Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Aina, Adekunle Kayode
Doctor of Philosophy - PhD
University of British Columbia
Protein aggregation-related diseases, in particular neurodegenerative diseases, are characterized by the aberrant perturbation of the underlying protein conformational ensemble. Effectively presenting epitopes using vaccines, to raise conformationally selective antibodies, is a central problem in treating neurodegenerative diseases. Parkinson’s and Alzheimer’s disease, which pathogenesis has been attributed to aberrant aggregates of alpha-synuclein and tau protein, respectively, are the two most common neurodegenerative diseases. Designing conformationally selective immunogens in silico often requires: 1.) an effective epitope scaffolding strategy that selectively targets pathologic aggregates known as oligomers while sparing the more abundant healthy monomers, with both the oligomeric and the monomeric forms having essentially identical amino acid sequences, and 2.) efficient methods and software for quantitative comparison of large conformational ensembles, which are currently not readily available. In this thesis, we apply various computational techniques including those based on information theory and principles of physics to address these two challenges. We computationally modeled and designed cyclic peptide and beta-helix protein immunogens to best mimic toxic oligomeric conformational ensembles of alpha-synuclein and tau protein computationally predicted epitopes, respectively. In both Parkinson’s and Alzheimer’s disease, our designed immunogens are predicted to be conformationally selective for toxic oligomers. Additionally, we developed a new generalized method for efficient representation and comparison of protein conformational ensembles. The method is up to 88 times faster while utilizing 48 times fewer computing cores than the readily available Encore software on a molecular dynamics-generated ensemble dataset. The methods developed and results presented in this thesis will not only accelerate the process of in silico conformation-specific immunogen design for protein aggregation-related diseases but have potential applications to antibody drug discovery and development in pharmaceutical biotechnology.
Computational Modeling and Designof Oligomer Selective Immunogens forParkinson’s and Alzheimer’s DiseasebyADEKUNLE KAYODE AINAB.Sc., University of Lagos, 2014M.Sc., University of Newfoundland, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(PHYSICS)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)March 2023© ADEKUNLE KAYODE AINA 2023The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:Computational Modeling and Design of Oligomer SelectiveImmunogens for Parkinson’s and Alzheimer’s Diseasesubmitted by Adekunle Kayode Ainain partial fulfillment of the requirements for the degree ofDoctor of Philosophy in PhysicsExamining Committee:Steven Plotkin, Professor, Physics and Astronomy, UBCSupervisorNeil Cashman, Professor, Medicine, UBCSupervisory Committee MemberJo¨rg Gsponer, Professor, Biochemistry and Molecular Biology, UBCSupervisory Committee MemberJoerg Rottler, Professor, Physics and Astronomy, UBCSupervisory Committee MemberCarl Michal, Associate Professor, Physics and Astronomy, UBCUniversity ExaminerSimcha Srebnik, Associate Professor, Chemical and Biological Engineering, UBCUniversity ExaminerJohn Straub, Professor, Chemistry, Boston University, USA)External ExamineriiAbstractProtein aggregation-related diseases, in particular neurodegenerative dis-eases, are characterized by the aberrant perturbation of the underlying pro-tein conformational ensemble. Effectively presenting epitopes using vaccines,to raise conformationally selective antibodies, is a central problem in treat-ing neurodegenerative diseases. Parkinson’s and Alzheimer’s disease, whichpathogenesis has been attributed to aberrant aggregates of α-synuclein andtau protein, respectively, are the two most common neurodegenerative dis-eases. Designing conformationally selective immunogens in silico often re-quires: 1.) an effective epitope scaffolding strategy that selectively targetspathologic aggregates known as oligomers while sparing the more abun-dant healthy monomers, with both the oligomeric and the monomeric formshaving essentially identical amino acid sequences, and 2.) efficient methodsand software for quantitative comparison of large conformational ensembles,which are currently not readily available.In this thesis, we apply various computational techniques including thosebased on information theory and principles of physics to address these twochallenges. We computationally modeled and designed cyclic peptide and β-helix protein immunogens to best mimic toxic oligomeric conformational en-sembles of α-synuclein and tau protein computationally predicted epitopes,respectively. In both Parkinson’s and Alzheimer’s disease, our designed im-munogens are predicted to be conformationally selective for toxic oligomers.Additionally, we developed a new generalized method for efficient represen-tation and comparison of protein conformational ensembles. The method isup to 88 times faster while utilizing 48 times fewer computing cores thanthe readily available Encore software on a molecular dynamics-generatediiensemble dataset.The methods developed and results presented in this thesis will not onlyaccelerate the process of in silico conformation-specific immunogen designfor protein aggregation-related diseases but have potential applications toantibody drug discovery and development in pharmaceutical biotechnology.iiiLay SummaryIn the work presented in this thesis, we proposed new methods for designingimmunogens on a computer for diseases that affect the nervous system. Weapplied these methods to Parkinson’s and Alzheimer’s disease, which arethe two most common diseases affecting the nervous system. Our resultspredicted that these methods are effective for making vaccines that can beused to develop antibody drugs to treat Parkinson’s and Alzheimer’s disease.The methods developed will not only speed up the process of designingimmunogens on a computer but have potential use in the drug developmentprocess in the biopharmaceutical industry.ivPrefaceThe work presented in this thesis has resulted in one US patent application,two peer-reviewed journal publications [1, 2], two manuscripts submitted topeer-reviewed journals, and one free publicly available software.A version of Chapter 2 has been published as Shawn C.C. Hsueh,Adekunle Aina, Andrei Yu. Roman, Neil R. Cashman, XubiaoPeng, and Steven S. Plotkin, 2022, Optimizing Epitope Confor-mational Ensembles Using α-Synuclein Cyclic Peptide “Glycin-del” Scaffolds: A Customized Immunogen Method for Generat-ing Oligomer-Selective Antibodies for Parkinson’s Disease, ACSChemical Neuroscience 13(15), 2261-2280 [1]. I was involved in theimplementation of methodology and software, data collection, data analy-sis, and data visualization. I wrote the manuscript with S.C.C.H. and itwas reviewed and edited by S.S.P. Full author contributions include; Con-ceptualization: S.S.P.; Methodology: S.C.C.H., X.P., A.A. and S.S.P.; Soft-ware: X.P., S.C.C.H., and A.A.; Data analysis: S.C.C.H., S.S.P., X.P., andA.A.; Visualization: S.C.C.H., X.P., A.A., and S.S.P.; Experimental data:A.Y.R.; Experimental data analysis: S.P. and S.C.C.H.; Resources: S.S.Pand N.R.C.; Writing—original draft: A.A., S.C.C.H., and S.S.P.; Writing—review and editing: S.S.P.Experimental results (not included in this thesis), which support the compu-tational method in Chapter 2, showing the ability of cyclic peptide “glycin-del” scaffolds to generate selective antibodies against toxic forms of α-synuclein implicated in diseases such as Parkinson’s has been published asGibbs Ebrima, Beibei Zhao, Andrei Roman, Steven S. Plotkin,Xubiao Peng, Shawn C.C. Hsueh, Adekunle Aina, Jing Wang,vClay Shyu, Calvin K. Yip, Sung-Eun Nam, Johanne M. Kaplan,and Neil R. Cashman, 2022, Rational Generation of MonoclonalAntibodies Selective for Pathogenic Forms of Alpha-Synuclein,Biomedicines 10 (9): 2168 [2]. I was involved in the computational mod-eling of the cyclic peptide “glycindel” scaffolds that were validated in thisexperimental work (see Ref. [1]). Full author contributions include; Com-putational modeling and data analysis: S.S.P., X.P., S.C.C.H., and A.A.;Experimental design: E.G., B.Z., A.Y.R., C.K.Y., J.M.K., and N.R.C.; Ex-periments and data analysis: E.G., A.Y.R., J.W., C.S., C.K.Y., and S.E.N.;Writing—original draft: J.M.K.; Writing—review and editing: B.Z. andN.R.C.A version of Chapter 3 has been submitted to a peer-reviewed journal asAdekunle Aina, Shawn C.C. Hsueh, Xubiao Peng, and Steven S.Plotkin, De novo computational design of a β-helix tau proteinscaffold: An oligomer-selective immunogen candidate forAlzheimer’s disease . I was responsible for conceptualization, develop-ment of methodology, implementation of methodology and software, datacollection, data analysis, and data visualization under the supervision ofS.S.P. I wrote the manuscript and it was reviewed and edited by S.S.P. Fullauthor contributions include; Conceptualization: A.A. and S.S.P.; Method-ology: A.A. and S.S.P.; Software: A.A., S.C.C.H., X.P. and S.S.P.; Dataanalysis: A.A., S.C.C.H. and S.S.P.; Visualization: A.A., X.P. and S.S.P.;Resources: S.S.P; Writing—original draft: A.A.; Writing—review and edit-ing: S.S.P.A US patent application on the work contained in Chapter 3 has been filedas Immunogens Targeting Oligomeric Tau and Methods of Gen-eration and Use Thereof, Inventors: Adekunle Aina and StevenS. Plotkin. I was responsible for the invention in this patent applicationunder the supervision of S.S.P.viA version of Chapter 4 has been submitted to a peer-reviewed journal asAdekunle Aina, Shawn C.C. Hsueh, and Steven S. Plotkin,Prothon: A local order parameter-based method for efficient com-parison of protein ensembles.. I was responsible for the conceptual-ization of the presented algorithms and methods and their implementationand validation. S.S.P. was the supervisor throughout the project. Fullauthor contributions include; Conceptualization: A.A.; Methodology: A.A.and S.S.P.; Software: A.A.; Data analysis: A.A. and S.C.C.H; Visualization:A.A.; Resources: S.S.P; Writing—original draft: A.A.; Writing—review andediting: S.S.P.NAME ABBREVIATIONComputational TeamA.A. Adekunle AinaS.C.C.H. Shawn C.C. HsuehX.P. Xubiao PengS.S.P. Steven S. PlotkinExperimental Team(Experimental results are not reported in this thesis.)N.R.C. Neil R. CashmanE.G. Ebrima GibbsJ.M.K. Johanne M. KaplanS.E.N. Sung-Eun NamA.Y.R. Andrei Yu. RomanC.S. Clay ShyuJ.W. Jing WangC.K.Y. Calvin K. YipB.Z. Beibei ZhaoviiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xxivAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Relevant terminology and definitions . . . . . . . . . . . . . 31.3 Protein aggregation and human diseases . . . . . . . . . . . . 51.3.1 α-synuclein and Parkinson’s disease . . . . . . . . . . 71.3.2 Tau and Alzheimer’s disease . . . . . . . . . . . . . . 81.4 Computer simulation . . . . . . . . . . . . . . . . . . . . . . 111.4.1 Molecular dynamics simulation . . . . . . . . . . . . . 111.4.2 Enhanced conformational sampling . . . . . . . . . . 12viii1.5 Information theory . . . . . . . . . . . . . . . . . . . . . . . 131.5.1 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . 131.5.2 Relative entropy and mutual information . . . . . . . 141.5.3 Jensen-Shannon divergence . . . . . . . . . . . . . . . 151.6 Dimensionality reduction . . . . . . . . . . . . . . . . . . . . 171.6.1 Principal component analysis . . . . . . . . . . . . . . 171.6.2 Multi-dimensional scaling . . . . . . . . . . . . . . . . 181.6.3 Stochastic proximity embedding . . . . . . . . . . . . 191.7 De novo computational protein design . . . . . . . . . . . . . 191.7.1 Backbone generation . . . . . . . . . . . . . . . . . . 201.7.2 Sequence design . . . . . . . . . . . . . . . . . . . . . 211.7.3 Sequence evaluation . . . . . . . . . . . . . . . . . . . 221.8 Research problems and objectives . . . . . . . . . . . . . . . 231.8.1 Research problems . . . . . . . . . . . . . . . . . . . . 231.8.2 Research objectives . . . . . . . . . . . . . . . . . . . 231.9 Research summary . . . . . . . . . . . . . . . . . . . . . . . . 232 Modeling α-synuclein cyclic peptide immunogen . . . . . . 272.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.1.1 α-synuclein epitope prediction . . . . . . . . . . . . . 312.1.2 Scaffolding of epitopes . . . . . . . . . . . . . . . . . 332.1.3 Generation of ensembles . . . . . . . . . . . . . . . . 342.1.4 Projecting ensemble distributions to lower dimension 392.1.5 Calculating ensemble overlap in 1D . . . . . . . . . . 402.1.6 Ensemble similarity measures . . . . . . . . . . . . . 402.1.7 The convergence of JSD and embedding depth . . . . 432.1.8 Evaluating off-pathway target criteria . . . . . . . . . 442.1.9 SMAA-TOPSIS ranking algorithm . . . . . . . . . . . 462.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 512.2.1 Comparing ensembles in reduced conformational space512.2.2 Scaffold screening criteria and scaffold ranking . . . . 54ix2.2.3 Embedding depth as a similarity measure comparedwith JSD . . . . . . . . . . . . . . . . . . . . . . . . . 562.2.4 Scaffold properties and their impact on performance . 582.2.5 Finding potential off-pathway targets . . . . . . . . . 622.2.6 Weighting the importance of ensemble properties . . 642.2.7 The role of glycindel immunogens in therapeutic de-velopment pipelines . . . . . . . . . . . . . . . . . . . 652.2.8 Other possible epitope scaffolding strategies . . . . . 663 De novo design of β-helix tau protein immunogen . . . . . 683.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.1.1 Prediction of epitopes . . . . . . . . . . . . . . . . . . 713.1.2 Epitope scaffolding using cyclic peptide glycindels . . 723.1.3 β-helix structure modeling . . . . . . . . . . . . . . . 733.1.4 β-helix sequence design and structure optimization . 753.1.5 Structure prediction with AlphaFold . . . . . . . . . . 763.1.6 Mechanical unfolding simulations . . . . . . . . . . . 763.1.7 Hamiltonian replica exchange molecular dynamics . . 773.1.8 Sampling conformational ensembles . . . . . . . . . . 783.1.9 Comparing conformational ensembles . . . . . . . . . 803.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 813.2.1 Prediction of tau epitopes . . . . . . . . . . . . . . . 813.2.2 Conformational selectivity of single-epitope cyclic pep-tide scaffolds . . . . . . . . . . . . . . . . . . . . . . . 833.2.3 Design of avidity-enhanced multi-epitope β-helix scaf-folds . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.2.4 AlphaFold predicts the designed β-helix structure . . 893.2.5 The designed β-helix scaffold is structurally and ener-getically stable . . . . . . . . . . . . . . . . . . . . . . 913.2.6 The designed β-helix scaffold is conformationally se-lective for a stressed protofibril model of tau oligomers 95x4 Efficient comparison of protein ensembles . . . . . . . . . . 974.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.1.1 Matrix representation of a protein ensemble . . . . . 1004.1.2 Vector representation of a protein ensemble . . . . . . 1014.1.3 Quantifying similarity between protein ensembles . . 1014.1.4 Cβ contact number local structural property . . . . . 1034.1.5 Measuring significant dissimilarity . . . . . . . . . . . 1034.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.2.1 Comparing computationally generated ensembles ofubiquitin . . . . . . . . . . . . . . . . . . . . . . . . . 1044.2.2 Comparing experimentally derived ensemble of tauK18 domain . . . . . . . . . . . . . . . . . . . . . . . 1084.2.3 Computational efficiency . . . . . . . . . . . . . . . . 1094.3 Code availability and usage . . . . . . . . . . . . . . . . . . . 1105 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116xiList of Tables2.1 Mean weights of SMAA-TOPSIS ranking criteria. . . 472.2 Ranking criteria and rankings for α-synuclein epi-tope scaffolds. The abbreviations JSDcf , JSDcm, JSDcs,Dc|m, and Dc|s correspond to JSDcyclic-fibril, JSDcyclic-monomer,JSDcyclic-stress, Dcyclic-in-monomer, andDcyclic-in-stress, respectively.OP corresponds to off-pathway targeting. . . . . . . . . . . . 483.1 Models of tau β-helix scaffold. Attributes of the designedβ-helix sequences with median (across five AlphaFold models)of the average per residue confidence (PLDDT) score ≥ 50%,and where each of the top three ranking Alphafold predictedstructures have RMSD from the Rosetta designed structure≤ 5 A˚. Models are sorted in order of decreasing values of themedian PLDDT score. . . . . . . . . . . . . . . . . . . . . . . 903.2 Designed sequences for models of tau β-helix scaffold.The corresponding amino acids for the four linkers as well asthe α-helix structure for each model in Table 3.1 are listed.Models are sorted in order of decreasing values of the medianPLDDT score. . . . . . . . . . . . . . . . . . . . . . . . . . . 914.1 Comparing intrinsically disordered ensembles of tauK18. The pairwise dissimilarity between 5 ensembles of tauK18 domain quantified using the Cβ contact number localstructural property implemented in Prothon. . . . . . . . . . 108xiiList of Figures1.1 Overview of the thesis. . . . . . . . . . . . . . . . . . . . 11.2 Schematic of the domains, mutation sites, and phos-phorylation sites in α-synuclein. All known disease-associatedmutations are found in the N-terminal domain. The C-terminaldomain consists of residues that are targets for phosphoryla-tion, which makes this domain a negative charge and mayinduce α-synuclein to misfold. Light red lines mark phos-phorylation sites and purple lines indicate disease-associatedmutations [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Schematic of the domains and splice isoforms of tauprotein. Exons 2, 3, and 10 of the MAPT gene encoding fortau protein are subject to alternative splicing resulting in sixisoforms of tau ranging from 352 to 441 amino acid residues.These tau isoforms differ according to the presence of 1, 2or absence of near-amino-terminal inserts (1N, 2N or 0N, re-spectively) and the presence or absence of the microtubule-binding domain repeat R2, yielding 3 or 4 carboxy-terminalrepeat domain (3R or 4R, respectively) tau species [4]. . . . 91.4 Illustration of principal component analysis (PCA) ofa two-dimensional data. PC1 is the first principal compo-nent, which indicates the direction of maximum data varianceand PC2 is the second principal component. . . . . . . . . . 18xiii2.1 Three-dimensional renderings for (2,3)EKTK cyclicpeptide, a scaffold of 57EKTK60 predicted epitope.(A) 3D licorice (stick) rendering with color assigned by theatom identity. (B) Rendering of the cyclic peptide in licorice,also showing the surface of the EKTK epitope. Colors areassigned by residue name, with glycine in gray, cysteine inorange, glutamate in blue, lysine in cyan, and threonine inmagenta. Images were rendered with PyMOL molecular vi-sualization system (https://pymol.org) . . . . . . . . . . 282.2 The workflow of modeling cyclic peptide “glycindel”scaffolds and in silico screening. . . . . . . . . . . . . . . 312.3 Collective coordinate epitope prediction for α-synuclein,using three criteria of increased SASA, loss of nativecontacts, and increased fluctuations (RMSF). (A) Sev-eral epitopes were predicted by each criterion; however, onlya single epitope 57EKTKEQ62 was predicted by (B) weightedaveraging. Chain E is not shown for ∆SASA because no epi-tope is predicted. (Figure adapted from Ref. [1]) . . . . . . . 332.4 Illustration of the embedding depth of the point xo ina multimodal distribution P (x). The embedding depth ofpoint xo is given by the integral over all parts of the distribu-tion with probability less than P (xo). Note there are 4 pointswith the same P (xi) = P (xo) and thus the same embeddingdepth. (Figure adapted from Ref. [1]) . . . . . . . . . . . . . 412.5 Convergence analysis for SPE and MDS dimensionalreduction. Convergence of dimensional reduction for (A)multidimensional scaling (MDS) for embedding depth and(B) stochastic proximity embedding (SPE) for JSDs. Bothquantities are plotted vs. the dimension of the reduction.The scaffold used here for illustration is (1,4)TKEQ. (Figureadapted from Ref. [1]) . . . . . . . . . . . . . . . . . . . . . . 42xiv2.6 The equilibrium ensemble distributions for the 59TKEQ62epitope projected by the multidimensional scaling (MDS)method [5] onto the first MDS dimension. For a givenepitope, different cyclic peptide scaffolds possess different dis-tributions, which will result in different overlap with the otherthree ensembles. By comparing the degree of ensemble over-lap, the conformational selectivity of a scaffold can be as-sessed. The scaffolds shown are (A) (1,4)TKEQ and (B)(2,3)TKEQ. . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.7 Measures for the rankings of all 16 epitope scaffolds,for three overlapping 4 residue sub-epitopes of 57EKTKEQ62in α-synuclein (top of each column). (A) Scaffoldedcyclic peptide ensemble dissimilarity to monomer (triangle),fibril (star), and stressed fibril (circle) ensembles, as measuredby Jensen-Shannon Divergence (JSD), showing the changes inensemble overlap with varying numbers of flanking glycines.(B) Scaffolded cyclic peptide ensemble embedding depth withinthe monomer (triangle), fibril (star), and stressed fibril (cir-cle) ensembles, showing the changes in ensemble embeddingwith varying number of flanking glycines. (C) Normalizedoff-pathway targeting values (OP) for scaffolds with varyingnumber of flanking glycines. Higher values indicate there isless predicted off-pathway targeting by a given scaffold. Theranks of the top 10 scaffolds are indicated in the figure panels,along with the rank for the highest ranking scaffold (15) forepitope 58KTKE61. (Figure adapted from Ref. [1]) . . . . . . 55xv2.8 Correlation matrices for measures of ensemble com-parison. Correlation matrices of the ensemble comparisonmeasures JSD and D, and three other scaffold properties: Dy-namic flexibility (RMSF) of an epitope, total residue lengthof the cyclic peptide scaffold, and the ranking, for α-synucleinepitopes (A) 57EKTK60, (B) 58KTKE61, and (C) 59TKEQ62.The number in each square (bottom-left) is the Pearson cor-relation coefficient. P is the p-value of the correlation coeffi-cients (top-right). (Figure adapted from Ref. [1]) . . . . . . . 572.9 Epitope-dependent correlation between scaffold prop-erties. Epitope-dependent correlation between (A) RMSFand scaffold length (number of residues in the scaffold), (B)ranking and scaffold length, (C) rank and the quantity JSDcm−JSDcs, and (D) rank and Dc|s − Dc|m, for α-synuclein epi-tope scaffolds. The Pearson correlation coefficient, r and thecorresponding p-values are given for 57EKTK60 (green trian-gles), 58KTKE61 (purple circles) and 59TKEQ62 (blue stars)scaffolds. The shaded areas around the fitted lines are the68% confidence intervals corresponding to the standard er-rors. (Figure adapted from Ref. [1]) . . . . . . . . . . . . . . 60xvi2.10 Off-pathway target analysis for (1,4)TKEQ. (A) Struc-tural ensemble distribution of cyclic peptide (1,4)TKEQ in1D along the first MDS component of the ensemble, alongwith the projected embedding of potential off-pathway tar-gets. Most of the off-pathway targets are located at the pe-riphery of the scaffold distribution. The actual calculation isperformed in 5D. Structures of PDB entries 2KKW and 1XQ8are rendered in ribbon schematics, and the epitope is renderedin Van der Waals surface. (B) The SASA distribution of(1,4)TKEQ, along with the SASA for the off-pathway targetstructures. (C) Only 1XQ8 and 2KKW show both notice-able structural similarity (Doff-target-in-cyclic(5D) > 5%) andSASA exposure (f(SASAoff-target-exceed-cyclic) > 5%). (Figureadapted from Ref. [1]) . . . . . . . . . . . . . . . . . . . . . . 633.1 Modeling tau β-helix structure. (A) Tau fibril fromAlzheimer’s disease brain (PDB ID: 5O3L) showing the sidechains on the left protofilament in the figure for the predictedepitopes: 315LSKVT319 (magenta), 343KLDFK347 (red), and365GGGN368 (light orange), and the 339VKSEKLDFKDRVQSKI354tau339-354 fragment (non-epitope portion in cyan) that sub-sumes the 343KLDFK347 epitope. (B) Segments of five chainsof the tau339-354 fragment are connected together with in-terchain linkers, to form a β-helix structure. Magenta dashlines indicate how glycine tripeptide linkers connect the C-terminus of one chain to the N-terminus of the next chain,and S352 is shown in yellow spheres. (C) The 7.9A˚ distancebetween the C-terminus of one chain and the N-terminus ofthe next chain in the tau fibril (black dotted line). All imageswere rendered with PyMOL molecular visualization system(https://pymol.org). . . . . . . . . . . . . . . . . . . . . 73xvii3.2 Distribution of (i, i+ 3) distances in a non-redundantdatabase of Protein Structures. The 7.9A˚ distance be-tween consecutive chains to be linked in our designed struc-ture (` in the plot) is well-within the distribution of distancesbetween Cα atoms separated by three amino acids (i, i + 3).The distribution shows several features that are labelled inthe figure: α (α-helical secondary structure), β (β-helicalsecondary structure), tr (transitional elements between sec-ondary structure and loop or turn). . . . . . . . . . . . . . . 753.3 Setup used for hamiltonian replica exchange molecu-lar dynamics (HREMD) simulations. The HREMD setup consists of 100 replicas (horizontal lines), each simulatedin an unfolding run to different degrees of unfolding Q0i for10 ns, followed by an equilibration run for 160 ns with eachreplica in its own harmonic potential centered at Q0i, followedby a production run in the same harmonic potential for 80 ns. 773.4 Prediction of tau epitopes. (A) Per residue normalizedincrease in solvent accessible surface area (∆SASA), loss ofnative contacts (∆Q), and local increase in root mean squaredfluctuations (∆RMSF). (B) Per residue weighted sum of ∆SASA,∆Q and ∆RMSF over all chains with the boundary chains inthe 5×2-chain, 2-protofibril structure A, B, I, and J havinghalf the weight of other chains. The zero point was set to anumerical value (7.5) that identified epitopes that are within5 amino acid long. The sequences shown in red font are thepredicted epitopes for tau. . . . . . . . . . . . . . . . . . . . 81xviii3.5 Conformational ensemble similarity. The dissimilaritybetween two conformational ensembles was quantified usingJSD (see Methods section 3.1.9), which is normalized to liebetween 0 (for identical ensembles) to 1 (for entirely differentensembles). Shown are the similarity between the epitopeensemble in the context of a scaffold and the stressed fib-ril oligomer model, versus the similarity between the epitopeensemble in the context of the scaffold and the monomer,for cyclic peptide scaffolds of the LSKVT epitope (triangles),cyclic peptide scaffolds of the KLDFK epitope (squares), andthe β-helix scaffold of the four KLDFK epitope repeats (cir-cles). The arrow indicates the direction of favorable confor-mational profile and the dashed line is the line y = x. . . . . 843.6 β-helix scaffold design strategy. (A) Five copies of tau-derived 16-residue 339VKSEKLDFKDRVQSKI354 repeatingsequence are linked serially by glycine tripeptide linkers (GGG);S352C substitutions are made in the first four repeats. Thesewere used to model (B) a β-helix structure, with disulfidebridges between residues C14 and C33 and residues C52 andC71. (C) Redesign of the last repeat (black box) and linkerresidues (gray boxes) to improve the stability of (D) the β-helix scaffold by creating interactions between the designedresidues. Last repeat is shown in yellow and linkers are shownin orange, both with licorice side chains. (E) The designedβ-helix structure (magenta) and AlphaFold predicted struc-ture (cyan) have Cα RMSD of 1.39A˚. All images were ren-dered with PyMOL molecular visualization system (https://pymol.org). . . . . . . . . . . . . . . . . . . . . . . . . . 86xix3.7 Rosetta energy and AlphaFold confidence for designedβ-helix structures. (A) Rosetta energy per residue (inRosetta energy units or REU) as a function of Cα RMSDto the Rosetta remodeled structure, for 10, 000 designed de-coys. Dashed line indicates low energy cuttoff of −3.41 REU,corresponding to 1% of decoys with energies below the cut-toff. (B) Per residue AlphaFold confidence (PLDDT) scorefor the top 3 ranked AlphaFold models as for the top rankedsequence. Dashed line indicates high confidence cuttoff of70%. The β-helix structure was rendered to show 1st ranked(C), 2nd ranked (D), and 3rd ranked (E) per residue confi-dence scores and colour coded as very high confidence (blue),high confidence (cyan), low confidence (yellow), and very lowconfidence (orange). All images were rendered with PyMOLmolecular visualization system (https://pymol.org) . . 88xx3.8 Computational characterization of the stability of β-helix scaffold. The (A) global and (B) local structural sta-bility in the free energy basin of the Rosetta designed struc-ture. (C) The mechanical stability measured by the averagecumulative work done during forced unfolding simulations(solid line), compared to fibronectin, a stable extra-cellularmatrix protein with similar length (dashed line), and an iso-lated (intrinsically disordered) tau monomer (dotted line),which serves as a negative control. (D) Thermodynamic sta-bility determined from the relative free energy surface alongthe fraction of native contacts Q (Eq. 3.4) order parameter.Snapshots from the first half (dotted), second half (dashed),and full 80ns trajectories (solid) in each umbrella are shown(see text). Inset images show representative snapshots of thestructures at the free energy minimum, where Q = 0.64, andwhere Q = 1 and Q = 0.1. The order parameters in pan-els (C) and (D) have opposite sense, as (C) considers pullingfrom the native state, and (D) considers folding free energysurface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.1 Representation and dimensionality reduction of ubiq-uitin ensembles. The folded (red) and partially folded (yel-low: 95% folded, magenta: 90% folded, cyan: 85% folded,green: 80% folded, and blue: 75% folded) ubiquitin ensem-bles are represented using Cβ contact number (CBCN) matrix(top) and RMSD matrix (bottom). Dimensionality reduc-tion to 2D using (left) principal component analysis (PCA)for (A) CBCN and (C) RMSD matrix representations and(right) t-distributed stochastic neighbor embedding (t-SNE)for (B) CBCN and (D) RMSD matrix representations. . . . 106xxi4.2 Comparing partially folded ensembles of ubiquitin.(A) Dissimilarity between varying degrees (75% < Q < 95%)of partially folded ensemble and the folded equilibrium ensem-ble of ubiquitin. Dissimilarity is quantified using Cβ contactnumber (circle) local structural property implemented in Pro-thon and Encore (triangle) The pairwise dissimilarity betweenthe 5 partially folded ensembles of ubiquitin in (A) using (B)Prothon and (C) Encore [6]. (D) Computational efficiencyof Prothon compared with Encore. Prothon calculations ranon a single core, while 48 cores were available to Encore. . . 1075.1 Overview of the thesis. . . . . . . . . . . . . . . . . . . . 112xxiiList of Programs4.1 Example Python script that computes dissimilarity betweenprotein ensembles using Prothon. . . . . . . . . . . . . . . . . 110xxiiiList of AbbreviationsAβ Amyloid-βAD Alzheimer’s diseaseALS Amyotropic lateral sclerosisBSA Bovine serum albuminCABA Cα-Cα bond angleCACN Cβ contact numberCATA Cα-Cα torsion angleCBCN Cβ contact numberCBD Corticobasal degenerationCC Collective coordinateCNS Central nervous systemCG Coarse-grainedCryo-EM Cryo-electron microscopyCTE Chronic traumatic encephalopathyDKL Kullback–Leibler divergenceFDA Food and Drug AdministrationFRET Fo¨rster resonance energy transferFTD Frontotemporal disordersHREMD Hamiltonian replica exchange molecular dynamicsIDP Intrinsically disordered proteinsJSD Jensen Shannon DivergenceJSDist Jensen Shannon DistanceKDE Kernel density estimationKLH Keyhole limpet hemocyaninMBAR Multistate Bennett Acceptance RatioxxivMD Molecular dynamicsMDS Multi-dimensional scalingMAP Microtubule-associated proteinNFT Neurofibrillary tanglesNMR Nuclear magnetic resonanceNAC Non-amyloid componentOP Off-pathwayPCA Principal component analysisPD Parkinson’s diseasePDB Protein data bankPED Protein ensemble databasePFF Preformed fibrilsPiD Pick’s diseasePLDDT Predicted local distance difference testPSP Progressive supranuclear palsyREMD Replica exchange molecular dynamicsREU Rosetta energy unitsRMSD Root mean squared deviationRMSF Root mean squared fluctuationsSASA Solvent accessible surface areaSNc Substantia nigra pars compactaSNCA Synuclein alphaSOD1 Superoxide dismutase 1SPE Stochastic proximity embeddingTDP43 TAR DNA-binding protein 43ThT Thioflavin Tt-SNE t-distributed stochastic neighbour embeddingUBC University of British ColumbiaxxvAcknowledgementsI would like to thank my supervisor Dr. Steven Plotkin, and my supervisorycommittee for their support and guidance during the research work presentedin this thesis.My appreciation goes to the University of British Columbia (UBC), ProMISTMNeurosciences, and MITACS for funding this research work.I am thankful to all the members of Plotkin Lab and the many students atthe Department of Physics and Astronomy and UBC at large for providingan enriching educational experience.To my family for all their sacrifices throughout my studies at UBC, I ammost grateful.xxviDedicationTo my beloved dad of blessed memory.xxviiChapter 1Introduction1.1 Thesis overviewThis thesis introduces new computational approaches and methods for mod-eling and design of immunogens to treat protein aggregation-related diseases.The thesis is organized into five chapters: three main chapters as shown inFig. 1.1, an introductory chapter, and a concluding chapter.Figure 1.1: Overview of the thesis.Chapter 1: IntroductionThe current chapter first gives an overview of this thesis, where the contentof each chapter is briefly described. Relevant terminology and definitionsare provided. Then a review of the background materials associated with1the work presented in this thesis, including protein aggregation and humandiseases, in particular Parkinson’s and Alzheimer’s disease, computer molec-ular simulation, information theory, dimensionality reduction, and de novocomputational protein design is presented. Finally, the research problemsand research objectives of this thesis are highlighted followed by a compre-hensive summary of the research work carried out in this thesis to achievethese objectives.Chapter 2: Modeling α-synuclein cyclic peptide immunogenIn this chapter, we developed a method for scaffolding and optimizing epi-tope conformational ensembles using “glycindel” cyclic peptides. We thenapplied this method to computationally predicted α-synuclein epitopes inthe design of immunogens for generating oligomer-selective therapeutic an-tibodies for Parkinson’s disease.Chapter 3: De novo design of β-helix tau protein immunogenThis chapter introduces a second method for scaffolding epitopes by de novodesign of a multi-epitope β-helix protein. We applied this method to designa β-helix tau protein scaffold that is suitable for eliciting oligomer-selectivetherapeutic antibodies for Alzheimer’s disease. We show through confor-mational ensemble analyses that the multi-epitope scaffolding approach ispredicted to be better in discriminating toxic tau oligomers than a “monova-lent” strategy utilizing a single instance of an epitope for immunogen design.Chapter 4: Efficient comparison of protein ensemblesIn this chapter, we developed and implemented an efficient method for thecomparison of protein conformational ensembles. The method is validatedusing conformational ensembles generated by molecular dynamics simula-tions of ubiquitin and can be up to two orders of magnitude faster than thereadily available Encore software [6].2Chapter 5: ConclusionThis chapter summarizes the main results obtained in Chapters 2, 3, and4, and provides potential future applications.1.2 Relevant terminology and definitionsAdjuvant: An adjuvant is an ingredient added to an immunogen that helpscreate a stronger immune response.Antibody: An antibody (or immunoglobulin) is a macromolecular proteinused by the immune system to identify and neutralize an antigen.Antigen: An antigen is a foreign agent or part of a foreign agent that reactswith the products of an immune response, e.g. antibodies, stimulated by aspecific immunogen. Some antigens can both induce an immune responseand react with the products of the immune response.Carrier: A carrier is a macromolecular protein, such as Bovine serum albu-min (BSA ) or Keyhole limpet hemocyanin (KLH), which is immunogenicand to which a non-immunogenic antigen may be conjugated to improveimmunogenicity.Epitope: An epitope is a specific region of an immunogen (or antigen) thatelicits an immune response. Epitopes are also known as antigenic determi-nants.Fibril: A fibril (or amyloid fibril) is a large structured aggregate of about40 or more monomers.Glycindel: A “glycindel” is a scaffold in which the non-epitope amino acidsare glycines.Immunogen: An immunogen is a foreign agent capable of inducing animmune response by stimulating B cells, T cells, or both of a host animal.3Immunization: The administration of an immunogen (or antigen) to ahost animal is referred to as immunization.Monomer: A monomer is a single polypeptide chain that makes up aprotein.Oligomer: An oligomer is a small amorphous aggregate of between 4 to 40monomers.Oligomer-selective: An immunogen is oligomer-selective if the immuno-gen mimics the conformation of an oligomer but not a monomer and fibril ofthe same protein. An antibody is oligomer-selective if it binds an oligomerbut not a monomer and fibril of the same protein.Scaffold: A scaffold (or epitope scaffold) is an immunogen consisting of anepitope and non-epitope amino acid residues, which restrain the epitope inconformational space.Scaffolding: The process of modeling or designing amino acids to preservethe conformation of an epitope is referred to as epitope scaffolding or simplyscaffolding.Vaccine: A vaccine consists of an immunogen, adjuvants, and sometimes acarrier.41.3 Protein aggregation and human diseasesProteins are biomolecular machines responsible for many of the biologicalprocesses in living organisms. Protein functions include, but are not limitedto, the catalysis of biochemical reactions, transportation of other biologicalmolecules, and chemical signaling [7]. Many proteins assume a specific nativefold; a unique three-dimensional (3D) structure to perform their functions.A protein fold performs specific functions through interaction with otherproteins or biomolecules such as DNA and RNA.Some proteins are, however, natively unstructured. Such proteins areknown as intrinsically disordered proteins (IDPs). IDPs are predominantin proteomes throughout all life forms [8]. Like natively structured pro-teins, many IDPs are biologically functional contrary to the structure defin-ing function hypothesis that forms the basis of most of our understandingof proteins today. Unlike natively structured proteins, however, IDPs arehighly prone to abnormal aggregation of monomeric forms of the proteinsto small oligomeric and large fibrillar aggregates [8].N* structures are intermediate structures that can form during the pro-cess of protein aggregation, which can lead to the formation of amyloid fib-rils. These structures are believed to be highly aggregation-prone and playa key role in the nucleation of fibril formation [9]. The timescale for fibrilformation is informed by the probability of observing aggregation-prone N*structures in the monomeric protein ensemble. Specifically, the formation ofN* structures is a stochastic process that depends on a number of factors,including the concentration of the protein, the temperature, the pH, andthe presence of cofactors or other molecules that can affect the aggregationprocess. The probability of observing N* structures can be influenced bythese factors, as well as by the intrinsic properties of the protein, such as itsprimary sequence and its propensity to form secondary structure elementsthat can promote aggregation [9]. Once N* structures form, they can serveas nucleation sites for the formation of amyloid fibrils, which are highlyordered, insoluble protein aggregates.Neurodegenerative diseases are a set of diseases affecting the central5nervous system. Protein aggregation is a biological hallmark of neurodegen-erative diseases. For example, the aggregation of amyloid beta (Aβ) andtau proteins in Alzheimer’s disease (AD) [10] and α-synuclein protein inParkinson’s disease (PD) [11]. A common feature observed in many neu-rodegenerative diseases is the alteration of the structure and aggregation ofspecific proteins, which results in their abnormal deposition. The aggrega-tion of these proteins results in a loss of their physiological function andmay lead to intra- or extra-cellular accumulation.The most common neurodegenerative disease is AD, characterized byprogressive memory loss and persistent deterioration in cognition, function,and behavior [12]. One of the main pathological observables in AD is theintra-neuronal accumulation of neurofibrillary tangles (NFTs) consisting oftwisted strands of tau protein [13]. Tau is a microtubule-associated pro-tein (MAP) abundant in the neurons of the central nervous system [14].Tau is an IDP that is highly soluble [15]. One of tau’s primary functionsis maintaining axonal microtubules’ stability, but its increased insolubilitycauses filamentous aggregates to develop, leading to neurons’ instability anddamage.After AD, PD is the second most common neurodegenerative diseaseand the fastest growing neurologic disease [3, 16]. PD is characterized bythe progressive loss of dopamine-generating neurons in the brain [17]. Move-ment is usually controlled by dopamine, which carries signals between thenerves in the brain. One of the key factors in the development of PD isthe deposition of aggregates of α-synuclein. However, Stephanie Janezic etal. [17] showed that the death of dopamine neurons of the substantia ni-gra pars compacta (SNc), which is a region of the brain, is independent ofα-synuclein aggregation in a PD transgenic mouse model. α-synuclein is ahighly soluble IDP [18, 19], predominantly produced in the neurons of thecentral nervous system and localized at presynaptic terminals [20].61.3.1 α-synuclein and Parkinson’s diseaseα-synuclein is an intrinsically disordered protein (IDP) with 140 amino acidssegmented into three domains: the N-terminal domain (residues 1–60), thecentral non-amyloid component (NAC) domain (residues 61–95), and the C-terminal domain (residues 96–140) [3, 19, 21–23] (see Fig. 1.2). α-synucleinwas first associated with Parkinson’s disease (PD) in 1997 when a missensemutation (A53T) was found in its SNCA encoding gene [3, 24].Figure 1.2: Schematic of the domains, mutation sites, and phospho-rylation sites in α-synuclein. All known disease-associated mutations arefound in the N-terminal domain. The C-terminal domain consists of residuesthat are targets for phosphorylation, which makes this domain a negativecharge and may induce α-synuclein to misfold. Light red lines mark phos-phorylation sites and purple lines indicate disease-associated mutations [3].All mutations in SNCA (synuclein alpha) encoding gene associated withPD are in the N-terminal domain, which has a highly conserved motif simi-lar to lipid-binding motifs responsible for α-synuclein association with mem-branes [3, 23, 25], and is involved in misfolding and aggregation [26, 27]. TheC-terminal domain is negatively charged and contains one serine and threetyrosine residues that can be phosphorylated, which may alter the structureof α-synuclein, leading to aberrant aggregation [28]. Although the normalphysiologic function of α-synuclein is not yet fully elucidated, the nativemonomeric form of α-synuclein helps to maintain presynaptic function andregulation of transmitter release [28]. However, α-synuclein aggregates havebeen shown to be toxic to neurons [29].Studies of synaptic homeostasis in animal models after over-expressing7or under-expressing α-synuclein have suggested that α-synuclein regulatesneurotransmitter release, synaptic activity, and plasticity [30]. Studies of α-synuclein aggregates in PD brains have suggested a pattern and distributionof pathology that correlates with the clinical progression of the disease.There is in vitro and in vivo evidence for cell-to-cell transmission of α-synuclein aggregates and pathology [31–35]The mechanism by which α-synuclein transmits from cell to cell is how-ever still unknown. It has been hypothesized that synaptic activity, in partic-ular synaptic vesicle exocytosis, leads to the release of α-synuclein from neu-ronal cells [36]. The binding of extracellular α-synuclein to the transmem-brane protein lymphocyte-activation gene 3 (LAG3) [37] or to complex N-linked glycans, has been associated with the intake of α-synuclein into neu-rons [3]. A transmission hypothesis for pathologic α-synuclein has emergedinvolving seeding and nucleation, cell-to-cell transmission, and eventual ag-gregation of toxic misfolded α-synuclein in a prion-like manner [38]. Manyin vitro and in vivo studies have previously shown that α-synuclein pathol-ogy can be induced and propagated through pathologic α-synuclein seeds inthe form of preformed fibrils (PFF) generated from recombinant pathologicmonomers [39], α-synuclein derived from brain homogenates of transgenicmice or human diseased brains [40, 41].A limiting factor in understanding the cell-to-cell transmission of α-synuclein is that it is not clearly known which forms of α-synuclein arepathogenic. There may be specific forms of α-synuclein aggregates that arepathogenic and more likely to propagate [42]. The toxic forms of α-synucleinwhich can seed and act as templates for endogenous α-synuclein in order totransmit in prion-like manner have been suggested to be soluble, prefibrillaroligomer or protofibril intermediates rather than the insoluble fibrils [3, 43–46].1.3.2 Tau and Alzheimer’s diseaseTau is a microtubule-associated protein found in neurons [47]. The assemblyof α and β tubulins results in the formation of microtubules. Tau binding8to tubulin promotes the assembly of microtubules and stabilization of themicrotubule network, which is required for axonal transport and neuronalhealth [48]. Tau is most prevalent in the central nervous system (CNS)with six isoforms, ranging from 352 to 441 amino acids, due to alternativemRNA splicing of exons 2, 3, and 10 of the microtubule-associated proteintau (MAPT) gene [4, 49, 50].Figure 1.3: Schematic of the domains and splice isoforms of tauprotein. Exons 2, 3, and 10 of the MAPT gene encoding for tau proteinare subject to alternative splicing resulting in six isoforms of tau rangingfrom 352 to 441 amino acid residues. These tau isoforms differ accordingto the presence of 1, 2 or absence of near-amino-terminal inserts (1N, 2Nor 0N, respectively) and the presence or absence of the microtubule-bindingdomain repeat R2, yielding 3 or 4 carboxy-terminal repeat domain (3R or4R, respectively) tau species [4].There are four principal domains in tau, which include the N-terminaldomain (NTD), proline-rich domain (PRD), microtubule-binding domain(MBD), and the C-terminal domain (CTD) (see Fig. 1.3). Exons 2 and3 are in the NTD, while exon 10 is in the MBD. The MBD is essentialfor maintaining microtubules by healthy tau, but it is also the putativedomain responsible for misfolding and aggregation in tauopathies [51–53].The MBD consists of four repeats R1, R2, R3, and R4, with R2 encodedby exon 10. There are three tau isoforms containing residues encoded byexon 10 (4R-tau) and lacking exon 10 residues (3R-tau), respectively (see9Fig. 1.3) [54]. In the healthy adult brain, there is an equal proportion of 3R-tau and 4R-tau [55]. Different tauopathies exhibit differential populations of3R-tau and 4R-tau. For instance, in AD, 3R-tau and 4R-tau co-aggregate,in contrast to progressive supranuclear palsy (PSP) pathologies, where onlythe 4R-tau aggregate, and frontotemporal disorders (FTD), where only 3R-tau aggregate [47, 56].The unstructured or disordered nature of tau [8] means it exhibits het-erogeneity of conformational states and the tendency to aggregate, makingit challenging to study experimentally. Experimental methods such as X-ray crystallography [57] and cryo-electron microscopy (Cryo-EM) [58] canreveal static structural information but not dynamic information of pro-cesses such as large protein conformational transformation and protein as-sembly. Experimental methods for studying dynamics include nuclear mag-netic resonance (NMR) [59], single-molecule fluorescence spectroscopy [60],temperature jump relaxation spectroscopy [61], and paramagnetic relaxationenhancement NMR [62]. However, these experimental techniques are inca-pable of obtaining atomic resolutions in both time and space.Despite previous studies on tau [63–66], the mechanism by which tauaggregates remains unknown. The abnormal post-translational modifica-tions, other than phosphorylation, may play a key role in tau aggregation[67, 68]. Although post-translational hyperphosphorylation of tau decreasesits binding affinity to tubulin, leading to the destabilization of microtubuleand neuronal dysfunction, it does not by itself promote tau aggregation. In-deed, hyperphosphorylation hinders tau aggregation in vitro [69]. However,other post-translational modifications such as acetylation could impair tauinteractions with microtubules and enhance tau aggregation [68, 70]. Tauaggregation may as well be as a result of the conformational transformationfrom an inert, nontoxic to a pathological, seed-competent form capable ofrecruiting healthy forms in self-assembly [67, 71, 72].The most common cause of dementia is Alzheimer’s disease (AD) [73].Progressive memory loss and cognitive decline are the clinical observables inAD patients [74]. There are about 50 million people with dementia world-wide and this number is expected to increase to more than 130 million people10by 2050. Dementia also has a huge economic impact with the total estimatedworldwide cost of over US $800 billion [75].One of AD’s main pathological features is the neurofibrillary tangles(NFT) formed by the abnormal aggregation of tau proteins in neurons [76].The deposition of NFTs in neurons is an hallmark of many other tauopathies,including PSP, FTD or Pick’s disease (PiD), chronic traumatic encephalopa-thy (CTE), and corticobasal degeneration (CBD) [77].1.4 Computer simulationComputer simulations have become an important tool for solving problemsthat are otherwise difficult and sometimes practically impossible to solveanalytically or for providing information that is difficult to obtain experi-mentally. The increase in computational power has facilitated the increasingpopularity of the use of computers to simulate biomolecular systems andprocesses. The general idea of any molecular simulation is to numericallycalculate, based on relevant model and theory, the properties of a physi-cal system. A very common method to simulate the time evolution of abiomolecular system is molecular dynamics (MD) [78, 79].1.4.1 Molecular dynamics simulationMolecular dynamics (MD) is a robust framework for simulating molecules,in particular biological molecules like proteins. MD simulation of a proteinwas first performed in the 1970s [80]. MD has been used to study proteinfolding, misfolding, and aggregation [66, 81, 82]. MD in protein simulationsis used to predict how each and every atom will move over time based onthe physics governing inter-atomic interactions [78, 79].Given the initial coordinates of all the atoms in a system, say protein inwater, and the potential between the atoms, Newton’s law of motion is usedto calculate the spatial position and the velocity of each atom as a functionof time. Thus the time evolution of the system is determined by solving11Eq. 1.1.Fi = mi∂2ri∂t2(1.1)for each atom i in the system. The resulting trajectory is a three-dimensionalatomic-level description of the system at every point during the simulatedtime interval [79].The force Fi, on atom i, is calculated from Fi = −∇i U(rN ), whereU(rN ) is the interaction potential which may include bonding potentials andlong-range potentials such as electrostatics and van der Waals interactions.The time average of a physical observable O is calculated by averagingover time along a trajectory as follows:O¯ = limt→∞1tt∫0dτ O(r(τ), r˙(τ)). (1.2)Ergodicity principle states that the average over periods of time along agiven trajectory of an observable is, at the limit, identical to the ensembleaverage of the same observable. That is, O¯ = 〈O〉. Ergodicity is importantwhen performing MD simulations [83]. MD simulation must be sufficientlylong such that it is longer than the relevant relaxation time in the system.Commonly used software for performing MD simulations include GRO-MACS [84], NAMD [85], CHARMM [86], Desmond [87], and OpenMM [88],while AMBER [89], CHARMM [90], and OPLS [91] are commonly used forcefields for performing MD simulations of proteins.1.4.2 Enhanced conformational samplingMD’s major challenge is the difficulty in simulating large biomolecular sys-tems and observing long timescale events such as protein aggregation due tolimited computational resources. This timescale challenge can be addressedeither by accelerating MD using powerful hardware [92–94] or utilizing en-hanced sampling techniques such as replica exchange MD (REMD) [95–97],biased MD [98, 99], accelerated MD [100], metadynamics [101], transitionpath sampling [102], and advanced analysis method such as constructing12Markov State Models (MSMs) [103–105].Replica exchange molecular dynamicsThe replica-exchange molecular dynamics (REMD) method [95, 106] wasintroduced by Yuji Sugita and Yuko Okamoto [95]. In the REMD method,multiple copies of the system known as replicas are run simultaneously atdifferent temperatures (TREMD) [107], Hamiltonian (HREMD) [108, 109]or other parameters [110], and exchanged at fixed time intervals. Exchangesbetween replicas are allowed based on the Metropolis criterion [111] to gen-erate a generalized ensemble. Since exchanges between neighboring replicaswith a close but different temperature or Hamiltonian can accelerate andenhance the convergence of MD simulations, REMD has been extensivelyused in generating equilibrium ensembles [95, 106–109, 112].1.5 Information theoryInformation theory is a statistical method specifically developed to quantifyinformation.1.5.1 EntropyEntropy is a measure of the uncertainty in a random variable. It is a mea-sure of the amount of information required on average to describe the vari-able [113]. Entropy is the fundamental quantity in information theory. Theentropy (or Shannon entropy) H(X) of a discrete random variable X withthe possible states x and probabilities p(x) is defined by Eq. 1.3 [113–115].H[X] = −∑x∈Xp(x) log2 p(x) (1.3)Joint entropyFor two discrete random variables X (with the possible states x) and Y(with the possible states y) and joint probabilities p(x, y), the joint entropy13H[X,Y] is given by Eq. 1.4 [113, 115].H[X,Y ] = −∑x∈X,y∈Yp(x, y) log2 p(x, y) (1.4)Conditional EntropyThe conditional entropy quantifies the average uncertainty in a random vari-able given the state of another random variable. For two discrete randomvariables X (with the possible states x) and Y (with the possible states y)and joint probabilities p(x, y), the conditional entropy H[X|Y ] of X givenY is defined by Eq. 1.5 [113, 115].H[X|Y ] = −∑x∈X,y∈Yp(x, y) log2 p(x|y) (1.5)It is intuitive to write the relationship between entropy, joint entropy, andconditional entropy as follows [113–115]:H[X,Y ] = H[X] +H[Y |X] (1.6)Eq. 1.6 states that the joint entropy of X and Y is equal to the entropy ofX alone, plus the remaining entropy of Y when X is known.1.5.2 Relative entropy and mutual informationThe relative entropy or Kullback–Leibler divergence (DKL [116]) betweentwo probability mass functions X1 =∣∣ p11, p12, p13, · · · p1n 〉 andX2 =∣∣ p21, p22, p23, · · · p2n 〉, which satisfy the constraints ∑ni=1 pji = 1 and0 ≤ pji ≤ 1 for all i = 1, 2, ..., n and j = 1, 2, is defined as [113]:DKL(X1, X2) =n∑i=1p1i log2p1ip2i(1.7)It can be shown that DKL is always non-negative and is zero if and only ifX1 = X2. However, DKL is not symmetric and does not satisfy the triangleinequality.14Mutual informationMutual information is a measure of the amount of information that onerandom variable contains about another random variable [113]. Given tworandom variables X and Y with marginal probability mass functions p(x)and p(y), respectively, and a joint probability mass function p(x, y). Themutual information I(X;Y ) between X and Y is defined as the relativeentropy between the joint distribution p(x, y) and the product distributionp(x)p(y) (Eq. 1.8 [113]).I(X;Y ) = DKL(p(x, y), p(x)p(y))=∑x∈X,y∈Yp(x, y) log2p(x, y)p(x)p(y)(1.8)It can be shown from Eq. 1.8 that: I(X;Y ) = H(X)−H(X|Y ) [113], mean-ing that the mutual information I(X;Y ) is the reduction in the uncertaintyof X due to the knowledge of Y . It follows that:I(X;X) = H(X)−H(X|X)= H(X)(1.9)Eq. 1.9 is the reason that entropy is sometimes referred to as self-information,since the mutual information of X with itself is the entropy of X.1.5.3 Jensen-Shannon divergenceThe Jensen-Shannon divergence (JSD [117–119]) is an information theoret-ical functional, which quantifies the difference between two probability dis-tributions. JSD is a symmetrized version of the Kullback–Leibler divergence(DKL [116]) or relative entropy.Given two probability distributions X1 =∣∣ p11, p12, p13, · · · p1n 〉 andX2 =∣∣ p21, p22, p23, · · · p2n 〉, which satisfy the constraints ∑ni=1 pji = 1 and0 ≤ pji ≤ 1 for all i = 1, 2, ..., n and j = 1, 2. Suppose w1 and w2 denotethe weights of the distributions X1 and X2, which satisfy the constraintsw1 + w2 = 1 and 0 ≤ wj ≤ 1. The JSD between the probability distribu-15tions X1 and X2 with weights w1 and w2, respectively, is defined by Eq. 1.10[120].JSD(X1, X2) = H[w1X1 + w2X2]− (w1H[X1] + w2H[X2]) (1.10)whereH[X] = −n∑i=1pi log2 pi (1.11)is the Shannon entropy of the probability distributionX = | p1, p2, p3, · · · pn 〉.Mathematical properties of JSD1. JSD is always non-negative and has a value of zero only if two proba-bility distributions are exactly the same.JSD(X1, X2) ≥ 0 (1.12)with JSD(X1, X2) = 0 if and only if X1 = X2.2. JSD is well defined even if probability distributions are not absolutelycontinuous. That is, JSD is well-defined even if p1i vanishes withoutvanishing p2i and vice versa.3. JSD is symmetric in its arguments. That is:JSD(X1, X2) = JSD(X2, X1) (1.13)These mathematical properties make JSD to be important for its applica-tion as a divergence (or difference) measure between probability distribu-tions [120]. JSD has been used for the analysis of DNA sequences [121, 122]and to quantify differences between protein ensembles [1, 6, 119].161.6 Dimensionality reductionHigh-dimensional datasets are common in many application domains, suchas images, texts, and biological data analysis. However, only a portion ofthe dimensions (or features) is usually useful for effective decision-making.The dimension of high-dimensional datasets generally needs to be reducedin order to use them, for example in machine learning modeling tasks or tovisualize the data. The difficulty of working with high-dimensional data isdue to the problem known as The Curse of Dimensionality: most statisticaland machine learning models perform poorly because of violations in thefundamental assumptions of the models [123].Many dimensionality reduction methods, including principal componentanalysis (PCA [124]), multi-dimensional scaling (MDS [5]), and stochas-tic proximity embedding (SPE [125]) have been developed to reduce high-dimensional data and to address the problem of The Curse of Dimensionality.Dimensionality reduction methods provide, for instance, a two-dimensionalembedding of abstract data that retains relevant high-dimensional proper-ties such as local distances between data points.1.6.1 Principal component analysisPrincipal component analysis (PCA [124]) is a linear transformation methodthat generates new dimensions, called principal components, by determiningthe maximum variance of the data [124, 126].17Figure 1.4: Illustration of principal component analysis (PCA) ofa two-dimensional data. PC1 is the first principal component, whichindicates the direction of maximum data variance and PC2 is the secondprincipal component.PCA projects highly-dimensional datasets to a new subspace where theprincipal components, which are orthogonal, are considered as the direc-tions of the maximum data variance (Fig. 1.4). In the PCA transformation,the first principal component has the highest variance, followed by the sec-ond principal component, and the subsequent principal components havedecreasing variances.1.6.2 Multi-dimensional scalingMulti-dimensional scaling (MDS [5]) is a non-linear transformation methodthat focuses on the relationships, such as the distance between data pointsin a multi-dimensional space [126]. There are two main approaches forMDS, including the classic metric MDS (also known as principal coordinateanalysis), which is the most widely used, and the non-metric MDS [5]. Ingeneral, MDS is not concerned with the actual data but with the pairwisedistances (or dissimilarities) between data points. MDS represents datapoints in reduced dimensions by calculating the distance (or dissimilarity)matrix such that more similar data are closer together and less similar data18are far apart [126]. Although MDS is known to be computationally expen-sive, it is a common method used for data visualization in lower dimensions,usually in 2D or 3D because of its distance relationship preserving charac-teristics.1.6.3 Stochastic proximity embeddingStochastic proximity embedding (SPE [125]) is a self-organizing algorithmfor dimensionality reduction that produces meaningful underlying reduceddimensions from high-dimensional data. SPE attempts to generate lower-dimensional embeddings that best preserve the Euclidean distance relation-ship between a set of data points. The method starts with an initial ar-rangement of the data points, and iteratively refines it by repeatedly se-lecting pairs of points at random, and adjusting their coordinates so thattheir respective proximities correlate as best as possible with their relativedistances.SPE has a learning rate parameter, which decreases during the itera-tive process in order to avoid oscillatory behavior [125]. Unlike MDS, SPEscales linearly with respect to the number of data points and can be ap-plied to very large data sets that are intractable by conventional embeddingmethods [125].1.7 De novo computational protein designDe novo computational protein design is transforming the field of proteinengineering [127]. De novo computational protein design has enabled theaccurate design of new protein sequences, not seen in nature, that fold intohighly stable protein structures [128–135]. Prior to de novo computationalprotein design, traditional methods for designing proteins utilized existingproteins with similar desired structures or functions, and high stability to al-low mutations necessary for introducing a new desired function. Traditionalmethods have been used to designed proteins to address many biotechnolog-ical challenges [136] such as engineering new catalysts [137, 138], therapeu-19tics [139, 140], biosensors [141, 142], and self-assembling nanomaterials [143].However, the reliance on existing, naturally evolved proteins for engi-neering new proteins makes this approach limited since the number of avail-able natural proteins that are suitable for modification is limited. Althoughthe number of protein structures available in structural databases, such asthe Protein Data Bank (PDB; https://www.rcsb.org/) continues toincrease, the desired structure with the right geometry and degree of stabil-ity for introducing a new desired function may be unavailable. In addition,natural evolution has designed proteins for use in specific biological con-texts that may be unsuitable for other biological environments, which limitsthe use of natural proteins for designing new protein structures and func-tions [136]. De novo computational protein design overcomes these limita-tions in traditional methods by allowing the possibility of an infinite numberof protein structures with suitable geometry for designing new protein struc-tures and functions [136].In general, there are three main steps in the process of de novo compu-tational protein design: 1.) generating compatible backbones to a specifiedtarget topology or structure, 2.) designing appropriate amino acid sequencesfor a given backbone, and 3.) evaluating the designed sequences against thetarget structure.1.7.1 Backbone generationThe design process starts by specifying a target protein topology or struc-ture and then generating suitable sequence-agnostic protein backbones. Theprotein backbone generation aims to obtain configurations that satisfy aset of predefined requirements, such as secondary structure elements, con-tacts, and bonds. Highly designable configurations, which are more likelyto support low-energy side-chain interactions, are then selected for sequencedesign. Many methods for generating protein backbones are knowledge-based since they rely on preexisting experimental structural data depositedin structural databases, such as the PDB (https://www.rcsb.org/).The most general method for generating protein backbones is the fragments20assembly method, which utilizes preexisting structural fragments to assem-ble, in principle, any arbitrary protein geometry. The fragments assemblymethod has been successfully applied to assemble diverse protein backbonegeometries [131, 133, 134, 144, 145].The main advantage of the fragment assembly method is that it cangenerate thousands of protein backbones with the specified secondary struc-ture, geometry, and other constraints in a relatively short time. However,a limitation of the fragments assembly method is its knowledge-based com-binatorial approach, in which complexity grows exponentially depending onthe number of predefined requirements that need to be satisfied in the targetbackbone. Hence, geometric constraints or biasing functions are sometimesused to guide fragment assembly toward desired features. For instance, dis-tance constraints can be used to favor non-local contacts between elementsdistant in the amino acid sequence to bring the N- and C-termini in closeproximity [136].1.7.2 Sequence designThe goal of the sequence design step is to find amino acid sequences thatminimize the energy function for a given protein backbone. The most widelyused software for computational protein design is Rosetta [146] and the mostgeneral algorithm for sequence design in Rosetta is the Packer, which per-forms optimization of the side chain placement for a fixed protein backboneusing simulated annealing [147]. It is known that the Packer can produce asuboptimal sequence design due to limitations in the energy functions andin the sequence sampling algorithms. To address these limitations, biasesare usually introduced into the Packer in order to find optimal side chainplacements. Biases are often introduced either by adding extra energy termsto the energy function or by restricting the amino acid identities allowed ateach residue position of a given protein backbone [136].Fixed-backbone sequence design is highly dependent on the startingprotein backbone and often yields similar sequences to the backbone tem-plate. Therefore, it may be a challenge to find suitable backbone templates21for fixed-backbone sequence design. Flexible-backbone sequence design, inwhich the given backbone is allowed to undergo small perturbation and en-ergy minimization, is usually employed for de novo sequence design in orderto find optimal and more diverse sequences that form well-packed, lowerenergy protein structures [148, 149]. The FastDesign protocol in Rosetta isone of the most powerful and widely used algorithms for flexible-sequencedesign, and is the method we use in Chapter 3 (Section 3.1.4).1.7.3 Sequence evaluationThe designed sequences can be evaluated using energy landscape calcula-tions. The Rosetta ab initio structure prediction protocol [150, 151] isa commonly used algorithm for designed sequence evaluation. Startingfrom an extended chain, the ab initio structure prediction protocol per-forms low-resolution, fragment insertion conformational sampling using theMonte Carlo sampling method [111], followed by high-resolution side chainoptimization and energy minimization. Thousands of independent foldingtrajectories are usually simulated to characterize the energy landscape. Thelowest energy structures from each trajectory are taken as the predictedstructures and the root mean square deviation (RMSD) between the de-signed structure and predicted structures are calculated in order to obtainan energy versus RMSD energy landscape profile. Good designs are identi-fied as those with funnel-shaped energy landscapes, which indicate a globalenergy minimum has been found for the designed structure and the exis-tence of a considerable energy difference from alternative conformations.Moreover, frequent sampling of near-native conformations shows that thedesigned structure is easily accessible [136].Other strategies for evaluating the designed sequences, instead of charac-terizing the energy landscape, include using accurate protein structure pre-diction algorithms like AlphaFold [152] to discard designs with low predic-tion scores and/or performing comprehensive molecular dynamics (MD) sim-ulations in explicit solvent to eliminate designs with poor stability [78, 79].A major limitation, however, of using MD for evaluating designed sequences22is that it remains a costly computational technique.1.8 Research problems and objectives1.8.1 Research problemsTwo main problems are addressed in this thesis:1. How to effectively present epitopes using immunogens to raise confor-mationally selective antibodies?2. How to efficiently compare protein conformational ensembles?1.8.2 Research objectivesThis thesis has three main objectives:• To develop methods for the computational design of immunogens thateffectively present epitopes suitable for eliciting conformationally se-lective therapeutic antibodies for treating protein aggregation-relateddiseases, especially neurodegenerative diseases.• To apply the developed methods for the computational design of im-munogens to Parkinson’s and Alzheimer’s disease, which are the twomost common neurodegenerative diseases.• To develop and implement an efficient computational method for quan-titative comparison of protein conformational ensembles.1.9 Research summaryEffectively presenting epitopes using immunogens, in order to raise confor-mationally selective antibodies through active immunization, is a centralproblem in treating protein misfolding diseases, particularly neurodegener-ative diseases such as Alzheimer’s disease or Parkinson’s disease [1, 2].23To address the first objective of this thesis, we seek to selectively targetconformations enriched in toxic, oligomeric propagating species while spar-ing the healthy forms of the protein that are often more abundant. To thisend, we computationally modeled scaffolded epitopes in cyclic peptides byinserting/deleting a variable number of flanking glycines (“glycindels”), tobest mimic a misfolding-specific conformation of an epitope of α-synucleinenriched in the oligomer ensemble, as characterized by a region most readilydisordered and solvent-exposed in a stressed, partially denatured protofibril.We screen and rank the cyclic peptide scaffolds of α-synuclein in silicobased on their ensemble overlap properties with the fibril, oligomer-model,and isolated monomer ensembles. We introduce a method for screeningagainst structured off-pathway targets in the human proteome, by selectingscaffolds with minimal conformational similarity between their epitope andthe same solvent-exposed primary sequence in structured human proteins.Different cyclic peptide scaffolds with variable numbers of glycines arepredicted computationally to have markedly different conformational en-sembles. Ensemble comparison and overlap was quantified by the Jensen-Shannon Divergence, and a new measure introduced in Ref. [1]—the em-bedding depth, which determines the extent to which a given ensemble issubsumed by another ensemble, and which may be a more useful measurein developing immunogens that confer conformational-selectivity to an an-tibody.Tau pathology is associated with many neurodegenetive disorders, in-cluding Alzheimer’s disease (AD), where the spatio-temporal pattern of tauneurofibrillary tangles strongly correlates with brain atrophy and degree ofcognitive impairment, suggesting that progression of AD may be curtailedby therapeutics selective to misfolded tau [77, 153–156].As a second method for modeling and designing immunogens by scaffold-ing epitopes, we introduce a new avidity-enhanced, multi-epitope approachfor protein misfolding immunogen design, which is predicted to mimic theconformational state of an exposed epitope in toxic tau oligomers. Misfolding-specific epitopes on tau were first predicted from the locally disordered re-gions of a stressed, protofibril oligomer. The measures of local disorder24used for the prediction included loss of native contacts, increased root meansquared (RMS) fluctuations, and increased solvent accessible surface area.The predicted tau epitope 343KLDFK347 was then scaffolded by designinga β-helix protein structure that incorporated multiple instances of the 16-residue tau fragment 339VKSEKLDFKDRVQSKI354.Using Rosetta [146], 10,000 sequences were designed and screened for thelinker portions of the β-helix scaffold, along with a C-terminal stabilizingα-helix that interacts with the linkers, to optimize the folded structure andstability of the scaffold. Structures were ranked by energy, and the lowest1% (82 unique sequences) were verified using AlphaFold [152].Several selection criteria are implemented to obtain a lead designed se-quence, including correct disulfide bonding pattern, high average confidencescore (PLDDT) for the top 5 models as obtained from AlphaFold, and struc-tural similarity between AlphaFold-predicted top ranking models and theRosetta designed structure (the Cα RMS deviation was < 1.4 A˚). The struc-ture was further validated using molecular dynamics (MD) simulations toconfirm mechanical stability against unfolding, free energetic stability usingHamiltonian replica exchange MD.Large-scale conformational ensemble analyses involving Jensen-ShannonDivergence show that the multi-epitope scaffolding approach, employed indesigning the β-helix scaffold, is predicted to be better in discriminatingtoxic tau oligomers than other “monovalent” strategies utilizing a singleinstance of an epitope for immunogen design.The realization of the dynamic nature of even natively structured pro-teins has made the comparison of protein conformational ensembles, asagainst single structural comparison, centrally important in structural bi-ology. However, software for quantitative comparison of protein conforma-tional ensembles are scarce and the readily available Encore software [6]involves methods that are computationally expensive and prohibitive forlarge ensembles.To address the third objective of this thesis, a new generalized methodis presented for efficient representation and comparison of protein conforma-tional ensembles. The method is based on the representation of a protein25ensemble as a vector of probability density functions. Each probability den-sity function represents the distribution of a local structural property suchas the Cβ contact number [157, 158], and is estimated using Gaussian ker-nel density estimation [159]. The dissimilarity between two conformationalensembles is quantified by the Jensen Shannon distance [160] between cor-responding probability density functions.The method is validated for conformational ensembles generated bymolecular dynamics simulations of ubiquitin and experimentally derived con-formational ensembles of truncated human tau protein consisting of the fourmicrotuble binding repeats. More importantly, the method is implementedand made freely available as a Python package, called Prothon, which is upto 88 times faster, while utilizing 48 times fewer computing cores, than theexisting Encore software [6] on the ubiquitin ensemble dataset.26Chapter 2Modeling α-synuclein cyclicpeptide immunogen1 A key step in the development of a therapeutic antibody or active vaccineis the immunization strategy [161], namely, the choice of protein epitopeand how it will be presented to an animal or human immune system. Bothprimary sequence and conformation of the epitope determine the particularprotein morphologies to which the resulting antibodies will be selective.Nowhere has conformational-selectivity been more important toimmunotherapies than in protein-aggregation related diseases [162]. Forthis class of diseases, an effective antibody must be able to spare healthyprotein and discriminate misfolded protein species that lead to molecularand cellular pathology [161]. Since the primary sequences of healthy andaberrant protein are generally the same, barring splice variants and perhapspost-translational modifications, the efficacy of an antibody is then due toits selective preference for binding to a misfolded conformation over healthyin vivo “native” conformations.For many proteins involved in misfolding and aggregation related diseasehowever, the native conformational ensemble is intrinsically disordered [163].Examples include amyloid-β (Aβ), tau protein, α-synuclein, and the low-complexity domains in FUS and TAR DNA-binding protein 43 (TDP43).Raising an antibody that avoids the majority of diverse conformations ofan intrinsically-disordered protein’s ensemble is a challenge. For example,1A version of this Chapter has been published as Shawn C.C. Hsueh, Adekunle Aina,Andrei Yu. Roman, Neil R. Cashman, Xubiao Peng, and Steven S. Plotkin, 2022, Opti-mizing Epitope Conformational Ensembles Using α-Synuclein Cyclic Peptide “Glycindel”Scaffolds: A Customized Immunogen Method for Generating Oligomer-Selective Antibodiesfor Parkinson’s Disease, ACS Chemical Neuroscience 13(15), 2261-2280 [1].27a peptide consisting of a contiguous fragment of native primary sequencetethered to an immunogen such as keyhole limpet hemocyanin (KLH) willlikely exhibit overlap in its presented ensemble with the ensemble of isolatednative monomer.Many neurodegenerative diseases, including Alzheimer’s disease (AD),Parkinson’s disease (PD), chronic traumatic encephalopathy (CTE) andamyotropic lateral sclerosis (ALS), spread throughout the brain via a prion-like mechanism involving soluble oligomers [161, 164–171]. Soluble oligomerscontain roughly between 4 to 40 chains of protein, which exist in a misfoldedconformational ensemble that is conformationally labile and very difficult toexperimentally characterize. We computationally model some key aspects ofthe oligomer ensemble using molecular dynamics, in order to predict disease-specific epitopes.Cyclic peptides, a subclass of macrocycles, are polymers of amino acidsthat have been conjugated to form a ring-like topology (Fig. 2.1). Theyhave been increasingly used as therapeutics, often as small protein moleculedrugs to bind targets [172–176].Figure 2.1: Three-dimensional renderings for (2,3)EKTK cyclicpeptide, a scaffold of 57EKTK60 predicted epitope. (A) 3D licorice(stick) rendering with color assigned by the atom identity. (B) Render-ing of the cyclic peptide in licorice, also showing the surface of the EKTKepitope. Colors are assigned by residue name, with glycine in gray, cys-teine in orange, glutamate in blue, lysine in cyan, and threonine in ma-genta. Images were rendered with PyMOL molecular visualization system(https://pymol.org)28In this thesis, we do not address the non-trivial problem of misfolding-specific epitope prediction, which has been treated elsewhere [177] (see Meth-ods Section 2.1.1). We focus instead on the problem of how to properlypresent a predicted epitope to the immune system of an animal (or human,in the case of active immunization), so that the resulting antibodies gener-ated by the animal are selective to disease-specific forms of the protein.We start from computationally generated ensembles of the α-synucleinfibril, isolated monomer, and stressed, partially disrupted proto-fibril as de-fined below, which is used as a model for the toxic oligomer—the form ofthe protein we wish to target with conformationally selective antibodies.The α-synuclein oligomer model was generated computationally. Althougholigomer structures involving select portions of the primary sequence con-strained into peptide macrocycles have been crystallized [178], no full-lengthα-synuclein oligomer structure or ensemble, or partial length α-synucleinoligomer structure containing our epitopes of interest, has been experimen-tally characterized at this time.We briefly review the epitope prediction method originally described inRef. [177], which is applied here to an α-synuclein protofibril. Given anepitope and an oligomer model, we then construct various cyclic peptideimmunogen constructs of that epitope by varying the number of glycinesflanking the epitope on the N- and C- termini, which we term “glycindel”scaffolds. Here we introduce only glycines as extrinsic amino acids, as theyare relatively non-immunogenic, which avoids potential immunological tar-geting of regions outside of the epitope of interest. Within this restrictedspace of extrinsic sequence and structure, we determine the optimal scaf-folding of the cyclic peptide construct, by maximizing the overlap with thestressed fibril ensemble and minimizing the ensemble overlap with either themonomer or the unstressed “native” fibril. We also minimize the tendencyof antibodies to a scaffolded epitope to elicit off-pathway targeting, by mini-mizing the conformational similarity to unrelated structured proteins in thehuman proteome that contain the epitope’s primary sequence.Using the above features as screening criteria, we used a ranking method[179] involving multi-criteria decision making analysis to systematically rank29the scaffolds from best to worst. Such a ranking allows for the experimental-ist to construct a reduced number of cyclic peptide scaffolds that are mostlikely to have the desired features of eliciting antibodies with conformation-ally selective binding to toxic oligomer species.The pipeline of the in silico screening method is given in Fig. 2.2. Eachstep is described in the Methods. In the Results, we visually depict the pro-jection of simulated ensembles in reduced conformational space, and we for-malize the ensemble overlap. We then develop the above-described methodto find off-pathway targets for a given scaffold, and rank 48 candidate cyclicpeptide scaffolds.Finally, we discuss the non-trivial question of weight assignments forranking candidates, alternate scaffolding methods, the validity of the vir-tual screening method, the benefits of in silico screening to facilitate moreefficient in vitro and in vivo screening, and the sensitivity or robustness ofepitope prediction depending on the structural model of the fibril used inthe epitope prediction algorithm.302.1 MethodsFigure 2.2: The workflow of modeling cyclic peptide “glycindel”scaffolds and in silico screening.2.1.1 α-synuclein epitope predictionIn our approach, we operate from the hypothesis that a partially disor-dered protofibril ensemble is enriched in oligomer-selective conformationalepitopes. That is, similar regions are exposed in both toxic oligomers andstressed protofibrils. If so, the stressed fibril may be used to predict oligomer-selective epitopes. This hypothesis is supported by previous in vitro and invivo experiments [177, 180, 181].The 57EKTKEQ62 epitope in α-synuclein was predicted by the CollectiveCoordinate (CC) algorithm [1], which has been used previously to predictmisfolding-specific epitopes in superoxide dismutase 1 (SOD1) [177]. TheCC algorithm predicts epitopes by identifying local unfolding events whena global denaturing stress is applied, where regions of a protein or multi-protein aggregate deviate structurally from their native structural conforma-tion. Three measures are used to quantify local disorder: increased solventaccessible surface area (∆SASA), loss of native contacts (∆Q), and increased31root mean squared fluctuations (∆RMSF).The procedure for predicting an epitope involves implementing a globalunfolding potential, which biases the system to have about 35 to23 of itstotal native contacts. For the prediction of α-synuclein epitopes we useda value of 0.65. Ten independent biased ensembles of an α-synuclein fib-ril structure (PDB ID: 2N0A) using the CC algorithm, as well as a single“native basin” ensemble of the fibril using molecular dynamics (MD) simula-tion [177], are generated to calculate ∆SASA, ∆Q and ∆RMSF. The “nativebasin”ensemble serves as a reference for calculating the above three differ-ence values. Multiple independent biasing simulations were performed inorder to ensure consistency in the regions of the fibril structure that are ob-served to have relatively higher values of ∆SASA, ∆Q and ∆RMSF, therebyavoiding predictions based on rare fluctuations that might be present in asingle biased simulation.Fig. 2.3 A shows the sequence motifs larger than 3 amino acids that arepredicted as epitopes by each of the three measures, for each of the 5 chainsin the protofibril structure (PDB 2N0A). Several epitopes were predictedby each measure. Fig. 2.3 B shows a relative per residue weighted sum of∆SASA, ∆Q and ∆RMSF over all chains with the boundary chains in thefibril structure having half the weight of other chains.Epitope 57EKTKEQ62,with the highest weighted sum (Ω), was taken as the final predicted epitopefor α-synuclein (Fig. 2.3 B).32Figure 2.3: Collective coordinate epitope prediction for α-synuclein,using three criteria of increased SASA, loss of native contacts, andincreased fluctuations (RMSF). (A) Several epitopes were predicted byeach criterion; however, only a single epitope 57EKTKEQ62 was predictedby (B) weighted averaging. Chain E is not shown for ∆SASA because noepitope is predicted. (Figure adapted from Ref. [1])2.1.2 Scaffolding of epitopesWe scaffold epitopes by constructing cyclic peptides containing both the epi-topes and a variable number of glycines. We refer to the resulting scaffoldsas glycindels. First, the predicted epitope (57EKTKEQ62), or a shortersequence that is subsumed by the epitope such as 57EKTK60, 58KTKE61or 59TKEQ62, is flanked on both sides with consecutive glycines. This isimplemented computationally by mutating the native flanking residues toglycine using SCWRL4 [182], a program for the prediction of protein side-chain conformations. In addition, one more residue is mutated to cysteine33on the N-terminal side of the sequence. Although in principle, other aminoacids or a combination thereof can be utilized, our choice of using glycineshelps to focus immunogenic effects to just the epitope, since glycine is rel-atively chemically inert compared to other amino acids, and has minimalimmunogenicity [183]. The cysteine is present to conjugate the peptides toimmunogens such as Bovine serum albumin (BSA) or Keyhole limpet hemo-cyanin (KLH) via a disulfide bond, increasing the likelihood of generatingantibodies to the scaffolded epitope.The topology of the cyclic peptide is obtained by head-to-tail linkage ofthe termini using a locally written Python script [1]. We refer to a cyclicpeptide epitope with n N-terminal glycines and m C-terminal glycines ascyclo(C-Gn-(Epitope)-Gm) or (n,m)Epitope (see Fig. 2.1). The cyclizedpeptide is then energy minimized in GROMACS [84, 184] using steepestdescent algorithm, before running equilibrium MD simulations.2.1.3 Generation of ensemblesGenerally, we collect four different equilibrium molecular dynamics (MD)ensembles for each epitope. These correspond to the epitope in the con-text of an isolated monomer, the fibril, the stressed fibril oligomer model,and the cyclic peptide scaffold. We perform MD simulations with theopen-source GROMACS [84, 184] package and the community-developedPLUMED library [185]. The force field used here for all ensemble samplingis CHARMM36m [89], which is a modified version of CHARMM36 with im-proved modeling for disordered proteins. Each epitope ensemble is obtainedspecifically as follows.Fibril ensembleThe conformational sampling starts from an existing experimentally re-solved α-synuclein structure determined by solid-state NMR [186] (PDBID: 2N0A). A protofibril composed of 5 chains (chains A-E of 2N0A) issolvated in 150mM Na and Cl aqueous solution, such that the system isneutral. After 50ps constant volume (NVT) and 150ps constant pressure34(NPT) equilibrium simulations under positional restraints on heavy atoms,we perform an equilibration MD simulation up to 100ns until the conver-gence is seen from RMSD during the simulation. A 20ns equilibration MDcontinued from the previous 100ns simulation is then performed, for collect-ing the “native basin”ensemble of the fibril, from which we sample snapshotsat 20ps intervals. Only configurations of the middle chains (chain B-D) arecollected in the ensemble, in order to reduce edge effects in the simulation.In total, the regularly spaced sampling results in 3003 configurations in thefibril ensemble obtained by this procedure. The above procedures of sol-vation and NVT-equilibration and NPT-equilibration are also implementedfor the other ensembles described below, before the MD production runs.Stressed fibril ensembleThe stressed fibril ensemble is a partially disordered fibril ensemble used topredict conformational epitopes similar to what might be presented by theoligomer. To generate this ensemble, a time-dependent global bias potentialV (Q, t) is implemented to partially unfold the α-synuclein fibril, whereV (Q, t) =12k(Q−Qc(t))2 (2.1)Q in equation (2.1) is a collective coordinate defined as the normalizedcount of the native contacts [1, 177]: Native contacts are pairs of heavy(non-hydrogen) atoms within 4.8 A˚ of each other that are in different aminoacids labeled by primary sequence residue index α, β, that satisfy |α− β| ≥3, and persist over 5 percent of the time in the first 100ns of equilibriumfibril simulation. Formally, the collective coordinate Q for any structurecharacterized by a set of heavy atom distances, rij , is defined as follows:Q =∑Nij Qij(rij)∑Nij 〈Qij(rij)〉native(2.2)whereQij(rij) =1− ( rijr0 )n1− ( rijr0 )m(2.3)35where we take r0 = 4.8 A˚, n = 6 and m = 12. Equation (2.3) approachesa step function for large m and n (for m > n), but is smooth and differen-tiable [177], which is a desirable property for the contact function. A contactfunction Qij(rij) is defined for each heavy-atom pair i, j in the list of nativecontacts, which rapidly goes to one when rij is slightly lower than r0 andrapidly goes to zero when rij is slightly larger than r0. The quantity in thenumerator of Q in equation (2.2) is the sum of Qij in an arbitrary structure,where∑Nij is summation over the native contact list, and the quantity inthe denominator is the Boltzmann average of the Qij in the fibril “nativebasin” ensemble. Thus, Q is typically a number between zero and unity.Qc(t) in equation (2.1) stands for the target value of the collective co-ordinate, Q. It is a time-dependent quantity that starts from a value corre-sponding to the counts of all native basin contacts in the fibril metastableequilibrium ensemble (Qc = 1), which is then taken to linearly decrease withtime, from Qc = 1 to Qc = 0.65 over 50 ns. Afterward, the bias is held fixedat Qc = 0.65 for 150ns. During the last 50ns of this second period when Qcis held fixed at 0.65, snapshots from the stressed fibril ensemble are collectedat an interval of 15ps.The above process is repeated 10 times, including the ramp down andsubsequent biased equilibration and sampling, to average the stochastic un-folding process of the protofibril and obtain a reliable biased ensemble. Thecapping chains at the ends of the fibril are discarded to avoid edge effects,yielding a total ensemble consisting of 50ns/15ps ∗ 3 chains ∗ 10 repeats =100000 sampled structures. A subset with 3500 configurations is randomlysampled from the total structural ensemble for efficiency of the calculation.In order to obtain an ensemble of the epitope that is partially disorderedand exposed to solvent, we add on additional constraint on SASA of theepitope in the ensemble, as follows. Among the 3500 configurations, wefurther discard those structures that have a lower epitope SASA than theequilibrium epitope SASA, generating a stressed fibril ensemble with ex-posed epitope consisting of 3407 configurations. We note that at this pointthe epitope has already been predicted, and the above calculations are forcomparison of the stressed/exposed protofibril ensemble with cyclic peptide36scaffold motifs.Monomer ensembleSince α-synuclein is an intrinsically disordered protein (IDP) [187], its equi-librium ensemble is relatively difficult to sample sufficiently by normal MDsimulation [188]. Here, we apply the method in Ref. [189] to generate anequilibrium monomer ensemble for α-synuclein. The steps involved in ourensemble generation include: 1.) Generation of a conformationally diverseensemble via the pivot algorithm and a “crankshaft” move wherein two ran-domly selected end points are fixed [189, 190], and 2.) Equilibration of eachpivot– and crankshaft–randomized structure for a short simulation time.The descriptions for these steps are as follows.The initial α-synuclein monomer configuration is obtained by extractinga single chain from the fibril structure (PDB ID: 2N0A). This structure isthen altered by employing a generalization of the pivot algorithm [191–194],which is an efficient algorithm for generating ensembles for a self-avoidingrandom walk, as well as a “crankshaft” move [189, 190] that randomizes φand ψ angles between two randomly-selected backbone atoms along the pep-tide chain, such that the randomly-selected backbone atoms remain fixed.Pivot moves and crankshaft moves are attempted with equal probability. Ifa move results in a steric clash, it is rejected, and the next randomly selectedmove is then attempted.We take a simple approximation wherein φ and ψ are sampled from a(2pi periodic) von Mises probability distribution with mean 0 and variance 1,i.e. ecosφ/(2piI0(1)), where I0 is the modified Bessel function of order 0. Piv-ot/crankshaft moves are repeatedly attempted until there are N successfulpivot/crankshaft moves, where N is the length of the chain. This processcompletely randomizes the conformation such that information about theoriginal structure is lost.After a randomized conformation is obtained, the structure is then sol-vated in a box determined by the principal axes wherein the peptide is atclosest 1.2 nm from the box edges. The structure is then energy minimized,37equilibrated in explicit modified TIP3P water and 150mM salt in an NVTensemble for 100ps, and then equilibrated in an NPT ensemble for 300ps.This process generated 1587 different structures as initial configurations.We then performed a 3ns equilibrium simulation starting from each of theabove initial configurations, collecting a snapshot every 1ns to be added tothe monomer ensemble. As a result, we obtained a monomer ensemble with4643 configurations (i.e. 93 simulations did not reach 3ns and 16 simulationsdid not reach 2ns within the simulation wall-clock time, due to variable sim-ulation box sizes). IDP ensemble generation is an active area of researchand several other methods of computational ensemble generation have beendeveloped [195].Scaffolded epitope ensemblesThe construction of the initial structure used for scaffold simulations isdescribed in Methods Section 2.1.2. After minimization, solvation, NVT-equilibrium and NPT-equilibrium simulation, a 300ns MD simulation is car-ried out, from which an initial ensemble is collected with constant samplinginterval of 40ps. Since the cysteine side chain has to be solvent-accessible toform a disulfide bond with the carrier protein (KLH or BSA), some config-urations were discarded if the SG atom in the cysteine was buried or if thesidechain of the cysteine pointed inside the cyclic peptide: The SG atomis defined as buried if its SASA is lower than 70% of that in an isolatedGly-Cys-Gly tripeptide (80A˚2). The cysteine side chain is defined as inwardpointing if its dihedral angle ψ (angle between CB atom and the backboneplane) is within [-90, 90] degrees. In practice, the scaffolded cyclic peptideensembles thus processed have a different number of configurations for eachcyclic construct, ranging from 2352 to 5468 configurations. The fraction ofthe ensemble that satisfied the above criteria varied from about 39% to 97%.382.1.4 Projecting ensemble distributions to lower dimensionWe first let N be the sum of the number of structures in all four ensembles:Monomer, fibril, stressed fibril, and cyclic peptide scaffolds (Here N rangesfrom 13369 to 16485). We then construct a pairwise root mean squareddeviation (RMSD) matrix that consists of the RMSD between any two epi-tope (EKTK, KTKE, or TKEQ) structures in any of the four ensembles.Each row of the N ×N matrix contains the distances (RMSD values) fromone structure. Two rows then constitute a 2-dimensional space giving thedistances to two structures determined by which rows have been chosen. Nrows, corresponding to the whole matrix, thus constitute an N -dimensionalspace where the location of each of N points, corresponding to each struc-ture, is determined by the set of distances (RMSD) to all other structures(including itself). The set of N structures is thus represented by a distribu-tion of points in an N -dimensional space.Multidimensional Scaling (MDS) [5] or Stochastic Proximity Embedding(SPE) [6, 125] was performed on the RMSD matrix to reduce the dimensionfrom N ×N to N ×D where D is the desired lower dimension. The valueof D depends on the application as described below. As well, whether MDSor SPE is used depends on the application, and will be described in detailin Sections 2.1.5, 2.1.6, and 2.1.8 below.Applying MDS or SPE results in an ensemble of points in a reduced num-ber of D dimensions. We then fit the effective distribution of the N pointsin D dimensions using kernel density estimation (KDE) [6, 159]. Since KDEperformance worsens exponentially with higher dimensional data sets as aresult of the so-called “curse of dimensionality” [196], a dimensional reduc-tion step is essential. A particular ensemble, e.g. the monomer structuralensemble, has a structural distance distribution in the RMSD matrix. Thisstructural distance distribution has a corresponding KDE distribution ofpoints. We refer to this KDE structural distance distribution as simply thestructural distribution below.392.1.5 Calculating ensemble overlap in 1DWe visualize the similarity between two ensembles intuitively by representingthem in 1D (this is not used as a ranking criterion). The overlap is the per-centage of a KDE distribution that overlaps with another KDE distribution.The formula we use here for the overlap is: Overlap = 1− 12∫∞−∞ |P −Q| dx,where x is the first MDS coordinate, and P (x) and Q(x) are two KDE dis-tributions in this 1D coordinate. For example, for two Gaussians of unitvariance and mean separation a, the overlap is 1− erf (a/(2√2)).2.1.6 Ensemble similarity measuresWe compare conformational ensembles of the epitope in the four differentcontexts, including monomer, fibril, stressed fibril and cyclic scaffold, usingtwo measures: Embedding Depth and Jensen-Shannon Divergence. Theseare defined as follows.Embedding depthThe embedding depth is most easily understood when taken as a measurebetween a single structure and a given ensemble. In this context, the em-bedding depth quantifies how deeply that structure is embedded within theensemble, when both structure and ensemble are projected onto some coor-dinate metric such as MDS coordinates. The structure-to-ensemble embed-ding depth Dδ(x−xo)|P , for a structure characterized by a point at x = xoembedded in a distribution P (x), is defined as the fraction of the ensemblethat has a lower KDE probability than the particular structure (Fig. 2.4):Dδ(x−xo)|P =∫ ∞−∞dxP (x)Θ (P (xo)− P (x)) . (2.4)In equation (2.4), Θ(P ) is the Heaviside step function, which returns 1 ifP > 0, otherwise 0.40Figure 2.4: Illustration of the embedding depth of the point xo ina multimodal distribution P (x). The embedding depth of point xo isgiven by the integral over all parts of the distribution with probability lessthan P (xo). Note there are 4 points with the same P (xi) = P (xo) and thusthe same embedding depth. (Figure adapted from Ref. [1])The mode of a distribution has an embedding depth of one because allof the ensemble has a lower KDE probability than the mode. On the otherhand, outliers of a distribution have embedding depths close to zero.The embedding depth of one distribution Q(x) within another P (x) canbe found by integrating equation (2.4) over the distribution Q(x):DQ|P =∫ ∞−∞dxQ(x)∫ ∞−∞dx′ P (x′)Θ(P (x)− P (x′)) . (2.5)The embedding depth between two distributions is in general non-reciprocal,in that DQ|P 6= DP |Q. It is straightforward to show that the embeddingdepth of a distribution within itself DP |P = 1/2. This follows because thespecial case of DP |P must be symmetric (reciprocal), so that switching x41and x′ in DP |P must yield the same equation. Therefore,DP |P =∫ ∞−∞∫ ∞−∞dx dx′ P (x)P (x′)Θ(P (x)− P (x′))=∫ ∞−∞∫ ∞−∞dx dx′ P (x)P (x′)12[Θ(P (x)− P (x′))+ Θ (P (x′)− P (x))]=∫ ∞−∞∫ ∞−∞dx dx′ P (x)P (x′)12(1) =12. (2.6)When used to compare two conformational ensembles, DA|B or DA-in-Brepresents the extent to which the ensemble A is subsumed by ensembleB. Asimilar concept in measuring the embedding of one ensemble in the other hasbeen introduced before in the context of statistics [197], but we are not awareof such a measure being previously applied to conformational ensemble com-parison. The embedding depth measures used for ranking (Dcyclic-in-stress,Dcyclic-in-monomer, and Dcyclic-in-fibril) are calculated in an MDS-reduced 3Dconformational space, where 95% of the matrix information can be preserved(Fig. 2.5A). Discrete, small sample size effects may also be considered forthe embedding depth, however these effects are unlikely to arise in practicefor conformational ensembles, which are typically large enough to achieveconvergence.Figure 2.5: Convergence analysis for SPE and MDS dimensionalreduction. Convergence of dimensional reduction for (A) multidimensionalscaling (MDS) for embedding depth and (B) stochastic proximity embed-ding (SPE) for JSDs. Both quantities are plotted vs. the dimension of thereduction. The scaffold used here for illustration is (1,4)TKEQ. (Figureadapted from Ref. [1])42Jensen-Shannon Divergence (JSD)The similarity between two different ensemble distributions is measured us-ing the Jensen-Shannon Divergence (JSD) [117–119], which is implementedhere using the ENCORE software [6]. JSD is a symmetrized and smoothedversion of the Kullback–Leibler divergence [198, 199], DKL, which is a dif-ference measure between two distributions. JSD is defined byJSD(P,Q) =12DKL(P,M) +12DKL(Q,M) (2.7)whereDKL(P,Q) =∫ ∞−∞P (x) log(P (x)Q (x))dx (2.8)where P (x) and Q(x) are two conformational ensembles in SPE-reduceddimensional space, and M is defined by the average of the two distributionsP and Q: M(x) = (P (x) +Q(x))/2.The value of the JSD measure depends on the dimensionality of theSPE-reduced space, with lower dimension tending to have smaller JSD (i.e.more overlap). The JSD values used for ranking cyclic peptide scaffolds(JSDcyclic-fibril, JSDcyclic-monomer, and JSDcyclic-stress) are produced by weightaveraging the JSD from 3D to 11D by the inverse of the SPE residuals ineach dimension (Fig. 2.5 for these residuals). By this measure, the higherdimensions contribute more to the weighted average JSD. The convergencetest in Section 2.1.7 shows that the information loss is about 3% in 3Dand the information loss is less than 1% in 11D for scaffold (1,4)TKEQ forexample (Fig. 2.5). JSD as calculated in equation (3.6) ranges from 0 tolog(2), but in this thesis, we normalize JSD to lie between 0 to 1.2.1.7 The convergence of JSD and embedding depthHere, we show the convergence of the dimension reduction performance onthe pairwise RMSD matrix that describes fibril, stressed fibril, monomerand (1,4)TKEQ ensemble. Stochastic Proximity Embedding (SPE) [6, 125]is performed to calculate JSD in reduced dimension. The different degreesof convergence in 3-11 dimensions (See Fig. 2.5B) motivated us to use a43weighted average JSD across several dimensions, by weighting the JSD ineach dimension by the inverse of the residual in that dimension. In practice,this weights higher dimensions more than lower dimensions.Multidimensional scaling (MDS) is performed to calculate embeddingdepth in reduced dimension. Since the residual quickly converged in dimen-sions of 3 or larger, (See Fig. 2.5A), we simply perform the embedding depthmeasure in 3D.The residual of the MDS and SPE are defined respectively as follows:ResidualMDS =∑i<j (dij − rij)2∑i<j r2ij(2.9)ResidualSPE =∑i<j(dij − rij)2rij/∑i<jrij (2.10)In equations (2.9) and (2.10), index i and j correspond to two differentrows in a pairwise RMSD matrix including the fibril ensemble, the stressedfibril ensemble, the monomer ensemble, and a given cyclic peptide scaffoldensemble. Before any dimensional reduction, the RMSD matrix is an N×Nmatrix, where N is the sum of the number of configurations of the abovefour ensembles, and the indices i and j run from 1 to N . dij and rij are theEuclidean distance between ith and jth row of the RMSD matrix in reduceddimension and in the original dimension, respectively.2.1.8 Evaluating off-pathway target criteriaWe search through the RCSB database (https://www.rcsb.org) of re-solved protein structures, to find potential off-pathway targets of antibodiesthat could be generated by each cyclic peptide scaffold. An off-pathwaytarget of concern meets three conditions: 1.) same primary sequence asthe epitope in the PDB structure, 2.) structural similarity to scaffoldedepitope, and 3.) sufficiently high solvent exposure so that it is likely to beantibody-accessible.The first criterion is assessed by finding “hits” when searching through44the RCSB database (e.g. any protein that contains one or more TKEQmotifs). The second criterion is assessed by the PDB entry’s structuralembedding depth in the scaffolded cyclic peptide ensemble. The embeddingdepth is calculated in the MDS-reduced 5D space of the RMSD matrix. Thethird criterion is assessed by finding the fraction of the glycindel–scaffoldedepitope ensemble with less solvent-accessible surface area (SASA) than thePDB entry (i.e. f(SASAoff-target-exceed-cyclic)).The severity of a potential off-pathway target for a given scaffold is deter-mined by summing, over all PDB structure “hits”, the product of the struc-tural embedding depth (Doff-target-in-cyclic) and the fraction of cyclic peptideensemble SASA exceeded (f(SASAoff-target-exceed-cyclic)). The criterion usedfor ranking (before a linear rescaling) is the negative of this severity , whichis represented by equation (2.11) below:OPunscaled = −∑PDB “hits”Doff-target-in-cyclic × f(SASAoff-target-exceed-cyclic)(2.11)By this convention, a higher (less negative) criterion value corresponds to amore favorable scaffold. SinceDoff-target-in-cyclic and f(SASAoff-target-exceed-cyclic)are very small for most RCSB entries (i.e. most entries are not of significantconcern), we employ a cut-off criterion wherein D and f have to both exceed5% for the entry to be included in a criteria calculation. Finally, the criteriaare linearly rescaled to be within the range [0,1].Sometimes, the epitope appears multiple times in a single RCSB PDBentry because of multiple deposited models, multiple chains or repetitiveepitope occurrence on a single chain. If such multiple occurrence happens,the Doff-target-in-cyclic and f(SASAoff-target-exceed-cyclic) in equation (2.11) aretaken as the average of the values over all epitope occurrences in the corre-sponding PDB entry.The search result in the RCSB database will also contain the fibrillar andstructured monomer α-synuclein entries. The fibril entries are excluded fromthe off-pathway target calculation, because we have already compared cyclicand fibril ensembles using JSDcyclic-fibril. We have also compared cyclic and45unstructured monomer ensembles using JSDcyclic-monomer, however monomerstructures in the RCSB database are kept because they are assumed tobe at least partially structured due to effects such as peptide-membraneinteractions.Weaker binding of antibodies has occasionally been observed in epitopemapping by alanine scans, particularly in longer epitopes. This binding tosingle point mutants occurs more commonly in the peripheral regions of theepitope, and may generally be an important consideration. Our epitopelengths are only 4aa however, so mutation of one amino acid would be asignificant 25% change in identity. We thus have not explored single pointmutants in the off-pathway analysis here.2.1.9 SMAA-TOPSIS ranking algorithmScaffolds are ranked using an adaptation of the so-called SMAA-TOPSISalgorithms, which stand for a combination of Stochastic Multi-criteria Ac-ceptability Analysis and Technique for Order Performance by Similarity toIdeal Solution [200]. The ranking algorithm we employ here uses a cumula-tive measure of the retention probability that a candidate is retained in thetop n leads [179]. The method generates a ranking of candidates when mul-tiple criteria are used for screening the candidates, and when those screeningcriteria have an unknown predictive importance a priori.The screening criteria as well as the importance weights for those criteriaare both subject to error, and an exact weight assignment for the importanceof the screening criteria is not needed. Instead, weight distributions areassigned, where the mean weight w represents the relative importance of eachcriterion and the standard deviation of the weight distribution represents theuncertainty in the importance for that criterion. The weight distribution istaken to be a uniform distribution:f (w) =12∆(if w −∆ < w < w + ∆)0 (elsewhere)(2.12)where w stands for the mean (or center) and ∆ stands for the distribution46width. In this thesis, all the criteria have ∆ = 0.5 (or equivalently standarddeviation σ of 0.288). The mean weights for each criterion are given inTable 2.1:Table 2.1: Mean weights of SMAA-TOPSIS ranking criteria.Criterion Mean weight wJSDcf 1JSDcm 11 - JSDcs 0.51- Dc|f 11- Dc|m 1Dc|s 0.5Off-target 1.5Subscript c=cyclic, f=fibril, s=stressed fibril, and m=monomer. See alsoTable 2.2.The ranking algorithm rescales all screening criteria to unity so weightscan be properly applied. The Ideal Best and Ideal Worst entries are givensimilarity screening criteria of either all 1’s or all 0’s respectively; Thesenumbers are given for each scaffold in Table 2.2. The table includes the3 sub-epitopes EKTK, KTKE, and TKEQ of the longer predicted epitopeEKTKEQ.47Table 2.2: Ranking criteria and rankings for α-synuclein epitope scaffolds. The abbreviations JSDcf ,JSDcm, JSDcs, Dc|m, and Dc|s correspond to JSDcyclic-fibril, JSDcyclic-monomer, JSDcyclic-stress, Dcyclic-in-monomer, andDcyclic-in-stress, respectively. OP corresponds to off-pathway targeting.Rank scaffold scaffold symbol JSDcf JSDcm JSDcs Dc|f (×10−5) Dc|m Dc|s OP0 Ibest Ibest 1.00000 1.000 0.000 0 0.000 1.000 1.0001 CGEKTKGGG (1,3)EKTK 0.99979 0.897 0.751 0 0.052 0.107 1.0002 CGGEKTKGGG (2,3)EKTK 0.99978 0.849 0.765 0 0.093 0.147 0.9793 CGGGEKTKGG (3,2)EKTK 0.99979 0.850 0.768 0 0.104 0.124 0.9594 CGEKTKGG (1,2)EKTK 0.99979 0.980 0.916 0 0.009 0.058 0.9865 CGGTKEQGGG (2,3)TKEQ 0.99833 0.869 0.740 12 0.128 0.177 0.8936 CGGEKTKGGGG (2,4)EKTK 0.99978 0.822 0.700 0 0.094 0.160 0.8927 CGGGEKTKGGGG (3,4)EKTK 0.99955 0.686 0.675 0 0.235 0.225 0.9718 CGEKTKG (1,1)EKTK 0.99979 0.961 0.951 0 0.011 0.019 1.0009 CGGGGEKTKGG (4,2)EKTK 0.99977 0.804 0.786 0 0.140 0.135 0.95210 CGGEKTKGG (2,2)EKTK 0.99967 0.886 0.875 0 0.082 0.061 1.00011 CGGTKEQGGGG (2,4)TKEQ 0.99974 0.905 0.871 0 0.144 0.084 1.00012 CGEKTKGGGG (1,4)EKTK 0.99974 0.889 0.917 0 0.070 0.061 1.00013 CGGTKEQGG (2,2)TKEQ 0.99979 0.975 0.976 0 0.058 0.038 1.00014 CGGGEKTKGGG (3,3)EKTK 0.99979 0.737 0.742 0 0.170 0.142 0.95815 CGGKTKEG (2,1)KTKE 0.99979 0.996 0.999 0 0.010 0.000 1.00016 CGGGTKEQGG (3,2)TKEQ 0.99951 0.904 0.903 0 0.122 0.049 0.99517 CGGGTKEQGGG (3,3)TKEQ 0.99974 0.911 0.877 0 0.193 0.076 0.99118 CGGEKTKG (2,1)EKTK 0.99979 0.948 0.962 0 0.058 0.022 0.98719 CGGTKEQG (2,1)TKEQ 0.99979 0.995 1.000 0 0.015 0.001 0.99120 CGKTKEGG (1,2)KTKE 0.99979 0.976 0.998 0 0.018 0.001 1.00021 CGTKEQGGGG (1,4)TKEQ 0.99979 0.972 0.943 0 0.037 0.044 0.91722 CGKTKEG (1,1)KTKE 0.99978 0.966 0.999 0 0.030 0.000 1.00023 CGTKEQG (1,1)TKEQ 0.99979 0.967 0.995 0 0.084 0.011 1.00024 CGGGKTKEGG (3,2)KTKE 0.99979 0.954 0.995 0 0.034 0.002 0.9844825 CGTKEQGG (1,2)TKEQ 0.99979 0.951 0.971 0 0.150 0.019 1.00026 CGGGGEKTKGGG (4,3)EKTK 0.99973 0.723 0.661 0 0.187 0.200 0.81127 CGGGEKTKG (3,1)EKTK 0.99979 0.964 0.991 0 0.043 0.004 0.91028 CGGGGTKEQGGG (4,3)TKEQ 0.99925 0.902 0.834 1 0.099 0.084 0.80129 CGGGGEKTKGGGG (4,4)EKTK 0.99931 0.509 0.649 0 0.452 0.331 1.00030 CGGGGTKEQG (4,1)TKEQ 0.99979 0.934 0.994 0 0.184 0.005 0.97331 CGKTKEGGG (1,3)KTKE 0.99956 0.917 0.997 7 0.142 0.000 0.94432 CGGGTKEQG (3,1)TKEQ 0.99979 0.925 0.991 0 0.100 0.007 0.89633 CGGGGKTKEG (4,1)KTKE 0.99969 0.816 0.962 0 0.196 0.013 0.98734 CGGGGEKTKG (4,1)EKTK 0.99979 0.879 0.919 0 0.091 0.035 0.83435 CGGGKTKEGGG (3,3)KTKE 0.99922 0.809 0.953 5 0.197 0.012 0.94036 CGGGGKTKEGGG (4,3)KTKE 0.99599 0.725 0.881 35 0.257 0.047 0.93237 CGGKTKEGG (2,2)KTKE 0.99873 0.859 0.942 13 0.349 0.056 0.93338 CGTKEQGGG (1,3)TKEQ 0.99978 0.922 0.936 0 0.070 0.054 0.73239 CGGGKTKEG (3,1)KTKE 0.99974 0.991 0.999 0 0.097 0.000 0.70540 CGGKTKEGGGG (2,4)KTKE 0.99791 0.708 0.947 6 0.312 0.017 0.88441 CGKTKEGGGG (1,4)KTKE 0.99929 0.757 0.969 0 0.239 0.004 0.77742 CGGGKTKEGGGG (3,4)KTKE 0.99958 0.706 0.901 0 0.548 0.089 0.96343 CGGGGTKEQGGGG (4,4)TKEQ 0.99861 0.840 0.726 2 0.142 0.144 0.51944 CGGKTKEGGG (2,3)KTKE 0.99966 0.822 0.976 0 0.091 0.004 0.59145 CGGGGKTKEGG (4,2)KTKE 0.99420 0.567 0.788 138 0.448 0.142 0.54746 CGGGGTKEQGG (4,2)TKEQ 0.99979 0.958 0.940 0 0.084 0.032 0.28147 CGGGGKTKEGGGG (4,4)KTKE 0.99445 0.586 0.829 90 0.267 0.045 0.41548 CGGGTKEQGGGG (3,4)TKEQ 0.99979 0.903 0.972 0 0.221 0.009 0.00049 Iworst Iworst 0.00000 0.000 1.000 105 1.000 0.000 0.00049All 48 scaffolds show strong dissimilarity to fibril, whereas other screen-ing criteria show more variance (Table 2.2). The compression of valuesfor JSDcf around unity means that all scaffolds perform similarly. For thiscriterion, the ideal worst entry is still taken to be 0 (although no scaffoldperformed that poorly), rather than the lowest value followed by a rescal-ing to 0. This procedure thus prevents insignificant discrepancies betweenscaffolds from being amplified. Similarly, the values of Dc|f are all either es-sentially zero or very small, so we take the ideal worst entry to be 1 and theideal best to be 0, to avoid ranking on statistically-insignificant differences.A server where the SMAA-TOPSIS algorithm may be run to rank the users’own data can be found at http://bjork.phas.ubc.ca. The server canselect and rank candidate leads from multiple competing screening tests thatwould otherwise make the selection of leads a nontrivial maximum-likelihoodranking problem [179].502.2 Results and DiscussionUsing the collective coordinates epitope prediction algorithm [177], aminoacid sequence 57EKTKEQ62 (residues 57-62 in α-synuclein) was predictedas a misfolding-specific epitope [201] (Fig. 2.3). To dissect the key aminoacids in this epitope, we have analyzed three separate contiguous sequencessubsumed by the epitope, namely 57EKTK60, 58KTKE61, and 59TKEQ62.2.2.1 Comparing ensembles in reduced conformationalspaceIn order to determine epitope scaffolds that may be capable of eliciting an-tibodies that are conformationally selective to soluble oligomers, the confor-mational ensemble of an epitope in a cyclic peptide scaffold is compared withthree other ensembles of the epitope, namely, the monomer, fibril, and thestressed (partially disordered) fibril. The stressed fibril is taken as a proxyfor the conformational ensemble of the epitope in a soluble oligomer as de-scribed in Methods Section 2.1.3. A desired cyclic peptide scaffolded epitopeconstruct that is oligomer-selective would have high ensemble similarity tothe stressed fibril, and as well, low ensemble similarity to the equilibriumfibril and isolated monomer.To determine the similarity between the four epitope ensembles (i.e.scaffold, stressed fibril, fibril, and monomer), we first generated these en-sembles by performing molecular dynamics (MD) simulations (see MethodsSection 2.1.3). The conformational similarity of the epitope between en-sembles is quantified in a reduced conformational space of the epitopes (seeMethods Section 2.1.4). For example, Fig. 2.6 shows the structural distri-butions in 1D for the four ensembles of epitope TKEQ, in two scaffolds.The two scaffolds chosen for this illustration are cyclo(CGTKEQGGGG) or(1,4)TKEQ, which stands for 1 glycine N-terminal to the TKEQ epitopeand 4 glycines C-terminal to the epitope, and cyclo(CGGTKEQGGG), or(2,3)TKEQ.51Figure 2.6: The equilibrium ensemble distributions for the59TKEQ62 epitope projected by the multidimensional scaling(MDS) method [5] onto the first MDS dimension. For a given epi-tope, different cyclic peptide scaffolds possess different distributions, whichwill result in different overlap with the other three ensembles. By com-paring the degree of ensemble overlap, the conformational selectivity of ascaffold can be assessed. The scaffolds shown are (A) (1,4)TKEQ and (B)(2,3)TKEQ.Although information may be lost when projecting high-dimensional en-sembles to lower dimensions, the distributions in Fig. 2.6 do illustrate howthe ensembles overlap. The fibril ensemble consists of a predominant sharpspike because of its rigid structure. On the other hand, the monomer en-semble is broadly distributed because it is natively unstructured and confor-mationally diverse. The stressed fibril ensemble distributes around the fibrilensemble because it is generated by forcing the partial unfolding of fibril bybiased MD. Each cyclic peptide scaffold possesses a different distribution.As well, the stressed fibril, monomer, and fibril ensembles are slightly differ-ent in each case of Fig. 2.6, because all structural distributions are distancedistributions based on RMSD, which are different for each scaffold ensemble.From the degree of overlap or similarity between a scaffolded cyclic peptideensemble and the other ensembles, we can assess whether the scaffold hasthe potential to raise oligomer-selective antibodies while sparing fibril andmonomer.52For example, both (1,4)TKEQ and (2,3)TKEQ scaffold ensembles havevery low overlap with the fibril ensemble (3% and 8% respectively) (seeMethods Section 2.1.5). Also, they both have high overlap with the stressedfibril, where (2,3)TKEQ is somewhat higher than (1,4)TKEQ (68% and47%). The above (low fibril overlap, high stressed fibril overlap) are desiredproperties of a conformationally selective immunogen. On the other hand,the scaffolds also have high overlap with isolated monomer ensemble, with(2,3)TKEQ having much higher overlap than that in (1,4)TKEQ (74% and47%). High overlap with the monomer ensemble is not a favorable propertybecause of the possibility of targeting healthy protein. Na¨ıvely from the 1Doverlap measure, (1,4)TKEQ may be better than (2,3)TKEQ, since it has ahigher ratio of stressed fibril ensemble overlap to monomer ensemble overlap(1.0 for (1,4)TKEQ vs. 0.92 for (2,3)TKEQ). However, with a more rigoroussimilarity measure analysis allowing for higher projected dimensions, and theranking algorithm in Section 2.1.9, (2,3)TKEQ actually ranks higher than(1,4)TKEQ.The similarity or overlap between ensembles is rigorously quantified bytwo measures, Jensen-Shannon Divergence (JSD) and embedding depth (seeMethods Section 2.1.6). JSD is a measure that represents the dissimilaritybetween two ensembles, which has been used previously to compare pro-tein ensembles [6, 119]. Embedding depth represents the extent to which agiven ensemble is subsumed by another, i.e. to what extent conformations inone ensemble are contained within another ensemble. It is a non-reciprocalmeasure that is introduced in Methods Section 2.1.6 to compare proteinconformational ensembles (see also Ref. [197]). For example, the embeddingdepth of the fibril ensemble within the stressed fibril ensemble in Fig. 2.6Ais 0.338, because fibril conformations are contained within the stressed fibrilensemble. Note that embedding depth between two identical ensembles is0.5, so 0.338 represents a large degree of embedding. On the other hand,the JSD between the two ensembles is 0.984, which represents two almostcompletely dissimilar ensembles. The efficacy of a scaffold to target a con-formational species may thus likely be better represented by the embeddingdepth than the JSD.532.2.2 Scaffold screening criteria and scaffold rankingIn Section 2.2.1, we showed that the various similarity measures that we haddefined between a scaffolded cyclic peptide epitope and other ensembles canbe optimized within the glycindel sequence space by varying the number offlanking N-terminal and C-terminal glycines (See Methods Section 2.1.2).The ensemble overlap of a given epitope with other ensembles can be tunedby changing the scaffolding residues. We thus computationally constructed4 × 4 = 16 scaffolds for each epitope, corresponding to the epitope beingflanked by anywhere between 1 and 4 glycines on each terminus or “side”,or 16× 3 = 48 total for epitopes 57EKTK60, 58KTKE61, and 59TKEQ62.Fig. 2.7 shows the results for three α-synuclein epitopes; 57EKTK60,58KTKE61, and 59TKEQ62, illustrating changes that can occur in ensemblesimilarity across all 48 scaffolds, as measured by Jensen-Shannon DivergenceJSD (see Methods Section 2.1.6), embedding depth DA|B (see Methods Sec-tion 2.1.6) and off-pathway target criteria OP (see Methods Section 2.1.8),by varying the number of flanking N-terminal and C-terminal glycines. De-tailed values are in Table 2.2. The changes in the values corresponding tothe fibril ensemble (JSDcyclic-fibril, and Dcyclic-in-fibril) are all very small on thescale of the plots, so they appear to remain unchanged across all scaffolds.In practice, this means that these two criteria do not contribute significantlyto the ranking between scaffolds. For epitopes 57EKTK60 and 58KTKE61,there is a generally decreasing trend of JSD with increasing scaffold length(total residue number in the cyclic peptide), and a generally increasing trendfor D with increasing scaffold length. These trends are less significant forepitope 59TKEQ62. We address this phenomenon further in Section 2.2.4.54Figure 2.7: Measures for the rankings of all 16 epitope scaffolds,for three overlapping 4 residue sub-epitopes of 57EKTKEQ62 in α-synuclein (top of each column). (A) Scaffolded cyclic peptide ensembledissimilarity to monomer (triangle), fibril (star), and stressed fibril (circle)ensembles, as measured by Jensen-Shannon Divergence (JSD), showing thechanges in ensemble overlap with varying numbers of flanking glycines. (B)Scaffolded cyclic peptide ensemble embedding depth within the monomer(triangle), fibril (star), and stressed fibril (circle) ensembles, showing thechanges in ensemble embedding with varying number of flanking glycines.(C) Normalized off-pathway targeting values (OP) for scaffolds with varyingnumber of flanking glycines. Higher values indicate there is less predictedoff-pathway targeting by a given scaffold. The ranks of the top 10 scaffoldsare indicated in the figure panels, along with the rank for the highest rankingscaffold (15) for epitope 58KTKE61. (Figure adapted from Ref. [1])The difficulty in manually assessing good scaffolds from multiple sim-ilarity measures led us to apply a systematic ranking method for the se-lection of the best performing scaffolds. The performance of each scaffold55is assessed by 7 ranking criteria, including JSDcyclic-fibril, JSDcyclic-monomer,1-JSDcyclic-stress, 1-Dcyclic-in-fibril, 1-Dcyclic-in-monomer, Dcyclic-in-stress and OP(the off-pathway target criterion). We formulate the ranking such that largevalues in all criteria are desired, so we thus subtract some JSD values from1 to convert dissimilarity to similarity, and we subtract some D values from1 to convert similarity to dissimilarity.Scaffolds are ranked with the SMAA-TOPSIS algorithm [179] using these7 criteria (see Methods Section 2.1.9). In the ranking algorithm, each crite-rion is assigned a weight for its relative importance; The weights used hereare given in Table 2.1. Since JSDcyclic-monomer and 1-Dcyclic-in-monomer bothrepresent the effect of monomer dissimilarity, the importance of monomerin the ranking amounts effectively to the sum of the two weights. Thesame applies to 1-JSDcyclic-stress and Dcyclic-in-stress, as well as JSDcyclic-fibriland 1- Dcyclic-in-fibril. Thus, the importance respectively for fibril, monomer,stressed fibril, and off-pathway target criteria are 2, 2, 1, 1.5. The rankingfor all 48 scaffolds is shown in Table 2.2. Such a ranking provides a ther-apeutic development strategy to predict which cyclic peptide scaffolds maybe most promising to use in an active immunization for antibody generationto oligomer targets of α-synuclein.2.2.3 Embedding depth as a similarity measure comparedwith JSDThe various ensemble similarity measures are compared with each other inFig. 2.8, which shows matrices of the Pearson’s correlation coefficient val-ues, across all the scaffolds in Table 2.2. JSD and embedding depth D arecompared for all scaffolds, along with three other scaffold properties: RootMean Squared Fluctuation of the epitope (RMSF), scaffold total residuelength, and the ranking of each scaffold. JSD is calculated between en-sembles by weight averaging values from 3 to 11 dimensions as describedin Section 2.1.6; Embedding depth D is calculated in 3-dimensions (3D) asdescribed in Section 2.1.6. The three JSDs (JSDcyclic-stress, JSDcyclic-fibril,JSDcyclic-monomer) have mutually positive correlations, as shown in the top-56left 3 × 3 matrices in Fig. 2.8A, B and C. This indicates that these JSDvalues may have implicit dependencies on one another and may contain somedegree of redundant information.Figure 2.8: Correlation matrices for measures of ensemble compari-son. Correlation matrices of the ensemble comparison measures JSD and D,and three other scaffold properties: Dynamic flexibility (RMSF) of an epi-tope, total residue length of the cyclic peptide scaffold, and the ranking, forα-synuclein epitopes (A) 57EKTK60, (B) 58KTKE61, and (C) 59TKEQ62.The number in each square (bottom-left) is the Pearson correlation coeffi-cient. P is the p-value of the correlation coefficients (top-right). (Figureadapted from Ref. [1])For epitope 59TKEQ62, the JSD correlations between cyclic peptide en-57sembles and fibril, stressed fibril, and monomer ensembles may result at leastin part from their flexibility, i.e. more flexibility of a cyclic peptide allowsmore conformational diversity, allowing in turn for more similar conforma-tions to the other ensembles, reducing the JSD. Conversely, a rigid scaffoldwould have a narrow structural distribution, and thus minimal overlap withany of the other ensembles, resulting in larger JSD. The JSD values of var-ious scaffolds thus have strong negative correlation with the RMSF for thisepitope (8th column/row in Fig. 2.8c). This anticorrelation of RMSF withJSD is recapitulated partially by the (weaker) correlation of RMSF with D.This effect may indicate a systematic deviation of conformational similar-ity for scaffolds of this epitope, and may suggest better targeting can beachieved for 57EKTK60 and 58KTKE61, where the anti-correlation of JSDwith RMSF is less significant.Embedding depth can help elucidate the implicit effects of scaffold rigid-ity. A rigid scaffold that is deeply embedded within the stressed fibril wouldbe a desirable candidate. Compared across scaffolds for a given epitope asin Fig. 2.8, an anticorrelation between Dc|s and RMSF would be ideal foroligomer targeting. This is not observed for any of our epitopes, but thecorrelations are not significant for 57EKTK60 and 58KTKE61, (p = 0.33 andp = 0.25) while for 59TKEQ62 the significance of the correlation of 0.76 isp = 0.0007. It is also worth noting that we are integrating a significantamount of information when investigating correlations across all scaffoldsfor a given epitope, in order to compare one epitope with another. Thevariance scaffold to scaffold for a given epitope is sufficiently large to allowfor highly ranked scaffolds for any of the epitopes. That said, the medianrankings for 57EKTK60, 58KTKE61, and 59TKEQ62 are 10.5, 37.5, and 25respectively, and 9 of the top 10 scaffolds are for 57EKTK60.2.2.4 Scaffold properties and their impact on performanceThe top 5-ranked scaffolds—(1,3)EKTK, (2,3)EKTK, (3,2)EKTK, (1,2)EKTK,and (2,3)TKEQ—all have substantially lower JSDcyclic-stress thanJSDcyclic-monomer, higher Dcyclic-in-stress than Dcyclic-in-monomer, and high off-58pathway (OP) target values (i.e. less off-pathway target severity) (Fig. 2.7and Table 2.2). JSDcyclic-fibril is approximately 1 for all scaffolds, and like-wise Dcyclic-in-fibril ≈ 0, so these two screening criteria cannot discriminatescaffolds.We found that scaffolds with more residues tend to have smaller JSDs,and larger embedding depths D (Fig. 2.7 and Fig. 2.8 “length” row/column).The trend is particularly apparent for 57EKTK60 scaffolds. It is likely thatthis trend is due to scaffold rigidity, since larger cyclic peptides have lessstructural constraint and more flexibility, allowing them to have higher over-lap with the other disordered ensembles. On the other hand, while RMSFcorrelated positively with peptide length for all epitopes, only 59TKEQ62achieved statistical significance (Fig. 2.9A), suggesting that the primarysequence of the epitope is as important as scaffold size in determining itsdynamics and flexibility, and thus its potential similarity to other ensembles.As another indicator that primary sequence determines epitope properties,scaffold size itself does not correlate significantly with a scaffold’s rankingperformance for 59TKEQ62 and 57EKTK60 (Fig. 2.9B), primarily becauseit is the relative overlap with the stressed fibril and monomer ensemblesthat determines the ranking. For 58KTKE61, the correlation of scaffold sizewith ranking is such that smaller scaffolds tend to perform significantly bet-ter (Fig. 2.9B), mostly because the strongest trend with increasing scaffoldlength is increased overlap with the monomer ensemble (Fig. 2.7), which isan undesirable trait. The rankings themselves for 58KTKE61 are generallylower than those for the other two epitopes.59Figure 2.9: Epitope-dependent correlation between scaffold proper-ties. Epitope-dependent correlation between (A) RMSF and scaffold length(number of residues in the scaffold), (B) ranking and scaffold length, (C)rank and the quantity JSDcm − JSDcs, and (D) rank and Dc|s − Dc|m, forα-synuclein epitope scaffolds. The Pearson correlation coefficient, r and thecorresponding p-values are given for 57EKTK60 (green triangles), 58KTKE61(purple circles) and 59TKEQ62 (blue stars) scaffolds. The shaded areasaround the fitted lines are the 68% confidence intervals corresponding tothe standard errors. (Figure adapted from Ref. [1])Plotting the scaffold rank vs. the difference in the JSDcm − JSDcs,as well as the difference Dc|s − Dc|m (Fig. 2.9C,D) gives an indication ofthe importance of the relative overlap between the stressed-fibril vs. themonomer ensembles. Both abscissae in Fig. 2.9C,D are plotted as desirablequantities—the larger the value, the better the performance (higher rankor lower numerical rank value). For epitopes 57EKTK60 and 58KTKE61,60there is a significant correlation between a scaffold’s rank and these relativeoverlap measures. For epitope 59TKEQ62, the correlation is not significanthowever, essentially because the variation in the off-pathway (OP) targetcriterion strongly affects the ranking for this epitope. This can be seen byretaining only those 59TKEQ62 scaffolds with OP above a threshold suchas 0.85 for example, and measuring the correlation for this reduced, filtereddataset. This reduced dataset consists of 11 out of 16 scaffolds and yieldsr = −0.68, p = 0.019 in Fig. 2.9C and r = −0.88, p = 0.0002 in Fig. 2.9D.Some epitopes tend to have better performance than others. 57EKTK60and 59TKEQ62 scaffolds are generally ranked higher than 58KTKE61 scaf-folds. As mentioned above, the median rankings for 57EKTK60, 59TKEQ62and 58KTKE61 are 10.5, 25, and 37.5 respectively. For the top 20 scaf-folds, there are 12 57EKTK60 scaffolds, 6 59TKEQ62 scaffolds, and only 258KTKE61 scaffolds, and 9 of the top 10 scaffolds are for 57EKTK60, withonly one 59TKEQ62 scaffold ranked 5th (Fig. 2.7). The poor performance of58KTKE61 scaffolds appears to be due to their systematically lower struc-tural similarity to the stressed fibril than to the unstructured monomerensemble, as shown in Fig. 2.7. The higher monomer similarity may itselfbe due to the higher conformational flexibility (RMSF) of 58KTKE61 scaf-folds, which is roughly twice as high on average as the RMSF of epitopes57EKTK60 or 59TKEQ62 (Fig. 2.9A). I.e. flexibility in the scaffold construc-tion could favor greater similarity to the monomer ensemble, because themonomer ensemble is inherently more conformationally diverse than that ofthe stressed fibril.Since a cyclic peptide has an inherent curvature which may more stronglyresemble the conformations of an epitope in a turn or bend, the averaged vir-tual bond angles representing the local curvatures of epitopes in the stressedfibril ensemble are calculated and compared. The virtual bond angle is de-fined as pi− 6 Cαi−1Cαi Cαi+1 in the kink model [202–204], where Cαi is the Cαatom of the ith amino acid. This angle has been shown to represent cur-vature in the continuum limit [205]. However, the curvature of 58KTKE61(1.13± 0.14) is not significantly lower than that of 57EKTK60 (1.18± 0.18)or 59TKEQ62 (1.10±0.16). As a result, the curvature itself does not explain61the lower performance of 58KTKE61.2.2.5 Finding potential off-pathway targetsIt is desirable to avoid off-pathway targets to minimize unwanted side-effects.To find the prevalence of unwanted targets in the proteome for a given epi-tope, we search through the RCSB database of resolved protein structures,to find proteins that might be potential off-pathway targets of antibodiesthat could be generated by each cyclic peptide scaffold (see Methods Sec-tion 2.1.8).To illustrate the procedure, we demonstrate the off-pathway target anal-ysis of (1,4)TKEQ scaffold here. Fig. 2.10A shows the scaffold ensemblefor (1,4)TKEQ, projected on the first MDS coordinate, along with all en-tries of the human proteome having known PDB strutures and containing59TKEQ62 motifs. The degree a PDB entry is embedded in the cyclic pep-tide ensemble is quantified as the embedding depth Doff-target-in-cyclic, and isrecorded as a percentage. Note that Fig. 2.10A is only for visualization; Theformal calculation of embedding depth, Doff-target-in-cyclic, is performed in 5dimensions (5D). Nevertheless, we can see from this figure that the epitopein the context of the various PDB structures is conformationally distinctfrom the epitope in the context of the cyclic peptide.62Figure 2.10: Off-pathway target analysis for (1,4)TKEQ. (A) Struc-tural ensemble distribution of cyclic peptide (1,4)TKEQ in 1D along thefirst MDS component of the ensemble, along with the projected embeddingof potential off-pathway targets. Most of the off-pathway targets are locatedat the periphery of the scaffold distribution. The actual calculation is per-formed in 5D. Structures of PDB entries 2KKW and 1XQ8 are renderedin ribbon schematics, and the epitope is rendered in Van der Waals sur-face. (B) The SASA distribution of (1,4)TKEQ, along with the SASA forthe off-pathway target structures. (C) Only 1XQ8 and 2KKW show bothnoticeable structural similarity (Doff-target-in-cyclic(5D) > 5%) and SASA ex-posure (f(SASAoff-target-exceed-cyclic) > 5%). (Figure adapted from Ref. [1])Fig. 2.10B indicates the distribution of the SASA for the (1,4)TKEQensemble, along with the SASA of TKEQ for all PDB entries in the humanproteome with 59TKEQ62 motifs. The SASA of the scaffolded cyclic peptideensemble ranges from 400A˚2 to 600A˚2, and serves as a good reference fromwhich to compare. The fraction of the cyclic peptide ensemble that has lower63SASA than a given PDB entry is defined as f(SASAoff-target-exceed-cyclic).We apply cutoff thresholds of 5% for both Doff-target-in-cyclic andf(SASAoff-target-exceed-cyclic) to all PDB entries containing the epitope. In thecase of (1,4)TKEQ, two PDB entries (1XQ8 [206] and 2KKW [207]) showboth noticeable structural similarity (Doff-target-in-cyclic > 5%) and solventexposure (f(SASAoff-target-exceed-cyclic) > 5%) relative to the (1,4)TKEQ en-semble (Fig. 2.10C). Many off-pathway targets, including 1XQ8 and 2KKWabove, are themselves deposited structures of monomeric α-synuclein. FibrilPDB entries of α-synuclein are excluded from the off-pathway target crite-rion calculation to avoid double counting the contribution of fibril to theranking. Of the many α-synuclein fibril structures in the PDB, the only oneidentified as an off-pathway target by the above cutoff criteria was 2N0A,which happens to be the PDB entry we used to generate the fibril ensembleand perform epitope prediction.On the other hand, the structured monomer entries still contribute tothe off-pathway target criterion because they are distinct from the simu-lated monomer ensemble. These monomer PDB entries are partly struc-tured (containing α-helices) by binding to micelles (e.g. PDB 2KKW and1XQ8), and are thought to be involved in various aspects of α-synucleinphysiology [206–211]. Thus, membrane-bound PDB monomer structuresare treated separately from the unstructured isolated monomer ensemble.2.2.6 Weighting the importance of ensemble propertiesRanking the peptide “glycindel” scaffolds here involved extensive confor-mational analysis and a ranking procedure with weighted criteria based onthis analysis. Assigning appropriate weights for each criterion is a non-trivialtask, which depends on biological intuition, and analyzing the consequencesarising from screening criteria with a given set of weights. For this spe-cific ranking, we put twice the weight on dissimilarity from the fibril andthe monomer than similarity to the stressed fibril. We chose this weight-ing scheme because the stressed fibril ensemble generation process contains64more prior assumptions, in which we hypothesize that a partially disorderedfibril ensemble is enriched in oligomer-selective conformational epitopes.The fibril ensemble is obtained by generating the “native basin” ensembleof the solid-state NMR resolved structure (PDB entry 2N0A). The monomerensemble is obtained by generating disordered conformations of an isolatedmonomer of α-synuclein. The confidence in the accuracy of the fibril en-semble and monomer ensemble are greater than that of the stressed fibriloligomer model ensemble. The off-pathway target criteria have a slightlyhigher weight than the similarity of stressed fibril, because minimal off-pathway target effects are desired and are key feature of monoclonal anti-body therapy.2.2.7 The role of glycindel immunogens in therapeuticdevelopment pipelinesThe in silico immunogen modeling and screening method developed hereprovides an additional route to aid the development and optimization ofa peptide immunogen that can be faster and cheaper than experiments.Experimental screening methods can then be performed on a subset oftop-ranked scaffolds to save available resources. Some examples of down-stream in vitro screening experiments are Thioflavin T (ThT) aggregationassays [212–214] , surface plasmon resonance (SPR) assays to measure bind-ing affinity to antibodies and conformational selectivity [179], and Fo¨rsterresonance energy transfer (FRET) assays [215] to measure aggregation ten-dency, since scaffolds that can trigger aggregation of normal α-synucleinmay have more contribution to the pathology because of greater seedingpropensity. These in vitro assays are typically followed by various in vivostudies as part of pre-clinical development. The ability to use computation-ally generated conformational ensembles as a screening method for candidateimmunogens can aid and accelerate therapeutic development.652.2.8 Other possible epitope scaffolding strategiesThe in silico screening method introduced in this Chapter can generallybe applied to various different scaffolding methods. There are many otherscaffolding methods that have been previously developed [134, 216–219] be-sides cyclizing the epitope with a variable number of glycine residues. Apartfrom these methods, several possible extensions of glycindel cyclic peptidescaffolding method may be directly implemented. For example, proline canbe used for scaffolding in addition to glycine, since it is relatively inert chem-ically compared to other amino acids, and it is also able to constrain thecyclic peptide ensemble by adding conformational rigidity [220], which maybe exploited to bias the scaffolded ensemble more effectively towards thestressed fibril ensemble. Large-scale computational design, which exploresa vastly larger phase space of possible sequences, may also be implemented,e.g. through Rosetta [134, 146]. This epitope scaffolding approach is thefocus of Chapter 3 of this thesis.While not common, epitopes of disease-specific antibodies may occasion-ally involve two or more requisite, discontiguous segments along the primarysequence of the peptide chain. Such a scenario arises, for example, in theanti-tau antibody zagotenemab, whose murine precursor was raised frompurified paired helical filaments as an immunogen [221]. Selective presen-tation of discontiguous epitopes can be facilitated by structural fixation ofpeptides, e.g. using cysteine–benzyl bromide chemical linkages [222]. Theantibodies raised by cyclic peptide glycindel scaffolds would not have thisproperty. Many other disease specific antibodies in clinical development forParkinson’s disease [223] as well as other neurodegenerative diseases [224]similarly target contiguous epitopes.Cyclic peptide ensembles can be constructed ab initio, while collect-ing ensembles for larger protein complexes (e.g. an antibody with givenparatope sequence) would typically require an experimentally resolved struc-ture or reliable prediction such as an AlphaFold model [152].66Different carrier proteins that conjugate to the scaffolded epitope suchas nanoparticles or lipid micelles have also been successfully implementedpreviously [225–228]. Similarly, a linear peptide epitope of CGTKEQGGGGconjugated to a much larger carrier can be simulated as a peptide with cys-teine SG atom spatially fixed at x = 0, and a boundary constraint such thatit is forbidden to access the half-space region x < 0. Such a peptide in factexhibits desirable ensemble overlap properties (Densemble-in-monomer=0.142,Densemble-in-stress=0.207, Densemble-in-fibril=0.000). Thus, conjugating on anon-interacting surface might be sufficient to modify the ensemble of theepitope to mimic the model oligomer. The above possible extension strate-gies are interesting future tests for computational and experimental studies.67Chapter 3De novo design of β-helixtau protein immunogen2,3 Tau is a microtubule-associated protein mainly found in the axonal partof neurons [47]. The assembly of α and β tubulins results in the formation ofmicrotubules. Tau binding to tubulin promotes the assembly of microtubulesand stabilization of the microtubule network, which is required for axonaltransport and neuronal health [48, 229, 230]. A hallmark of pathology inAlzheimer’s disease as well as other tauopathies is the formation of tauoligomers and fibrils [161, 231], which in turn destabilizes microtubules andthus intracellular trafficking [232]. Destabilization of microtubules leads toneuronal and synaptic loss [233, 234], and promotes neuroinflammation [155,235].Neurodegenerative disorders involving tau pathology, collectively knownas tauopathies, include frontotemporal dementia (FTD) or Pick’s disease(PiD), chronic traumatic encephalopathy (CTE), corticobasal degeneration(CBD), progressive supranuclear palsy (PSP), and Alzheimer’s disease (AD)[77]. The presence of tau lesions strongly correlates with the progression ofthese diseases [153–156]. Alternative splicing gives rise to alternate isoformshaving variable numbers of microtubule binding domains [77], which dur-ing pathology aggregate to different fibril morphologies (e.g. [236, 237]) on2A version of this Chapter has been submitted to a peer-reviewed journal asAdekunle Aina, Shawn C.C. Hsueh, Xubiao Peng, and Steven S. Plotkin, De novocomputational design of a β-helix tau protein scaffold: An oligomer-selective immunogencandidate for Alzheimer’s disease3A US patent application on the work contained in this Chapter has been filed asImmunogens Targeting Oligomeric Tau and Methods of Generation and Use Thereof,Inventors: Adekunle Aina and Steven S. Plotkin68different energy landscapes [238].While the pathogenesis is not yet fully understood, the aberrant presenceof extracellular Amyloid-β (Aβ) plaques and intracellular tau-containingneurofibrillary tangles in AD brains make both Aβ and tau proteins the twomain therapeutic targets [161]. Safely targeting therapeutically relevantepitopes on Aβ or tau is nevertheless a herculean task [239]. Immunogensare highly effective therapeutic agents employed in the public health sectorto trounce diseases. After two decades of research and development, im-munogens for treating AD have been unsuccessful [240–243]. However, therecent approval of the first immunotherapy against AD by the United StatesFood and Drug Administration (FDA), although amidst some controversy,has reactivated interest in immunotherapeutic strategies for combating AD.AADvac1, the first immunotherapy targeting tau, was advanced to clinicaltrials in 2013 [244]. Over the following decade, more than a dozen immuno-gens targeting tau have been developed and advanced to clinical trials [155].A common strategy employed in the design of these immunogens is the in-corporation of a single instance of an identified epitope. Nevertheless, it isthe aggregated, oligomeric forms of the protein which have been shown tobe toxic [161]. This motivates a strategy wherein key epitopes of the proteinare scaffolded in such a way as to present multiple copies of the epitope ina polyvalent immunogen.The problem of designing an effective immunogen to treat a protein mis-folding disease such as AD is two-fold, involving both epitope identificationand selective targeting to pathogenic species. Epitopes must be identifiedthat are disease-specific and induce strong and long-lasting immunity [245],and the presentation of the immunogenic, disease-specific epitopes must se-lectively target pathogenic species while sparing healthy proteins. The epi-tope in the healthy protein often has an identical and unmodified primaryamino acid sequence as the toxic species.Immunogens induce an ensemble of immunogen-specific antibodies, whichrecognize various epitopes on the immunogen. T cells recognize MHC-presented linear peptide sequences, while B cells recognize both linear andconformational epitopes that are exposed on antigenic surfaces [243, 246].69In the present application, an effective immunogen must induce antibodiesthat selectively bind to misfolded conformations in toxic forms of the pro-tein over healthy “native” conformations (Chapter 2 and Ref. [1]). Like itspredecessors tested in clinical trials, there remain concerns regarding the ef-ficacy of the recently approved Aβ-targeting antibody aducanumab for thetreatment of AD [247–250]. It is therefore important to continue to innovatenew approaches to combat AD.In this Chapter we rationally design an immunogen that captures theconformational ensemble of misfolding-specific epitopes in tau protein, char-acterized by regions most readily disordered and solvent-exposed in a stressed,partially disordered fibril. We achieved this by designing an epitope scaffoldthat is primarily a β-helix that incorporates multiple instances of the tar-geted epitope, and which is stabilized by a single α-helix. Conformationalanalyses show that this scaffold presents the misfolding-specific epitopesin conformations distinct from those in either the intrinsically disorderedmonomer, or the amyloid fibril, more effectively than an approach of scaf-folding a single epitope in either a linear peptide, cyclic peptide, or in asingle protein immunogen. The designed immunogen may be suitable foreliciting therapeutic antibodies that are selective for toxic tau oligomers inAlzheimer’s disease, providing that the species of oligomer retains some de-gree of conformational similarity to high-molecular-weight fibrils and protofib-rils.703.1 Methods3.1.1 Prediction of epitopesTo predict tau epitopes, two conformational ensembles were generated, onefor tau fibril and the other for a partially unfolded fibril, which serves as amodel for tau oligomers. This oligomer-selective epitope prediction methodposits that a partially unfolded protofibril ensemble is enriched in oligomer-selective conformational epitopes [177], and has been supported by previousexperimental evidence [180, 181].The fibril ensemble was generated by performing a 30.1 ns moleculardynamics (MD) simulation, starting from a tau fibril structure (PDB ID:5O3L) extracted from an AD patient brain [236]. To generate the partiallyunfolded fibril ensemble, ten independent 150 ns bias MD simulations wereperformed in order to average over the stochastic process of unfolding. Dur-ing the first 50 ns of the bias simulations, the number of native contactswas linearly decreased to 60% of its native value. A native contact was de-fined being formed when heavy atoms belonging to residues with a sequenceseparation ≥ 3 are within 4.8 A˚ over 95 percent of the time in a 100 nsequilibrium fibril simulation. This determines the total number N of nativecontacts. After 50 ns, the bias of 60% native contacts was fixed for theremaining 100 ns of simulation.The bias potential V (Q, t) is implemented to globally unfold the taufibril structure along the fraction of native contacts Q reaction coordinate,which takes the following form:V (Q, t) =12k(Q−Q0(t))2 (3.1)whereQ =∑Nij Qij(rij)∑Nij 〈Qij(rij)〉native(3.2)In Eq. (4.11), the sum in the numerator runs over the N native con-tacts that may be formed in a given conformation, while the sum in thedenominator runs over the N native contacts in a member of the native71conformational ensemble and is then averaged over conformations sampledduring the 100 ns equilibrium simulation of the native fibril structure. Qijin Eq. (4.10) is defined by a contact function for each atom pair i, j withcontact separated by distance rij , using the following formula:Qij(rij) =1− ( rijr0 )n1− ( rijr0 )m. (3.3)In Eq. (3.3), we take r0 = 4.8 A˚, n = 6 and m = 12, to obtain a sigmoidalfunction that rapidly goes to one as rij falls below r0, and rapidly goes tozero as rij becomes larger than r0. All simulations were performed in explicitsolvent (TIP3P water model, and 150 mM NaCl) at 300 K and 1 bar usingGROMACS [84, 184] and the CHARMM36m force field [89] with periodicboundary conditions.Using the fibril ensemble as a reference, epitopes were predicted basedon the consensus of three measures that quantified local disorder, includ-ing loss of native contacts (∆Q), increased root mean squared fluctua-tions (∆RMSF), and increased solvent accessible surface area (∆SASA). SeeChapter 2 or Ref.s [1, 177] for a more detailed description of this approachfor predicting misfolding-specific epitopes.3.1.2 Epitope scaffolding using cyclic peptide glycindelsAs described in Results section 3.2.1, 3 regions emerge from the collective co-ordinates prediction as candidate misfolding-specific epitopes: 315LSKVT319,343KLDFK347, and 365GGGN368 (see Fig. 3.1 A). The 365GGGN368 epitopewas not pursued further due to it’s lack of sequence complexity and expectedlack of immunogenicity.To scaffold a single instance of the predicted 315LSKVT319 or 343KLDFK347epitope, we computationally constructed “glycindel” cyclic peptides follow-ing the procedure described in Chapter 2. Briefly, each cyclic peptide scaf-fold consists of the epitope flanked on the N- and C-termini by n and mglycines respectively. We refer to these scaffolds as cyclo(C-Gn-(EPITOPE)-Gm)or (n,m)EPITOPE, where C is a cysteine residue for conjugating a scaffold72to carriers such as Keyhole limpet hemocyanin (KLH) in order to increaseimmunogenicity. Cyclic peptide construction is implemented computation-ally by mutating the corresponding flanking residues to glycine or cysteine inthe native fibril structure using SCWRL4 [182]. The topology of the cyclicpeptide is obtained by head-to-tail backbone linkage, which is then energyminimized using a steepest descent algorithm in GROMACS [84, 184].Figure 3.1: Modeling tau β-helix structure. (A) Tau fibril fromAlzheimer’s disease brain (PDB ID: 5O3L) showing the side chains on theleft protofilament in the figure for the predicted epitopes: 315LSKVT319(magenta), 343KLDFK347 (red), and 365GGGN368 (light orange), and the339VKSEKLDFKDRVQSKI354 tau339-354 fragment (non-epitope portion incyan) that subsumes the 343KLDFK347 epitope. (B) Segments of five chainsof the tau339-354 fragment are connected together with interchain linkers,to form a β-helix structure. Magenta dash lines indicate how glycine tripep-tide linkers connect the C-terminus of one chain to the N-terminus of thenext chain, and S352 is shown in yellow spheres. (C) The 7.9A˚ distancebetween the C-terminus of one chain and the N-terminus of the next chainin the tau fibril (black dotted line). All images were rendered with PyMOLmolecular visualization system (https://pymol.org).3.1.3 β-helix structure modelingThe initial β-helix backbone was modeled using a repeating unit of 16 aminoacid sequence spanning the tau fragment 339VKSEKLDFKDRVQSKI354(tau339-354) [251, 252], which subsumes the 343KLDFK347 predicted epitope(see Fig. 3.1A). Five tau339-354 repeating sequences were connected serially73with glycine tripeptide (GGG) linkers to form a single chain, β-helix peptidewith a total of 92 residues (Fig. 3.1 B).The distance between the Cα carbon of the C-terminal residue of tau339-354 on one chain and the Cα carbon of the N-terminal residue of tau339-354on the next consecutive chain in the tau fibril structure (PDB ID: 5O3L)was calculated to be ≈ 7.9A˚ (Fig. 3.1 C). We thus hypothesized that anideal linker length would be about 3 amino acids, and investigated the distri-bution of distances in a non-redundant database of 26,900 structures [253].Figure 3.2 shows the distribution of distances between Cα atoms of aminoacids separated by (i, i + 3). We find several expected features, includ-ing peaks corresponding to α-helical and β-sheet secondary structure, alongwith an additional peak at ≈ 9A˚ separation corresponding to transitionsfrom (α, β) secondary structures to loops or turns [254] These sequenceswere often initiated or terminated by glycines or prolines. The 7.9A˚ dis-tance of our linkers (magenta bar labelled ` in Fig. 3.2) is in the middleof this distribution, supporting the hypothesis that a 3-amino linker wascompatible in length and would not frustrate our designed structure.In order to stabilize the designed scaffold, the serine at amino acid po-sition 352 was mutated to cysteine for all but the last tau339-354 repeat,amounting to four S352C mutations in the structure (Fig. 3.1B). The S352Csubstitution introduces two disulfide bonds in the scaffold, which are intro-duced to improve the structural stability of the β-helix structure.The structure of the designed sequence was predicted using AlphaFold[152] (see Methods section 3.1.5 for further details), a deep learning algo-rithm for accurate protein structure prediction. Five models were generatedby AlphaFold, and the model with the highest average confidence score thatalso formed the designed disulfide bonds between residues 14 and 33 andbetween residues 52 and 71 was selected as the initial model for the β-helixstructure.To further improve stability of the initial model, the structure of the C-terminal repeat sequence was redesigned to form an α-helix structure usingthe RosettaRemodel algorithm [255], while imposing the constraint that thedistance between the N- and the C- termini Cα atoms of the whole β-helix74Figure 3.2: Distribution of (i, i + 3) distances in a non-redundantdatabase of Protein Structures. The 7.9A˚ distance between consecutivechains to be linked in our designed structure (` in the plot) is well-within thedistribution of distances between Cα atoms separated by three amino acids(i, i + 3). The distribution shows several features that are labelled in thefigure: α (α-helical secondary structure), β (β-helical secondary structure),tr (transitional elements between secondary structure and loop or turn).structure is ≈ 3.5A˚. This remodeling step creates an interaction interfacebetween the C-terminal α-helix and the GGG linkers. Furthermore, theremodeling allows for head-to-tail cyclization of the scaffold if needed, sincethe termini are now in spatial proximity.3.1.4 β-helix sequence design and structure optimizationStarting from the designed β-helix structure with C-terminal α helix dis-cussed above, the Rosetta protein design software [129, 146] was used tofurther optimize the sequence and overall structure of the modeled tau β-helix. PyRosetta [256] (Linux release 311 64Bit) was used for all Rosettadesigns. The FastDesign protocol was used to pack all residues, and to ap-ply sequence design to (only) the four linkers and the C-terminal α-helixresidues, using the REF15 scoring function [257]. All 20 naturally occur-ring amino acid residues were allowed in the designed residue positions. A75MoveMapFactory was set up to allow the minimization of all bond lengths,bond angles, and torsion angles. The design protocol was repeated ten thou-sand times to generate 10,000 decoys of the β-helix structure.3.1.5 Structure prediction with AlphaFoldDeepMind’s AlphaFold (version 2), a deep learning structure prediction al-gorithm that showed the best performance at CASP14 by a significant mar-gin [152, 258] (https://github.com/deepmind/alphafold), was installed lo-cally and trained, searching through the full database current as of January01, 2020, and the model obtained was used to predict the structures of se-lected Rosetta designed β-helix scaffold decoys from their primary sequencealone.3.1.6 Mechanical unfolding simulationsTo determine mechanical stability of the tau β-helix scaffold, unfolding sim-ulations were performed. Ten independent forced unfolding simulations wereperformed along the reaction coordinate Q (the fraction of native contacts)over the course of 100 ns, each using PLUMED [185], OpenMM [88] simu-lation engine, and the CHARMM36m force field [89]. A native contact wasdefined to be between heavy atoms within 0.45 nm, belonging to residues αand β with a sequence separation |α − β| > 3. The reaction coordinate Qof an arbitrary conformation X is defined as follows [259]:Q(X) =1N∑(i,j)11 + exp [β(rij(X)− λr0ij)](3.4)where the sum runs over N pairs of native contacts (i, j), rij(X) is thedistance between atoms i and j in conformation X, and r0ij is the nativedistance between atoms i and j. The parameters β and λ were taken to be50 nm−1 and 1.5 respectively. A time-dependent harmonic potential V (Q, t)(Eq. 4.11) was applied to move the center of the bias linearly from Q0 = 1to Q0 = 0 over the simulation time. The spring constant k in Eq. (4.11) wastaken to be 107 kJ·mol−1.763.1.7 Hamiltonian replica exchange molecular dynamicsHamiltonian replica exchange molecular dynamics (HREMD) simulations[109, 260] were performed to determine the free energy surface (i.e. potentialof mean force (PMF)) along the fraction of native contacts Q (Eq. 3.4). Theset up consists of 100 replicas with time-independent harmonic restraintscentered at positions equally spaced betweenQ = 1 andQ = 0. The strengthof the harmonic restraint k was taken to be 105 kJ·mol−1 for all replicas forthe production run (80 ns for each replica). Before the production run,the protein must be unfolded and equilibrated in each harmonic potentialrestraint. The unfolding run is performed in 10 ns for each replica, and thesystem in each of the 100 harmonic potentials is equilibrated for 160 ns inthe equilibration run.Figure 3.3: Setup used for hamiltonian replica exchange moleculardynamics (HREMD) simulations. The HREMD set up consists of 100replicas (horizontal lines), each simulated in an unfolding run to differentdegrees of unfolding Q0i for 10 ns, followed by an equilibration run for 160ns with each replica in its own harmonic potential centered at Q0i, followedby a production run in the same harmonic potential for 80 ns.77The initial configurations before unfolding in each of the replicas wereobtained by seeding all 100 replicas with the Rosetta-designed native struc-ture, and applying the time-dependent harmonic restraints with correspond-ing center linearly decreased from Q = 1 to Q = Q0i during the unfoldingrun. Here, Q0i, 0 < i < 99, is the center of the harmonic restraint usedfor each replica during the equilibration and production runs. Q0i is differ-ent for each of the replicas, increasing linearly from 0.01 to 1 see Fig. 3.3).Because the interactions stabilizing the protein are stronger at higher native-ness, in practice we linearly decrease the strength of the harmonic restraintsduring the unfolding run as a function of time, from a spring constant ofk = 107 to k = 105 kJ·mol−1. The spring constant then remains fixed atk = 105 kJ·mol−1 during the equilibration and production runs. Exchangesbetween neighbouring replicas were attempted every 1 ps (500 steps). Thesimulation, including the initial and the production runs, ran for 250 ns perreplica for a total of 25µs for all replicas. Conformations were sampled at 10ps intervals from each replica in the production run and used to determinethe unfolding free energy profile along Q by solving the Multistate BennettAcceptance Ratio (MBAR) equations [261, 262].3.1.8 Sampling conformational ensemblesAll-atom molecular dynamics (MD) simulations were performed in explicitsolvent (TIP3P water model, 150 mM NaCl) at a temperature of 300Kand pressure of 1 bar using GROMACS [84, 184] and CHARMM36m forcefield [89] to generate ensembles for tau fibril, tau oligomer, tau monomer,cyclic peptide scaffolds, and β-helix scaffold.Fibril ensemble: The fibril ensemble was generated by performing 30.1ns MD simulation starting from a tau fibril structure (PDB ID: 5O3L).Conformations were sampled at equal time intervals of 1 ns for a total of30.1× 10× 10 = 3010 single-chain conformations (there are 10 chains in thesystem) in the fibril ensemble.78Oligomer ensemble: The oligomer was modeled as a partially unfoldedfibril. Simulations were performed as described in Methods section 3.1.1.Conformations were sampled at equal time intervals of 1 ns from the last≈ 42 ns of ten independent biased simulations of 10 chains, for a total of42× 10× 10 = 4200 single-chain conformations in the oligomer ensembleMonomer ensemble: The free energy landscape of an intrinsically disor-dered protein (IDP) such as tau is rugged and weakly funneled. Therefore, itis very challenging to generate an equilibrium ensemble for an IDP throughdirect MD simulation. The strategy that was used previously in Chapter 2and in Ref.s [1, 189] was therefore employed. In brief, two steps are involved.Firstly, a highly diverse conformational ensemble with 10,000 configurationswas generated by using the pivot algorithm [192, 263] , along with crankshaftmoves [264] that randomize torsion angles between two randomly-selectedfixed backbone atoms. Secondly, each feasible conformation generated wasenergy minimized, and then a 3 ns MD simulation was performed. The lastconformation from each simulation was collected to obtain a total of 7166conformations in the monomer ensemble.Cyclic peptide ensembles: Each cyclic peptide scaffold was simulated for300 ns using conventional MD. Conformations were then sampled at equaltime intervals of 100 ps from the last 250 ns of the simulation, for a total of2500 conformations in each cyclic peptide scaffold ensemble.β-helix scaffold ensembles: For the β-helix peptide ensembles, we per-formed 100-replica HREMD simulations for a total of 25 µs (see Methodssection 3.1.7). A number Ni of conformations determined from Eq. 3.5 weresampled randomly from the ith replica, so that replicas were Boltzmann-weighted:Ni = 1250× e−∆Fi . (3.5)Here, ∆Fi is the relative free energy (in kBT) of the ith replica (see Fig. 3.8D). A total of 2393 conformations were sampled for each of four instancesof KLDFK motif in the β-helix scaffold.793.1.9 Comparing conformational ensemblesConformational ensembles are compared using Jensen-Shannon Divergence(JSD) [118, 119], which we implemented using the ENCORE software [6].JSD is a symmetrized version of the Kullback–Leibler divergence [116], DKL,which is a measure of the difference between two probability distributionsP and Q, defined byJSD(P,Q) =12DKL(P,M) +12DKL(Q,M) (3.6)whereM =P +Q2(3.7)andDKL(P,Q) =∫ ∞−∞P (x) log(P (x)Q (x))dx . (3.8)The probability distribution representing an ensemble is obtained by creat-ing a root mean squared deviation (RMSD) matrix of all structures in allensembles to be compared. The dimension of this high-dimensional RMSDmatrix is then reduced using the Stochastic Proximity Embedding (SPE)method [125]. Since the value of the JSD depends on the dimension of theSPE-reduced space, weighted average JSD values from 3D to 11D are used,with weights taken as the inverse of the SPE residuals in each dimension.The JSD is normalized to lie between 0 (for identical ensembles) to 1 (forentirely different ensembles).803.2 Results and Discussion3.2.1 Prediction of tau epitopesFigure 3.4: Prediction of tau epitopes. (A) Per residue normalizedincrease in solvent accessible surface area (∆SASA), loss of native contacts(∆Q), and local increase in root mean squared fluctuations (∆RMSF). (B)Per residue weighted sum of ∆SASA, ∆Q and ∆RMSF over all chains withthe boundary chains in the 5×2-chain, 2-protofibril structure A, B, I, and Jhaving half the weight of other chains. The zero point was set to a numericalvalue (7.5) that identified epitopes that are within 5 amino acid long. Thesequences shown in red font are the predicted epitopes for tau..We predicted misfolding-specific epitopes in tau protein using the proce-dure described in Methods section 3.1.1, which has previously been used topredict misfolding-specific epitopes in α-synuclein (Chapter 2 and Ref.s [1,2]), superoxide dismutase (SOD1) [177], and Aβ [180, 181]. An equallyweighted sum of three measures of local disorder, including loss of native81contacts (∆Q), increased root mean squared fluctuations (∆RMSF), andincreased solvent accessible surface area (∆SASA) were used to predict epi-topes. Fig. 3.4A shows the per residue normalized values for ∆SASA, ∆Q,and ∆RMSF. As a necessary condition for a candidate epitope, a contigu-ous string of residues must satisfy a consistent decrease in Q, an increase inSASA, and a value of ∆RMSF greater than the average across all residuesin 8 of 10 independent simulations for all metrics. Figure 3.4B shows theper residue weighted sum of ∆SASA, ∆Q and ∆RMSF over all chains withthe boundary chains A, B, I, and J in the fibril structure having half theweight of other chains. Mathematically, we ploted the function Ω (Eq. 3.9)versus the residue index.Ω =12(RA +RB +RI +RJ) +RC +RD +RE +RF +RG +RH , (3.9)whereR = (SASA/SASAmax) + (Q/Qmax) + (RMSF/RMSFmax) (3.10)The zero point of function Ω was set at 7.5 to identify epitopes that areabout 5-residues long. Three motifs above the zero point, 315LSKVT319,343KLDFK347, and 365GGGN368, were thus predicted as misfolding-specificepitopes for tau.In summary, a protofibril region is used as a model to predict oligomer-selective epitopes. These regions of peptide sequence are conformationallydistinct from either those in an isolated monomer (because they are pre-sented in a stressed fibril conformation), or those in the fibril itself (becausethey were selected as being disordered from the fibril when stressed). Thisrecipe has been successful in identifying oligomer-selective antibodies in α-synuclein [1, 2]. The problem then turns to how to properly scaffold thepredicted epitope in order to present it in a conformation similar to that inthe stressed fibril. For α-synuclein, this has been successfully achieved bycyclic peptide “glycindel” scaffolds (Chapter 2 and Ref.s [1, 2]). We nowturn to this analysis for the above-predicted epitopes.823.2.2 Conformational selectivity of single-epitope cyclicpeptide scaffoldsOur goal at this stage is to design scaffolds that are selective for toxic tauoligomers. In other words, we aim to design scaffolds that present epitopesin similar conformations to those present on toxic tau oligomers, that aredifferent from conformations presented by healthy tau monomers, or fibril,as we wish to target paracrine species that have the potential to spreadpathology by prion-like propagation [161, 265]To this end, we constructed cyclic peptides (see Methods section 3.1.2) toscaffold two of the three predicted tau epitopes, including 315LSKVT319 and343KLDFK347 epitopes. We did not construct scaffolds for the 365GGGN368predicted tau epitope because it consists of mostly glycine (GLY) residues,which are less immunogenic than other side chains. Each constructed cyclicpeptide scaffold consists of a single instance of either the 315LSKVT319 or343KLDFK347 epitope flanked by between one to four variable numbers ofGLY on the N- and/or the C-terminus. Hence, we constructed a total of 4×4or 16 cyclic peptide scaffolds for each of the 315LSKVT319 and 343KLDFK347epitopes.To determine the conformational selectivity of the constructed cyclicpeptide scaffolds in silico, we sampled the conformational ensemble of eachepitope in four different contexts: The fibril, oligomer, monomer, and each of16×2 = 32 cyclic peptide scaffolds, by performing all-atom MD simulationsin explicit solvent (see Methods section 3.1.8.) Each cyclic peptide epitopeensemble was then compared to the same epitope ensemble in the contextof the fibril, oligomer, and monomer. We used Jensen-Shannon Divergence(JSD) to quantify the degree of similarity between two conformational en-sembles (see Methods section 3.1.9). Glycindel scaffolds were genericallydistinct from the fibril, with JSD values between scaffold and fibril rangingfrom 0.96 to 1.00. We thus focused on comparisons with the monomer andstressed fibril oligomer model ensembles.We seek epitope scaffolds with both high similarity (low JSD) to theoligomer ensemble, and low similarity (high JSD) to the monomer ensem-83ble. Fig. 3.5 shows the conformational ensemble dissimilarity (JSD) to theoligomer vs. JSD to the monomer, for each of the 32 cyclic peptide scaffolds(16 scaffolds each for tau 315LSKVT319 and 343KLDFK347 epitopes).Figure 3.5: Conformational ensemble similarity. The dissimilarity be-tween two conformational ensembles was quantified using JSD (see Methodssection 3.1.9), which is normalized to lie between 0 (for identical ensembles)to 1 (for entirely different ensembles). Shown are the similarity between theepitope ensemble in the context of a scaffold and the stressed fibril oligomermodel, versus the similarity between the epitope ensemble in the contextof the scaffold and the monomer, for cyclic peptide scaffolds of the LSKVTepitope (triangles), cyclic peptide scaffolds of the KLDFK epitope (squares),and the β-helix scaffold of the four KLDFK epitope repeats (circles). Thearrow indicates the direction of favorable conformational profile and thedashed line is the line y = x..Several observations are apparent from Fig. 3.5. In general, 315LSKVT319scaffolds sample epitope ensembles that are more similar to both the monomerand the oligomer ensembles than 343KLDFK347 scaffolds. There is a pos-itive correlation between the similarity between scaffold and oligomer andthe similarity between scaffold and monomer, with Pearson correlation co-efficient r = 0.71 for all the cyclic peptide scaffolds, moderate correlationfor the 315LSKVT319 epitope scaffolds (r = 0.56), and strong correlation for84the 343KLDFK347 epitope scaffolds (r = 0.92). This correlation shows thatas the cyclic peptide scaffolds become less similar to the monomer (increas-ing JSD), which is desirable, they also become less similar to the oligomer(increasing JSD), which is undesirable. It is worth noting that the JSD be-tween monomer and oligomer is 0.54, more similar than any of the scaffoldsto the oligomer, and more similar than any of the KLDFK scaffolds to themonomer. The more similar the monomer and oligomer ensembles are, thestronger the correlation we expect in the data of Fig. 3.5.The desired scaffold should be more similar to the oligomer than themonomer, which would put the data point for a scaffold below the y = xdashed line in Fig. 3.5. The result here shows an unfavorable result thatthe typical conformations explored by glycindel cyclic peptide scaffolds of315LSKVT319 and 343KLDFK347 epitopes are predicted to be more similar tothose of an isolated monomer of tau than an oligomer model using a stressedfibril. We note that this result is in contrast to glycindel scaffolding ofepitopes for α-synuclein, which were able to predict scaffolds having greatersimilarity to oligomers in Chapter 23.2.3 Design of avidity-enhanced multi-epitope β-helixscaffoldsFrom the above result, none of the 32 cyclic peptide scaffolds are predictedto be more selective for tau oligomers than monomers. We therefore de-signed a single-chain β-helical scaffold consisting of multiple instances ofthe 343KLDFK347 epitope. We chose the 343KLDFK347 epitope because ofits location in the tau fibril structure (Fig. 3.1 A).85Figure 3.6: β-helix scaffold design strategy. (A) Five copies of tau-derived 16-residue 339VKSEKLDFKDRVQSKI354 repeating sequence arelinked serially by glycine tripeptide linkers (GGG); S352C substitutions aremade in the first four repeats. These were used to model (B) a β-helix struc-ture, with disulfide bridges between residues C14 and C33 and residues C52and C71. (C) Redesign of the last repeat (black box) and linker residues(gray boxes) to improve the stability of (D) the β-helix scaffold by creatinginteractions between the designed residues. Last repeat is shown in yel-low and linkers are shown in orange, both with licorice side chains. (E)The designed β-helix structure (magenta) and AlphaFold predicted struc-ture (cyan) have Cα RMSD of 1.39A˚. All images were rendered with PyMOLmolecular visualization system (https://pymol.org)..The epitope 343KLDFK347 is a motif which is part of a larger contiguoussequence in the tau monomer, 339VKSEKLDFKDRVQSKI354 (tau339-354),that has close spatial proximity between its N- and C-termini within thetau fibril structure PDB 5O3L. Tau structures in the PDB are polymorphic,often depending on the disease phenotype. We have chosen a tau structureassociated with AD, however other tau structures in the PDB also satisfy thecondition that the N- and C-termini of V339 and I354 are in close spatialproximity (e.g. PDBs 6NWP and 6NWQ involved in chronic traumaticencephalopathy). The strategy used here should potentially be applicable86to this disease as well. Beta-helical structures have been observed in naturein other contexts, for example antifreeze proteins [251, 252].To design β-helix peptide scaffolds, we tethered 5 copies of tau339-354 se-quence with glycine (GLY) tripeptides (GGG) (see Fig. 3.1). We then madea S352C (serine 352 to cysteine (CYS)) mutations in the first four copies ofthe sequence, with the intention of designing two disulfide bridges that wouldimprove the stability of the scaffold (Fig. 3.6 A). Indeed AphaFold [152]predicts a β-helix structure (Fig. 3.6 B) with the S352C substitutions, butpredicts a disordered peptide without the S352C substitutions (see Methodssection 3.1.5).All 5 AlphaFold models predicted a β-helix structure for the five-repeatsequence (with S352C substitutions) with high average per residue confi-dence scores of 89%, 92%, 89%, 88%, and 85% for the 1st through 5thAlphaFold models, respectively. The formation of β-helix structure alwaysput cysteines C352 in successive repeats of tau339-354 within 4.8 A˚ of eachother. Two disulfide bonds, between cysteines in the 1st and 2nd repeats,and between cysteines in the 3rd and 4th repeats, were predicted as intendedby only the third and fifth AlphaFold models; the other three models pre-dicted only one of the two disulfide bonds.We thus used the 3rd AlphaFold model with the two designed disulfidebonds and higher confidence score (89%) as the initial β-helix structuralmodel for redesign. To further improve the stability of β-helix structuralmodel, we remodeled the amino acids starting from the last GGG linkerand including the linker and the last tau339-354 repeat (see Methods sec-tion 3.1.2). The last tau339-354 repeat was remodeled to an α-helix struc-ture in a conformation that is docking and interacting with all the linkers(Fig. 3.6 D). For both linker and α-helix, we allowed for the possibility ofany of the 20 naturally occurring amino acids to occur in all remodeled posi-tions. Finally, all four linkers and α-helix residues were designed to optimizethe sequence and structure of the β-helix scaffold (Fig. 3.6 D) (see Methodssection 3.1.4).Ten thousand (10,000) decoys of β-helix scaffold were generated duringthe design phase using Rosetta [129, 146]. Fig. 3.7 A plots the Rosetta en-87ergy per residue of the designed decoys against the Cα root mean squareddeviation (RMSD) from the starting Rosetta-remodeled structure, with en-ergy = 1.98 Rosetta energy units (REU). The RMSD for all designed decoysis below 1 A˚ except for one outlying decoy with an RMSD of 1.13 A˚. All thedesigned decoys have energies below −3 REU per residue, which is signifi-cantly lower than the energy of the starting structure.Figure 3.7: Rosetta energy and AlphaFold confidence for designedβ-helix structures. (A) Rosetta energy per residue (in Rosetta energyunits or REU) as a function of Cα RMSD to the Rosetta remodeled struc-ture, for 10, 000 designed decoys. Dashed line indicates low energy cuttoffof −3.41 REU, corresponding to 1% of decoys with energies below the cut-toff. (B) Per residue AlphaFold confidence (PLDDT) score for the top3 ranked AlphaFold models as for the top ranked sequence. Dashed lineindicates high confidence cuttoff of 70%. The β-helix structure was ren-dered to show 1st ranked (C), 2nd ranked (D), and 3rd ranked (E) perresidue confidence scores and colour coded as very high confidence (blue),high confidence (cyan), low confidence (yellow), and very low confidence(orange). All images were rendered with PyMOL molecular visualizationsystem (https://pymol.org)883.2.4 AlphaFold predicts the designed β-helix structureTo validate the feasibility that a designed sequence folds into the designedβ-helix structure, AlphaFold was used to predict the structure from the de-signed sequences alone (see Methods section 3.1.5). A distribution of energywas constructed for the 10,000 decoys and the lowest 1% of energy defined acutoff that included 82 unique sequences. The structures of these 82 uniquesequences were then predicted with AlphaFold. AlphaFold outputs 5 mod-els per sequence, with each model predicting one structure. Table 3.1 showsthe average per residue confidence score; the predicted local distance differ-ence test (PLDDT) score for the median ranking model of the 5, and the CαRMSD from the Rosetta-designed β-helix structure for the three top rankingmodels for 28 selected sequences. The 28 selected sequences (see Table 3.2for the designed sequences) are those from the 82 lowest energy sequencesthat satisfy two criteria: 1.) They have an average per residue confidencescore for the median ranking model ≥ 50%, and 2.) each of the three topranking models has a Cα RMSD from the remodeled β-helix structure ≤ 5A˚.To characterize the structural and energetic stability of a representativedesigned sequence in silico, several selection criteria were imposed. We se-lected a sequence that 1.) has a low energy; it is among the 1% lowest energydecoys, corresponding to an energy cutoff of −3.41 REU per residue, 2.) hasa high structure prediction score; a median confidence score (across 5 mod-els) ≥ 70, which is the threshold for high confidence structure prediction forAlphaFold [152]. That is, at least three AlphaFold models must have highconfidence scores (see Fig. 3.7 B), and 3.) has the designed structure acrossall the top three models; it is predicted to have i) the designed β-helixstructure, and ii) correctly forms the two designed disulfide bonds. Thepredicted β-helix structure was rendered to show the 1st ranked (Fig. 3.7C), 2nd ranked (Fig. 3.7 D), and 3rd ranked (Fig. 3.7 E) per residue confi-dence scores and colour coded as very high confidence (blue), high confidence(cyan), low confidence (yellow), and very low confidence (orange).Table 3.1 shows that Model 0 is the only sequence satisfying these strin-89Table 3.1: Models of tau β-helix scaffold. Attributes of the designedβ-helix sequences with median (across five AlphaFold models) of the averageper residue confidence (PLDDT) score ≥ 50%, and where each of the topthree ranking Alphafold predicted structures have RMSD from the Rosettadesigned structure ≤ 5 A˚. Models are sorted in order of decreasing values ofthe median PLDDT score.ModelPLDDT(%)Energy(REU)RMSD1(A˚)RMSD2(A˚)RMSD3(A˚)0 71.99 −314.43 1.39 1.38 1.381 69.89 −316.14 1.57 1.39 1.502 69.17 −315.10 1.37 1.84 1.583 65.91 −314.57 1.37 1.32 1.354 65.14 −314.34 1.43 1.50 1.625 64.05 −314.17 2.03 1.89 1.966 61.19 −317.04 1.41 1.81 1.947 60.85 −314.18 1.74 1.68 1.628 60.47 −314.04 1.90 2.20 1.619 59.83 −314.71 2.13 1.97 2.1810 59.45 −314.71 1.75 1.60 1.8811 59.13 −315.34 1.53 1.47 1.5612 59.06 −315.02 1.32 1.92 1.6513 58.81 −314.40 1.52 1.86 2.2314 57.85 −315.06 1.38 1.59 1.7915 57.76 −315.02 1.83 1.75 1.8716 57.46 −313.85 1.55 1.40 1.6217 57.08 −315.97 1.87 1.49 1.6418 56.39 −315.47 1.34 1.87 1.6619 55.55 −316.86 1.86 1.64 1.8020 54.17 −314.87 1.66 1.83 1.4821 53.99 −314.46 2.05 2.83 2.3422 53.93 −317.23 1.61 1.39 2.3623 51.75 −314.89 2.34 2.28 2.5324 51.47 −313.95 1.51 1.59 1.8425 51.46 −314.32 4.72 4.87 4.8626 51.16 −316.30 1.40 2.40 2.1827 50.22 −316.25 1.67 1.80 1.77gent selection criteria. The Rosetta designed structure and AlphaFold pre-dicted structure for Model 0 have Cα RMSD of 1.39A˚ (Fig. 3.6 E).90Table 3.2: Designed sequences for models of tau β-helix scaffold.The corresponding amino acids for the four linkers as well as the α-helixstructure for each model in Table 3.1 are listed. Models are sorted in orderof decreasing values of the median PLDDT score.Model Link1 Link2 Link3 Link4 Helix0 GGF DAF GPF DSF DYEQMKYYEKLIDIYA1 GGF DAF GPF DSF DKEKAKEYEKLIDIYA2 GGF DAF GPF DSF DKEKMKDYERLIDTYA3 GGG TAF GPF DSF DYEKMKEYEKYIEIYA4 GGA DAF GPF DSF NEEKMKEYEKYIEIYA5 GGF DAF GPF DEF DYEAMKWYEWLIEVYA6 GGF DAF GPF DSF DKEQMKEYEKLIEIYA7 GGA DAF GPY ESF DEEAMKEYEKYIEIYA8 GGF DAF GPF DSF DEEQMKWYEWLIEVYA9 GGA DAF GPY DSF DEEAMKEYEKYIEIYA10 GGF DAF GPF DSF DKEQMKKFEELIEKHA11 GGG TAF GPF ESF DKEKMKEYEKYIDIYA12 GGF DAF GPF ESF DEEQMKWYEWLIDVYA13 GGF TAF GPF DSF DKEQMKEYEKLIEIYA14 GGG DAF GPF DSF DKEQMKEYEKYIETYA15 GGG DAF GPF ESF DEEAMKEYEKYIEIYA16 GGG DAF GPF DSF DEEQMKYYEKYIEIYA17 GGF DAF GPF DSF DKEKMKWYEWLIDVYA18 GGA DAF GPF DSF DEEQMKEYEKYIEIYA19 GGF DAF GPF DSF DEEQMKEYEKLIDIYA20 GGG DAF GPF DSF IEEEMKKYEDYIEKYA21 GGF DAF GPF DSF DKEQAKRYMQLVDIYA22 GGG DAF GPF DSF DEEQMKYYEWYIEVYG23 GGF DAF GPF DSF DEEKMKKYLKLIEIYA24 GGG TAF GPF ESF DEEQMKEYEKYIDIYA25 GGG GPF GPY ESF NEEEMKEYEKYIDIYA26 GGG DAF GPF DSF DEEQMKEYEKYIEIYA27 GGG TAF GPF ESF DEEQMKYYEEVIEKTA3.2.5 The designed β-helix scaffold is structurally andenergetically stableOne of the most important pharmacological properties for a peptide suchas the designed tau β-helix scaffold intended for use as an immunogen isstability. To this end, the stability of the selected β-helix scaffold (i.e. Model0 ) was characterized in silico. All simulations were performed in explicitsolvent (0.15mM NaCl) at 300K and 1bar using GROMACS [184] with the91CHARMM36m force field [89], and periodic boundary conditions.MetastabilityTo check the structural stability of the scaffold in the free energy basin ofthe designed structure, a 100 ns all-atom MD simulation starting from thedesigned structure was performed, and the last 50 ns was used for analysis.Heavy-atom root mean square deviation (RMSD) and Cα root mean squarefluctuation (RMSF) were used to quantify the global and local stability,respectively. The RMSD vs. time plot in Fig. 3.8A shows that the scaffoldis globally structurally stable within the simulation time. The RMSD fromthe starting structure of the sampled conformations is below 2 A˚. Apartfrom five N-terminus residues with RMSF between 1.5 A˚ to 3.5 A˚ (Fig. 3.8B), the per residue local fluctuations remain below the size of a carbon atom(1.4 A˚) for all residues, suggesting a high structural stability for the scaffoldin the free energy basin of the designed structure.Mechanical stabilityTo quantify mechanical stability, ten independent forced unfolding simula-tions were performed (see Methods section 3.1.6). The cumulative averagework done by the applied forces to unfold the β-helix scaffold structure asa function of the native contact order parameter Q (Eq. 3.4) was taken asa measure of mechanical stability. The work performed in a given trajec-tory generally averages out the stochastic effects of forces and is a smoothfunction of the order parameter [266, 267]. Here, the work performed wasaveraged over ten independent simulations to further average out stochasticeffects during the unfolding process. For comparison, the analogous calcula-tion was performed to assess the mechanical stability of isolated fibronectintype III domain of human tenascin (PDB ID: 1TEN) [268, 269] and taumonomer (chain A from PDB ID: 5O3L) [236], which serve as positive andnegative controls respectively. The force-field and simulation model (all-atom in TIP3P solvent) used for all proteins are the same, so no additionalnormalization across time, energy, or force is required for accurate compar-92Figure 3.8: Computational characterization of the stability of β-helix scaffold. The (A) global and (B) local structural stability in the freeenergy basin of the Rosetta designed structure. (C) The mechanical stabilitymeasured by the average cumulative work done during forced unfolding sim-ulations (solid line), compared to fibronectin, a stable extra-cellular matrixprotein with similar length (dashed line), and an isolated (intrinsically dis-ordered) tau monomer (dotted line), which serves as a negative control. (D)Thermodynamic stability determined from the relative free energy surfacealong the fraction of native contacts Q (Eq. 3.4) order parameter. Snapshotsfrom the first half (dotted), second half (dashed), and full 80ns trajectories(solid) in each umbrella are shown (see text). Inset images show representa-tive snapshots of the structures at the free energy minimum, where Q = 0.64,and where Q = 1 and Q = 0.1. The order parameters in panels (C) and (D)have opposite sense, as (C) considers pulling from the native state, and (D)considers folding free energy surface.ison [270]. Figure 3.8 C shows that the mechanical stability of the scaffoldis comparable to that of fibronectin, a stable extra-cellular matrix proteinwith similar length (92 versus 90 amino acids).93Thermodynamic stabilityWe also determined the thermodynamic stability of the β-helix scaffold, byperforming a Hamiltonian replica exchange molecular dynamics (HREMD)simulation to determine the free energy surface as a function of Q (seeMethods section 3.1.7). The HREMD simulation consists of 100 replicaswith harmonic restraints centered at positions equally spaced between thefraction of native contacts Q = 0 to Q = 1. Each replica was simulated for250 ns for a total of 25 µs. A total of 8000 conformations were sampled at 10ps intervals from the last 80 ns of each replica to determine the relative freeenergy of unfolding along Q for the scaffold. Figure 3.8 D shows a largelydownhill free energy surface towards higher degrees of nativeness, until thefree energy minimum of the scaffold at Q = 0.64. There is a weak metastableminimum near Q ≈ 0.9, but entropic forces bias the global minimum towardsa lower degree of native contacts.Nevertheless, the global minimum ensemble has a large amount of nativestructural similarity: The average RMSD of this ensemble is 1.25 A˚, and ifwe ignore the largely disordered N-terminal 13 residues, the RMSD of theremainder is 0.45 A˚. Fig. 3.8 D also shows representative snapshots of theconformations sampled at Q = 0.64, Q = 0.1, and Q = 1. The Q = 0.64snapshot shows that most of the lost contacts are the result of the flexibleN-terminus (c.f. Fig. 3.8 B). Overall, this result shows that the designedscaffold is thermodynamically stable in a largely structured, β-helical con-formation with a stabilizing α-helix. We note that as an immunogen proxyfor an oligomer, which generally are conformationally labile and thus elu-sive to structural determination [161], some degree of partial disorder mayactually be a favorable feature of the designed scaffold.943.2.6 The designed β-helix scaffold is conformationallyselective for a stressed protofibril model of tauoligomersTo determine the conformational selectivity of the designed β-helix scaffoldfor a stressed fibril model of tau oligomers (c.f. Fig. 3.5A), the confor-mation of the predicted 343KLDFK347 epitope was sampled in the contextof monomer, stressed protofibril oligomer, and β-helix scaffold (see Meth-ods section 3.1.8). Four different KLDFK ensembles, corresponding to thefour KLDFK instances in the β-helix scaffold sequence, were separately an-alyzed for the β-helix scaffold. Each KLDFK scaffold ensemble was thencompared with the monomer and the oligomer ensembles, respectively, us-ing the Jensen-Shannon divergence (JSD) similarity measure (see Methodssection 3.1.9).Here, we compare the conformational selectivity of a multi-epitope β-helix scaffold to single-epitope cyclic peptide scaffolds for the tau 343KLDFK347epitope. Figure 3.5A shows that the β-helix scaffold is predicted to be moreselective for tau oligomers than are cyclic peptide glycindel scaffolds. Forthe same conformational similarity to the oligomer, three of the four β-helixensembles clearly show lower similarity (higher JSD) to the monomer thanKLDFK cyclic peptide scaffolds. Similarly, for the same conformational dis-imilarity to the monomer, three β-helix ensembles show higher similarity(lower JSD) to the oligomer than all of the KLDFK cyclic peptide scaffolds.The N-terminal KLDFK motif has an ensemble that is more similar to themonomer than that of the other three epitope repeats. This is expectedsince the N-terminus of the β-helix scaffold is relatively flexible, assumingthe accuracy of the force field used in the simulations (CHARMM36m [89])(Fig. 3.8 D).In Chapter 2 and Refs. [1, 2] we have constructed single-epitope cyclicpeptide glycindel scaffolds to successfully generate α-synuclein oligomer-selective antibodies, following a similar procedure to the one described inMethods section 3.1.2. Therefore, this analysis cannot rule out the ability ofa single-epitope cyclic peptide scaffold to raise oligomer-selective antibodies.95In conclusion, the accumulation of abnormal forms of tau protein inneurons is a hallmark of Alzheimer’s disease (AD). Despite progress over thepast decade, immunotherapies targeting tau have not yet yielded a clinicallyapproved therapeutic. We report a new approach for immunogen design thatincorporates multiple copies of a targeted epitope in a β-helix structure,mimicking the aggregated, oligomeric state of the epitope in disease formsof the underlying protein. Conformational ensemble analyses show thatthe β-helix scaffold developed here are predicted to discriminate models ofabnormal forms of tau better than single-epitope scaffolds targeting the sameepitope.96Chapter 4Efficient comparison ofprotein ensembles4 One of the fundamental principles that has influenced protein science is thestructure-function paradigm: The idea that, for proteins with a reliable andstable three-dimensional (3D) structure, the fold invariably determines theprotein’s functions [271–273]. Protein structures are central to molecularbiology and are used for example in synthetic biology [274–277] and in drugdesign [276, 278, 279].Comparing protein structures is a common and useful practice in struc-tural biology for the understanding of functional and evolutionary relation-ships [271–273, 280–282]. Consequently, several quantitative measures forcomparing protein structures have been developed; the most commonly useddissimilarity measure is the distance-based global root mean square devia-tion (RMSD) of atomic positions. This has however been shown to be oneof the least representative of the degree of structural dissimilarity comparedto contact-based methods, such as Cβ-Cβ pairwise distances, that are morerobust and relevant [283]. For this reason and other limitations, such as thedependence of RMSD on the accuracy of the superposition of protein struc-tures, flexible regions, and protein length, more accurate measures includingthe global distance test total score (GDT-TS) and template modeling score(TM-score) are used during Critical Assessment of techniques for proteinStructure Prediction (CASP) competitions to quantify the similarity be-tween computationally predicted structures and experimentally determined4A version of this Chapter has been submitted to a peer-reviewed journal asAdekunle Aina, Shawn C.C. Hsueh, and Steven S. Plotkin, Prothon: A local orderparameter-based method for efficient comparison of protein ensembles.97structures [258, 283, 284].Additionally, proteins are dynamic systems and explore a vast conforma-tional space. Thus, comparisons between individual structures often needto be generalized to comparisons between ensembles of structures to accu-rately characterize macrostates of proteins. Unfolded states, partially un-folded states, or intrinsically disordered proteins (IDPs) require an ensembledescription to properly characterize them. Comparisons between ensemblesof structures have thus been developed to treat these systems.Unlike protein structure comparison, for which many metrics are avail-able, efficient methods and software for comparing protein structural en-sembles are much less common. The first attempt to quantitatively mea-sure the dissimilarity between structural ensembles was an extension of theglobal RMSD [285]. A different approach was proposed by Kresten Lindorff-Larsen and Jesper Ferkinghoff-Borg [119], which involves the estimation ofthe underlying probability distributions of protein conformational ensemblesand the quantification of the overlap between these probability distributionsusing a symmetrized form of the Kullback Leibler divergence [6, 119, 286].Three methods were proposed for estimating the underlying probability den-sities, including quasi-harmonic approximation, conformational clustering,and dimensionality reduction [119], with all the three methods having seriouslimitations pointed out by the authors. While the quasi-harmonic approxi-mation method is relatively fast, it is only effective for ensembles that canbe described by a multivariate normal distribution. The other two methodsrequire the calculation of all pairwise global RMSDs, a calculation scalingas 12(N + M)(N + M + 1), where N and M are the ensemble sizes, whichcan be prohibitively expensive for large ensembles, due to the optimizationof the structural superposition of structures that is required. For example,using current computing power on the Digital Research Alliance of Canadacedar computing cluster (https://alliancecan.ca), to compare twoensembles of 15000 structures each of a peptide of 76 amino acids takes 58hours (2 days and 10 hours) on a single core and 7 hours on 48 cores runningin parallel.On the other hand, large ensembles are now routinely generated from98molecular dynamics (MD) simulations, and it is often useful to compareprotein ensembles generated from MD simulations using different force fields,simulation parameters, solvent conditions, or amino acid sequence. IDPs donot have a well-defined native structure, but exist as an equilibrium ensembleof diverse conformations, which interconvert rapidly [287–290]. For thesepractical situations involving large conformational ensembles, there is a needfor an effective quantitative measure and software for comparing structuralensembles, which does not require the computationally expensive process ofstructural superposition.To address the problem of the high computational cost required foroptimal structural alignment, as well as the potential issues of accuracymentioned above that are associated with the use of the global RMSD ofatomic positions as a structural dissimilarity measure, contact-based mea-sures and measures utilizing internal coordinates, for example torsion an-gles, for structural comparison have previously been proposed [283, 291].More recently, a measure for comparing IDP ensembles based on Cα-Cαdistance matrices was described in Ref. [292]. Although the method de-scribed in reference [292] does not require the alignment of structures, andso is superposition-independent, therefore requiring relatively lower compu-tational cost, it only considers distance distribution averages rather thanthe full distributions themselves.In the present work, we introduce and implement a new generalizedmethod for the efficient representation and comparison of protein confor-mational ensembles. The method involves the utilization of the JensenShannon Distance (JSDist) metric for the quantification of the differencebetween probability density functions representing the distributions of a lo-cal structural property of polypeptide chains that constitute the proteinensemble under consideration. A related approach for comparing conforma-tional ensembles was previously introduced by McClendon et al., in whichthe Kullback-Leibler Divergence was used to quantify the differences be-tween the distributions of the torsion angles [293]. In principle, any localstructural property can be used in our method. Local structural proper-ties including per residue solvent accessible surface area (SASA) [294, 295],99virtual Cα-Cα bond angle (CABA) and torsion angle (CATA) [296], Cαcontact number (CACN), and Cβ contact number (CBCN) [157, 158] wereimplemented. Our method was implemented using the Python program-ming language and is made available as a Python package, called Prothon,for easy access to the computational structural biology scientific commu-nity. Prothon provides an easy-to-use protein ensemble comparison programand a simple code framework for extension to include other local structuralproperties. We provide a GitHub page with the Python source code athttps://github.com/PlotkinLab/Prothon.4.1 DescriptionIn this section, we describe the algorithm for the efficient representation andcomparison of protein conformational ensembles implemented as a Pythonpackage called Prothon.4.1.1 Matrix representation of a protein ensembleConsider a protein ensemble Xm,n with m number of conformations. Let θbe a local structural property, such as the per residue Cβ contact number(CBCN) [157, 158] (see section 4.1.4), of a polypeptide chain, and n thenumber of θ values, which characterize each conformation that make upensemble Xm,n. Ensemble Xm,n can then be represented by an m×n matrixgiven by Eq. 4.1.Xm,n =θ1,1 θ1,2 θ1,3 · · · θ1,nθ2,1 θ2,2 θ2,3 · · · θ2,nθ3,1 θ3,2 θ3,3 · · · θ3,n.......... . ....θm,1 θm,2 θm,3 · · · θm,n(4.1)Each row of matrix Xm,n is a vector representing a conformationCm = | θm,1, θm,2, θm,3, · · · θm,n 〉, and each column is an ensembleθn = ( θ1,n, θ2,n, θ3,n, · · · θm,n ) of corresponding local values of θ in all100conformations in the protein ensemble.4.1.2 Vector representation of a protein ensembleThe matrix representing a protein ensemble, as described in section 4.1.1,can be written as a vector Xm,n of θn ensembles (see Eq. 4.2).Xm,n = | θ1, θ2, θ3, · · · θn 〉 (4.2)Each ensemble θn can further be transformed into a one-dimensional (1D)probability density function, so that:Xm,n = | p1, p2, p3, · · · pn 〉 (4.3)The probability density function representing each θn is determined by Gaus-sian kernel density estimation, which we implemented using SciPy [159].4.1.3 Quantifying similarity between protein ensemblesHere, we propose an efficient and effective dissimilarity measure for proteinconformational ensembles by the comparison of probability density functionsrepresenting a local property distribution using the Jensen Shannon Distance(JSDist) metric. The JSDist is an information theory-based measure forcomparing two probability distributions. A related non-metric version ofJSDist, the Jensen Shannon Divergence (JSD), has been used to quantifythe dissimilarity between protein ensembles in Chapters 2 and 3 and inprevious studies [1, 6], although often employing procedures which requirehigh computational cost and/or have limited practical applicability to largeensembles.The ensemble representation as described in section 4.1.2, allows forthe calculation of both local and global similarity between two protein en-sembles. Given two protein ensembles Xm1,n =∣∣ pX1 , pX2 , pX3 , · · · pXn 〉and Ym2,n =∣∣ pY1 , pY2 , pY3 , · · · pYn 〉, which are represented with vectors ofprobability density functions (pXn and pYn ) of a local structural property,the dissimilarity between ensembles Xm1,n and Ym2,n is estimated as the101n-dimensional vector, termed here as the dissimilarity vector given by:D = | D1, D2, D3, · · · Dn 〉 , (4.4)The components of D are the JSDist between the probability densities rep-resenting corresponding local structural property values in the polypeptidechains that make up Xm,n and Ym,n (Eq. 4.5).Dn(pXn , pYn ) =√12[DKL(pXn , pn) +DKL(pYn , pn)]12 (4.5)wherepn = (pXn + pYn )/2 (4.6)andDKL(pXn , pn) =d∑i=1pXi,n log2(pXi,npi,n)(4.7)is the Kullback Leibler divergence between pXn and pn probability densi-ties [286]. It is noteworthy to mention that Dn has a lower and upper boundof 0 and 1 respectively. A value of 0 indicates that two ensembles are iden-tical while a value of 1 suggests that they are completely different.The global difference D (Eq. 4.8), between ensembles Xm,n and Ym,n, iscalculated as the average across the n local differences.D =1nn∑i=1Di (4.8)Motif similarity between ensembles can also be determined in a similar fash-ion by averaging over local structural property belonging to a motif. Thecomputational cost to calculate the described similarity measure scales lin-early with n, where n is the number of local structural property values.1024.1.4 Cβ contact number local structural propertyThe Cβ contact number (CBCN) implemented in Prothon is defined by thenumber of Cβ atoms on other residues located within a sphere of radius rocentred on the Cβ atom of the residue of interest (Eq. 4.9).CBCN(i) =1NN∑j=111 + exp [β(rij − r0)] (4.9)where the sum runs over N Cβ atoms j in contact with Cβ atom i, and rij isthe distance between Cβ atoms i and j, belonging to residues i and j with asequence separation |i− j| > 2. The parameters β and ro were taken to be50 nm−1 and 1 nm, respectively. A similar method for calculating contactnumber was previously adopted by Kinjo et al. [157] and Zheng Yuan [158].4.1.5 Measuring significant dissimilarityTo compare two protein ensembles Xm1,n and Ym2,n, we consider only localdissimilarities (i.e. Dn) between the ensembles that are statistically signif-icant relative to dissimilarities within each ensemble. N samples of eachensemble are generated by randomly sampling (with replacement) m1 andm2 conformations from ensembles Xm1,n and Ym2,n, respectively. The localdissimilarities Dn are then calculated between the N samples within thesame ensemble and across different ensembles, which results in N2 inter-ensemble sample differences, and 2× (N2 ) intra-ensemble sample differences.In this present work we take N = 5 samples of each ensemble so that thereare 25 inter-ensemble and 20 intra-ensemble sample differences, respectively.The statistical significance of local dissimilarities Dn are calculated using theMann–Whitney U test [159, 297, 298], which is a non-parametric test of thenull hypothesis: the probability of x being greater than y is equal to theprobability of y being greater than x for randomly selected values x and yfrom two populations.1034.2 ValidationThe validity and computational efficiency of the introduced method for thecomparison of protein ensembles is demonstrated here with computationallygenerated, experimentally derived, structured, and intrinsically disorderedprotein ensembles.4.2.1 Comparing computationally generated ensembles ofubiquitinUbiquitin is a regulatory protein that exists in all eukaryotic cells. It per-forms various functions through conjugation to many different target pro-teins [299]. Ubiquitin consists of 76 amino acids and has a molecular massof about 8.6 kDa.To generate conformational ensembles for the natively structured pro-tein ubiquitin, we used the 3D coordinates of its atoms downloaded fromthe protein data bank (PDB ID: 1UBQ [300]) as the initial state to performmolecular dynamics (MD) simulations in CHARMM36m force field [89] us-ing GROMACS [184]. All simulations were performed in explicit solvent(TIP3P water model, and 150 mM NaCl) at 300 K and 1 bar with periodicboundary conditions. 5 independent MD runs each were performed for thefolded state and 5 partially folded states of ubiquitin. Each MD run was for50 ns. The partially folded states were obtained by performing global un-folding MD simulations, using PLUMED [185], along a collective coordinateQ (see Eq. 4.10), which defines the fraction of native contacts.Q(X) =1N∑(i,j)11 + exp [β(rij(X)− λr0ij)](4.10)where the sum runs over N pairs of native contacts (i, j), rij(X) is thedistance between atoms i and j in conformation X, belonging to residues aand b with a sequence separation |a− b| > 3, and r0ij is the native distancebetween atoms i and j. Native contacts were taken to be between atomswithin 0.45 nm in the native structure. The parameters β and λ were takento be 50 nm−1 and 1.5 respectively. Similar method for defining fraction of104native contacts was previously adopted by Best et al. [259] .A time-dependent harmonic potential V (Q, t) (Eq. 4.11) was applied tomove the center of the bias linearly fromQ0 = 1 toQ0 = 0.75, 0.80, 0.85, 0.90,0.95, respectively for 5 partially folded states. The global unfolding bias wasapplied for 10 ns and then kept fixed for 40 ns.V (Q, t) =12k(Q−Q0(t))2 (4.11)The spring constant k in Eq. (4.11) was taken to be 107 kJ·mol−1.Conformations were sampled at equal time intervals of 40 ps from thelast 40 ns of five independent simulations, for a total of 4000040 × 5 = 5000conformations in each of the folded and partially folded ensemble.The degree of nativeness (or foldedness) of ubiquitin was taken as thefraction of native contacts Q. To visualize these ensembles, we representedthem as a CBCN m× n matrix (see Matrix representation of a protein en-semble) and as a pairwise RMSD m × m matrix (as used in Encore [6]),where m = 30000 is the total number of structures and n = 70 is the num-ber of Cβ atoms in each structure. The high dimensional CBCN and RMSDmatrices were then reduced to 2-dimensions (2D) using principal compo-nent analysis (PCA, [124]) and t-distributed stochastic neighbor embedding(t-SNE, [301]) dimensionality reduction methods (see Fig. 4.1). PCA andt-SNE were implemented using Scikit-learn [302]. In Fig. 4.1, the ensemblesare color coded as folded (red) and partially folded (yellow: 95% folded,magenta: 90% folded, cyan: 85% folded, green: 80% folded, and blue: 75%folded). At this 2D level of resolution, whereby the PCA explained varianceis 39% and 44% for CBCN and RMSD matrices, respectively, the ensem-bles are more easily distinguishable for the CBCN matrix representation(Fig. 4.1 A and B) than the pairwise RMSD matrix representation (Fig. 4.1C and D). As expected for these ubiquitin ensembles, the spatial proximityof structures in the partially folded ensembles to structures in the folded en-semble decreases with decreasing degree of foldedness (i.e. yellows are closerthan blues are to red) and the degree of spread increases with decreasing de-gree of foldedness (i.e. there is more spatial variation for blue than yellow.)105Figure 4.1: Representation and dimensionality reduction of ubiqui-tin ensembles. The folded (red) and partially folded (yellow: 95% folded,magenta: 90% folded, cyan: 85% folded, green: 80% folded, and blue:75% folded) ubiquitin ensembles are represented using Cβ contact number(CBCN) matrix (top) and RMSD matrix (bottom). Dimensionality reduc-tion to 2D using (left) principal component analysis (PCA) for (A) CBCNand (C) RMSD matrix representations and (right) t-distributed stochas-tic neighbor embedding (t-SNE) for (B) CBCN and (D) RMSD matrixrepresentations.(see Fig. 4.1 A and B). These observed relationships between the ensemblesusing CBCN matrix are visually absent when using the RMSD matrix (seeFig. 4.1 C and D).Fig. 4.2 A shows the dissimilarity of partially folded ensembles of ubiq-uitin from the folded (equilibrium) ensemble at different degrees of native-ness: 75% < Q < 95% at 5% intervals, quantified using Cβ contact number(CBCN) local structural property as implemented in Prothon, and global106RMSD structural property as implemented in Encore dimensionality reduc-tion method in 11D [6].Figure 4.2: Comparing partially folded ensembles of ubiquitin. (A)Dissimilarity between varying degrees (75% < Q < 95%) of partially foldedensemble and the folded equilibrium ensemble of ubiquitin. Dissimilarity isquantified using Cβ contact number (circle) local structural property imple-mented in Prothon and Encore (triangle) The pairwise dissimilarity betweenthe 5 partially folded ensembles of ubiquitin in (A) using (B) Prothon and(C) Encore [6]. (D) Computational efficiency of Prothon compared withEncore. Prothon calculations ran on a single core, while 48 cores were avail-able to Encore.Both the CBCN local structural property and the global RMSD struc-tural property are able to distinguish the partially folded ensembles fromthe folded ensemble and correctly determine the order of nativeness with-out prior knowledge of how the ensembles were obtained (see Fig. 4.2 A).Fig.s 4.2 B and C show the heatmap of pairwise dissimilarity between the5 partially folded ensembles of ubiquitin as quantified using CBCN andRMSD, respectively. As expected, the dissimilarity increases (becomes less107darkened) as one moves away in all 4 directions (up, down, left, and right)from the leading diagonal, where dissimilarity is zero (black) when usingCBCN (see Fig. 4.2 B). This observation is also generally true when us-ing RMSD, although, an exception is noticeable, e.g. the ensemble at 90%nativeness is more dissimilar to the ensemble at 75% nativeness than theensemble at 95% nativeness, which is unexpected. These results show thatthe methods of protein ensemble representation and protein ensemble com-parison as implemented in Prothon are effective.4.2.2 Comparing experimentally derived ensemble of tauK18 domainTau is an intrinsically disordered protein (IDP), whose misfolding and aggre-gation is implicated in many neurodegenerative diseases including Alzheimer’sdisease (AD), Pick’s disease (PiD), chronic traumatic encephalopathy (CTE),corticobasal degeneration (CBD), and progressive supranuclear palsy (PSP)[77]. Tau K18 domain (tauK18) is a 130-residue truncated human tau pro-tein consisting of the four microtuble binding repeats of tau. Five ensemblesof tauK18 were download from the Protein ensemble database (PED) [303].These ensembles represent different models of tauK18 ensemble that werederived by first sampling random coil conformations and then selecting thoseconformations that fit experimental data [304].Table 4.1: Comparing intrinsically disordered ensembles of tau K18.The pairwise dissimilarity between 5 ensembles of tau K18 domain quanti-fied using the Cβ contact number local structural property implemented inProthon.Dissimilarity Ensemble 2 Ensemble 3 Ensemble 4 Ensemble 5Ensemble 1 0.029 0.028 0.031 0.028Ensemble 2 - 0.026 0.029 0.028Ensemble 3 - - 0.026 0.027Ensemble 4 - - - 0.029Table 4.1 shows the pairwise conformational dissimilarity of the 5 tauK18ensembles. Conformational dissimilarity here was quantified using the Cβ108contact number (CBCN) local structural property implemented in Prothon.The dissimilarity values are small and similar (dissimilarity ≈ 0.03), sug-gesting that all 5 ensembles represent similar ensemble in agreement withthe result obtained by Tamas Lazar et al. [292].4.2.3 Computational efficiencyTo evaluate the computational efficiency of Prothon, we recalculated thepairwise dissimilarity between 5 ubiquitin partially folded ensembles de-scribed in section 4.2.1. The calculation of the pairwise ensemble dissimilar-ity was repeated 6 times using Prothon and the publicly available programEncore [6], respectively. For each ith run, where i, 1 ≤ i ≤ 6, is an integer,conformations were selected from the 5000 conformations that make up eachensemble at i regular frame intervals, for a total of ≈ 1i ×5000 conformationsin each ensemble. Since Prothon is currently a serial code, each run used asingle core on a 2020 MacBook Pro, while 48 cores were available for Encore,which has parallel code, on the Digital Research Alliance of Canada cedarcomputing cluster (https://alliancecan.ca).Fig. 4.2 D shows the wall clock time required to calculate the pairwiseensemble dissimilarity for the 5 ubiquitin partially folded ensembles withvarying number of conformations in each ensemble using Prothon and En-core, respectively. While the time required to run Encore increases exponen-tially with the number of conformations, the time required to run Prothonessentially remains the same at ≈ 300 seconds = 5 minutes. When i = 6and each ensemble had 16 × 5000 = 834 conformations, it takes Encore 596seconds = 9 minutes and 56 seconds, which is twice that of Prothon (whichtakes 298 seconds = 4 minutes and 58 seconds), to run. When i = 1 andeach ensemble had 11 × 5000 = 5000 conformations, the time it takes Encoreto run balloons to 28,406 seconds = 7 hours, 53 minutes, and 26 seconds,which is more than 88 times that of Prothon (which takes 322 seconds =5 minutes and 22 seconds) despite Encore using 48 times more computingcores than Prothon.1094.3 Code availability and usageProthon is freely available. Users can run Prothon by downloading the Python package file Prothon.py fromgithub under the GPLv3 license at (https://github.com/PlotkinLab/Prothon. The snippet of code inProgram 4.1, which can be downloaded at https://github.com/PlotkinLab/Prothon, shows how to useProthon to calculate ensemble dissimilarity in only 10 lines of Python code. The exact code was used to generatethe data for the plot in Fig. 4.2 A.Program 4.1 Example Python script that computes dissimilarity between protein ensembles using Prothon.1 from Prothon import Prothon23 data = [ ’Q100 . dcd ’ , ’Q75 . dcd ’ , ’Q80 . dcd ’ , ’Q85 . dcd ’ , ’Q90 . dcd ’ , ’Q95 . dcd ’ ]4 topology = ’ topology . pdb ’56 prothon = Prothon ( data=data , topology=topology )7 ensembles = prothon . en s emb l e r ep r e s en ta t i on ( measure=’CBCN’ )89 d i s s i m i l a r i t y = [ ]1011 for ensemble in ensembles [ 1 : ] :12 d = prothon . e n s e m b l e d i s s i m i l a r i t y ( ensemble , ensembles [ 0 ] )13 d i s s i m i l a r i t y . append (d [ 0 ] )1415 print ( d i s s i m i l a r i t y )110The Prothon class is first imported from the Prothon package (line 1), followed by the creation of a Prothonobject (line 6) initialized with a list of the ensembles (line 3) to be compared and the topology (in pdb format) ofthe conformations contained in these ensembles. The dcd format has been used for the ensemble data here but anyformat supported by the MDTraj package [295] is supported. The Prothon ensemble repesentation function is thenused to represent the ensembles as described in this Chapter using the Cβ contact number (CBCN) local struc-tural property (line 7). To calculate the dissimilarity between two ensembles, the Prothon ensemble dissimilarityfunction is used (line 12), which returns a list “d” of the global dissimilarity, local dissimilarity, and the p valuesfor the local dissimilarity. The global dissimilarity between each ensemble and the first ensemble is saved (line 13)to the dissimilarity list (created in line 9), which is finally displayed in line 15.111Chapter 5ConclusionIn the work presented in this thesis, we proposed two epitope scaffoldingstrategies for the computational modeling and design of oligomer-selectiveimmunogens for protein aggregation-related diseases, and developed a newgeneralized method for efficient quantitative comparison of protein confor-mational ensembles (Fig. 5.1).Figure 5.1: Overview of the thesis.Firstly, we presented an epitope scaffolding method using cyclic peptideswith a computational screening technique that predicts cyclic peptide im-munogen candidates with a desired conformational ensemble that has thepotential to raise oligomer-selective antibodies. This scaffolding methodwas applied to model a pool of 48 cyclic peptide immunogen candidates,which scaffold the α-synuclein epitope in a restricted sequence space using112flanked glycines and a cysteine for immunogen conjugation (i.e. “glycindel”scaffolds). The aim was to find cyclic peptide scaffolds that resemble theconformation of the epitope in the context of an oligomer. These cyclic pep-tides can then be used as immunogens to raise oligomer-selective antibodies.Several highly-ranked cyclic peptide immunogens from this study havebeen used in active immunizations for the purpose of raising such oligomer-selective antibodies [2]. Other scaffolding and design strategies may be ex-plored as well to improve the selectivity and avidity of the elicited antibodies,which forms the basis for our second epitope scaffolding strategy as brieflydescribed in the following.Secondly, we introduced a novel method for scaffolding epitopes to targettoxic forms of proteins implicated in protein aggregation-related diseases.This method entails the design of scaffolds that connect several chains in anaggregated structure by designed linkers, to incorporate multiple repeats ofa target epitope. This construction is intended to guide the conformationalensemble explored by the epitope towards those conformations present inaggregated conformations, which we hypothesize would present the epitopein disease-associated forms of the underlying protein. The prediction of whatepitopes to scaffold in this manner would depend on the application; in ourcontext, the epitopes were predicted to be those on the accessible surface ofan oligomer.The method was applied to tau, a microtuble-binding protein whose lossof function and tangle formation in neurons is associated with many neurode-generative diseases, including Alzheimer’s disease and other tauopathies.Oligomer-selective tau epitopes were predicted by stressing the fibril to in-duce a partially disordered fibril, which serves as a predictive model forepitopes that are likely to be exposed on the surface of oligomers.Four copies of the predicted tau 343KLDFK347 epitope were incorporatedin the final design of a β-helix scaffold. The structure of the designed scaffoldwas validated with AlphaFold, and it is gratifying to see that the Rosetta-designed structure and AlphaFold-predicted structure are nearly identical,with a Cα RMS deviation of 1.39 A˚. In silico characterization of the designedscaffold shows that it is predicted to be thermodynamically stable, which113is an important property of a molecule intended for use as an immunogen.Furthermore, we showed that the multi-epitope scaffolding approach is pre-dicted to be better in discriminating models of abnormal forms of tau fromisolated tau monomer, than single-epitope scaffolding approaches, such asin cyclic peptide “glycindel” scaffolds.The multi-epitope scaffolding approach introduced in this thesis canstraightforwardly be applied to proteins implicated in other protein aggregation-related diseases, such as tau protein in chronic traumatic encephalopathy(CTE), α-synuclein in Parkinson’s disease, SOD1 in amyotrophic lateralsclerosis (ALS), TDP43 in frontotemporal dementia (FTD), and Huntingtinin Huntington’s disease. Experimental characterization of the designed tauβ-helix scaffold is ongoing work.One of the requirements for designing conformationally selective im-munogens in silico is the comparison of large conformational ensembles.However, efficient methods/software for quantitative comparison of largeconformational ensembles are currently not readily available. Therefore,we developed a new generalized method for the efficient representation andcomparison of protein ensembles.Our newly developed method was implemented in the Python program-ming language and made freely available as a Python package called Prothonto the computational structural biology community. The method involvesthe representation of a protein ensemble as a vector of probability densityfunctions. Each probability density function is estimated, using Gaussiankernel density estimation, from the distribution of a local structural prop-erty of the polypeptide chains that make up the ensemble. The dissimilaritybetween two protein ensembles is then quantified by the Jensen Shannondistance between corresponding probability density functions.The method was validated using computationally generated partiallyfolded ensembles of ubiquitin, and experimentally derived intrinsically dis-ordered ensemble of tau protein with the Cβ contact number (CBCN) localstructural property. In principle, any local structural property can be used.Therefore, in addition to CBCN, other local structural properties includingper residue solvent accessible surface area (SASA) [294, 295], virtual Cα-Cα114bond angle (CABA) and torsion angle (CATA) [296], and Cα contact num-ber (CACN) have also been implemented in Prothon. Prothon was shown tobe effective in correctly distinguishing computationally generated ensemblesof ubiquitin and experimentally derived ensembles of tau protein. 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Thesis/Dissertation
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Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Plotkin, Steven
Computational modeling and design of oligomer selective immunogens for Parkinson’s and Alzheimer’s disease
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