Branching Brownian motion models for cell developmental trajectories
department or school: Science, Faculty of
department or school: Mathematics, Department of
data provider: DSpace
degree campus: UBCV
creator: Gadhiwala, Nitya
issued: 2023-08-30T22:23:14Z
issued: 2023
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: Recent advances in single cell sequencing has led to the availability of gene expression data. We model the trajectories of cells in gene expression space using a diffusion and gradient drift process that also undergoes branching. We recover the law on paths of this process given time marginals using an entropy minimization problem. The optimization is over the set of all processes with the same branching mechanism and given marginals. We prove that among these the one which minimizes the relative entropy with respect to a reference branching Brownian motion is the ground truth. The above result has been proved earlier for models that don't consider branching. This thesis extends it for the case with branching.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/85714
note: Branching Brownian motion models forcell developmental trajectoriesbyNitya GadhiwalaBachelor of Mathematics (Honours), Indian Statistical Institute, 2021A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Mathematics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2023© Nitya Gadhiwala 2023The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:Branching Brownian motion models for cell developmental trajectoriessubmitted by Nitya Gadhiwala in partial fulfillment of the requirements forthe degree of Master of Sciencein Mathematics.Examining Committee:Omer Angel, Professor, Department of Mathematics, UBCCo-supervisorGeoffrey Schiebinger, Assistant Professor, Department of Mathematics, UBCCo-supervisoriiAbstractRecent advances in single cell sequencing has led to the availability of geneexpression data. We model the trajectories of cells in gene expression spaceusing a diffusion and gradient drift process that also undergoes branching.We recover the law on paths of this process given time marginals usingan entropy minimization problem. The optimization is over the set of allprocesses with the same branching mechanism and given marginals. Weprove that among these the one which minimizes the relative entropy withrespect to a reference branching Brownian motion is the ground truth. Theabove result has been proved earlier for models that don't consider branching.This thesis extends it for the case with branching.iiiLay SummaryA cell, over the course of it's lifetime, traces out a path in gene expressionspace. Upon it's death, it divides into a random number of cells. Usingmodern technologies such as single cell sequencing, we can obtain snapshotsof these paths in gene expression space. We use optimal transport to fit amodel of branching diffusion with gradient drift to the above …
has type: Thesis/Dissertation
date issued: 2023-11
is shown at: 10.14288/1.0435667
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Angel, Omer
contributor: Schiebinger, Geoffrey
type: Text
identifier URI: http://hdl.handle.net/2429/85714