{"Affiliation":[{"label":"Affiliation","value":"Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"Aggregated Source Repository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Tosefsky, Kira","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."},{"label":"Creator","value":"Kwon, Woo Joo","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"Date Available","value":"2018-11-28T18:33:05Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"Date Issued","value":"2018-03-26","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Description":[{"label":"Description","value":"The development of multidrug resistant bacteria in response to antibiotic treatment is one of the chief problems facing modern medicine. We sought to investigate the effect of different antibiotic treatment regimens and bacterial population characteristics on the development of the multidrug resistant bacteria in a population under selective pressure from two antibiotics. We built a deterministic compartmental model in Python to simulate an E.coli population under selective pressure from benzylpenicillin and cephaloglycin. Baseline parameters were obtained from the literature. After adjusting six parameters and compiling results after two hours, we found that the final population size of the multidrug resistant strain decreased in response to increased mutation and growth rates and decreased horizontal gene transfer rates, while variations in the other parameters produced more complex trends.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"Digital Resource Original Record","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/67918?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"FullText":[{"label":"Full Text","value":"    A Python simulation model of the development of multidrug resistant E.coli in an individual host    Kira Tosefsky and Woo Joo Kwon  March 26, 2018   1 Abstract:  The development of multidrug resistant bacteria in response to antibiotic treatment is one of the chief problems facing modern medicine. We sought to investigate the effect of different antibiotic treatment regimens and bacterial population characteristics on the development of the multidrug resistant bacteria in a population under selective pressure from two antibiotics. We built a deterministic compartmental model in Python to simulate an E.coli population under selective pressure from benzylpenicillin and cephaloglycin. Baseline parameters were obtained from the literature. After adjusting six parameters and compiling results after two hours, we found that the final population size of the multidrug resistant strain decreased in response to increased mutation and growth rates and decreased horizontal gene transfer rates, while variations in the other parameters produced more complex trends. Introduction: Current understanding of antibiotic resistance development points to random mutation (i.e. not induced by the presence of antibiotics) as the origin of resistance, and horizontal gene transfer as a principal mechanism of its proliferation. Under selective pressure from antibiotics, resistant phenotypes bear a selective advantage over susceptible phenotypes, resulting in the competitive exclusion of susceptible phenotypes by resistant phenotypes over multiple generations, and ultimately in the development of resistant infections unresolvable by traditional medical approaches. Varying solutions have been proposed and practiced in an attempt to minimize the growth of resistant bacteria in populations under antibiotic pressure. The first approach, termed mixing, involves concurrent administration of two antibiotics, in the hopes that bacteria resistant to one antibiotic will be susceptible to, and thus eradicated by, the other. The  2 drawback to administration of two antibiotics is the potential for the development and proliferation of bacteria resistant to both antibiotics. Another approach, termed cycling, repeatedly administers two different antibiotics in succession rather than in tandem. Which of these approaches more effectively limits the proliferation of bacteria resistant to both antibiotics given particular characteristics of a population - the most problematic of these populations from a clinical perspective - is a continued matter of debate.  Because characterization of time-varying infectious population composition in vivo is generally not feasible, simulation modelling of population dynamics under selective pressure from antibiotics offers a useful means of characterizing population dynamics in response to antibiotic administration and for determining optimal treatment regimens.  To analyze the effects of different treatment regimens, we created a deterministic compartmental model for E.coli population under selective pressure from two beta-lactam (B-lactam) antibiotics, benzylpenicillin, antibiotic \u201cA\u201d, and cephaloglycin, antibiotic \u201c B\u201d, against which some bacteria in the population develop resistance via mutation.  Methods: B-lactam antibiotics function by binding and inactivating cytoplasmic membrane enzymes, penicillin binding proteins (PBPs), critical for maintaining and adapting the structure of the bacterial cell wall (Lepage et al. 1995). If a sufficient proportion of PBPs in a cell are inactivated, cell lysis results (Olofsson 2005).  The kinetics of the interaction between PBPs and beta-lactams have been described using a three-step model:                      k1                 k2               k3 E + C   \u2192 \u2190   E-C   \u2192   E-C*   \u2192   E + P                          (1)          k-1  3 Where K is the equilibrium constant for the formation of PBP-beta lactam complex, K = k1\/k-1, E-C* is the acyl-enzyme and P is the inactivated product following dissociation of the complex. Referring to benzylpenicillin as antibiotic \u201cA\u201d and cephaloglycin as antibiotic \u201cB\u201d, the following differential equation were used to describe the change in their concentrations:  !\"#!$ = \t\u2212\ud835\udc36\ud835\udc4e(\ud835\udc58\ud835\udc4e + \ud835\udc58\ud835\udc53\ud835\udc4e\t \u00d7 \t\ud835\udc381)       (2a) !\"2!$ = \t\u2212\ud835\udc36\ud835\udc4f(\ud835\udc58\ud835\udc4f + \ud835\udc58\ud835\udc53\ud835\udc4f\t \u00d7 \t\ud835\udc382)       (2b) where ka and kb are the spontaneous decay rates of the antibiotics, and kfa and kfb are the rates of formation of the acyl enzyme adduct (E-C*), kfa = k2a\/Ka, kfb = k2b\/Kb, assuming a rapid equilibrium in the first step of the mechanism described above. These equations describe both the first-order decay of beta lactams and the second order rate of formation of acyl-enzyme adduct.  The rate of change in free enzyme concentration is described by a more complex differential equation, since free enzyme is regenerated in the final step of the mechanism: E1 = (-E1\t\u00d7\tkfa\t\u00d7\tCa + k3a \u00d7 E1)\t\u00d7 \t 556        (3a) E2 = (-E2\t\u00d7\tkfb\t\u00d7\tCb + k3b \u00d7 E2)\t\u00d7 \t 556                         (3b) where 556 represents an adjustment for changing population size, assuming enzyme synthesis rates are proportional to the number of cells. At the same time, the total enzyme concentrations (the sum of bound and unbound enzymes), is assumed to be proportional to the total population size, S. Thus, Etot1 = 7656 \t\u00d7 \t\ud835\udc46 and Etot2 = 7656 \t\u00d7 \t\ud835\udc46, where  7656 represents the initial ratio of enzyme to population size.   4 Since the proportion of unbound PBPs, E1 and E2, is the critical factor in determining mortality rates for each population, we assign the variable Q to this proportion: Q1 =  797$:$9         (4a)             Q2 = 7;7$:$;                                                      (4b)  Growth rate constants, r, are then given by the following equations for each population: P: r1 = (rmax - rminab)\t\u00d7\tQ1\t\u00d7\tQ2 + rminab                           (5) A: r2 = (rmax - rmina)\t\u00d7\tQ1 + rmina                                        (6) B: r3 = (rmax - rminb)\t\u00d7\tQ2 + rminb                                        (7) AB: r4 = rmax                                                    (8) where rmax is the maximum growth rate constant under no antibiotic pressure, and rmin is the growth rate constant when all PBPs are bound (Olofsson et. Al 2005).  Incorporating these growth rate constants into the logistic growth model, we obtain the following growth rates: P: g1 = r1 \u00d7\t1.0 \u00d7\t(<=5)<                                             (9) A: g2 = r2 \u00d7\t1.0 \u00d7\t(<=5)<                                           (10) B: g3 = r3 \u00d7\t1.0 \u00d7\t(<=5)<                                            (11) AB: g4 = r4 \u00d7\t1.0 \u00d7\t(<=5)<                                         (12) Where K is the carrying capacity of the total population. Accounting for the effects of the immune system, a term  Phagr\t\u00d7\t__(population P, A, B, or AB)___ \u00d7 >?#@(>?#@A5))           (13) is subtracted from each of the above equations, where \u201cPhagr\u201d represents the killing rate of phagocytes and \u201cPhag\u201d the number of phagocytes at the infection site.  5 Concurrently, ma and mb were assigned to the mutation rates resulting in formation of the resistant genes for antibiotic A and B, respectively while l1, l2, l3 and l4 described the rates of loss of resistant plasmids from each of the populations and t1, t2, t3 and t4 described the rates of horizontal gene transfer of the plasmids. Thus, the differential equations describing the change in population size of each population, P, A, B, and AB, were encoded as follows and illustrated in Fig. 1: !>($)!$ \t= (g1 \u00d7\tP) + (t1 \u00d7\tA \u00d7\tP) - (t2 \u00d7\tB \u00d7\tP) \u00d7\tdt + (l1 \u00d7\tA \u00d7\tP) \u00d7\tdt + (l2 \u00d7\tB \u00d7\tP) \u00d7\tdt \u2013 (Phagr \u00d7\tP) \u00d7\t( >?#@(>?#@A5)) \u2013 (ma \u00d7\tP) \u2013 (mb \u00d7\tP) + (ma \u00d7\tmb) \u00d7\tP      (14) !B($)!$  = (g2 \u00d7\tA) + (t1 \u00d7\tA \u00d7\tP) - (t3 \u00d7\tA \u00d7\tAB) - (l1 \u00d7\tA \u00d7\tP) + (l3 \u00d7\tA \u00d7\tAB)                      - Phagr \u00d7\tA \u00d7\t( >?#@(>?#@A5)) + ma \u00d7\tP - mb \u00d7\tA                                (15) !C($)!$  = (g3 \u00d7\tB) + (t2 \u00d7\tA \u00d7\tP)  - (t4 \u00d7\tB \u00d7\tAB) - (l2 \u00d7\tB \u00d7\tP) + (l4 \u00d7\tA \u00d7\tAB)  - Phagr \u00d7\tB \u00d7\t( >?#@(>?#@A5)) + mb \u00d7\tP - ma \u00d7\tB                              (16) !BC($)!$  = (g4 \u00d7\tAB) + (t3 \u00d7\tA \u00d7\tAB) + (t4 \u00d7\tB \u00d7\tAB) - (l3 \u00d7\tA \u00d7\tAB) - (l4 \u00d7\tB \u00d7\tAB)  - Phagr \u00d7\tAB \u00d7\t( >?#@(>?#@A5)) + ma \u00d7\tmb \u00d7\tP + mb \u00d7\tA + ma \u00d7\tB            (17)     6        Baseline parameters for E.coli growth and mortality rates both in the absence and presence of antibiotic pressure were taken from Dagata et al. (2008), as were estimates of carrying capacity, phagocytic killing rates and numbers and bacterial population levels in a typical infection. Parameters for enzyme kinetics were taken from Lepage et al. (1995). All baseline parameter values are listed in Table 1.  Euler integration was performed over a time period of T = 2 hours, with a time step of dt = 10-6 hours.  Table 1: Baseline Parameters Symbol Meaning Value Units P Parent population size 106 # cells A  Population size of antibiotic-A resistant  1 # cells Fig. 1. Illustration of the compartmental model upon changes in population size are based.  The python program simulates the above situation using equations 14-17.     7 B Population size of antibiotic-B resistant  1 # cells AB  Population size of antibiotic-A and antibiotic-B resistant  1 # cells S  Total population size (initial) 1000003 # cells  C0  Antibiotic dose of A  40\t\u00d7\t10-6 M C0  Antibiotic dose of B 40 \u00d7\t10-6 M Ka  Rate of degradation of A, based on 100 min half-life  0.10395 \u00d7\t4 hr-1  Kb  Rate of removal of B, based on 400 min half-life   0.10395 hr-1 Rmax Max cell division rate (no antibiotic pressure); assume mortality rate in absence of antibiotics is negligible  2.7726\/24 hr-1 Rmina Cell division rate under pressure from antibiotic B (to which bacteria \u201cA\u201d are susceptible), mortality rate = 1.9  (2.7726 - 1.9)\/24   \u00d7\t16.6626\/24 in vivo div. Rate, but under no competition   hr-1 Rminb  Cell division rate under pressure from antibiotic A (to which bacteria \u201cB\u201d are susceptible), mortality rate = 2.1 (2.7726 - 2.1)\/24  hr-1 Rminab  Cell division rate under pressure from antibiotic A and B, mortality rate = 1.9 + 2.1 (2.7726 - 1.9 - 2.1)\/24 hr-1 K Carrying capacity, to maintain infection threshold of 10^6 bacteria  108 # cells Phag  Total number of phagocytes at infection site  332711  # cells Phagr  Killing rate of phagocytes  33.6038\/24  hr-1 l1, l2, l3, l4 Horizontal gene transfer rates  10-3\/24  hr-1  Rates of resistant plasmid loss   10-6 hr-1  Mutation rates, ma and mb  1.42*10^-9 hr-1, cells-1  8 kda Dissociation constant of E*C for A 3600*2.1*(10^-3 hr-1 K3b Dissociation constant of E*C for B 3600*10^-4 hr-1 k2a\/kda = kfa  Pseudo-first order rate constant for PCB acylation for A 331000*3600 hr-1 k2b\/kdb = kfb  Pseudo-first order rate constant for PCB acylation for B 30000*3600 hr-1 Ma  Mutation rate for genetic element producing resistance to antibiotic a  1.42*10^-9 Fraction of cells  Mb  Mutation rate for genetic element producing resistance to antibiotic b  1.42*10^-9  Fraction of cells  We then adjusted parameters to investigate the following effects on the population size of multidrug resistant bacteria at time T, our factor of interest: a) Antibiotic dose volume b) Horizontal gene transfer rates  c) Mutation rates  d) Growth rate of bacterial population e) Timing of antibiotic administration, relative to timing of infection (as measured by the initial population size at timing of first administration)  f) The effect of mixing versus cycling regimens, with introduction of the \u201csecond\u201d antibiotic at different time intervals following introduction of the first antibiotic.   For each parameter adjustment, we plotted population size of AB at time t against the adjusted parameter to investigate relevant trends. Results and Discussion: The population size of AB resistant bacteria decayed with increasing population growth rate according to a second order polynomial best fit, as shown below:  9     This result suggests that by increasing the maximum growth rate of the population, more sensitive bacteria are able to proliferate despite the antibiotic selection factor against them, exerting greater competitive inhibition on resistant strains.  0200000040000006000000800000010000000120000001400000016000000180000000 0.2 0.4 0.6 0.8 1 1.2 1.4Population of AB (Number of Cells) at T Growth Rate Constant (hr-1) Final AB Population Size vs. Max Growth Rate Model Data Poly. (Model ) 10   The effect of antibiotic dose volume on the population of strain AB at time T decays sharply, stabilizing beyond a concentration of 0.0002 M. This suggests that increasing the antibiotic dose beyond this concentration, though not increasing the risk of resistance infection, does not present any therapeutic benefit.  149895001498960014989700149898001498990014990000149901000 0.0002 0.0004 0.0006 0.0008 0.001 0.0012Population of AB (number of cells) at TDose Concentration (M)AB Population Size vs. Antibiotic Concentration (M)Model Data 11   The relationship between horizontal gene transfer rates and the number of AB bacteria is particularly interesting, as it presents a threshold below which AB strain bacteria are effectively unable to proliferate (number of cells at time T < 1). Above this threshold, AB strain bacteria are able to proliferate and reach population levels in the millions at time T. The threshold horizontal gene transfer rate was identified around 10-5 transfers per cell division, suggesting that therapies capable of suppressing horizontal gene transfer rates below this level may be exceptionally effective in limiting the proliferation of multidrug resistant strains.     020000004000000600000080000001000000012000000140000001600000018000000200000000 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 0.00045Population of AB (number of cells) at T Gene Transfer Rate (hr^-1 cells^-1)Final Population Size of AB  vs. Horizontal Gene Transfer Rate 12   Surprisingly, the number of AB bacteria varied inversely with mutation rates of the genes resulting in resistance. While we expected that increasing mutation rates would increase the number of bacteria transformed to both single-drug resistant strains and the multi-drug resistant strain, the unexpected result can be explained from an ecological standpoint. The accelerated transformation of parental strains into single-drug resistant strains results in the multidrug resistant strain competing with a greater number of single-drug resistant individuals, with a higher relative fitness than the parental competitors. As a result, the multidrug resistant bacteria have a reduced fitness advantage in this environment, limiting their population growth.  14978000149800001498200014984000149860001498800014990000149920000 2E-09 4E-09 6E-09 8E-09 1E-08 1.2E-08 1.4E-08 1.6E-08Population of AB (number of cells) at TMutation Rate (hr-1 cell-1)Population of AB Bacteria vs. Mutation RateData Model 13    We investigated the effect of timing of antibiotic treatment with respect to timing of infection by adjusting the initial population size at the time of antibiotic administration, assuming that the population would have grown to a larger size without antibiotic pressures present in the interval between infection and treatment commencement. We see that early administration of antibiotic is most effective in minimizing the number of AB bacteria at time T. For larger initial population sizes above 4 \u00d7\t106 and below the carrying capacity (107), the number of AB bacteria at time T stabilizes around 3 \u00d7\t106. For initial populations above the carrying capacity, however, there are significant jumps in the number of AB bacteria at time T, suggesting that antibiotic administration becomes significantly less effective after the bacterial population has reached its carrying capacity.  050000001000000015000000200000002500000030000000350000000 2000000 4000000 6000000 8000000 10000000AB Population SizeInitial Population SizeAB Population Size vs. Initial Population Size 14   The effect of antibiotic cycling on the proliferation of AB bacteria was also unpredicted. With antibiotic A representing the antibiotic with shorter half-life (by a factor of 4), we examined the effects of delaying the introduction of antibiotic B after the introduction of A by various time intervals. While delaying the introduction of B by up to T\/3 hours, no difference was seen between the number of AB bacteria at time T as compared to a mixing regimen. However, beyond a delay of T\/3 hours, there was a significant jump in number of AB bacteria at time T.  14980000149900001500000015010000150200001503000015040000150500000 0.5 1 1.5 2Population of AB (number of cells) at T Time Delay of Administration of B after A (hr)Final Population of AB vs. Time Delay of B 199000001992000019940000199600001998000020000000200200000 0.5 1 1.5 2Population of AB (number of cells) at T Time Delay of Administration of A (hr)Final Population of AB vs. Time Delay of A   15  This relationship was reversed when delaying the introduction of antibiotic A, wherein delays less than T\/3 hours resulted in larger populations of AB bacteria at time T, while delays beyond this conferred a significant reduction in the number of AB bacteria. However, the minimum population of AB bacteria achieved by any delay of introduction of antibiotic A was significantly higher than the minimum population size achieved with mixing or delay of antibiotic B by any time interval < T. Thus, a mixing regimen, or a cycling regimen wherein introduction of a longer half-life antibiotic is delayed up to T\/3 hours appears to minimize the population size of antibiotic resistant bacteria at time T\/3.  Conclusion: While the quantitative information provided by our data has limited applicability due to the specificity of parameter estimates, the qualitative information it provides about the relationship between the development of multidrug resistant bacterial infections and various population characteristics or treatment regimens has potential applicability to a variety of pathogenic systems. Further, parameters entered into the program itself can be easily adjusted to produce results more applicable to other pathogenic systems for which the effects of changes in various parameters are challenging to pinpoint in an in vivo system          16 References: Lepage, S., Lakaye, B., Galleni, M., Thamm, I., Crine, M., Groslambert, S., & Fr\u00e8re, J. (1995). Saturation of penicillin-binding protein 1 by ?-lactam antibiotics in growing cells of Bacillus licheniformis. Molecular Microbiology, 16(2), 365-372. doi:10.1111\/j.1365-2958.1995.tb02308.x Dagata, E. M., Dupont-Rouzeyrol, M., Magal, P., Olivier, D., & Ruan, S. (2008). The Impact of Different Antibiotic Regimens on the Emergence of Antimicrobial-Resistant Bacteria. PLoS ONE, 3(12). doi:10.1371\/journal.pone.0004036 Olofsson, S. K., Geli, P., Andersson, D. I., & Cars, O. (2005). Pharmacodynamic Model To Describe the Concentration-Dependent Selection of Cefotaxime-Resistant Escherichia coli. Antimicrobial Agents and Chemotherapy, 49(12), 5081-5091. doi:10.1128\/aac.49.12.5081-5091.2005   17 Appendix:  Code:  import matplotlib.pyplot as plt #for plotting population sizes, frequencies at time t import math import numpy #for arrays  t0 = 0 #begin administration of antibiotics at t = t0 = 0 t = t0 #initialize time  #define constant mutation rates ma = 1.42*(10**-9) #ma = mutation rate of genetic element -> resistance to antibiotic a, benzylpenicillin mb = 1.42*(10**-9) #mb = mutation rate of genetic element -> resistance to antibiotic b, cephaloglycin  #initialize populations at t = t0 P = 10**6#parent population A = 1#resistant population A, resistant to benzylpenicillin B = 1#resistant population B, resistant to cephaloglycin AB = 1#resistant population AB, resistant to benzylpenicillin + cephaloglycin S0 = A + P + B + AB#total population S = S0#initialize total population  #convert popultion sizes to floats float(P) float(A) float(B) float(AB) float(S)  #Initialize concentrations of antibiotics administered C0 = 40*10**-6 Ca = C0 Cb = C0\/2 #half the concentration of cephaloglycin administered (due to longer half-life, as per clinical convention) ka = 0.10395*4 #rate of spontaneous degradation of benzylpenicillin, half-life = 100 min kb = 0.10395 #rate of spontaneous degradation of cephaloglycin, half-life = 400 min  #convert concentrations to floats float(Ca) float(Cb)   18  E0 = 0.266*10**-9 #initial (equivalent) concentrations of PBP1 and PBP2  #define enzyme PBP1 (binds benzylpenicillin, \"a\") kinetic parameters kfa = 331000*3600#second order rate of formation of acyl-enzyme, E-C*, M^-1 s^-1 k3a = 2.1*(10**-3)*3600#first order rate of dissociation of E-C* into E + P (enzyme + acylated antibiotic), s^-1 E1 = E0#initialize free PBP1 concentration Etot1 = E0#initialize total PBP1 concentration at t = t0  #convert concentrations + kinetic parameters to floats float(E0) float(kfa) float(k3a) float(E1) float(Etot1)  #initialize PBP2 (binds cephaloglycin, \"b\") kinetic parameters kfb = 30000*3600##second order rate of formation of acyl-enzyme, E-C*, M^-1 s^-1 k3b = 3600*10**-4#first order rate of dissociation of E-C* into E + P (enzyme + acylated antibiotic), s^-1 E2 = E0#initialize free PBP2 concentration Etot2 = E2#initial total PBP2 concentration at t = t0  #convert enzyme concenrations + kinetic parameters to floats float(kfb) float(k3b) float(E2) float(Etot2)  #define proportions of free PBPs for each PBP Q1 = E1\/Etot1#proportion of free PBP1s Q2 = E2\/Etot2#proportion of free PBP2s d1 = Etot1\/S#constant ratio of total PBP1s (free + bound) to population size (enzyme\/cell) d2 = Etot2\/S#constant ratio of total PBP2s (free + bound) to population size (enzyme\/cell)  #convert ratios to floats float(Q1) float(Q2)  #Set growth rate constants for each subpopulation rmax = 2.7726\/24 #max growth rate constant under no antibiotic selective pressure, hr^-1 rmina = (2.7726 - 1.9)\/24#minimum growth rate of pop. all PBP2s bound to antibotic b, no PBP1s bound, hr^-1  19 rminb = (2.7726 - 2.1)\/24#minimum growth rate of pop. with all PBP1s bound to antibiotic a, no PBP2s bound, hr^-1 rminab = (2.7726 - 1.9 - 2.1)\/24#minimum growth rate of pop. with all PBP1s and PBP2s bound, hr^-1 r1 = (rmax - rminab)*Q1*Q2 + rminab#growth rate constant of pop.P susceptible to antibotic a and b, reduction in growth rate proportional to proportion bound PBPs, hr^-1 r2 =(rmax - rmina)*Q1 + rmina#growth rate constant of pop.A susceptible to antibotic b, reduction in growth rate proportional to proportion bound PBP2s, hr^-1 r3 = (rmax - rminb)*Q2 + rminb#growth rate constant of pop.B susceptible to antibotic a, reduction in growth rate proportional to proportion bound PBP1s, hr^-1 r4 = rmax#growth rate constant of pop. AB, not affected by action of antibiotics, hr^-1  #convert growth rate constants to floats float(rmax) float(rmina) float(rminb) float(r1) float(r2) float(r3) float(r4)  #set logistic growth equation parameters K = 10**8 #carrying capacity, cells float(K)  #logistic growth equations, cells\/hr g1 = r1*1.0*(K - S)\/K#for pop P g2 = r2*1.0*(K - S)\/K#for pop A g3 = r3*1.0*(K - S)\/K#for pop B g4 = r4*1.0*(K - S)\/K#for pop AB  #convert growth rates to floats float(g1) float(g2) float(g3) float(g4)   #Define frequencies of each subpopulation FreqP = P\/S FreqA = A\/S FreqB = B\/S FreqAB = AB\/S   20 #convert frequencies to floats float(FreqP) float(FreqA) float(FreqB) float(FreqAB)  #Set up arrays P_fin = [] A_fin = [] B_fin = [] AB_fin = [] S_fin = [] time = [] Ca_fin = [] Cb_fin = [] r1_fin =[] r2_fin =[] r3_fin =[] r4_fin =[] g1_fin = [] g2_fin =[] g3_fin = [] g4_fin = [] E1_fin = [] E2_fin = [] Etot1_fin = [] Etot2_fin =[] Q1_fin = [] Q2_fin =[] FreqP_fin =[] FreqA_fin = [] FreqB_fin = [] FreqAB_fin =[]  #Define immune response parameters Phagr = 33.6038\/24 #constant killing rate of phagocytes, cells^-1, hr^-1 Phag = 332711#constant number of phagocytes at site of infection  #convert phagocyte # and killing rate to floats float(Phagr) float(Phag)  #rates of horizontal gene transfer, cell^-1 hr^-1 t1 = (10**-3)\/(2.1*24)  21 t2 = (10**-3)\/(2.1*24) t3 = (10**-3)\/(2.1*24) t4 = (10**-3)\/(2.1*24)  #convert horizontal gene transfer rates to floats float(t1) float(t2) float(t3) float(t4)  #Loss of resistance plasmid rates, cell^-1 hr^-1 l1 = (10**-6) l2 = (10**-6) l3 = (10**-6) l4 = (10**-6)  #convert loss of resistance rates to floats float(l1) float(l2) float(l3) float(l4)  #Inialize the stop time and time step T = 2#final time, hr dt = 10**-6, #time step  #convert start\/stop time and time step to floats float(t) float(T) float(dt)  while t <= T: #iterate through loop until t < T #update population sizes     P = P + g1*P*dt + (t1*A*P)*dt - (t2*B*P)*dt + (l1*A*P)*dt + (l2*B*P)*dt - Phagr*P*(Phag\/(Phag + S))*dt - ma*P*dt - mb*P*t - ma*mb*P*dt     A = A + (g2*A)*dt + (t1*A*P)*dt - (t3*A*AB)*dt - (l1*A*P)*dt + (l3*A*AB)*dt - Phagr*A*(Phag\/(Phag + S))*dt + ma*P*dt- mb*A*dt     B = B + (g3*B)*dt + (t2*A*P)*dt - (t4*B*AB)*dt - (l2*B*P)*dt + (l4*A*AB)*dt - Phagr*B*(Phag\/(Phag + S))*dt + mb*P*dt - ma*B*dt     AB = AB + (g4*AB)*dt + (t3*A*AB)*dt + (t4*B*AB)*dt - (l3*A*AB)*dt - (l4*B*AB)*dt - Phagr*AB*(Phag\/(Phag + S))*dt + ma*mb*P*dt + mb*A*dt + ma*B*dt     S = P + A + B + AB     t = t + dt   22 #update concentrations     if t < T\/2 or t > (T\/2 + dt):         Ca = Ca - Ca*ka*dt - Ca*kfa*E1*dt         Cb = Cb - Cb*kb*dt - Cb*kfb*E2*dte     else:         Ca = C0 + Ca - Ca*ka*dt - Ca*kfa*E1*dt         Cb = C0 + Cb - Cb*kb*dt - Cb*kfb*E2*dt  #update growth rate constants     r1 = 1.0*(rmax - rminab)*Q1*Q2 + rminab     r2 = 1.0*(rmax - rmina)*Q2 + rmina     r3 = 1.0*(rmax - rminb)*Q1 + rminb     r4 = 1.0*rmax  #update growth rates     g1 = r1*1.0*(K - S)\/K     g2 = r2*1.0*(K - S)\/K     g3 = r3*1.0*(K - S)\/K     g4 = r4*1.0*(K - S)\/K  #update enzyme concentrations     Etot1 = d1*S#total number PBP1s (free + bound) proportional to total number of cells     E1 = (E1 -kfa*E1*Ca + k3a*(E1)*S\/S0)*dt      E2 = (E2 + -kfb*E2*Cb + k3b*(E2)*S\/S0)*dt     Etot2 = d2*S#total number PBP2s (free + bound) proportional to total number of cells  #update proportion of free enzymes     Q1 = E1\/Etot1     Q2 = E2\/Etot2  #update frequencies     FreqP = P\/S     FreqA = A\/S     FreqB = B\/S     FreqAB = AB\/S   #append values for each loop in arrays     P_fin.append(P)     A_fin.append(A)     B_fin.append(B)     AB_fin.append(AB)     time.append(t)  23     Ca_fin.append(Ca)     Cb_fin.append(Cb)     S_fin.append(S)     r1_fin.append(r1)     r2_fin.append(r2)     r3_fin.append(r3)     r4_fin.append(r4)     g1_fin.append(g1)     g2_fin.append(g2)     g3_fin.append(g3)     g4_fin.append(g4)     E1_fin.append(E1)     E2_fin.append(E2)     Etot1_fin.append(Etot1)     Etot2_fin.append(Etot2)     Q1_fin.append(Q1)     Q2_fin.append(Q2)     FreqP_fin.append(FreqP)     FreqA_fin.append(FreqA)     FreqB_fin.append(FreqB)     FreqAB_fin.append(FreqAB)      print(FreqAB)     if (T - dt) < t < T + dt:         print(AB)#print population size at time T #Plot plt.figure(1)#population frequencies vs. time plt.plot(time, FreqP_fin, label=\"P\") plt.plot(time, FreqA_fin, label=\"B\") plt.plot(time, FreqB_fin, label=\"A\") plt.plot(time, FreqAB_fin, label=\"AB\") plt.xlabel(\"time(hours)\") plt.ylabel(\"Phenotype Frequencies\") plt.legend() plt.show() plt.figure(2)#population frequencies vs. antibiotic a concentration plt.plot(Ca_fin, FreqP_fin, label = \"P\") plt.plot(Ca_fin, FreqA_fin, label= \"A\") plt.plot(Ca_fin, FreqB_fin, label=\"B\") plt.plot(Ca_fin, FreqAB_fin, label=\"AB\") plt.xlabel(\"Concentration of A\") plt.ylabel(\"Phenotype Frequencies\") plt.legend() plt.show()  24 plt.figure(3)#population frequencies vs. antibiotic b concentration plt.plot(Cb_fin, FreqP_fin, label = \"P\") plt.plot(Cb_fin, FreqA_fin, label= \"A\") plt.plot(Cb_fin, FreqB_fin, label=\"B\") plt.plot(Cb_fin, FreqAB_fin, label=\"AB\") plt.xlabel(\"Concentration of B\") plt.ylabel(\"Phenotype Frequencies\") plt.legend() plt.show() plt.figure(6)#total population vs. time plt.plot(time, S_fin, label=\"total population\") plt.legend() plt.show() plt.figure(4)#concentration of a vs. time plt.plot(time, Ca_fin, label=\"Ca\") plt.xlabel(\"time(hours)\") plt.ylabel(\"Concentration of A\") plt.legend() plt.show() plt.figure(5)#concentration of b vs. time plt.plot(time, Cb_fin, label=\"Cb\") plt.xlabel(\"time(hours)\") plt.ylabel(\"Concentratinon of B\") plt.legend() plt.show()   ","attrs":{"lang":"en","ns":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","classmap":"oc:AnnotationContainer"},"iri":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","explain":"Simple Knowledge Organisation System; Notes are used to provide information relating to SKOS concepts. 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