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Reference: Tamas Szekely Jr., (2014). Stochastic modelling and simulation in cell biology. DPhil. University of Oxford.Citable link to this page:


Stochastic modelling and simulation in cell biology

Abstract: Modelling and simulation are essential to modern research in cell biology. This thesisfollows a journey starting from the construction of new stochastic methods fordiscrete biochemical systems to using them to simulate a population of interactinghaematopoietic stem cell lineages.The first part of this thesis is on discrete stochastic methods. We develop two newmethods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoermethods. These are based on the Richardson extrapolation technique, which is widelyused in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true.The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method.The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver.Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remainsaccurate even when simulation time is speeded up. This is a useful property forsimulating the complex systems that researchers are often interested in today.The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupledcells.In brief, this thesis contains four main sets of contributions: two new high-accuracydiscrete stochastic methods that have been numerically tested, an improvement thatcan be used with any leaping method that introduces vectorisation as well as how touse a common stepsize adapting scheme, and an investigation of the effects of couplinglineages in a heterogeneous population of haematopoietic stem cell niche lineages.

Digital Origin:Born digital Type of Award:DPhil Level of Award:Doctoral Awarding Institution: University of Oxford Notes:This thesis is not available on ORA.


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 Bibliographic Details

Issue Date: 2014

Copyright Date: 2014 Identifiers

Urn: uuid:f9b8dbe6-d96d-414c-ac06-909cff639f8c Item Description

Type: thesis;

Language: en Keywords: Stochastic simulation tau-leap higher-order stochastic methods stem cells population dynamicsSubjects: Biology Computational biochemistry Cell Biology (see also Plant sciences) Biology and other natural sciences (mathematics) Computer science (mathematics) Mathematical biology Probability theory and stochastic processes Stem cells (clinical sciences) Biology (medical sciences) Chemical kinetics Tiny URL: ora:9396


Author: Tamas Szekely Jr. - institutionUniversity of Oxford facultyMathematical, Physical and Life Sciences Division - Department of Comp



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