Dissertation/Thesis Abstract

Simulation and Control of Biological Stochasticity
by Rackauckas, Christopher Vincent, Ph.D., University of California, Irvine, 2018, 209; 10827971
Abstract (Summary)

Stochastic models of biochemical interactions elucidate essential properties of the network which are not accessible to deterministic modeling. In this thesis it is described how a network motif, the proportional-reversibility interaction with active intermediate states, gives rise to the ability for the variance of biochemical signals to be controlled without changing the mean, a property designated as mean-independent noise control (MINC). This noise control is demonstrated to be essential for macro-scale biological processes via spatial models of the zebrafish hindbrain boundary sharpening. Additionally, the ability to deduce noise origin from the aggregate noise properties is shown.

However, these large-scale stochastic models of developmental processes required significant advances in the methodology and tooling for solving stochastic differential equations. Two improvements to stochastic integration methods, an efficient method for time stepping adaptivity on high order stochastic Runge-Kutta methods termed Rejection Sampling with Memory (RSwM) and optimal-stability stochastic Runge-Kutta methods, are combined to give over 1000 times speedups on biological models over previously used methodologies. In addition, a new software for solving differential equations in the Julia programming language is detailed. Its unique features for handling complex biological models, along with its high performance (routinely benchmarking as faster than classic C++ and Fortran integrators of similar implementations) and new methods, give rise to an accessible tool for simulation of large-scale stochastic biological models.

Indexing (document details)
Advisor: Nie, Qing
Commitee: Chen, Long, Enciso, German
School: University of California, Irvine
Department: Mathematics
School Location: United States -- California
Source: DAI-B 80/01(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Applied Mathematics, Systematic biology, Developmental biology
Keywords: Adaptive time stepping, Julia, Noise control, Rejection sampling, Runge-Kutta, Stochastic
Publication Number: 10827971
ISBN: 9780438304307
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