dc.description.abstract | Systems Biology is an actively emerging interdisciplinary area between biology and
applied mathematics, based on the idea of treating biological systems as a whole
entity which is more than the sum of its interrelated components. One of the major goals of systems biology is to reveal, understand, and predict such properties
through the development of mathematical models based on experimental data. In
many cases, predictive models of systems biology are described by large systems
of nonlinear differential equations. Quantitative identification of such systems requires the solution of inverse problems on the identification of parameters of the
system. This dissertation explores the inverse problem for the identification of the
finite dimensional set of parameters for systems of nonlinear ordinary differential
equations (ODEs) arising in systems biology. Two numerical methods are implemented. The first method combines the ideas of Pontryagin optimization or Bellman’s quasilinearization with sensitivity analysis and Tikhonov’s regularization.
The method is applied to various biological models such as the classical LotkaVolterra system, bistable switch model in genetic regulatory networks, gene regulation and repressilator models from synthetic biology. The numerical results and
application to real data demonstrate the superlinear convergence with convergence
rate close to quadratic. The method proved to be extremely effective in moderate scale models of systems biology. The results are published in a recent paper Mathematical Biosciences, 305(2018), 133-145. To address adaptation and scalability
of the method for large-scale models of systems biology the modification of the
method is developed by embedding a method of staggered corrector for sensitivity
analysis and by enhancing multi-objective optimization which enables application
of the new method to large-scale models with practically non-identifiable parameters based on multiple data sets, possibly with partial and noisy measurements.
The new method is applied to benchmark model of three-step pathway modelled by
8 nonlinear ODEs with 36 unknown parameters and two control input parameters.
The numerical results demonstrate the superlinear convergence with minimum five
data sets and with minimum measurements per data set. The method is extremely
robust with respect to partial and noisy measurements, and in terms of required
number of measurements for each component of the system. Optimal choice of the
Tikhonov regularization parameter significantly improves convergence rate, precision and convergence range of the algorithm. Software package qlopt is developed
for both methods and posted in GitHub. MATLAB package AMIGO2 is used
to demonstrate advantage of qlopt over most popular methods/software such as
lsqnonlin, fmincon and nl2sol in an equivalent setting. | en_US |