Stochastic modeling of biochemical systems with filtering and smoothing

Download

index.pdf

Date

2019

Author

Haksever, Merve

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

245
views

258
downloads

Deterministic modeling approach is the traditional way of analyzing the dynamical behavior of a reaction network. However, this approach ignores the discrete and stochastic nature of biochemical processes. In this study, modeling approaches, stochastic simulation algorithms and their relationships to each other are investigated. Then, stochastic and deterministic modeling approaches are applied to biological systems, Lotka-Volterra prey-predator model, Michaelis-Menten enzyme kinetics and JACK-STAT signaling pathway. Also, numerical solutions for ODE system and realizations obtained through stochastic simulation algorithms are compared. In general, it is not possible to assess all elements of the state vector of biochemical systems. Hence, some statistical models are used to obtain the best estimation. Filtering and smoothing distributions can be obtained via Bayes’ rule. However, as an alternative to approximate these distributions Monte Carlo methods might be used. In the second part, bootstrap particle filter algorithm is derived and applied to birthdeath process. Estimated probability distribution functions are compared according to number of particles used.

Subject Keywords

Biochemistry., Mathematical modeling, simulation algorithms, filtering, smoothing.

URI

http://etd.lib.metu.edu.tr/upload/12624344/index.pdf
https://hdl.handle.net/11511/44920

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Efficient Surface Integral Equation Methods for the Analysis of Complex Metamaterial Structures Yla-Oijala, Pasi; Ergül, Özgür Salih; Gurel, Levent; Taskinen, Matti (2009-03-27) Two approaches, the multilevel fast multipole algorithm with sparse approximate inverse preconditioner and the surface equivalence principle algorithm, are applied to analyze complex three-dimensional metamaterial structures. The efficiency and performance of these methods are studied and discussed.
Stochastic modelling of biochemical networks and inference of modelparameters Purutçuoğlu Gazi, Vilda (null, Springer, 2018-01-01) There are many approaches to model the biochemical systems deterministically or stochastically. In deterministic approaches, we aim to describe the steady-state behaviours of the system, whereas, under stochastic models, we present the random nature of the system, for instance, during transcription or translation processes. Here, we represent the stochastic modelling approaches of biological networks and explain in details the inference of the model parameters within the Bayesian framework.
Neural network calibrated stochastic processes: forecasting financial assets Giebel, Stefan; Rainer, Martin (Springer Science and Business Media LLC, 2013-03-01) If a given dynamical process contains an inherently unpredictable component, it may be modeled as a stochastic process. Typical examples from financial markets are the dynamics of prices (e.g. prices of stocks or commodities) or fundamental rates (exchange rates etc.). The unknown future value of the corresponding stochastic process is usually estimated as the expected value under a suitable measure, which may be determined from distribution of past (historical) values. The predictive power of this estimati...
Online state estimation for discrete nonlinear dynamic systems with nonlinear noise and interference Demirbaş, Kerim (2015-01-01) This paper presents a real-time recursive state filtering and prediction scheme (PR) for discrete nonlinear dynamic systems with nonlinear noise and random interference, such as undesired random jamming or clutter. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple composite hypothesis testing. The PR outperforms both the sampling importance resampling (SIR) particle filter and auxiliary sampling importance resampling (ASIR) particle filter; wh...
Frequency estimation of a single real-valued sinusoid: An invariant function approach Candan, Çağatay; Çelebi, Utku (2021-08-01) An invariant function approach for the computationally efficient (non-iterative and gridless) maximum likelihood (ML) estimation of unknown parameters is applied on the real-valued sinusoid frequency estimation problem. The main attraction point of the approach is its potential to yield a ML-like performance at a significantly reduced computational load with respect to conventional ML estimator that requires repeated evaluation of an objective function or numerical search routines. The numerical results ind...

Citation Formats

M. Haksever, “Stochastic modeling of biochemical systems with filtering and smoothing,” Thesis (M.S.) -- Graduate School of Applied Mathematics. Scientific Computing., Middle East Technical University, 2019.