PH.D DEFENCE - PUBLIC SEMINAR

Analysis of bio-pathway models using parallel architectures

Speaker
Mr Ramanathan Rajendiran
Advisor
Dr Wong Weng Fai, Associate Professor, School of Computing


05 Jul 2017 Wednesday, 09:30 AM to 11:00 AM

Executive Classroom, COM2-04-02

Abstract:

We study models of bio-pathways that arise in systems biology. Often a bio-pathway can be viewed as a network of bio-chemical reactions. One can then model the network as a dynamical system. In this talk, we explore two classes of such models, namely, a single system of ordinary differential equations and hybrid dynamical systems. Hybrid systems are multi-mode dynamical systems which evolve over continuous time. The dynamics in each mode is governed by a mode-specific system of differential equations and at discrete instances there can be instantaneous jumps between modes depending typically on the current continuous state.

Both these models --- especially when used in systems biology context--- are difficult to analyze and the analysis methods one develops are usually computationally intensive and hence difficult to scale. With this as motivation, we broadly explore the twin themes of: (i) Probabilistic approximations of ODEs systems and hybrid systems accompanied by a probabilistic verification technique known as statistical model checking, (ii) GPU based implementations of the SMC procedures and the related analysis techniques.

In the first part of the talk, we consider single systems of ODEs. We first recall a previously developed approximation technique in which a system of ODEs is first approximated as a dynamic Bayesian network (DBN). We show how the construction of the DBN can be parallelized via a GPU implementation.

Next we present a parallelized statistical model checking (SMC) based analysis method for ODEs systems. The core component of this technique is an online procedure for verifying whether a numerically generated trajectory of a model satisfies a dynamical property. We then show how this method can be applied to parameter estimation of bio-pathways to achieve significant performance improvement.

The next part of the talk focuses on analysis of hybrid systems. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. Based on this, we develop a probabilistic approximation scheme in which the hybrid system can be approximated as a discrete-time Markov chain. However, it is not computationally feasible to compute this Markov chain for high-dimensional systems. Hence we construct a simulation based method for sampling the paths of the Markov chain and carrying out SMC based verification. This probabilistic approximation scheme is then parallelized using a GPU implementation.

We have applied our methods to a number of realistic models. The results indicate that our approximation schemes scale well and can be applied in a number of different settings.