Stochastic algorithms for biochemical processes

After the completion of the human genome sequencing (and of a lot of other genomes), the main challenge for the modern biology is to understand complex biological processes such as metabolic pathways, gene regulatory networks and cell signalling pathways, which are the basis of the functioning of living cells. This goal can only be achieved by using mathematical modelling tools and computer simulation techniques, to integrate experimental data and to make predictions on the system behaviour that will be then experimentally checked, so as to gain insights into the working and the general principles of organization of biological systems. In the study of biological systems, the use of stochastic methods is motivated by the fact that these systems are usually composed by many chemical interactions among a large number of chemical species, but the molecular quantities involved can be small (few tens of molecules), and the noise plays a major role in the system’s dynamics. One major problem related to stochastic methods is that they are difficult to implement analytically; hence, they are implemented by means of numerical simulations whose computation time is usually very expensive. In this thesis we provide a discrete and stochastic framework for the modelling, simulation and analysis of biological and chemical systems, which overcomes the limitations of a variant of membrane systems, called DPPs, and of the classic stochastic algorithms. This novel method combines, in particular, the descriptive power of DPPs with the efficiency of tau-leaping algorithm. This approach, called tau-DPP, exploits the membrane structure and the system definition of DPPs, with the aim of describing multiple volume systems, and uses a modified version of the tau-leaping algorithm for the efficient description of the system behaviour. The framework of tau-DPP has been applied to ecological, biological and chemical systems. In general, the study of such kind of models requires the knowledge of many numerical factors for a complete and accurate description of biological systems, like molecular species quantities and reaction rates, which represent an indispensable quantitative information to perform computational investigations of the system behaviour. The lack and the inaccuracy of these information bring about the challenging problem of developing suitable techniques to automatically estimate the correct values to all parameters in order to reproduce the expected dynamics in the best possible way. In this thesis, we consider the application of two optimisation techniques, genetic algorithms and particle swarm optimizer, to tackle this problem. In particular, we test and compare the performances of genetic algorithms and particle swarm optimization to the aim of identify the most suitable optimisation technique for the parameter estimation. Finally, the problem related to the exploration of the parameters space of a biochemical system is described. Usually, this kind of analysis is achieved by means of large numbers of independent simulations where each execution is performed with a particular parametrisation. To efficiently tackle this problem, we present the implementation of a parameter sweep application on a grid framework.