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Developing a Kalman filter-based method to estimate the probability distribution of stochastic systems in biology
Student(en):

 Betreuer:

Ruess Jakob
Beschreibung:

Project Context

In order to display the proper response to different external input stimuli, such as changes in temperature or the presence of food sources, cells have evolved complicated mechanisms to regulate their internal processes. All those mechanisms have to be based on what is possible in the cell: chemical reactions that are based on random collisions and interactions of molecules and are thus inherently random. To robustly carry out their function, cells need to tightly control this molecular noise.

Using mathematical models, systems biology researcher try to understand the functioning of such mechanisms with the ultimate goal of finding ways to intervene in a targeted way, e.g. in order to repair malfunctions (such as in cancer) or to optimize the production of biofuels or drugs. Given the inherent molecular noise of chemical reactions, gaining a proper understanding of how cells work and controlling their function requires models that include randomness. Such models are often very hard to analyze and give rise to many challenges for mathematicians and engineers.

Project goal

The goal of this project is to develop a Kalman filter-based method to approximate the time evolution of the probability distribution of continuous-time Markov chain models for chemical reaction systems. The student will initially become familiar with the chemical master equation and existing techniques for the approximation of its solution, namely finite state projection and stochastic simulation and then develop a Kalman filter-based method to combine the two approximation techniques. Ideally the method should then be extended such that it can serve as a state estimator for the probability distribution of system components that cannot be measured in experiments. The method will be evaluated on a standard model of gene expression.



Weitere Informationen 		Professor:

John Lygeros
Projektcharakteristik:

Typ:
Art der Arbeit: 50% theory, 50% simulation
Voraussetzungen: Candidates for this project should possess good Matlab skills and basic knowledge of stochastic processes and statistics. No biology background is required.
Anzahl StudentInnen: 1
Status: taken
Projektstart:
Semester: SS 2012