Improving stochastic simulations of complex chemical systems with bitwise arithmetic

With his strong tradition in biological physics, UMR168 is an ideal place to develop project at the boundary between physics and biology, with a direct experimental counterpart. 

The Gillespie algorithm is a powerful computational tool to simulate the dynamics of a system of interacting chemical species in regimes where particle numbers are small, and stochastic fluctuations are large [1]. This well-known algorithm becomes computationally demanding when one attempts to sample a large number of configurations, e.g. looking for rare samples in the dynamics, or simulating a large number of species or reactions. In this internship, we propose to develop a new method to increase the computational yield of the algorithm, by leveraging the boolean representation of numbers as they are stored in a computer [2].

This method allows for simulating simultaneously multiple copies of the system, which share the same random number used to draw the system samples. Because the random-number generation is the bottleneck of the simulation, this parallel algorithm yields a significant gain in performance. Most importantly, given that the copies of the system are initialized with random, independent initial conditions, their dynamics is independent, and it allows for sampling a broader part of the system’s configuration space. Different applications of the algorithm will be explored in the context of simulating complex chemical systems, which are typically non-well mixed and contains a large number of species and reactions.

The student will be tasked with the numerical implementation of this parallel Gillespie algorithm, and with its application to a few representative models of interacting chemical species. The student will acquire valuable interdisciplinary skills, such as proficiency in C++, and getting familiar with models of chemical-reaction networks.

The internship will take place at UMR 168, Institut Curie, and at Gulliver Laboratory, UMR 7083, ESPCI, Paris. For further information see https://sites.google.com/site/michelecastellana/internship-proposals.

References

[1] D. T. Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics, 22(4):403–434, December 1976.

[2] M. Palassini and S. Caracciolo. Universal Finite-Size Scaling Functions in the 3-d Ising Spin Glass. Phys. Rev. Lett., 82(25):5128, 1999. Number: 25

We are looking for a student with a good background in programming.