Particle-based stochastic reaction diffusion methods have become a
popular approach for studying the behavior of cellular processes in
which both spatial transport and noise in the chemical reaction process
can be important. While the corresponding deterministic, mean-field
models given by reaction-diffusion PDEs are well-established, there are
a plethora of different stochastic models that have been used to study
biological systems, along with a wide variety of proposed numerical
solution methods.
In this talk I will motivate our interest in such methods by first
summarizing several applications we have studied, focusing on how the
complicated ultrastructure within cells, as reconstructed from X-ray CT
images, might influence the dynamics of cellular processes. I will then
introduce our attempt to rectify the major drawback to one of the most
popular particle-based stochastic reaction-diffusion models, the lattice
reaction-diffusion master equation (RDME). We propose a modified version
of the RDME that converges in the continuum limit that the lattice
spacing approaches zero to an appropriate spatially-continuous model.
Time-permitting, I will discuss several questions related to calibrating
parameters in the underlying spatially-continuous model.
Seminar series
Date
Thu, 05 Feb 2015
Time
16:00 -
17:00
Location
L3
Speaker
Samuel Isaacson
Organisation
Boston University