arXiv subjects

S. Setayeshgar

Publications and source records attributed to S. Setayeshgar.

5 recordsLinked to original sources

arXiv2003

Application of Coarse Integration to Bacterial Chemotaxis

We have developed and implemented a numerical evolution scheme for a class of stochastic problems in which the temporal evolution occurs on widely-separated time scales, and for which the slow evolution can be described in terms of a small number of moments of an underlying probability distribution. We demonstrate this method via a numerical simulation of chemotaxis in a population of motile, independent bacteria swimming in a prescribed gradient of a chemoattractant. The microscopic stochastic model, which is simulated using a Monte Carlo method, uses a simplified deterministic model for excitation/adaptation in signal transduction, coupled to a realistic, stochastic description of the flagellar motor. We show that projective time integration of ``coarse'' variables can be carried out on time scales long compared to that of the microscopic dynamics. Our coarse description is based on the spatial cell density distribution. Thus we are assuming that the system ``closes'' on this variable so that it can be described on long time scales solely by the spatial cell density. Computationally the variables are the components of the density distribution expressed in terms of a few basis functions, given by the singular vectors of the spatial density distribution obtained from a sample Monte Carlo time evolution of the system. We present numerical results and analysis of errors in support of the efficacy of this time-integration scheme.

physics.comp-ph↗

arXiv2003

Physical limits to biochemical signaling

Many crucial biological processes operate with surprisingly small numbers of molecules, and there is renewed interest in analyzing the impact of noise associated with these small numbers. Twenty--five years ago, Berg and Purcell showed that bacterial chemotaxis, where a single celled organism must respond to small changes in concentration of chemicals outside the cell, is limited directly by molecule counting noise, and that aspects of the bacteria's behavioral and computational strategies must be chosen to minimize the effects of this noise. Here we revisit and generalize their arguments to estimate the physical limits to signaling processes within the cell, and argue that recent experiments are consistent with performance approaching these limits.

physics.bio-ph↗

arXiv2002

Exploring defective eigenvalue problems with the method of lifting

Consider an N x N matrix A for which zero is a defective eigenvalue. In this case, the algebraic multiplicity of the zero eigenvalue is greater than the geometric multiplicity. We show how an inflated (N+1) x (N+1) matrix L can be constructed as a rank one perturbation to A, such that L is singular but no longer defective, and the nullvectors of L can be easily related to the nullvectors of A. The motivation for this construction comes from linear stability analysis of an experimental reaction-diffusion system which exhibits the Turing instability. The utility of this scheme is accurate numerical computation of nullvector(s) corresponding to a defective zero eigenvalue. We show that numerical computations on L yield more accurate eigenvectors than direct computation on A.

math-ph↗

arXiv1998

Turing Instability in a Boundary-fed System

The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations (Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experiments.

patt-sol↗

arXiv1998

Numerical Bifurcation Diagram for the Two-Dimensional Boundary-fed CDIMA System

We present numerical solution of the chlorine dioxide-iodine-malonic acid reaction-diffusion system in two dimensions in a boundary-fed system using a realistic model. The bifurcation diagram for the transition from non-symmetry breaking structures along boundary feed gradients to transverse symmetry breaking patterns in a single layer is numerically determined. We find this transition to be discontinuous. We make connection with earlier results and discuss prospects for future work.

patt-sol↗