title: Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.
abstract: Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity.
  
  
  
  In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method.
  
  
  
  Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.
authors.affiliation: Department of Computer Science, Virginia Tech, Blacksburg, 24061, VA, USA.
authors.forename: Minghan
authors.initials: M
authors.lastname: Chen
authors.affiliation: Department of Computer Science, Virginia Tech, Blacksburg, 24061, VA, USA.
authors.forename: Fei
authors.initials: F
authors.lastname: Li
authors.affiliation: Department of Computer Science, Virginia Tech, Blacksburg, 24061, VA, USA.
authors.forename: Shuo
authors.initials: S
authors.lastname: Wang
authors.affiliation: Department of Computer Science, Virginia Tech, Blacksburg, 24061, VA, USA. ycao@cs.vt.edu.
authors.forename: Young
authors.initials: Y
authors.lastname: Cao
mesh_terms: D016935:Caulobacter crescentus / Q000378:metabolism; D004058:Diffusion; D008954:Models, Biological; D017711:Nonlinear Dynamics; D013269:Stochastic Processes
keywords: Hill function; Hybrid method; Reaction diffusion master equation (RDME); Stochastic simulation