3 research outputs found
Algorithm for Mesoscopic Advection-Diffusion
In this paper, an algorithm is presented to calculate the transition rates
between adjacent mesoscopic subvolumes in the presence of flow and diffusion.
These rates can be integrated in stochastic simulations of reaction-diffusion
systems that follow a mesoscopic approach, i.e., that partition the environment
into homogeneous subvolumes and apply the spatial stochastic simulation
algorithm (spatial SSA). The rates are derived by integrating Fick's second law
over a single subvolume in one dimension (1D), and are also shown to apply in
three dimensions (3D). The proposed algorithm corrects the derived rates to
ensure that they are physically meaningful and it is implemented in the AcCoRD
simulator (Actor-based Communication via Reaction-Diffusion). Simulations using
the proposed method are compared with a naive mesoscopic approach, microscopic
simulations that track every molecule, and analytical results that are exact in
1D and an approximation in 3D. By choosing subvolumes that are sufficiently
small, such that the Peclet number associated with a subvolume is sufficiently
less than 2, the accuracy of the proposed method is comparable with the
microscopic method, thus enabling the simulation of
advection-reaction-diffusion systems with the spatial SSA.Comment: 12 pages, 9 figures. Submitted to IEEE Transactions on NanoBioscienc
An Unstructured Mesh Convergent Reaction-Diffusion Master Equation for Reversible Reactions
The convergent reaction-diffusion master equation (CRDME) was recently
developed to provide a lattice particle-based stochastic reaction-diffusion
model that is a convergent approximation in the lattice spacing to an
underlying spatially-continuous particle dynamics model. The CRDME was designed
to be identical to the popular lattice reaction-diffusion master equation
(RDME) model for systems with only linear reactions, while overcoming the
RDME's loss of bimolecular reaction effects as the lattice spacing is taken to
zero. In our original work we developed the CRDME to handle bimolecular
association reactions on Cartesian grids. In this work we develop several
extensions to the CRDME to facilitate the modeling of cellular processes within
realistic biological domains. Foremost, we extend the CRDME to handle
reversible bimolecular reactions on unstructured grids. Here we develop a
generalized CRDME through discretization of the spatially continuous volume
reactivity model, extending the CRDME to encompass a larger variety of
particle-particle interactions. Finally, we conclude by examining several
numerical examples to demonstrate the convergence and accuracy of the CRDME in
approximating the volume reactivity model.Comment: 35 pages, 9 figures. Accepted, J. Comp. Phys. (2018
Incorporating active transport of cellular cargo in stochastic mesoscopic models of living cells
We propose a new multiscale method to incorporate active transport of cargo particles in biological cells in stochastic, mesoscopic models of reaction-transport processes. Given a discretization of the computational domain, we find stochastic, convective mesoscopic molecular fluxes over the edges or facets of the subvolumes and relate the process to a corresponding first order finite volume discretization of the linear convection equation. We give an example of how this can be used to model active transport of cargo particles on a microtubule network by the motor proteins kinesin and dynein. In this way we extend mesoscopic reaction-diffusion models of biochemical reaction networks to more general models of molecular transport within the living cell.eSSENC