4,724 research outputs found
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
Partial differential equations for self-organization in cellular and developmental biology
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field
The Two Regime method for optimizing stochastic reaction-diffusion simulations
The computer simulation of stochastic reaction-diffusion processes in biology is often done using either compartment-based (spatially discretized) simulations or molecular-based (Brownian dynamics) approaches. Compartment-based approaches can yield quick and accurate mesoscopic results but lack the level of detail that is characteristic of the more computationally intensive molecular-based models. Often microscopic detail is only required in a small region but currently the best way to achieve this detail is to use a resource intensive model over the whole domain. We introduce the Two Regime Method (TRM) in which a molecular-based algorithm is used in part of the computational domain and a compartment-based approach is used elsewhere in the computational domain. We apply the TRM to two test problems including a model from developmental biology. We thereby show that the TRM is accurate and subsequently may be used to inspect both mesoscopic and microscopic detail of reaction diffusion simulations according to the demands of the modeller
Reaction rates for mesoscopic reaction-diffusion kinetics
The mesoscopic reaction-diffusion master equation (RDME) is a popular
modeling framework, frequently applied to stochastic reaction-diffusion
kinetics in systems biology. The RDME is derived from assumptions about the
underlying physical properties of the system, and it may produce unphysical
results for models where those assumptions fail. In that case, other more
comprehensive models are better suited, such as hard-sphere Brownian dynamics
(BD). Although the RDME is a model in its own right, and not inferred from any
specific microscale model, it proves useful to attempt to approximate a
microscale model by a specific choice of mesoscopic reaction rates. In this
paper we derive mesoscopic reaction rates by matching certain statistics of the
RDME solution to statistics of the solution of a widely used microscopic BD
model: the Smoluchowski model with a mixed boundary condition at the reaction
radius of two molecules. We also establish fundamental limits for the range of
mesh resolutions for which this approach yields accurate results, and show both
theoretically and in numerical examples that as we approach the lower
fundamental limit, the mesoscopic dynamics approach the microscopic dynamics
Mechanical and Systems Biology of Cancer
Mechanics and biochemical signaling are both often deregulated in cancer,
leading to cancer cell phenotypes that exhibit increased invasiveness,
proliferation, and survival. The dynamics and interactions of cytoskeletal
components control basic mechanical properties, such as cell tension,
stiffness, and engagement with the extracellular environment, which can lead to
extracellular matrix remodeling. Intracellular mechanics can alter signaling
and transcription factors, impacting cell decision making. Additionally,
signaling from soluble and mechanical factors in the extracellular environment,
such as substrate stiffness and ligand density, can modulate cytoskeletal
dynamics. Computational models closely integrated with experimental support,
incorporating cancer-specific parameters, can provide quantitative assessments
and serve as predictive tools toward dissecting the feedback between signaling
and mechanics and across multiple scales and domains in tumor progression.Comment: 18 pages, 3 figure
Detailed simulations of cell biology with Smoldyn 2.1.
Most cellular processes depend on intracellular locations and random collisions of individual protein molecules. To model these processes, we developed algorithms to simulate the diffusion, membrane interactions, and reactions of individual molecules, and implemented these in the Smoldyn program. Compared to the popular MCell and ChemCell simulators, we found that Smoldyn was in many cases more accurate, more computationally efficient, and easier to use. Using Smoldyn, we modeled pheromone response system signaling among yeast cells of opposite mating type. This model showed that secreted Bar1 protease might help a cell identify the fittest mating partner by sharpening the pheromone concentration gradient. This model involved about 200,000 protein molecules, about 7000 cubic microns of volume, and about 75 minutes of simulated time; it took about 10 hours to run. Over the next several years, as faster computers become available, Smoldyn will allow researchers to model and explore systems the size of entire bacterial and smaller eukaryotic cells
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