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Lattice Microbes: high-performance stochastic simulation method for the reaction-diffusion master equation.

ABSTRACT: Spatial stochastic simulation is a valuable technique for studying reactions in biological systems. With the availability of high-performance computing (HPC), the method is poised to allow integration of data from structural, single-molecule and biochemical studies into coherent computational models of cells. Here, we introduce the Lattice Microbes software package for simulating such cell models on HPC systems. The software performs either well-stirred or spatially resolved stochastic simulations with approximated cytoplasmic crowding in a fast and efficient manner. Our new algorithm efficiently samples the reaction-diffusion master equation using NVIDIA graphics processing units and is shown to be two orders of magnitude faster than exact sampling for large systems while maintaining an accuracy of !0.1%. Display of cell models and animation of reaction trajectories involving millions of molecules is facilitated using a plug-in to the popular VMD visualization platform. The Lattice Microbes software is open source and available for download at http://www.scs.illinois.edu/schulten/lm

SUBMITTER: Roberts E

PROVIDER: S-EPMC3762454 | biostudies-other | 2013 Jan

REPOSITORIES: biostudies-other

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Lattice Microbes: high-performance stochastic simulation method for the reaction-diffusion master equation.

Roberts Elijah E Stone John E JE Luthey-Schulten Zaida Z

Journal of computational chemistry 20120925 3

Spatial stochastic simulation is a valuable technique for studying reactions in biological systems. With the availability of high-performance computing (HPC), the method is poised to allow integration of data from structural, single-molecule and biochemical studies into coherent computational models of cells. Here, we introduce the Lattice Microbes software package for simulating such cell models on HPC systems. The software performs either well-stirred or spatially resolved stochastic simulatio ...[more]

PMID: 23007888

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Project description:BACKGROUND: Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins), conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. RESULTS: We describe STEPS, a stochastic reaction-diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction-diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. CONCLUSION: STEPS simulates models of cellular reaction-diffusion systems with complex boundaries with high accuracy and high performance in C/C++, controlled by a powerful and user-friendly Python interface. STEPS is free for use and is available at http://steps.sourceforge.net/

Project description:BackgroundThe concentration gradient of Bicoid protein which determines the developmental pathways in early Drosophila embryo is the best characterized morphogen gradient at the molecular level. Because different developmental fates can be elicited by different concentrations of Bicoid, it is important to probe the limits of this specification by analyzing intrinsic fluctuations of the Bicoid gradient arising from small molecular number. Stochastic simulations can be applied to further the understanding of the dynamics of Bicoid morphogen gradient formation at the molecular number level, and determine the source of the nucleus-to-nucleus expression variation (noise) observed in the Bicoid gradient.ResultsWe compared quantitative observations of Bicoid levels in immunostained Drosophila embryos with a spatially extended Master Equation model which represents diffusion, decay, and anterior synthesis. We show that the intrinsic noise of an autonomous reaction-diffusion gradient is Poisson distributed. We demonstrate how experimental noise can be identified in the logarithm domain from single embryo analysis, and then separated from intrinsic noise in the normalized variance domain of an ensemble statistical analysis. We show how measurement sensitivity affects our observations, and how small amounts of rescaling noise can perturb the noise strength (Fano factor) observed. We demonstrate that the biological noise level in data can serve as a physical constraint for restricting the model's parameter space, and for predicting the Bicoid molecular number and variation range. An estimate based on a low variance ensemble of embryos suggests that the steady-state Bicoid molecular number in a nucleus should be larger than 300 in the middle of the embryo, and hence the gradient should extend to the posterior end of the embryo, beyond the previously assumed background limit. We exhibit the predicted molecular number gradient together with measurement effects, and make a comparison between conditions of higher and lower variance respectively.ConclusionQuantitative comparison of Master Equation simulations with immunostained data enabled us to determine narrow ranges for key biophysical parameters, which for this system can be independently validated. Intrinsic noise is clearly detectable as well, although the staining process introduces certain limits in resolution.

Dataset Information

Lattice Microbes: high-performance stochastic simulation method for the reaction-diffusion master equation.

Publications

Lattice Microbes: high-performance stochastic simulation method for the reaction-diffusion master equation.

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