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STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies.

Hepburn I, Chen W, Wils S, De Schutter E - BMC Syst Biol (2012)

Bottom Line: 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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Theoretical Neurobiology, University of Antwerp, Campus Drie Eiken, Universiteitsplein 1, Wilrijk 2610, Belgium. erik@oist.jp

ABSTRACT

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/

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Example tetrahedral and cubic spine meshes. The ideal geometry for Spine #4 (A) represented by a cubic mesh of 2576 cubes (B) and by a tetrahedral mesh of 2571 tetrahedrons (C). The mesh surfaces are displayed in CUBIT.
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Figure 4: Example tetrahedral and cubic spine meshes. The ideal geometry for Spine #4 (A) represented by a cubic mesh of 2576 cubes (B) and by a tetrahedral mesh of 2571 tetrahedrons (C). The mesh surfaces are displayed in CUBIT.

Mentions: For each spine shape, first an adaptive tetrahedral mesh was generated in CUBIT with the coarsest mesh (minimal number of tetrahedrons) permissible by the software, and then a cubic mesh was generated in MesoRD from CSG input, with the cube size controlled to result in a mesh with a similar number of subvolumes to the tetrahedral mesh (further information about the meshes can be found in Additional file 3). Furthermore, for each spine a more detailed (greater number of subvolumes) tetrahedral and cubic mesh was generated, with a close match between the number of tetrahedral and cubic subvolumes. The more detailed meshes typically approached the approximate minimum subvolume size for a system of slow diffusion and fast reaction previously discussed, and so are approximately the most detailed mesh that would be acceptable for simulation. Figure 4 shows spine #4 represented by both a tetrahedral mesh and cubic mesh in the coarser case.


STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies.

Hepburn I, Chen W, Wils S, De Schutter E - BMC Syst Biol (2012)

Example tetrahedral and cubic spine meshes. The ideal geometry for Spine #4 (A) represented by a cubic mesh of 2576 cubes (B) and by a tetrahedral mesh of 2571 tetrahedrons (C). The mesh surfaces are displayed in CUBIT.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3472240&req=5

Figure 4: Example tetrahedral and cubic spine meshes. The ideal geometry for Spine #4 (A) represented by a cubic mesh of 2576 cubes (B) and by a tetrahedral mesh of 2571 tetrahedrons (C). The mesh surfaces are displayed in CUBIT.
Mentions: For each spine shape, first an adaptive tetrahedral mesh was generated in CUBIT with the coarsest mesh (minimal number of tetrahedrons) permissible by the software, and then a cubic mesh was generated in MesoRD from CSG input, with the cube size controlled to result in a mesh with a similar number of subvolumes to the tetrahedral mesh (further information about the meshes can be found in Additional file 3). Furthermore, for each spine a more detailed (greater number of subvolumes) tetrahedral and cubic mesh was generated, with a close match between the number of tetrahedral and cubic subvolumes. The more detailed meshes typically approached the approximate minimum subvolume size for a system of slow diffusion and fast reaction previously discussed, and so are approximately the most detailed mesh that would be acceptable for simulation. Figure 4 shows spine #4 represented by both a tetrahedral mesh and cubic mesh in the coarser case.

Bottom Line: 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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Theoretical Neurobiology, University of Antwerp, Campus Drie Eiken, Universiteitsplein 1, Wilrijk 2610, Belgium. erik@oist.jp

ABSTRACT

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/

Show MeSH
Related in: MedlinePlus