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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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Subvolume size. The model described in the text is simulated for different uniform meshes over a range of tetrahedron sizes, all within the acceptable upper and lower bound of 0.4 μm to 0.02 μm, and each mesh representing the same geometry. Mean results for 10 iterations in each case are identical for each mesh size with no errors, demonstrating the accuracy of the well-mixed approximation in this range.
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Figure 3: Subvolume size. The model described in the text is simulated for different uniform meshes over a range of tetrahedron sizes, all within the acceptable upper and lower bound of 0.4 μm to 0.02 μm, and each mesh representing the same geometry. Mean results for 10 iterations in each case are identical for each mesh size with no errors, demonstrating the accuracy of the well-mixed approximation in this range.

Mentions: Figure 3 shows the simulation of this system in STEPS with three different tetrahedral meshes representing the same total volume of one cubic micron. The three meshes are reasonably regular and range from the upper bound of accepted subvolume size (with approximately 100 tetrahedrons) to a size of 30 nanometers (approximately 350,000 tetrahedrons). There are no significant errors in results and no discrepancies between the different mesh sizes, showing that the spatial Gillespie method is accurate over this range for this simple problem.


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

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

Subvolume size. The model described in the text is simulated for different uniform meshes over a range of tetrahedron sizes, all within the acceptable upper and lower bound of 0.4 μm to 0.02 μm, and each mesh representing the same geometry. Mean results for 10 iterations in each case are identical for each mesh size with no errors, demonstrating the accuracy of the well-mixed approximation in this range.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Subvolume size. The model described in the text is simulated for different uniform meshes over a range of tetrahedron sizes, all within the acceptable upper and lower bound of 0.4 μm to 0.02 μm, and each mesh representing the same geometry. Mean results for 10 iterations in each case are identical for each mesh size with no errors, demonstrating the accuracy of the well-mixed approximation in this range.
Mentions: Figure 3 shows the simulation of this system in STEPS with three different tetrahedral meshes representing the same total volume of one cubic micron. The three meshes are reasonably regular and range from the upper bound of accepted subvolume size (with approximately 100 tetrahedrons) to a size of 30 nanometers (approximately 350,000 tetrahedrons). There are no significant errors in results and no discrepancies between the different mesh sizes, showing that the spatial Gillespie method is accurate over this range for this simple problem.

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