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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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Validation of reaction–diffusion. A. Lack of effect of diffusion in STEPS (points with error bars showing the sd) on first-order irreversible reaction (analytical solution, full line) with uniform initial concentration. Setting the diffusion constant to zero did not change the simulation results (not shown). B. Diffusion does not significantly affect stationary distribution of molecule that undergoes a zero-order production reaction and second order reaction with clamped species when tetrahedron size is larger than acceptable minimum. STEPS simulation (histogram) compared to analytical solution to chemical master equation (open circles).
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Figure 9: Validation of reaction–diffusion. A. Lack of effect of diffusion in STEPS (points with error bars showing the sd) on first-order irreversible reaction (analytical solution, full line) with uniform initial concentration. Setting the diffusion constant to zero did not change the simulation results (not shown). B. Diffusion does not significantly affect stationary distribution of molecule that undergoes a zero-order production reaction and second order reaction with clamped species when tetrahedron size is larger than acceptable minimum. STEPS simulation (histogram) compared to analytical solution to chemical master equation (open circles).

Mentions: In testing the combined simulation of chemical reactions and diffusion we were limited by the paucity of available analytical solutions. A first simple test was to add diffusion to an irreversible first-order reaction with an initial uniform concentration of the reagent. Diffusion should not affect this process, which is confirmed (30 of 30 points fell within 95% confidence interval) (Figure 9A). Next, a very discrete reaction–diffusion problem, typically containing only about 10 molecules in the system, was analyzed. This consisted of two reactions: a zero-order reaction and second order reaction [38]. Ensuring that subvolume size was larger than the accepted lower bound, and significantly larger than the “critical value” discussed in [38], the deviation of the stationary distribution of the reactant from the analytical solution to the master equation was small (Figure 9B).


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

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

Validation of reaction–diffusion. A. Lack of effect of diffusion in STEPS (points with error bars showing the sd) on first-order irreversible reaction (analytical solution, full line) with uniform initial concentration. Setting the diffusion constant to zero did not change the simulation results (not shown). B. Diffusion does not significantly affect stationary distribution of molecule that undergoes a zero-order production reaction and second order reaction with clamped species when tetrahedron size is larger than acceptable minimum. STEPS simulation (histogram) compared to analytical solution to chemical master equation (open circles).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 9: Validation of reaction–diffusion. A. Lack of effect of diffusion in STEPS (points with error bars showing the sd) on first-order irreversible reaction (analytical solution, full line) with uniform initial concentration. Setting the diffusion constant to zero did not change the simulation results (not shown). B. Diffusion does not significantly affect stationary distribution of molecule that undergoes a zero-order production reaction and second order reaction with clamped species when tetrahedron size is larger than acceptable minimum. STEPS simulation (histogram) compared to analytical solution to chemical master equation (open circles).
Mentions: In testing the combined simulation of chemical reactions and diffusion we were limited by the paucity of available analytical solutions. A first simple test was to add diffusion to an irreversible first-order reaction with an initial uniform concentration of the reagent. Diffusion should not affect this process, which is confirmed (30 of 30 points fell within 95% confidence interval) (Figure 9A). Next, a very discrete reaction–diffusion problem, typically containing only about 10 molecules in the system, was analyzed. This consisted of two reactions: a zero-order reaction and second order reaction [38]. Ensuring that subvolume size was larger than the accepted lower bound, and significantly larger than the “critical value” discussed in [38], the deviation of the stationary distribution of the reactant from the analytical solution to the master equation was small (Figure 9B).

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