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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 reactions. A. First-order irreversible reaction. Mean for 1000 iterations of STEPS (points with error bars showing the sd) matches the analytical solution (full line, broken lines are the predicted sd). B. First-order reversible reaction. The STEPS simulation (mean of 100 iterations) evolves correctly to the predicted steady state concentrations. C, D. Second order irreversible reaction. With equal reactant concentrations the evolution in time of the inverse of the concentration of one of the source species in comparison to the analytical solution is shown (C) and with unequal reactant concentrations the comparison of the source species ratio with the analytical solution is shown (D).
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Figure 6: Validation of reactions. A. First-order irreversible reaction. Mean for 1000 iterations of STEPS (points with error bars showing the sd) matches the analytical solution (full line, broken lines are the predicted sd). B. First-order reversible reaction. The STEPS simulation (mean of 100 iterations) evolves correctly to the predicted steady state concentrations. C, D. Second order irreversible reaction. With equal reactant concentrations the evolution in time of the inverse of the concentration of one of the source species in comparison to the analytical solution is shown (C) and with unequal reactant concentrations the comparison of the source species ratio with the analytical solution is shown (D).

Mentions: One of our simplest validation systems, the first-order irreversible reactions system, is also perhaps one of our most important due to the fact that we test the resulting noise from our implementation of the SSA. This vital aspect of stochastic reaction–diffusion simulator output is usually insufficiently tested, often with simple visual comparison of the amplitude of the noise from the output of two different simulators. The standard deviation matched the analytical solution to the chemical master equation closely, and the mean behavior also behaved as expected (20 of 20 points fell in the 95% CI) (Figure 6A).


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 reactions. A. First-order irreversible reaction. Mean for 1000 iterations of STEPS (points with error bars showing the sd) matches the analytical solution (full line, broken lines are the predicted sd). B. First-order reversible reaction. The STEPS simulation (mean of 100 iterations) evolves correctly to the predicted steady state concentrations. C, D. Second order irreversible reaction. With equal reactant concentrations the evolution in time of the inverse of the concentration of one of the source species in comparison to the analytical solution is shown (C) and with unequal reactant concentrations the comparison of the source species ratio with the analytical solution is shown (D).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Validation of reactions. A. First-order irreversible reaction. Mean for 1000 iterations of STEPS (points with error bars showing the sd) matches the analytical solution (full line, broken lines are the predicted sd). B. First-order reversible reaction. The STEPS simulation (mean of 100 iterations) evolves correctly to the predicted steady state concentrations. C, D. Second order irreversible reaction. With equal reactant concentrations the evolution in time of the inverse of the concentration of one of the source species in comparison to the analytical solution is shown (C) and with unequal reactant concentrations the comparison of the source species ratio with the analytical solution is shown (D).
Mentions: One of our simplest validation systems, the first-order irreversible reactions system, is also perhaps one of our most important due to the fact that we test the resulting noise from our implementation of the SSA. This vital aspect of stochastic reaction–diffusion simulator output is usually insufficiently tested, often with simple visual comparison of the amplitude of the noise from the output of two different simulators. The standard deviation matched the analytical solution to the chemical master equation closely, and the mean behavior also behaved as expected (20 of 20 points fell in the 95% CI) (Figure 6A).

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