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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 simulations. A. SBML model of calcium oscillations in astrocytes simulated in STEPS with the deterministic solver Wmrk4 (results plotted at 4 second intervals) shows perfect agreement with BioModels Online simulation. B. SBML model in a femtoliter compartment is simulated in STEPS with the stochastic solver Wmdirect (results plotted at 0.8 second intervals) and compared to BioModels Online deterministic simulation. Shown are cAMP and Ca signals, which are controlled by Events. Small stochastic differences are noticeable between simulations.
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Figure 12: Example simulations. A. SBML model of calcium oscillations in astrocytes simulated in STEPS with the deterministic solver Wmrk4 (results plotted at 4 second intervals) shows perfect agreement with BioModels Online simulation. B. SBML model in a femtoliter compartment is simulated in STEPS with the stochastic solver Wmdirect (results plotted at 0.8 second intervals) and compared to BioModels Online deterministic simulation. Shown are cAMP and Ca signals, which are controlled by Events. Small stochastic differences are noticeable between simulations.

Mentions: Imported models may be directly simulated in STEPS using the deterministic solver or the well-mixed stochastic solver, although many models are not suitable for stochastic simulation without some modification. It is worth noting that SBML models may potentially form the basis of simulations in the spatial stochastic solver, but not without some modifications; for example diffusion coefficients and non-uniform initial conditions must currently be defined outside of SBML.Figure 12A shows a deterministic simulation in STEPS of model BIOMD0000000184 from the BioModels Database in comparison to a BioModels Online Simulation. This model of spontaneous calcium oscillations in astrocytes [50] contains two compartments (cytoplasm and endoplasmic reticulum) with transport reactions between them. Some reactions in the model can be represented as fundamental reactions, but some reactions contain complex maths, which is therefore converted to Python structures allowing for solution by the approximate method. Figure 12A shows close agreement between the STEPS simulation and the BioModels Online Simulation, and also matches the published results [50] (not shown).


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 simulations. A. SBML model of calcium oscillations in astrocytes simulated in STEPS with the deterministic solver Wmrk4 (results plotted at 4 second intervals) shows perfect agreement with BioModels Online simulation. B. SBML model in a femtoliter compartment is simulated in STEPS with the stochastic solver Wmdirect (results plotted at 0.8 second intervals) and compared to BioModels Online deterministic simulation. Shown are cAMP and Ca signals, which are controlled by Events. Small stochastic differences are noticeable between simulations.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 12: Example simulations. A. SBML model of calcium oscillations in astrocytes simulated in STEPS with the deterministic solver Wmrk4 (results plotted at 4 second intervals) shows perfect agreement with BioModels Online simulation. B. SBML model in a femtoliter compartment is simulated in STEPS with the stochastic solver Wmdirect (results plotted at 0.8 second intervals) and compared to BioModels Online deterministic simulation. Shown are cAMP and Ca signals, which are controlled by Events. Small stochastic differences are noticeable between simulations.
Mentions: Imported models may be directly simulated in STEPS using the deterministic solver or the well-mixed stochastic solver, although many models are not suitable for stochastic simulation without some modification. It is worth noting that SBML models may potentially form the basis of simulations in the spatial stochastic solver, but not without some modifications; for example diffusion coefficients and non-uniform initial conditions must currently be defined outside of SBML.Figure 12A shows a deterministic simulation in STEPS of model BIOMD0000000184 from the BioModels Database in comparison to a BioModels Online Simulation. This model of spontaneous calcium oscillations in astrocytes [50] contains two compartments (cytoplasm and endoplasmic reticulum) with transport reactions between them. Some reactions in the model can be represented as fundamental reactions, but some reactions contain complex maths, which is therefore converted to Python structures allowing for solution by the approximate method. Figure 12A shows close agreement between the STEPS simulation and the BioModels Online Simulation, and also matches the published results [50] (not shown).

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