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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 diffusion. In all panels the analytical solution is compared with the mean for 10 (A-C) or 30 (D) iterations of the STEPS simulation at three different times after start of the simulation. A. 3D diffusion in an infinite volume from a point source. B. 1D diffusion in a finite tube: all the molecules are positioned at the border (distance = 0) initially. C. 1D diffusion in a semi-infinite tube with the concentration at the border (distance = 0) clamped. D. 1D diffusion in a finite tube with a constant and equal influx of the same species of molecule at both ends (displacement = −5 and +5).
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Figure 8: Validation of diffusion. In all panels the analytical solution is compared with the mean for 10 (A-C) or 30 (D) iterations of the STEPS simulation at three different times after start of the simulation. A. 3D diffusion in an infinite volume from a point source. B. 1D diffusion in a finite tube: all the molecules are positioned at the border (distance = 0) initially. C. 1D diffusion in a semi-infinite tube with the concentration at the border (distance = 0) clamped. D. 1D diffusion in a finite tube with a constant and equal influx of the same species of molecule at both ends (displacement = −5 and +5).

Mentions: We first tested the most universal case: 3D diffusion from a point source in an infinite volume (Figure 8A), which has a known analytical solution for the time and evolution of the radial mean concentration [47]. While we could ensure the absence of boundary effects, it was not possible to mimic a point source in a tetrahedral mesh. The small deviations between the analytical solution and the STEPS simulation at short distances from the source for early simulation times are due to the finite volume of this source (see Additional file 4). At further distances or later times the match between the mean of the STEPS simulation showed no significant deviation from the analytical solution.


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 diffusion. In all panels the analytical solution is compared with the mean for 10 (A-C) or 30 (D) iterations of the STEPS simulation at three different times after start of the simulation. A. 3D diffusion in an infinite volume from a point source. B. 1D diffusion in a finite tube: all the molecules are positioned at the border (distance = 0) initially. C. 1D diffusion in a semi-infinite tube with the concentration at the border (distance = 0) clamped. D. 1D diffusion in a finite tube with a constant and equal influx of the same species of molecule at both ends (displacement = −5 and +5).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Validation of diffusion. In all panels the analytical solution is compared with the mean for 10 (A-C) or 30 (D) iterations of the STEPS simulation at three different times after start of the simulation. A. 3D diffusion in an infinite volume from a point source. B. 1D diffusion in a finite tube: all the molecules are positioned at the border (distance = 0) initially. C. 1D diffusion in a semi-infinite tube with the concentration at the border (distance = 0) clamped. D. 1D diffusion in a finite tube with a constant and equal influx of the same species of molecule at both ends (displacement = −5 and +5).
Mentions: We first tested the most universal case: 3D diffusion from a point source in an infinite volume (Figure 8A), which has a known analytical solution for the time and evolution of the radial mean concentration [47]. While we could ensure the absence of boundary effects, it was not possible to mimic a point source in a tetrahedral mesh. The small deviations between the analytical solution and the STEPS simulation at short distances from the source for early simulation times are due to the finite volume of this source (see Additional file 4). At further distances or later times the match between the mean of the STEPS simulation showed no significant deviation from the analytical solution.

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