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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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Comparison between cubic and tetrahedral spine meshes. A scatter plot of the properties of the tetrahedral meshes (red triangles; many points overlap) and the cubic meshes (blue squares; some overlap) representing geometry which consists of a spherical head joined to a cylindrical neck to approximate dendritic spines. All properties were plotted as a ratio of measured value/ideal value. A. The coarsest meshes ranging from approximately 2500–3000 subvolumes per mesh. B. The more detailed meshes ranging from approximately 11000 to 16000 subvolumes per mesh.
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Figure 5: Comparison between cubic and tetrahedral spine meshes. A scatter plot of the properties of the tetrahedral meshes (red triangles; many points overlap) and the cubic meshes (blue squares; some overlap) representing geometry which consists of a spherical head joined to a cylindrical neck to approximate dendritic spines. All properties were plotted as a ratio of measured value/ideal value. A. The coarsest meshes ranging from approximately 2500–3000 subvolumes per mesh. B. The more detailed meshes ranging from approximately 11000 to 16000 subvolumes per mesh.

Mentions: For all meshes the volume and surface area of both the head and neck regions were measured and compared. Figure 5 shows a plot of the normalized measurements. All meshes appeared to represent the spine head volume quite accurately, yet the cubic meshes often failed to represent the neck volume sufficiently, and only a marginal improvement was noticeable in the more detailed meshes. This demonstrates that, while one could always find an optimal cube size to represent any one region of a geometry accurately, the cube size will not necessarily suffice for other regions which may have different morphologies. This is a clear drawback for cubic meshes, which originates from the need for all subvolumes to be of the same size. Any error in volume will of course produce an error in reaction rates as well as for diffusion rates. It may be possible with a very detailed mesh to represent all regions sufficiently, yet a larger number of subvolumes means a slower simulation and may result in loss of accuracy caused by the small subvolume size.


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

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

Comparison between cubic and tetrahedral spine meshes. A scatter plot of the properties of the tetrahedral meshes (red triangles; many points overlap) and the cubic meshes (blue squares; some overlap) representing geometry which consists of a spherical head joined to a cylindrical neck to approximate dendritic spines. All properties were plotted as a ratio of measured value/ideal value. A. The coarsest meshes ranging from approximately 2500–3000 subvolumes per mesh. B. The more detailed meshes ranging from approximately 11000 to 16000 subvolumes per mesh.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Comparison between cubic and tetrahedral spine meshes. A scatter plot of the properties of the tetrahedral meshes (red triangles; many points overlap) and the cubic meshes (blue squares; some overlap) representing geometry which consists of a spherical head joined to a cylindrical neck to approximate dendritic spines. All properties were plotted as a ratio of measured value/ideal value. A. The coarsest meshes ranging from approximately 2500–3000 subvolumes per mesh. B. The more detailed meshes ranging from approximately 11000 to 16000 subvolumes per mesh.
Mentions: For all meshes the volume and surface area of both the head and neck regions were measured and compared. Figure 5 shows a plot of the normalized measurements. All meshes appeared to represent the spine head volume quite accurately, yet the cubic meshes often failed to represent the neck volume sufficiently, and only a marginal improvement was noticeable in the more detailed meshes. This demonstrates that, while one could always find an optimal cube size to represent any one region of a geometry accurately, the cube size will not necessarily suffice for other regions which may have different morphologies. This is a clear drawback for cubic meshes, which originates from the need for all subvolumes to be of the same size. Any error in volume will of course produce an error in reaction rates as well as for diffusion rates. It may be possible with a very detailed mesh to represent all regions sufficiently, yet a larger number of subvolumes means a slower simulation and may result in loss of accuracy caused by the small subvolume size.

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