Limits...
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/

Show MeSH

Related in: MedlinePlus

STEPS import of a tetrahedral mesh with realistic geometry. The mesh is reconstructed from a surface triangular mesh provided at http://synapses.clm.utexas.edu/anatomy/Ca1pyrmd/radiatum/K24/K24.stm . For a test simulation in STEPS molecules are distributed uniformly and the system is then visualized in CUBIT.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3472240&req=5

Figure 2: STEPS import of a tetrahedral mesh with realistic geometry. The mesh is reconstructed from a surface triangular mesh provided at http://synapses.clm.utexas.edu/anatomy/Ca1pyrmd/radiatum/K24/K24.stm . For a test simulation in STEPS molecules are distributed uniformly and the system is then visualized in CUBIT.

Mentions: The mesh importing utilities in STEPS also provide a more advanced, flexible way to simulate systems with complex geometries. Traditionally, meshes for subvolume-based SSA simulations have been constructed from combinations of standard geometry primitives such as cubes, spheres and cylinders [9], where geometry features are highly abstracted. A typical representative of this method is the Constructive Solid Geometry (CSG), adopted by MesoRD for geometry construction. This type of mesh is relatively easy to construct, but the highly abstracted models may not reflect real geometry constraints to the system and may produce inaccurate simulation results (see Results). A better, yet more challenging approach is to reconstruct volume meshes from biological data based on closed surface meshes. However, the surface meshes derived from series of electron microscope images [35] are commonly unclosed and have small intersecting surfaces, thus they cannot be used directly in volume mesh generation. This problem can be solved by semi-manually preprocessing the surface meshes using mesh manipulation tools such as MeshLab [36]. Once volume meshes are generated from the cleaned-up surface meshes, they can be imported to STEPS for simulations. Figure 2 gives an example STEPS simulation running in a reconstructed mesh with realistic geometry.


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

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

STEPS import of a tetrahedral mesh with realistic geometry. The mesh is reconstructed from a surface triangular mesh provided at http://synapses.clm.utexas.edu/anatomy/Ca1pyrmd/radiatum/K24/K24.stm . For a test simulation in STEPS molecules are distributed uniformly and the system is then visualized in CUBIT.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: STEPS import of a tetrahedral mesh with realistic geometry. The mesh is reconstructed from a surface triangular mesh provided at http://synapses.clm.utexas.edu/anatomy/Ca1pyrmd/radiatum/K24/K24.stm . For a test simulation in STEPS molecules are distributed uniformly and the system is then visualized in CUBIT.
Mentions: The mesh importing utilities in STEPS also provide a more advanced, flexible way to simulate systems with complex geometries. Traditionally, meshes for subvolume-based SSA simulations have been constructed from combinations of standard geometry primitives such as cubes, spheres and cylinders [9], where geometry features are highly abstracted. A typical representative of this method is the Constructive Solid Geometry (CSG), adopted by MesoRD for geometry construction. This type of mesh is relatively easy to construct, but the highly abstracted models may not reflect real geometry constraints to the system and may produce inaccurate simulation results (see Results). A better, yet more challenging approach is to reconstruct volume meshes from biological data based on closed surface meshes. However, the surface meshes derived from series of electron microscope images [35] are commonly unclosed and have small intersecting surfaces, thus they cannot be used directly in volume mesh generation. This problem can be solved by semi-manually preprocessing the surface meshes using mesh manipulation tools such as MeshLab [36]. Once volume meshes are generated from the cleaned-up surface meshes, they can be imported to STEPS for simulations. Figure 2 gives an example STEPS simulation running in a reconstructed mesh with realistic geometry.

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