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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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Simulator efficiency. Test system simulation runtimes in STEPS, MesoRD and Smoldyn. Filled circles show points where the simulation is calculated to be accurate and open circles show where simulation may be inaccurate. A. Low number of molecules initial condition. Left panel: STEPS and MesoRD simulation runtimes at different number of subvolumes describing the same total mesh volume. Right panel: Smoldyn runtimes with varying number of simulation iterations due to a change in time-step. B. High number of molecules initial condition, which is the only difference from simulations shown in A. Notice different y-scale between A and B but not between left panels and right panels.
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Figure 11: Simulator efficiency. Test system simulation runtimes in STEPS, MesoRD and Smoldyn. Filled circles show points where the simulation is calculated to be accurate and open circles show where simulation may be inaccurate. A. Low number of molecules initial condition. Left panel: STEPS and MesoRD simulation runtimes at different number of subvolumes describing the same total mesh volume. Right panel: Smoldyn runtimes with varying number of simulation iterations due to a change in time-step. B. High number of molecules initial condition, which is the only difference from simulations shown in A. Notice different y-scale between A and B but not between left panels and right panels.

Mentions: Figure 11 shows simulation times in STEPS, MesoRD and Smoldyn for the test system for two different models, which differ only by the total number of molecules as the initial condition. All simulators are very fast in the most efficient case (very large time-step in Smoldyn, only one volume in STEPS, eight subvolumes in MesoRD) but may be inaccurate. As we then decrease efficiency and increase accuracy we can see that simulation time eventually scales approximately linearly for all simulators, although MesoRD initially scales logarithmically. In the first model a total of 5500 molecules were injected, which corresponds to a concentration of ~0.3 μM, and during simulation the total number of molecules increased to around 6000. The estimated upper limit of acceptable subvolume size in STEPS corresponds to approximately 300 tetrahedrons in the mesh, making the results for a 454 tetrahedron mesh accurate with a simulation time of 13 seconds. The estimate for a cubic mesh puts an acceptable number of cubes at approximately 380 (a small discrepancy from the tetrahedral case arising from the different geometry), giving the fastest simulation with acceptable accuracy at 512 subvolumes in the MesoRD mesh with a simulation time of 66 seconds (it was in fact not possible to generate a 7x7x7 mesh of 343 cubes). The fastest reaction in the system has a characteristic time of 1 ms, so a time-step of 0.1 ms was estimated as the upper-bound for accuracy in Smoldyn with a runtime of 73 seconds. So, at the estimate for the most efficient conditions with acceptable accuracy, STEPS runtime was more than 5 times faster than MesoRD and Smoldyn. As we increase accuracy further in Smoldyn with 10 times more iterations the runtime slows to 726 seconds (not plotted), and with approximately 10 times more subvolumes in STEPS (4520) and MesoRD (4096) STEPS slows to 109 seconds compared to 169 seconds for MesoRD. So, in the lower molecule number case, at the most efficient simulation possible for acceptable conditions STEPS appears to perform favorably, and as we increase detail STEPS appears to maintain an advantage over the other two simulators. At the most detailed meshes tested for STEPS (13871 tetrahedrons) and MesoRD (13824 cubes) runtime was 263 seconds in STEPS and 347 seconds in MesoRD (not plotted).


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

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

Simulator efficiency. Test system simulation runtimes in STEPS, MesoRD and Smoldyn. Filled circles show points where the simulation is calculated to be accurate and open circles show where simulation may be inaccurate. A. Low number of molecules initial condition. Left panel: STEPS and MesoRD simulation runtimes at different number of subvolumes describing the same total mesh volume. Right panel: Smoldyn runtimes with varying number of simulation iterations due to a change in time-step. B. High number of molecules initial condition, which is the only difference from simulations shown in A. Notice different y-scale between A and B but not between left panels and right panels.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 11: Simulator efficiency. Test system simulation runtimes in STEPS, MesoRD and Smoldyn. Filled circles show points where the simulation is calculated to be accurate and open circles show where simulation may be inaccurate. A. Low number of molecules initial condition. Left panel: STEPS and MesoRD simulation runtimes at different number of subvolumes describing the same total mesh volume. Right panel: Smoldyn runtimes with varying number of simulation iterations due to a change in time-step. B. High number of molecules initial condition, which is the only difference from simulations shown in A. Notice different y-scale between A and B but not between left panels and right panels.
Mentions: Figure 11 shows simulation times in STEPS, MesoRD and Smoldyn for the test system for two different models, which differ only by the total number of molecules as the initial condition. All simulators are very fast in the most efficient case (very large time-step in Smoldyn, only one volume in STEPS, eight subvolumes in MesoRD) but may be inaccurate. As we then decrease efficiency and increase accuracy we can see that simulation time eventually scales approximately linearly for all simulators, although MesoRD initially scales logarithmically. In the first model a total of 5500 molecules were injected, which corresponds to a concentration of ~0.3 μM, and during simulation the total number of molecules increased to around 6000. The estimated upper limit of acceptable subvolume size in STEPS corresponds to approximately 300 tetrahedrons in the mesh, making the results for a 454 tetrahedron mesh accurate with a simulation time of 13 seconds. The estimate for a cubic mesh puts an acceptable number of cubes at approximately 380 (a small discrepancy from the tetrahedral case arising from the different geometry), giving the fastest simulation with acceptable accuracy at 512 subvolumes in the MesoRD mesh with a simulation time of 66 seconds (it was in fact not possible to generate a 7x7x7 mesh of 343 cubes). The fastest reaction in the system has a characteristic time of 1 ms, so a time-step of 0.1 ms was estimated as the upper-bound for accuracy in Smoldyn with a runtime of 73 seconds. So, at the estimate for the most efficient conditions with acceptable accuracy, STEPS runtime was more than 5 times faster than MesoRD and Smoldyn. As we increase accuracy further in Smoldyn with 10 times more iterations the runtime slows to 726 seconds (not plotted), and with approximately 10 times more subvolumes in STEPS (4520) and MesoRD (4096) STEPS slows to 109 seconds compared to 169 seconds for MesoRD. So, in the lower molecule number case, at the most efficient simulation possible for acceptable conditions STEPS appears to perform favorably, and as we increase detail STEPS appears to maintain an advantage over the other two simulators. At the most detailed meshes tested for STEPS (13871 tetrahedrons) and MesoRD (13824 cubes) runtime was 263 seconds in STEPS and 347 seconds in MesoRD (not plotted).

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