Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Schaff, James C.; Gao, Fei; Li, Ye; Novak, Igor L.; Slepchenko, Boris M.

doi:10.1371/journal.pcbi.1005236

Cited by 28 publications

(21 citation statements)

References 56 publications

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“…To see this figure in color, go online. environment; we are also unaware of any other systems biology software offering a spatial hybrid deterministic/ stochastic solver (9).…”

Section: Resultsmentioning

confidence: 99%

“…When the copy numbers are low, a spatial stochastic simulator using the Smoldyn simulation engine (8) is available. VCell even has a solver for spatial hybrid deterministic/stochastic simulations (9), to accommodate systems containing some species at high copy number (modeled as continuous concentrations and PDEs) and others at low copy number (modeled with stochastic reaction kinetics and Brownian motion).…”

Section: Introductionmentioning

confidence: 99%

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Compartmental and Spatial Rule-Based Modeling with Virtual Cell

Blinov

Schaff

Vasilescu

et al. 2017

Biophysical Journal

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In rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations deterministic solvers or the Smoldyn stochastic simulator.

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“…To see this figure in color, go online. environment; we are also unaware of any other systems biology software offering a spatial hybrid deterministic/ stochastic solver (9).…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Compartmental and Spatial Rule-Based Modeling with Virtual Cell

Blinov

Schaff

Vasilescu

et al. 2017

Biophysical Journal

Self Cite

View full text Add to dashboard Cite

show abstract

“…3 can be used to produce compartmental deterministic (ODE), compartmental stochastic, compartmental network-free, spatial deterministic (PDE), spatial stochastic, and spatial hybrid deterministic/stochastic simulations. We believe that VCell is unique in making all these approaches available within one unified software environment; we are also unaware of any other systems biology software offering a spatial hybrid deterministic/stochastic solver(9).…”

Section: Resultsmentioning

confidence: 99%

“…When the copy numbers are low, a spatial stochastic simulator using the Smoldyn simulation engine (8) is available. VCell even has a solver for spatial hybrid deterministic/stochastic simulations (9), to accommodate systems containing some species at high copy number (modeled as continuous concentrations and partial differential equations) and others at low copy number (modeled with stochastic reaction kinetics and Brownian motion).…”

Section: Introductionmentioning

confidence: 99%

Compartmental and spatial rule-based modeling withVirtual Cell(VCell)

Blinov

Schaff

Vasilescu

et al. 2017

Preprint

View full text Add to dashboard Cite

In rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation (ODE) and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the novel rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations (PDE) deterministic solvers or the Smoldyn stochastic simulator.

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“…In Table 1 , we describe advantages and limitations for some of the more common methods. Hybrid approaches, such as the method described in [ 21 ], that mix particle simulations with a deterministic partial differential equation solver are most similar to the approach we take here.…”

Section: Introductionmentioning

confidence: 99%

Particle-based simulations of polarity establishment reveal stochastic promotion of Turing pattern formation

2018

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Polarity establishment, the spontaneous generation of asymmetric molecular distributions, is a crucial component of many cellular functions. Saccharomyces cerevisiae (yeast) undergoes directed growth during budding and mating, and is an ideal model organism for studying polarization. In yeast and many other cell types, the Rho GTPase Cdc42 is the key molecular player in polarity establishment. During yeast polarization, multiple patches of Cdc42 initially form, then resolve into a single front. Because polarization relies on strong positive feedback, it is likely that the amplification of molecular-level fluctuations underlies the generation of multiple nascent patches. In the absence of spatial cues, these fluctuations may be key to driving polarization. Here we used particle-based simulations to investigate the role of stochastic effects in a Turing-type model of yeast polarity establishment. In the model, reactions take place either between two molecules on the membrane, or between a cytosolic and a membrane-bound molecule. Thus, we developed a computational platform that explicitly simulates molecules at and near the cell membrane, and implicitly handles molecules away from the membrane. To evaluate stochastic effects, we compared particle simulations to deterministic reaction-diffusion equation simulations. Defining macroscopic rate constants that are consistent with the microscopic parameters for this system is challenging, because diffusion occurs in two dimensions and particles exchange between the membrane and cytoplasm. We address this problem by empirically estimating macroscopic rate constants from appropriately designed particle-based simulations. Ultimately, we find that stochastic fluctuations speed polarity establishment and permit polarization in parameter regions predicted to be Turing stable. These effects can operate at Cdc42 abundances expected of yeast cells, and promote polarization on timescales consistent with experimental results. To our knowledge, our work represents the first particle-based simulations of a model for yeast polarization that is based on a Turing mechanism.

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Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Cited by 28 publications

References 56 publications

Compartmental and Spatial Rule-Based Modeling with Virtual Cell

Compartmental and Spatial Rule-Based Modeling with Virtual Cell

Compartmental and spatial rule-based modeling withVirtual Cell(VCell)

Particle-based simulations of polarity establishment reveal stochastic promotion of Turing pattern formation

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