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P40: Modeling multi-state molecules with a pythonic STEPS interface
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**Jules Lallouette**, **Erik De Schutter**

Molecules involved in biological signaling pathways can, in some cases, exist in a very high number of different functional states. Well-studied examples include the Ca2+/calmodulin dependent protein kinase II (CaMKII), or receptors from the ErbB family. Through a combination of binding sites, phosphorylation sites, and polymerization, these molecules can form complexes that reach exponentially increasing numbers of distinct states. This phenomenon of combinatorial explosion is a common obstacle when trying to establish detailed models of signaling pathways.

Classical approaches to the stochastic simulation of chemical reactions require the explicit characterization of all reacting species and all associated reactions. This approach is well suited to population based methods in which there are a relatively low number of different molecules that can be present at relatively high concentrations. Since each state of multi-state complexes would however have to be modeled as a distinct specie, the combinatorial explosion that we mentioned earlier makes these approaches inapplicable.

Two separate problems need to be tackled: the "specification problem" which requires a higher level of abstraction in the definition of complexes and reactions ; and the "computation problem" that requires efficient methods to simulate the time evolution of reactions involving multi-state complexes. Rule based modeling (RBM) [2] tackles the former problem by allowing modelers to write "template" reactions that only contain the parts of the complexes actually involved in the reaction. Network-free methods together with particle-based methods [4] usually tackle the latter problem by only considering the states and reactions that are accessible from the current complex states and thus avoiding the computation of the full reaction network.

STEPS is a spatial stochastic reaction-diffusion simulation software that implements population based methods to simulate reaction-diffusion processes on realistic tetrahedral meshes [3]. In an effort to tackle the "specification problem" in STEPS, we present in this poster a novel, more pythonic, interface to STEPS that allows intuitive declaration of both classical and multi-state complexes reactions. Significant emphasis was put on simplifying model declaration, data access, and data saving during simulations.

To specifically tackle the "computation problem" in STEPS, we present a hybrid population/particle based method to simulate reactions involving multi-state complexes. By preventing the formation of arbitrarily structured macromolecules, we lower the computational cost of the pattern matching step necessary to identify potential reactants [1]. This diminished computational cost allows us to simulate larger spatial systems. We discuss these performance improvements and present examples of stochastic spatial simulations involving 12 subunits CamKII complexes which would have previously been intractable in STEPS.

References

1\. M. L. Blinov, et al. Graph theory for rule-based modeling of biochemical networks. Lect. Notes Comput. Sc., 2006.

2\. L. A. Chylek, et al. Innovations of the rule-based modeling approach. Systems Biol., 2013

3\. I. Hepburn, et al. Steps: efficient simulation of stochastic reaction–diffusion models in realistic morphologies. BMC Syst. Biol., 2012.

4\. J. J. Tapia, et al. Mcell-r: A particle-resolution network-free spatial modeling framework. In Modeling Biomolecular Site Dynamics, Springer, 2019.

**Speakers**

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Molecules involved in biological signaling pathways can, in some cases, exist in a very high number of different functional states. Well-studied examples include the Ca2+/calmodulin dependent protein kinase II (CaMKII), or receptors from the ErbB family. Through a combination of binding sites, phosphorylation sites, and polymerization, these molecules can form complexes that reach exponentially increasing numbers of distinct states. This phenomenon of combinatorial explosion is a common obstacle when trying to establish detailed models of signaling pathways.

Classical approaches to the stochastic simulation of chemical reactions require the explicit characterization of all reacting species and all associated reactions. This approach is well suited to population based methods in which there are a relatively low number of different molecules that can be present at relatively high concentrations. Since each state of multi-state complexes would however have to be modeled as a distinct specie, the combinatorial explosion that we mentioned earlier makes these approaches inapplicable.

Two separate problems need to be tackled: the "specification problem" which requires a higher level of abstraction in the definition of complexes and reactions ; and the "computation problem" that requires efficient methods to simulate the time evolution of reactions involving multi-state complexes. Rule based modeling (RBM) [2] tackles the former problem by allowing modelers to write "template" reactions that only contain the parts of the complexes actually involved in the reaction. Network-free methods together with particle-based methods [4] usually tackle the latter problem by only considering the states and reactions that are accessible from the current complex states and thus avoiding the computation of the full reaction network.

STEPS is a spatial stochastic reaction-diffusion simulation software that implements population based methods to simulate reaction-diffusion processes on realistic tetrahedral meshes [3]. In an effort to tackle the "specification problem" in STEPS, we present in this poster a novel, more pythonic, interface to STEPS that allows intuitive declaration of both classical and multi-state complexes reactions. Significant emphasis was put on simplifying model declaration, data access, and data saving during simulations.

To specifically tackle the "computation problem" in STEPS, we present a hybrid population/particle based method to simulate reactions involving multi-state complexes. By preventing the formation of arbitrarily structured macromolecules, we lower the computational cost of the pattern matching step necessary to identify potential reactants [1]. This diminished computational cost allows us to simulate larger spatial systems. We discuss these performance improvements and present examples of stochastic spatial simulations involving 12 subunits CamKII complexes which would have previously been intractable in STEPS.

References

1\. M. L. Blinov, et al. Graph theory for rule-based modeling of biochemical networks. Lect. Notes Comput. Sc., 2006.

2\. L. A. Chylek, et al. Innovations of the rule-based modeling approach. Systems Biol., 2013

3\. I. Hepburn, et al. Steps: efficient simulation of stochastic reaction–diffusion models in realistic morphologies. BMC Syst. Biol., 2012.

4\. J. J. Tapia, et al. Mcell-r: A particle-resolution network-free spatial modeling framework. In Modeling Biomolecular Site Dynamics, Springer, 2019.

Sunday July 19, 2020 7:00pm - 8:00pm CEST

Slot 07

Slot 07