Compartmental and spatial rule-based modeling with Virtual Cell (VCell)

11 In rule-based modeling, molecular interactions are systematically specified in the form of reaction rules 12 that serve as generators of reactions. This provides a way to account for all the potential molecular 13 complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule14 based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of 15 rules and merger of networks generated automatically (using the BioNetGen modeling engine) with 16 hand-specified reaction networks. VCell provides a number of ordinary differential equation (ODE) and 17 stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from 18 these networks, and agent-based network-free simulation of the rules. In this work, compartmental and 19 spatial modeling of rule-based models has been implemented within VCell. To enable rule-based 20 deterministic and stochastic spatial simulations and network-free agent-based compartmental 21 simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the 22 new rule-based formalism, every reactant and product pattern and every reaction rule are assigned 23 locations. We also introduce the novel rule-based concept of molecular anchors. This assures that any 24 species that has a molecule anchored to a predefined compartment will remain in this compartment. 25 Importantly, in addition to formulation of compartmental models, this now permits VCell users to 26 seamlessly connect reaction networks derived from rules to explicit geometries to automatically 27 generate a system of reaction-diffusion equations. These may then be simulated using either the VCell 28 partial differential equations (PDE) deterministic solvers or the Smoldyn stochastic simulator. 29