  Detailed modeling and simulation of biochemical systems is complicated by the
problem of combinatorial complexity, an explosion in the number of species and
reactions due to myriad protein-protein interactions and post-translational
modifications. Rule-based modeling overcomes this problem by representing
molecules as structured objects and encoding their interactions as
pattern-based rules. This greatly simplifies the process of model
specification, avoiding the tedious and error prone task of manually
enumerating all species and reactions that can potentially exist in a system.
From a simulation perspective, rule-based models can be expanded
algorithmically into fully-enumerated reaction networks and simulated using a
variety of network-based simulation methods, provided that the network is not
exceedingly large. Alternatively, rule-based models can be simulated directly
using particle-based kinetic Monte Carlo methods. This "network-free" approach
produces exact stochastic trajectories with a computational cost that is
independent of network size. However, memory and run time costs increase with
the number of particles, limiting the size of system that can be feasibly
simulated. Here, we present a hybrid particle/population simulation method that
combines the best attributes of both the network-based and network-free
approaches. The method takes as input a rule-based model and a user-specified
subset of species to treat as population variables rather than as particles.
The model is then transformed by a process of "partial network expansion" into
a dynamically equivalent form that can be simulated using a population-adapted
network-free simulator. The transformation method has been implemented within
the open-source rule-based modeling platform BioNetGen, and resulting hybrid
models can be simulated using the particle-based simulator NFsim.
