2018 # Generalizing Gillespie’s Direct Method to Enable Network-Free Simulations

**Abstract:** Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gi…

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“…It could be a system of nonlinear ODEs that are numerically integrated to generate deterministic time courses for each chemical species. It could also be a stochastic model simulated using Gillespie's direct method [18], for example, or a network-free method [19], such as that implemented in NFsim [20]. In network-free methods, the system state is tracked in terms of the set of molecules currently present in the system, without enumerating all possible chemical species and reactions (which could be too many to practically enumerate).…”

confidence: 99%

“…It could be a system of nonlinear ODEs that are numerically integrated to generate deterministic time courses for each chemical species. It could also be a stochastic model simulated using Gillespie's direct method [18], for example, or a network-free method [19], such as that implemented in NFsim [20]. In network-free methods, the system state is tracked in terms of the set of molecules currently present in the system, without enumerating all possible chemical species and reactions (which could be too many to practically enumerate).…”

confidence: 99%

“…KMC procedures are also useful for studying systems, such as cell signaling networks, that have large state spaces 4 arising from the combinatorial number of chemical species that can be generated by biomolecular interactions of interest 5 . For such systems, it may be impracticable, even with the aid of a computer, to enumerate the chemical species that are potentially populated.…”

confidence: 99%

“…For such systems, it may be impracticable, even with the aid of a computer, to enumerate the chemical species that are potentially populated. Nonetheless, simulations can be performed by formulating rules to represent biomolecular interactions 5 and then using these rules as event generators in a so-called network-free simulation algorithm 4 , such as that implemented in the NFsim software package 6,7 . In a networkfree simulation (of cell signaling dynamics), stochastic effects may be negligible 8 .…”

confidence: 99%

“…However, if the state of one tyrosine residue does not influence the state of others, then the same system of interactions could be fully captured with only 2 n equations. One way to overcome the combinatorial explosion problem is with network-free simulation algorithms that avoid the explicit specification or derivation of all possible states [32–36]. A second option is model reduction, in which an approximate model is derived by neglecting sparsely populated species [37].…”

confidence: 99%