Table 1.

Common modeling methodologies for self-assembly. The table lists principal techniques for self-assembly modeling, some systems biology software packages implementing them, and some notable applications in self-assembly modeling.

Reaction Representation	Description	Software Packages	Applications
Law of Mass Action (Deterministic)	Expresses any well-mixed chemical system as a collection of coupled non-linear first order differential equations which typically must be numerically integrated. PDEs must be used when space is explicitly included	BioNetGen [15], COPASI [82], VCell [146], DBSolve [66]	Virus Assembly: [125, 173, 27, 70], Metabolomic Networks[90]
SSA/Gillespie Approaches	Provides a way to simulate kinetically correct trajectories consistent with the Chemical Master Equation	Moleculizer [114], BioNetGen [15], VCell [146], DESSA [218]	Virus assembly: [184, 97]
Spatial Stochastic	Usually combine Gillespie or Stochastic Langevin with diffusion or subunit geometry	MCell [182], StochSim [108], VCell [146], Smoldyn [4], SRSim [69]	Geometric Constraints with Diffusion: [68], Amyloid-Beta: [192]
Rule-Based	Primarly network-free rule-based methods which may incorporate stochasticity and spatial modeling	RuleMonkey [32], BioNetGen, ML-Space [13], VCell [164], SRSim [69]	Multivalent ligand-receptor interactions: [213], Prion Aggregation [154], Virus Assembly: [167, 218]
Brownian Dynamics	An explicitly spatial model where Brownian motion is computed with the Langevin equation	Smoldyn [4], MCell [182]	Multiscale Reaction-Diffusion [58], Virus Assembly: [167, 71, 128, 46, 47, 17], Crowding/Amyloids: [205], Clathrin Cage Formation: [87]