ERODE

ERODE performs exact reduction and analysis of stochastic reaction networks and associated differential equations to compute lumped models that preserve stochastic dynamics under mass-action kinetics.

Key Features:

• Exact lumping method: Implements an exact lumping method for stochastic reaction networks with mass-action kinetics to reduce model complexity while preserving stochastic dynamics.
• Species equivalence relations: Establishes equivalence relations between species to form reduced networks where each macro-species is stochastically equivalent to the sum of its constituent species.
• Initial-state independence: Produces reductions whose stochastic equivalence holds irrespective of the system's initial state.
• Parameter-independent equivalences: Encodes kinetic parameters as additional species to enable equivalences that do not depend on specific parameter values.
• Largest species equivalence algorithm: Includes an efficient algorithm to determine the largest species equivalence for maximal lumping.
• Projection computation: Computes projections that maintain the dynamics relevant to user-specified observables.
• Numerical solution and stochastic simulation: Provides numerical solution and stochastic simulation capabilities for dynamical systems derived from reaction networks.
• Minimization of dynamical systems: Supports minimization procedures for dynamical systems arising from stochastic reaction networks.
• Data formats: Supports import and export in SBML (Systems Biology Markup Language) and Matlab formats.

Scientific Applications:

• Signaling pathway models: Reduction and analysis of signaling pathway models while preserving essential stochastic dynamics.
• Epidemic processes on complex networks: Model reduction and analysis of epidemic processes on complex networks to retain key stochastic behavior.
• Cellular regulatory processes with intrinsic noise: Analysis and simplification of cellular regulatory systems where stochastic noise substantially affects dynamics.

Methodology:

Uses an exact lumping method for mass-action stochastic reaction networks by establishing species equivalence relations and computing projections; encodes kinetic parameters as species to obtain parameter-independent equivalences and employs an efficient algorithm to compute the largest species equivalence that yields reduced macro-species stochastically equivalent to sums of original species irrespective of initial state.