DelaySSAToolkit.jl

DelaySSAToolkit.jl models reaction systems by incorporating explicit time delays to simulate non‑Markovian dynamics for the study of biological, chemical, ecological, and genetic processes.

Key Features:

• Non‑Markovian modeling: Represents reaction systems with non‑Markovian dynamics via explicit time delays that capture history-dependent behavior.
• Delay stochastic simulation: Implements various exact formulations of the delay stochastic simulation algorithm (delay SSA) for exact simulation of delayed reactions.
• Intermediate-step representation: Encodes multiple implicit intermediate reaction steps as time delays to reduce model complexity while retaining temporal fidelity.
• Kinetic fidelity: Enables accurate simulation of reaction kinetics influenced by time‑dependent factors and delayed events.
• High‑performance implementation: Implemented in Julia to support efficient numerical computing for large‑scale and complex models.

Scientific Applications:

• Gene regulatory networks: Models delayed transcriptional and translational processes in gene regulatory networks.
• Chemical kinetics: Simulates chemical reactions where intermediate states have significant lifetimes.
• Population dynamics: Studies ecological population dynamics with time‑lagged interactions.
• Genetic systems: Explores inheritance and genetic processes influenced by temporal delays.

Methodology:

Uses various exact formulations of the delay stochastic simulation algorithm (delay SSA) to simulate non‑Markovian reaction systems with explicit time delays; implemented in Julia.