DelaySSA: stochastic simulation of biochemical systems and gene regulatory networks with or without time delays.

Stochastic Simulation Algorithm (SSA) is crucial for modeling biochemical reactions and gene regulatory networks. Traditional SSA is characterized by Markovian property and cannot naturally model systems with time delays. Several algorithms have already been designed to handle delayed reactions, yet few easy-to-use implementations exist. To address these challenges, we have developed DelaySSA, an R package that implements currently available algorithms for SSA with or without delays. Meanwhile, we also provided Matlab and Python versions to support wider applications. We demonstrated its accuracy and validity by simulating two classical models: the Bursty model and Refractory model. We then tested its capability to simulate the RNA Velocity model, where it successfully reproduced both the up- and down-regulation stages in the phase portrait. Finally, we extended its application to simulate a gene regulatory network of lung cancer adeno-to-squamous transition (AST) and qualitatively analyzed its bistability behavior by approximating the Waddington's landscape. Modeling the therapeutic intervention of a SOX2 degrader as a delayed degradation reaction, AST is effectively blocked and reprogrammed back to the adenocarcinoma state, providing a useful clue for targeting drug-resistant AST in the future. Taken together, DelaySSA is a powerful and easy-to-use software suite, facilitating accurate modeling of various kinds of biological systems and broadening the scope of stochastic simulations in systems biology.