Efficient formulation of the rejection-based algorithm for biochemical reactions with delays

The rejection-based stochastic simulation algorithm (RSSA) is an exact simulation for realising temporal behaviour of biochemical reactions. It reduces the number of propensity updates during the simulation by using propensity bounds of reactions to select the next reaction firing. We present in this paper a new efficient formulation of RSSA and extend it for incorporating biochemical reactions with time delays. Our new algorithm explicitly keeps track of the putative firing times of reactions and uses these to select the next reaction firing. By using such a representation, it can efficiently handle biochemical reactions with delays and achieve computational efficiency over existing approaches for exact simulation.