Parameter-preserving model order reduction of chemical master equations with a priori error bound

The stochastic kinetics of biomolecular reactions within a cell are modeled by a continuous-time and discrete-state Markov process, where the state is defined by molecular copy numbers that transition by chemical reactions. The governing equation, known as the Chemical Master Equation (CME), is numerically solved to analyze stochastic chemical reactions. However, the extensive state space poses a challenge in the high computational cost required for solving the CME, so it isn't easy to perform repeated simulations for various parameters to search for parameters that achieve a desired chemical reaction. In this paper, we propose a model reduction method that systematically reduces the states of the CME by projection while preserving the rate parameters in the model to be able to search for the parameter space efficiently. The proposed approach is a tailored extension of the balanced truncation based method and provides a guaranteed upper bound of the approximation error.