Structured Projection-Based Model Reduction with Application to Stochastic Biochemical Networks
For researchers modeling stochastic biochemical networks, this work provides a theoretically grounded reduction technique that maintains network structure, though it is incremental as it builds on existing LNA time-scale separation.
The authors propose a structured projection-based model reduction method for the Linear Noise Approximation (LNA) of the Chemical Master Equation, proving mean-square convergence and deriving convex optimization algorithms. Applied to a yeast glycolysis model, the method preserves network structure and reduces complexity.
The Chemical Master Equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason more simple approximations to the CME have been proposed. In this work we focus on one such model, the Linear Noise Approximation. Specifically, we consider implications of a recently proposed LNA time-scale separation method. We show that the reduced order LNA converges to the full order model in the mean square sense. Using this as motivation we derive a network structure preserving reduction algorithm based on structured projections. We present convex optimisation algorithms that describe how such projections can be computed and we discuss when structured solutions exits. We also show that for a certain class of systems, structured projections can be found using basic linear algebra and no optimisation is necessary. The algorithms are then applied to a linearised stochastic LNA model of the yeast glycolysis pathway.