Inferring reaction rates from lagged molecular data without full state enumeration
Koopman Operator Inference for the Chemical Master Equation
Computational Engineering, Finance, and Science
Summary
Understanding how molecules change in chemical reactions often requires tracking many possible states, which can be overwhelming. This work shows a way to estimate reaction speeds using data pairs from molecules observed at two times, without needing to handle all possible molecular states. They use a mathematical technique called extended dynamic mode decomposition to simplify the problem and improve accuracy by adding smart functions related to the reactions. Tests on simulated reaction networks show their method helps recover reaction rates more reliably from limited data.
What this means in practice
- •For computational chemists: Estimate reaction kinetics from time-lagged molecular data without simulating huge state spaces.
- •For biochemical modelers: Improve parameter inference in stochastic biochemical networks by incorporating derived functions to reduce bias.
Authors
Aditya Dendukuri, Linda Petzold
Abstract
We infer kinetic rates of stochastic reaction networks from molecular-state pairs separated by a fixed time lag, without constructing the large state space of the Chemical Master Equation. Extended dynamic mode decomposition estimates the finite-time evolution of selected functions of the molecular state. A matrix logarithm then gives a projected generator whose species rows determine the rates through the known reaction stoichiometry. A finite set of functions introduces a systematic bias. We construct additional functions from the reaction channels and prove that each level of closure moves the first bias term to higher order. Spectral formulas identify the omitted modes responsible for this bias and show when the logarithm amplifies sampling error. Exact calculations and experiments on five reaction networks confirm the predicted error behavior and show when the added functions improve finite-sample rate recovery.