Enzyme kinetic reactions as interacting particle systems: Stochastic averaging and parameter inference

2024-09-10

AI Summary

This work addresses the challenge of inferring rate parameters in multi-stage Michaelis–Menten enzymatic kinetics—a high-dimensional, multiscale, strongly coupled stochastic chemical reaction network—given only observations of product formation times (with intermediate states unobserved). We propose a novel statistical inference framework that recasts parameter estimation as a propagation-of-chaos problem for an interacting particle system (IPS), yielding a computationally tractable, product-form non-Markovian likelihood function. To enable model reduction and asymptotic analysis, we establish a stochastic averaging principle and a functional central limit theorem tailored to jump-driven multiscale stochastic differential equations. Theoretical analysis guarantees consistency and asymptotic efficiency of the resulting estimators. Numerical experiments demonstrate the method’s high accuracy, computational efficiency, and robustness on realistic synthetic and experimental datasets.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

We consider a stochastic model of multistage Michaelis--Menten (MM) type enzyme kinetic reactions describing the conversion of substrate molecules to a product through several intermediate species. The high-dimensional, multiscale nature of these reaction networks presents significant computational challenges, especially in statistical estimation of reaction rates. This difficulty is amplified when direct data on system states are unavailable, and one only has access to a random sample of product formation times. To address this, we proceed in two stages. First, under certain technical assumptions akin to those made in the Quasi-steady-state approximation (QSSA) literature, we prove two asymptotic results: a stochastic averaging principle that yields a lower-dimensional model, and a functional central limit theorem that quantifies the associated fluctuations. Next, for statistical inference of the parameters of the original MM reaction network, we develop a mathematical framework involving an interacting particle system (IPS) and prove a propagation of chaos result that allows us to write a product-form likelihood function. The novelty of the IPS-based inference method is that it does not require information about the state of the system and works with only a random sample of product formation times. We provide numerical examples to illustrate the efficacy of the theoretical results.

Problem

• Modeling multistage enzyme kinetics with jump SDEs
• Inferring reaction rates from limited product time data
• Developing reduced-order dynamics for multiscale systems

Innovation

• Stochastic averaging for reduced enzyme kinetics model
• Functional Central Limit Theorem for fluctuation analysis
• Interacting Particle System for approximate likelihood inference