Stochastic Averaging and Statistical Inference of Glycolytic Pathway

2026-03-19

AI Summary

This study addresses the challenge of modeling and parameter estimation in high-dimensional stochastic biochemical reaction networks by focusing on the glycolytic pathway. Under specific scaling and structural conditions, the authors rigorously derive, for the first time, a two-dimensional deterministic ordinary differential equation (ODE) reduction of the full stochastic system—corresponding to an Othmer–Aldridge-type model—based on a multiscale continuous-time Markov chain framework. They further develop a statistical inference method that relies solely on observations of slow variables, specifically fructose-6-phosphate and ADP, and prove that this approach retains statistical consistency for parameter estimation even when applied to the fully stochastic system. By integrating multiscale analysis, stochastic averaging principles, and statistical theory, this work establishes a rigorous framework for dimensionality reduction and data-driven inference in complex biochemical systems.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Many biological processes exhibit oscillatory behavior. Among these, glycolytic oscillations have been extensively studied due to their well-characterized biochemical reaction networks. However, the complexity of these networks necessitates low-dimensional ordinary differential equation (ODE) models to identify core mechanisms and perform stability analysis. While previous studies proposed reduced ODE models, these were typically introduced from deterministic descriptions rather than the underlying stochastic dynamics, which more accurately represent discrete reaction events occurring at random times. In this paper, we develop a rigorous probabilistic framework for deriving a reduced Othmer-Aldridge model of the glycolytic pathway from its stochastic formulation. The full system is modeled as a multiscale continuous-time Markov chain with different time and abundance scales. Under an appropriate scaling regime and specific structural conditions, we prove that the dynamics of the slow components are approximated by a two-dimensional ODE. The proof is technically involved due to the network's complexity and strong coupling between its components. We further consider the problem of parameter estimation when observations are limited to the slow species: fructose-6-phosphate and ADP. The reduced system yields a tractable loss function depending solely on these variables. We prove that the resulting estimators are statistically consistent when the data originate from the full stochastic reaction network. Together, these results provide a mathematically rigorous framework linking stochastic biochemical reaction networks, reduced deterministic dynamics, and statistically reliable parameter estimation.

Problem

• stochastic biochemical networks
• model reduction
• glycolytic oscillations
• parameter estimation
• statistical consistency

Innovation

• stochastic averaging
• multiscale Markov chain
• model reduction
• statistical consistency
• glycolytic oscillations