A Symbolic and Statistical Learning Framework to Discover Bioprocessing Regulatory Mechanism: Cell Culture Example

TL;DR

Bioprocess modeling faces intrinsic stochasticity and limited data, challenging reliable discovery of regulatory mechanisms. The authors propose a symbolic and statistical learning framework that models cell culture dynamics with stochastic differential equations and a mixture of $K$ candidate regulatory mechanisms, jointly learning kinetic parameters $\boldsymbol{\vartheta}_k$ and weights $\boldsymbol{w}$ under $\sum_k w_k=1$. They develop a likelihood-based Bayesian inference pipeline using Metropolis-adjusted Langevin dynamics (MALA) with adjoint sensitivity to achieve efficient posterior exploration and robustness, including a theoretical asymptotic consistency result (Theorem 1) that concentrates posterior mass on the true mechanism and parameters as data grows. An empirical study on a representative CHO cell culture network demonstrates improved predictive fidelity and the ability to recover missing regulatory modules under data-limited conditions, highlighting the approach’s potential for advancing intelligent digital twins in biomanufacturing.

Abstract

Bioprocess mechanistic modeling is essential for advancing intelligent digital twin representation of biomanufacturing, yet challenges persist due to complex intracellular regulation, stochastic system behavior, and limited experimental data. This paper introduces a symbolic and statistical learning framework to identify key regulatory mechanisms and quantify model uncertainty. Bioprocess dynamics is formulated with stochastic differential equations characterizing intrinsic process variability, with a predefined set of candidate regulatory mechanisms constructed from biological knowledge. A Bayesian learning approach is developed, which is based on a joint learning of kinetic parameters and regulatory structure through a formulation of the mixture model. To enhance computational efficiency, a Metropolis-adjusted Langevin algorithm with adjoint sensitivity analysis is developed for posterior exploration. Compared to state-of-the-art Bayesian inference approaches, the proposed framework achieves improved sample efficiency and robust model selection. An empirical study demonstrates its ability to recover missing regulatory mechanisms and improve model fidelity under data-limited conditions.

Figures (2)

• Figure 1: (a) Schematic of a simple metabolic reaction network with green and blue represent extracellular and intracellular metabolites. Reactions with flux rate modeling using M-M kinetics are shown in Red. (b) Illustration of enzyme regulatory mechanisms (Created with BioRender.com). (1) Standard Catalysis: Under baseline conditions, the substrate binds to the enzyme's active site, leading to catalysis without regulatory interference. (2) Competitive Inhibition: A competitive inhibitor binds to the enzyme's active site, preventing substrate binding and thus inhibiting catalysis. (3) Non-Competitive Inhibition: A non-competitive inhibitor binds to a distinct allosteric site, allowing substrate binding but impairing catalytic activity, resulting in reduced reaction rates without affecting substrate affinity. (4) Allosteric Activation: An allosteric activator binds to an allosteric site, inducing a conformational change that enhances enzyme activity by either improving substrate binding affinity, increasing catalytic turnover, or both.
• Figure 2: Asymptotic consistency of the posterior distributions of $\bm{\theta}$ and $\bm{w}$ across iterations.