Enzyme-Substrate Complex Formation Modulates Diffusion-Driven Patterning In Metabolic Pathways

TL;DR

This study models how reversible enzyme-substrate interactions influence spatial pattern formation in metabolic pathways through diffusion-driven instabilities, providing insights into mesoscale biochemical organization.

Contribution

It introduces a reaction-diffusion model incorporating enzyme-substrate complexes and analyzes their impact on pattern formation, extending previous effective kinetics models.

Findings

Reversible enzyme binding alters the conditions for Turing instability.

Enzyme-substrate interactions influence pattern selection and slow heterogeneity emergence.

Numerical simulations validate analytical predictions of pattern formation dynamics.

Abstract

Spatial organization in metabolic pathways can arise from the interplay between enzymatic reaction kinetics and diffusion-driven instabilities. In this work we investigate how reversible enzyme--substrate binding influences pattern formation in a two-step metabolic pathway. Starting from a mechanistic description in which the substrate reversibly binds to the first enzyme before catalytic conversion, we formulate a three-species reaction--diffusion system that explicitly incorporates the enzyme--substrate complex. We first analyse the homogeneous dynamics and determine the unique steady state of the kinetic system. Exploiting the separation of time scales between the rapid binding kinetics and the slower evolution of metabolite concentrations, we derive a reduced two-variable model using a quasi-steady-state approximation for the enzyme-substrate complex. This reduction preserves the essential nonlinear coupling between catalytic reactions and spatial transport. Linear stability and weakly nonlinear analysis reveal conditions for diffusion-driven (Turing) instability and show that reversible enzyme binding significantly modifies the location and extent of the instability region compared to models with effective kinetics. Numerical simulations confirm the analytical predictions and demonstrate how enzyme-substrate interactions reshape pattern selection and slow the emergence of spatial heterogeneity. These results provide a mechanistic link between enzyme binding kinetics, diffusion-driven pattern formation, and mesoscale metabolic organization. The proposed framework offers a tractable approach for studying spatial patterning in enzymatic networks and may help explain the emergence of structured biochemical domains such as those associated with liquid--liquid phase separation.