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

arXiv:2512.15737v2 Announce Type: replace
Abstract: We investigate how enzymatic binding kinetics regulate diffusion-driven instabilities 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 two reaction-diffusion models: a simplified system with effective kinetics and an extended model that explicitly includes the enzyme-substrate complex. The latter exhibits a structural degeneracy at critical parameter values due to a continuous family of homogeneous equilibria. To enable direct comparison and analytical progress, we introduce a reduced non-degenerate formulation via a quasi-equilibrium closure that encodes the influence of complex formation into effective reaction terms while preserving the nonlinear coupling between catalytic turnover and spatial transport.
We show that explicit enzyme-substrate binding shifts the homogeneous steady state, modifies relaxation dynamics, and substantially alters the size and location of the Turing instability region relative to the simplified model. Numerical simulations are in close agreement with weakly nonlinear predictions, illustrating how reversible binding reshapes pattern selection and slows the development of spatial heterogeneity. These results establish a quantitative link between enzyme-substrate binding kinetics, diffusion-driven instabilities, and mesoscale spatial organization, including structures associated with liquid-liquid phase separation (LLPS). The proposed framework provides a mechanistic route by which association, dissociation, and catalytic rates jointly regulate the robustness and structure of spatial metabolic patterns, and can be extended to broader classes of compartmentalized biochemical networks.