Emergent Nonlinearity in Active Molecular Chemotaxis

Understanding chemotaxis at the molecular level is challenging, as individual enzyme molecules cannot sense chemical gradients across their nanometer-sized bodies. Typical theoretical models encompass chemotaxis under constant, externally imposed gradients; however, this overlooks a critical feedback loop, where the active enzymes themselves reshape the imposed gradients through catalysis. In this work, we investigate the principles of active molecular chemotaxis using a Fokker-Planck model for an ATP-driven kinase-phosphatase system. Using experimentally relevant enzyme concentration ranges (∼nM), we demonstrate that the chemotactic velocity of enzymes does not simply respond linearly to chemical gradients, as commonly observed in microscale systems driven by diffusiophoresis. Instead, it emerges from a nonlinear coupling between the enzyme's spatial distribution, its conformational state (free/bound-state ratio), and chemical gradients modulated by catalytic reactions. As a result, the spatial profile of chemotactic velocity transitions between monotonic and nonmonotonic regimes, depending on substrate availability. Furthermore, we find that high catalyst concentrations can amplify the effective interaction between enzymes, forming a cascade that is critical for collective assemblies such as metabolon formation. To understand these complex interactions, we construct chemotactic velocity maps as a function of enzyme concentration, energy, and substrate availability, offering a set of design principles. This work clarifies the distinct roles of energy, gradients, and enzyme free/bound states in molecular motion, highlighting a fundamental difference between nano and microscale systems, and provides a theoretical framework for designing advanced autonomous active molecular systems.