Enzymes show two distinct transport behaviors in the presence of their substrates in solution. First, their diffusivity enhances with an increasing substrate concentration. In addition, enzymes perform directional motion toward regions with a high substrate concentration, termed as chemotaxis. While a variety of enzymes has been shown to undergo chemotaxis, there remains a lack of quantitative understanding of the phenomenon. Here, we derive a general expression for the active movement of an enzyme in a concentration gradient of its substrate. The proposed model takes into account both the substrate-binding and catalytic turnover step, as well as the enhanced diffusion of the enzyme. We have experimentally measured the chemotaxis of a fast and a slow enzyme: urease under catalytic conditions and hexokinase for both full catalysis and for simple noncatalytic substrate binding. There is good agreement between the proposed model and the experiments. The model is general, has no adjustable parameters, and only requires three experimentally defined constants to quantify chemotaxis: enzyme-substrate binding affinity (Kd), Michaelis-Menten constant (KM), and level of diffusion enhancement in the associated substrate (α).
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