  Enzymes show two distinct transport behaviors in the presence of their
substrates in solution. First, their diffusivity enhances with increasing
substrate concentration. In addition, enzymes perform directional motion toward
regions with high substrate concentration, termed chemotaxis. While a variety
of enzymes has been shown to undergo chemotaxis, there remains a lack of
quantitative understanding of the phenomenon. Here, we provide 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 effect. 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 non-catalytic 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
({\alpha}).
