  Enzyme-based systems have been shown to undergo directional motion in
response to their substrate gradient. Here, we formulate a kinetic model to
analyze the directional movement of an ensemble of protein molecules in
response to a gradient of the ligand. A similar analysis has been performed to
probe the motion of enzyme molecules in response to a gradient of the substrate
under catalytic conditions. In both cases, a net movement up the
ligand/substrate gradient is predicted when the diffusivity of the
ligand/substrate-bound protein is lower than that of the unbound protein
(positive chemotaxis). Conversely, movement down the ligand/substrate gradient
is expected when the diffusivity of the ligand/substrate-bound protein is
higher than that of the unbound protein (negative chemotaxis). The work
underscores the critical importance of measuring the diffusivity of the bound
protein and compare it with that of the free protein.
