A theory of macromolecular chemotaxis

A macromolecule in a gradient of a cosolute that is preferentially (relative to the solvent) either attracted to or excluded from the domain of the macromolecule should experience a thermodynamic force and move, respectively, up or down the gradient. A theory of chemotactic forces arising from such preferential interactions, especially short-range ligand binding and excluded volume interactions, is developed via an extension of Kirkwood-Buff theory. The ligand binding result is confirmed for both non-ionic and ionic cosolutes by standard solution thermodynamics. The effect of increasing the electrolyte concentration to diminish the electrostatic free energy of a charged macromolecule is also treated formally via an electrostatic macromolecule-electrolyte preferential interaction coefficient. For short-range interactions, the induced chemotactic velocity is attributed entirely to tangential tractions at the interface between the macromolecule and its surrounding solution. The velocity of a spherical macromolecule driven by such tractions is derived by a hydrodynamic calculation for steady-state creepy flow with a partial slip boundary condition. Qualitative comparisons of theoretical predictions with experimental observations of Zheng and Pollack pertaining to charged microspheres near the surfaces of non-ionic gels suggest that the reported exclusion zones are due to chemotaxis induced by gradients of base (NaOH) (or acid (HCl)) and salt. With a single adjustable parameter, namely, the ratio of slip length to area per surface carboxyl (or amidine) group, this theory yields nearly quantitative agreement with many observations. The estimated slip length for the microspheres is comparable to that obtained for bovine serum albumen by fitting the chemotactic theory to two reported cross-diffusion coefficients. When a solution with a gradient of NaOH is placed in contact with a smooth glass wall, chemotactic surface tractions are predicted to cause convection of the solution toward the acidic end of the gradient, as observed in preliminary experiments.