Substrate concentration dependence of the diffusion-controlled steady-state rate constant.
The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a local-density approximation. By solving the strictly linearized equation for the time-independent case with absorbing boundary conditions, we present an analytic expression for the diffusion-limited steady-state rate constant for small substrate concentrations in terms of an effective second virial coefficient B2*. Comparisons to Brownian dynamics simulations excluding hydrodynamic interactions show excellent agreement up to bulk number densities of B2*rho0 < approximately = 0.4 for hard sphere and repulsive Yukawa-like interactions between the substrates. Our study provides an alternative way to determine the second virial coefficient of interacting macromolecules experimentally by measuring their steady-state rate constant in diffusion-controlled reactions at low densities.
Dzubiella
J
J
NSF Center for Theoretical Biological Physics (CTBP), University of California, San Diego, La Jolla, California 92093-0365, USA. jdzubiella@ucsd.edu
McCammon
J A
JA
D016880:Anisotropy; D001703:Biophysics / Q000379:methods*; D002627:Chemistry, Physical / Q000379:methods*; D004058:Diffusion; D007700:Kinetics; D015233:Models, Statistical; D008962:Models, Theoretical; D010825:Physics / Q000379:methods; D011336:Probability; D014867:Water / Q000737:chemistry
D014867:Water