Kinetics of diffusion-controlled enzymatic reactions with charged substrates

PACS Codes: 82.45.Tv, 87.15.VvMSC Codes: 92C30Electrostatically steered diffusion-reaction processes exist widely in chemistry and biochemistry [1,2]. Ionic screening effects were first described by using the well-known Debye-Hückel limiting law (DHL) [3]. The DHL implemented within transition state theory [4] is still often used to estimate the kinetics of enzyme-substrate reactions. E.g., the dependence of the rate constant on ionic strength for the diffusion-controlled reaction of acetylcholine (charge = +1) catalyzed by acetylcholinesterase can be described approximately by [5]:where kon, and are second-order association rate constants at the specified ionic strength I, zero ionic strength, and infinite ionic strength, respectively. zE and zI are the charges of the enzyme and substrate involved in the interaction. The DHL says that the rate constant (in an electrostatically-steered process) decays exponentially with the increase of the square root of ionic strength, as is observed under some conditions [5-8]. However, because the DHL is based on an excess free energy described by the linearized Poisson-Boltzmann model of an ionic solution, it is assumed that the ionic species involved obey a Boltzmann distribution, i.e. are in an equilibrium state. The contributions of solute-solute interactions to the excess free energy are ignored in the theory. Moreover, in diffusion-influenced reactions, the substrate distribution is not in an equilibrium state. Therefore, the DHL only applies for low ionic strengths, and very dilute substrate concentrations. However, in real biological systems, the substrate concentration can be quite high; e.g., the acetylcholine concentration can reach about 300 mM when released from vesicles in synapses [9].The finite concentration effect was recently studied using Brownian dynamics simulation [10], and later theoretical work was done for the condition of weak substrate-substrate interaction or low substrate density [11]. Both works are