Model for solvent viscosity effect on enzymatic reactions

Abstract

Why reaction rate constants for enzymatic reactions are typically inversely proportional to fractional power exponents of solvent viscosity remains to be already a thirty years old puzzle. Available interpretations of the phenomenon have not led to consensus among researches about its origin. They invoke to either a modification of 1. the conventional Kramers' theory or that of 2. the Stokes law. We show that there is an alternative interpretation of the phenomenon at which neither of these modifications is in fact indispensable. Basing on an analogy from the theory of adsorption on heterogeneous surfaces we reconcile 1. and 2. with the experimentally observable dependence. We assume that an enzyme solution in solvent with or without cosolvent molecules is an ensemble of samples with different values of the viscosity for the movement of the system along the reaction coordinate. We assume that this viscosity consists of the contribution with the weight q from cosolvent molecules and that with the weight 1− q from protein matrix and solvent molecules. We introduce heterogeneity in our system with the help of a distribution over the weight q. The function of the distribution is a unique characteristic of the solution of enzymes (type of the enzyme, cosolvent molecular weight, pH, temperature, etc.). We verify the obtained solution of the integral equation for the unknown function of the distribution by direct substitution. We conclude that even at linear relationship between the solvent viscosity and that for the movement of the system along the reaction coordinate our approach enables us to obtain the required dependence. All parameters of the model are related to experimentally observable values. The meaning of fractional exponents appears to be the characteristic for the behavior of the distribution with the variation of the weight q. Our approach yields the existence of the limit value for the fractional power exponent with the decrease of cosolvent molecular weight that is in agreement experimental data known from the literature. This limit value is determined by the properties of the protein structure and thus is a unique characteristic of the type of the enzyme only rather than that of the solution. General formalism is exemplified by the analysis of literature experimental data for oxygen escape from hemerythin.

Direct enzymatic esterification of cotton and Avicel with wild-type and engineered cutinases

“…Different dielectric constants could explain different abilities to recognize cellulose, since solvent polarity affects the strength of noncovalent interactions either the ones involved in CBM N1 binding (Aquino et al 2002) or in the structure stability of CBM N1, which has a relatively low maximum stability compared to other single-domain globular proteins (Creagh et al 1998). The factor viscosity would work against the binding in vegetable oil (Sitnitsky 2010) but given the duration of the experiment and the mechanical agitation, viscosity may play a minor role.…”

The effect of viscosity-increasing agents on ATP synthesis in chloroplast thylakoids

“…In fact, the observed rate of the ATP hydrolysis corresponded to the rate of the action of the enzyme (25-27 turnovers per s), while ATP synthesis is provided by the rate of 200-280 rps and could be even 400-600 rps [16]. It is logical to assume that the limiting stage in the case of the relatively slow Ca 2+ dependent hydrolysis is the inhibition of conformational changes of the enzyme during catalysis due to the increase in the intramolec ular friction [4].…”

“…This can be recorded experimentally by inhibi tion of the activity of a particular enzyme in the presence of viscosity increasing reagents. On the other hand, the increase in the viscosity can influence the processes by the mechanism of intramolecular fric tion, i.e., can affect the enzyme itself by slowing the conformational transitions in its active center [4].…”

Prospects of Using Biocatalysis for the Synthesis and Modification of Polymers

“…These factors limit the maximum molecular weight of the polymer obtained by enzymatic polymerization under the conditions of a pure monomer melt or its solution in a particular solvent, whereas an increase in temperature leads to inactivation of the biocatalyst. In addition, with an increased viscosity, the activity of the enzyme and the rate of polymer synthesis decrease [ 220 , 221 ].…”