Dear Harith,

The attached paper is a good example for your observation, however, the study was done on the effect of viscosity on enzyme catalysis.

Biol Proced Online. 2003; 5: 108–115.

Published online 2003 May 1. doi:  10.1251/bpo52

PMCID: PMC154660

Measuring Solution Viscosity and its Effect on Enzyme Activity

Salvador Uribe2 and José G. Sampedro 1

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Abstract

In proteins, some processes require conformational changes involving structural domain diffusion. Among these processes are protein folding, unfolding and enzyme catalysis. During catalysis some enzymes undergo large conformational changes as they progress through the catalytic cycle. According to Kramers theory, solvent viscosity results in friction against proteins in solution, and this should result in decreased motion, inhibiting catalysis in motile enzymes. Solution viscosity was increased by adding increasing concentrations of glycerol, sucrose and trehalose, resulting in a decrease in the reaction rate of the H+-ATPase from the plasma membrane of Kluyveromyces lactis. A direct correlation was found between viscosity (η) and the inhibition of the maximum rate of catalysis (V max). The protocol used to measure viscosity by means of a falling ball type viscometer is described, together with the determination of enzyme kinetics and the application of Kramers’ equation to evaluate the effect of viscosity on the rate of ATP hydrolysis by the H+-ATPase.

Keywords: Viscosity, Trehalose

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Introduction

In proteins, processes involving conformational change are slowed by medium viscosity (1). The effect of viscosity on the rate of protein-dependent chemical reactions was originally described by Kramers (2). Kramers’ treatment was applied to protein folding and to other protein processes involving structural movements, such as folding or catalysis (3, 4). Following synthesis, proteins acquire a number of different conformations before reaching the “native” form. Likewise, denaturing involves passage through different unfolded states (5). In enzymes, during catalysis or ligand binding conformational changes occur, at least in the active site (6). Furthermore, many enzymes may exhibit widely different structural conformations, distinguishable by protease sensitivity, antibody recognition, circular dichroism or fluorescence (7). Thus, according to Kramers’ theory, enzymes alternating between widely different conformations during catalysis should be inhibited by viscosity (1). One such case is carbon-monoxy-myoglobin embedded in a trehalose glass matrix, where trehalose inhibits the release of carbon monoxide (8).

The E1E2-ATPases undergo large conformational changes during catalysis as they alternate between states E1 and E2 (9). Indeed, states E1 and E2 exhibit different sensitivity to proteases and antibodies (10). Thus, the isolated E1E2, H+-ATPase (EC 3.6.1.35) from Kluyveromyces lactis was chosen to study the inhibitory effects of increasing concentrations of different viscosogenic compounds on the rate of ATP hydrolysis. As predicted by Kramers’ theory (1), at 20°C, trehalose, sucrose or glycerol increased solvent viscosity while inhibiting the H+-ATPase, mainly through a decrease in V max (11). In addition, increasing the temperature resulted in diminished effects viscosity on the V max (11). Here, the method used to measure viscosity, the determination of enzyme kinetics and the application of Kramers’ theory to evaluate the effect of viscosity on enzyme activity are described in detail.

Analysis of enzyme kinetics

Initial velocities of ATP hydrolysis were plotted against the concentration of ATP. The iterative program Microcal Origin 6.0® (Microcal Software Inc. MA) was used to analyse the data by non-linear regression. The Hill equation [eq 2] which describes a cooperative behaviour for enzyme kinetics was used in the fitting of the initial velocity data:

v = V max ·S n / ( S 0.5 n + S n ) [2]

where v is the initial velocity, V max is the maximum velocity, S is the concentration of the varied substrate, S0.5 is the substrate concentration where v = 0.5V max and n is the Hill coefficient which in some cases describes the probable number of active sites.

The Arrhenius relation, normally used in biochemistry, does not contain a term that accounts for the restricting effect of molecular motions by the medium on the rate of a given reaction. In this regard, Kramers’ theory has been used to describe the effect of viscosity on the behavior of protein reactions where conformational changes are involved (1): in a diffusion dependent, enzyme-catalyzed reaction [eq 3], where the substrate binds to the enzyme to yield the product

the rate of product formation (k cat) is inhibited by the friction of the solvent with the protein, i.e. friction increases the activation energy needed to reach the transition state (14). In turn, friction is a function of viscosity η. Thus, the reaction rate constant depends linearly on η as showed in equation [eq 4] as described by Jacob and Schmid (1)

k= η-1 exp (- ΔU/RT) [4]

where k is the rate constant for the reaction (k cat or V max for enzyme catalyzed reactions), η is the macroscopic viscosity of the solvent, R is the gas constant (8.314 J (K mol)-1), T is the absolute temperature and ?U is the free energy barrier imposed by solvent friction. At a fixed temperature, any increase in viscosity would be expected to result in an increase in ΔU. When plotting V max versus η-1 a straight line is obtained which has a slope of 1, indicating that at the given temperature, there is a complete dependence of the rate of reaction on solution viscosity. In cases where friction does not exist, the reaction rate depends solely on the true activation energy and on temperature; thus η is replaced by the time constant (τ) or, as τ=k 0-1, by k 0 -1 (1). To assess whether the catalytic activity of the H+-ATPase is inhibited by viscosity as predicted by Kramers’ relation (1), the V max data, defined as V max0/V max were plotted against the solvent relative viscosity, defined as η/η0. Where V max0 and η0 are respectively the V max and the viscosity in the absence of trehalose and V max and η are the observed values at each trehalose concentration.

Hoping this will be helpful,

Rafik

thank you Rafik Karaman... it looks good research. 

hi,

the problem of diffusion controlled reaction was tackled in several papers as for example:

Begum F, Zhao H, Simon SL. Modeling methyl methacrylate free radical

polymerization: reaction in hydrophilic nanopores. Polymer 2012;53(15):

3238-44.

Begum F, Zhao H, Simon SL. Modeling methyl methacrylate free radical

polymerization: reaction in hydrophobic nanopores. Polymer 2012;53(15):

3261-8.

Martins J, Melo E. Molecular mechanism of lateral diffusion of py10-PC and

free pyrene in fluid DMPC bilayers. Biophys J 2001;80(2):832-40.

Devanne T, Bry A, Raguin N, Sebban M, Palmas P, Audouin L, et al. Radiochemical

ageing of an amine cured epoxy network. Part II: kinetic modeling.

Polymer 2005;46(1):237-41.

Richaud E, Le Gac PY, Verdu JV. Thermooxidative aging of polydicyclopentadiene in glassy state. Polym Degrad Stab 2014;102:95-104.

Dušek K. Diffusion control in the kinetics of cross-linkingOriginal Research Article

Polym Gels Networks 1996;4(5–6):383-404.

regards