Solventquality dependent contact formation dynamics in proteins
Abstract
The mean time of contact formation between two ends of a protein chain shows power law dependence with respect to the number of residues, $\tau_{CF} \sim N^{\alpha}$. Fluorescence quenching measurements based on triplettriplet energy transfer show variation in the value of scaling exponent $\alpha$ for different proteinsolvent systems. Here, starting from a nonMarkovian diffusion equation supplemented with an exponential sink term that accounts for the energy transfer reaction between donor and acceptor groups, we calculate the mean time of contact formation using the WilemskiFixman closure approximation. The nonMarkovian diffusionreaction equation includes the effects of solvent quality and hydrodynamic interaction in a meanfield fashion. It shows that the contact formation dynamics is mainly governed by two time scales, the reciprocal of the intrinsic rate of quenching $(k_0^{ET})^{1}$, and the relaxation time $\tau_0 = \eta b^3/k_B T$ of the coarsegrained residue of an effective size $b$ with solvent viscosity $\eta$. In the limit of $k_0^{ET} \tau_0 \ll 1$, the dominating effect of the reactioncontrolled kinetics yields the scaling exponents as $0.89$, $1.47$ and $1.79$ in poor, theta and good solvents respectively. In the opposite limit $k_0^{ET} \tau_0 \gg 1$, the dominating influence of the diffusioncontrolled kinetics results in $\alpha$ as $1.90$, $2.17$, $2.36$ for a freelydraining and $1.31$, $1.77$, $2.06$ for a nonfreelydraining chain in poor, theta and good solvents respectively. In the intermediate limit, $k_0^{ET} \tau_0 \approx 1$, the increase in the number of residues switches the kinetics from reactioncontrolled at low $N$ to diffusioncontrolled at large $N$. These general results suggest that experimental estimates of the scaling exponents reflect solventquality dependence of the mean contact formation time in the reactioncontrolled limit.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 arXiv:
 arXiv:1506.00073
 Bibcode:
 2015arXiv150600073K
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Physics  Biological Physics
 EPrint:
 4 Figures