Rate processes for conformational dynamics controlled by passage through fluctuating geometrical bottlenecks are studied using a path integral formalism. When the fluctuations of the bottlenecks relax exponentially, we recover Zwanzig's previous results obtained using a diffusion equation approach. The kinetic rate is inversely proportional to the viscosity from the solvents. For the case where the bottleneck relaxes according to a stretched exponential (Kohlrausch-Williams-Watts ) law (we use its Fourier transform which is approximately a Cole-Davidson law), one still obtains exponential kinetics at long times with an effective rate constant. This rate coeffkient is inversely proportional to a fractional power of viscosity from the solvents. As in the exponential case, the survival probability follows a non-exponential behaviour for short times. The statistics of the kinetic rates for simple exponential relaxing solvents and complex non-exponential relaxing solvents are also compared and discussed.

Statistics and dynamics of solvent controlled conformation dynamics and reactions

248th National Meeting (2014)

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