Fluctuations of the environment

Our main conclusion is that random fluctuations of the environment can slow down the extinction of genetic variability by up to 10 times in comparison with the absence of fluctuation. The slowing down is brought about when the range of the optimum fluctuation has about the same value as the longterm diffo ence in mean fitness. 

Assuming that the fluctuation of the environment of the initial and final system oscillates like a harmonic oscillator, then the enthalpies are given by (compare with Fig. 6.3)... 

Simulating the Fluctuations of the Environment and Nuclear Quantum Mechanical Effects 11177... 

It is important to clarify here that the description of PT processes by curve crossing formulations is not a new approach nor does it provide new dynamical insight. That is, the view of PT in solutions and proteins as a curve crossing process has been formulated in early realistic simulation studies [1, 2, 42] with and without quantum corrections and the phenomenological formulation of such models has already been introduced even earlier by Kuznetsov and others [47]. Furthermore, the fact that the fluctuations of the environment in enzymes and solution modulate the activation barriers of PT reactions has been demonstrated in realistic microscopic simulations of Warshel and coworkers [1, 2]. However, as clarified in these works, the time dependence of these fluctuations does not provide a useful way to determine the rate constant. That is, the electrostatic fluctuations of the environment are determined by the corresponding Boltzmann probability and do not represent a dynamical effect. In other words, the rate constant is determined by the inverse of the time it takes the system to produce a reactive trajectory, multiplied by the time it takes such trajectories to move to the TS. The time needed for generation of a reactive trajectory is determined by the corresponding Boltzmann probability, and the actual time it takes the reactive trajectory to reach the transition state (of the order of picoseconds), is more or less constant in different systems. 

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