On the Rate Distribution Analysis of Kinetic Data Using the Maximum Entropy Method:  Applications to Myoglobin Relaxation on the Nanosecond and Femtosecond Timescales

We discuss the application of the maximum entropy method (MEM) to the extraction of rate distributions from kinetics experiments on the nanosecond to femtosecond time scale. We first present simulations to show the effects of data truncation (typical of nanosecond experiments) on rate distributions recovered by MEM. The stretched exponential decay is considered as an example to demonstrate that if the true distribution of rates for the underlying process includes faster time scales than are contained within the experimental data set, MEM can introduce unwarranted features that extend into the slower regions of rate space. This observation has relevance to the application of MEM to obtain rate distributions from kinetic experiments involving the relaxation of complex molecules like proteins, where features in the distribution are sometimes interpreted as static distributions of protein conformational substates. As an experimental example, we present an MEM analysis of the temperature dependence of the geminate rebinding kinetics of carbonmonoxy myoglobin near room temperature and find a barrier height of 18 kJ/mol. We also consider the application of MEM to ultrafast pump−probe transient absorption data, where one needs to take into account the possibility of nonmonotonicity in the kinetics and the finite pulse autocorrelation width that effectively convolves into the observed material responses. The MEM analyses of the femtosecond photophysics of Mb and MbNO, monitored at several wavelengths in the visible region, are presented as examples.