Continuous time Markov models of the kinetics of protein folding and fluorescent protein blinking

We develop continuous time Markov models for a pair of biophysical problems. The first problem is the kinetic mechanism of protein folding. We develop a model that aims to explain the nine-order-of-magnitude dependence of folding rates on protein size and the predominance of two-state folding kinetics. In our model, secondary structures, which are intrinsically unstable in isolation, are stabilized and directed towards the native state by cooperative interactions with neighboring secondary structures along the folding routes. The model fits folding-rate data on a set of 82 proteins and can be applied to estimate the distribution of intrinsic folding rates for proteins in the proteomes of cells. The second problem is the analysis of fluorescent protein blinking in super-resolution microscopy. We develop an aggregated continuous time Markov model for quantifying the fluorescent proteins in a diffraction-limited volume. Using a maximum-likelihood approach, we apply the model to study the in vitro photophysics of the protein Dendra2 and to quantify the number of FliM molecules in bacterial flagellar motors. The end goal of the method is to count proteins in molecular assemblies with single molecule precision