Mean first passage time analysis reveals rate-limiting steps, parallel pathways and dead ends in a simple model of protein folding

Mean first passage time analysis reveals rate-limiting steps, parallel pathways and dead ends in a simple model of protein folding Abstract. – We have analyzed dynamics on the complex free energy landscape of protein folding in the FOLD-X model, by calculating for each state of the system the mean first passage time to the folded state. The resulting kinetic map of the folding process shows that it proceeds in jumps between well-defined, local free energy minima. Closer analysis of the different local minima allows us to reveal secondary, parallel pathways as well as dead ends. Proteins are polymers with several hundred degrees of freedom, so it is natural to think of protein folding as (diffusive) motion on a complex potential energy surface. This landscape picture has become popular in the wider protein folding community during the last decade [1, 2], and clearly invites the question of the nature of the surface: ruggedness, presence of kinetic traps, funnels etc. One problem with answering such questions is that the concept of folding rate, used to describe simple two-state kinetics, can not be generalized to a property that is defined for each configuration of the protein, so it is not useful for describing local kinetics. In this Letter, we use the inverse rate, the mean first passage time (MFPT) which can be calculated for each configuration [3], to analyze the kinetics of folding. Our results clearly reveal kinetic barriers that can not be predicted from the one-dimensional projection of the free energy landscape, and allow us to construct an improved reaction coordinate. Workable, detailed models of protein folding energetics and kinetics do not exist. Instead, we work with the FOLD-X model [4], which is rather simplified, but takes experimental knowledge into account. FOLD-X and similar models [5, 6, 7] are based on the observation that the folding rate of small proteins is correlated with the entropy cost of ordering the chain in a near-native geometry, implying that this happens before the transition state. Non-native interactions are hereby rendered less likely, and the models only consider interactions present