A coarse-grained model for force-induced protein deformation and kinetics.
Force-induced changes in protein conformation are thought to be responsible for certain cellular responses to mechanical force. Changes in conformation subsequently initiate a biochemical response by alterations in, for example, binding affinity to another protein or enzymatic activity. Here, a model of protein extension under external forcing is created inspired by Kramers' theory for reaction rate kinetics in liquids. The protein is assumed to have two distinct conformational states: a relaxed state, C(1), preferred in the absence of external force, and an extended state, C(2), favored under force application. In the context of mechanotransduction, the extended state is a conformation from which the protein can initiate signaling. Appearance and persistence of C(2) are assumed to lead to transduction of the mechanical signal into a chemical one. The protein energy landscape is represented by two harmonic wells of stiffness kappa(1) and kappa(2), whose minima correspond to conformations C(1) and C(2). First passage time t(f) from C(1) to C(2) is determined from the Fokker-Plank equation employing several different approaches found in the literature. These various approaches exhibit significant differences in behavior as force increases. Although the level of applied force and the energy difference between states largely determine equilibrium, the dominant influence on t(f) is the height of the transition state. Distortions in the energy landscape due to force can also have a significant influence, however, exhibiting a weaker force dependence than exponential as previously reported, approaching a nearly constant value at a level of force that depends on the ratio kappa(1)/kappa(2). Two model systems are used to demonstrate the utility of this approach: a short alpha-helix undergoing a transition between two well-defined states and a simple molecular motor.