Effect of solvent on collective motions in globular protein

Two molecular dynamics simulations on bovine pancreatic trypsin inhibitor (BPTI), have been made, one in vacuum, the other in water, in order to assess the effect of the solvent water on collective motions. Principal component analysis has been performed to determine collective modes, the principal components, which are assumed to behave as effectively independent harmonic oscillators. Projection of the protein's motion in water onto the plane defined by the first two principal components shows a clustering effect in the trajectory, absent in the vacuum trajectory. This is thought to be due to many local minima in the free energy surface caused by solute-solvent interactions. In order to assess the viscous effect of the solvent, friction coefficients for the principal components were determined by analyzing their velocity correlation functions in terms of the Langevin equation for an independent damped oscillator. Consistent with this analysis is that all modes have friction coefficients centered on the value of 47 cm-1 in a range of +/- 10 cm-1. With this friction coefficient, all modes of effective frequencies below 23.5 cm-1 display overdamped motion. By assuming the harmonic approximation for the conformational energy surface for BPTI in vacuum to be valid for BPTI in water, and treating each mode as an independent damped oscillator with a friction coefficient of 47 cm-1, the shift to higher frequencies in the water spectrum relative to the vacuum spectrum could be almost exactly reproduced, indicating this shift is due solely to the viscous effect of the solvent. By analyzing the time correlation functions of the first four principal components it is found that they can be very well described as independent damped oscillators each with a friction coefficient of 47 cm-1.