From Protein Structure to Function with Bioinformatics.pdf

9 Protein Dynamics: From Structure to Function 233assumption of a harmonic potential. In fact, PCA can be used to study the degreeof anharmonicity in the molecular dynamics of the simulated system. For proteins,it was shown that at physiological temperatures, especially the majormodes of collective fluctuation that are frequently functionally relevant, aredominated by anharmonic fluctuations (Amadei et al. 1993; Hayward et al. 1995).9.3 Collective Coordinate Sampling AlgorithmsAnalyzing MD simulations in terms of collective coordinates (obtained e.g. byPCA or NMA) reveals that only a small subset of the total number of degreesof freedom dominates the molecular dynamics of biomolecules. As proteinfunction could in many cases been linked to these essential subspace modes(e.g. Brooks and Karplus 1983; Gō et al. 1983; Levitt et al. 1983), the dynamicswithin this low-dimensional space was termed “essential dynamics” (ED).This not only aids the analysis and interpretation of MD trajectories but alsoopens the way to enhanced sampling algorithms that search the essential subspacein either a systematic or exploratory fashion (Grubmüller 1995; Amadeiet al. 1996).9.3.1 Essential DynamicsThe first attempts in this direction were aimed at a simulation scheme inwhich the equations of motion were solely integrated along a selection of primaryprincipal modes, thereby drastically reducing the number of degrees offreedom (Amadei et al. 1993). However, these attempts proved problematicbecause of non-trivial couplings between high- and low-amplitude modes,even though after diagonalization the modes are linearly independent (orthogonal).Therefore, instead, a series of techniques has prevailed that take intoaccount the full-dimensional simulation system and enhance the motion alonga selection of principal modes. The most common of these techniques areconformational flooding (Grubmüller 1995) and ED sampling (Amadei et al.1996; de Groot et al. 1996a, b). In conformational flooding, an additionalpotential energy term that stimulates the simulated system to explore newregions of phase space is introduced on a selection of principal modes,whereas in ED sampling a similar goal is achieved by geometrical constraintsalong a selection of principal modes. With these techniques a sampling efficiencyenhancement of up to an order of magnitude can be achieved, providedthat a reasonable approximation of the principal modes has been obtainedfrom a conventional simulation. However, due to the applied structural orenergetic bias on the system, the ensemble generated by ED sampling and