ABSTRACT
CONTENTS 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 17.2 Extended Sampling Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
17.2.1 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 17.2.2 Constraint Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 17.2.3 Conformational Flooding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 17.2.4 Principal Component Restraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
17.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 17.3.1 Characterization of the Free Energy Surface Around the
Native Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 17.3.2 Rapid Conformational Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 17.3.3 Large Conformational Motions: Allosteric Transitions,
Unfolding, Folding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 17.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
Correlated motions in biological macromolecules provide a key to understanding and regulation of function. For example, binding to proteins of small molecules [1] as well as of other macromolecules [2] frequently occurs via structural rearrangements accomplished by concerted displacements of several structural elements. Thus, dynamic cross-correlations between distant sites were shown to have important implications for the design of protease inhibitors [3]. Establishing a consistent framework connecting structure, energy landscape, dynamics, and function, however, is still a challenge [4, 5]. Experiments do not offer direct access to atomic description of correlated
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motion, and the experimental data need to be interpreted in the framework of an appropriate model [6-9]. The determination of correlated motions by computational means is more straightforward. They can be predicted from one representative structure using a description of intramolecular interaction at different levels of detail (normal mode analysis, Gaussian network model) [10-14] or deduced from an ensemble of structures using multivariate statistics [7,15-19].Moleculardynamics (MD) simulation is onemeansof generating ensembles. However, large-scale correlated motions, in principle, amenable to simulation, pose a sampling problem [4,20], since the amplitude of significant motions is large, while the energy landscape is still rugged. This results in slow timescales of motion along these directions in conformational space. Extrapolation of motions along collective coordinates obtained from nor-
mal mode or simplified normal mode calculations are very instructive, and examples can be found elsewhere in this book. The most important collective coordinates are in many cases astonishingly stable and similar results can be obtained with different methods or approximations. That the directions of the slowest frequency normal mode (obtained at 0 K) should be similar to those obtained from principal component analysis of MD trajectories at nonzero temperature canbynomeansbe taken for granted, since themolecule in an MD trajectory does sample the potential energy surface close to a local minimum, which is explored by normal mode calculations (see Figure 17.1). The simple extrapolation of motion along normal modes or principal components of motion poses the additional problem that the resulting structures are necessarily distorted and hence need to be minimized. An in-detail study of the energetic landscape of the region around thenative structure or ofmajor structural transition is therefore difficult to achieve. Schematically, one can imagine the energy surface in the direction of a low
frequencymode as illustrated in Figure 17.1, being essentially flat in thenative basin, with many minima and subminima.
