ABSTRACT
CONTENTS 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
18.1.1 Biomolecular Simulations and Enhanced Conformation Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
18.1.2 AQualitative Picture of the Conformational Energy Landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
18.1.3 Objectives and Basic Strategies for Enhanced Conformation Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
18.2 Using Collective Coordinates for Enhanced Conformation Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 18.2.1 Collective Coordinate Descriptions of Protein Dynamics . . . 370 18.2.2 Enhanced Sampling Methods Employing Collective
Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 18.3 The Amplified Collective Motion Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
18.3.1 The Weak Coupling Method for Constant Temperature MD Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
18.3.2 The ACM Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 18.3.3 Using ANM to Guide Atomic Simulations in the ACM
Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 18.3.4 The Amplified Collective Motion-Assisted Minimum
Escaping (ACM-AME) Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 18.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
18.4.1 Interdomain Motions of Bacteriophage T4 Lysozyme. . . . . . . . 378 18.4.2 Folding of an S-Peptide Analog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 18.4.3 ACM-AME Sampling of Peptide Conformations . . . . . . . . . . . . . 383
18.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
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18.1.1 Biomolecular Simulations and Enhanced Conformation Sampling
The atomic simulation of biomacromolecular systems has become an indispensable tool in structural biology [1]. In general, such simulations involve solving the Newton’s equations of motion:
d⇀xi dt
= ⇀vi,
d⇀v dt
= − ⇀∇ iV(⇀x1,⇀x2, . . . ,⇀xNa)
mi , i = 1, . . . ,Na
(18.1)
where {⇀xi, i = 1, . . . ,Na} are the atomic coordinates, Na the number of atoms, and V(⇀x1,
⇀x2, . . . , ⇀xNa) the potential energy function. As a result, we
obtain the trajectory of the system, {⇀xi(t), i = 1, . . . ,Na}, for a period of time t = [0, ttot]. For any specific biological question, it is well known that the adequateness
of this tool persistently relies on two issues (1) whether the potential energy function V(⇀x1,
⇀x2, . . . , ⇀xNa) is of appropriate accuracy for the question, and
(2) whether the parts of the conformational space relevant to the question can be sufficiently sampled within the time period t = [0, ttot], so that reliable ensemble averages can be obtained. The above two issues are closely related: more detailed potential energy
functions (hopefully with higher accuracy) usually require more expensive computations for each energy and energy derivative evaluation of a single conformation, resulting in shorter ttot or, equivalently, more restricted sampling in the conformational space given the same amount of computation. Thus, depending on the problem at hand, we frequently need to trade accuracy for efficiency, or vice versa. During the last few decades, tremendous progresses have been made to
addressboth themodel accuracyandsamplingefficiency issues in atomic simulations of protein dynamics. Some of the techniques have been developed for specific purposes, while others with a general purpose that atomic simulations employing them can address problems of wider range and with more biological significance. Among them, techniques achieving enhanced conformational sampling have found wide applications.
