Publisher Summary The vibrational spectrum of a molecule is determined by its three-dimensional structure and its vibrational force field. An analysis of this (usually infrared (IR) and Raman) spectrum can therefore provide information on the structure and on intramolecular and intermolecular interactions. The more probing the analysis, the more detailed is the information that can be obtained. Detailed analyses of the vibrational spectra of macromolecules, however, have provided a deeper understanding of structure and interactions in these systems. An important advance in this direction for proteins came with the determination of the normal modes of vibration of the peptide group in N-methylacetamide, and the characterization of several specific amide vibrations in polypeptide systems. Extensive use has been made of spectra-structure correlations based on some of these amide modes, including attempts to determine secondary structure composition in proteins. Polypeptide molecules exhibit many more vibrational frequencies than the amide modes. Over the years, some normal-mode calculations have provided greater insight into the spectra of particular molecules. However, these have often been based on approximate structures or have employed limited force fields. These force fields can now serve as a basis for detailed analyses of spectral and structural questions in other polypeptide molecules. The aim of this chapter is to present these recent developments in the vibrational spectroscopy of peptides, polypeptides, and proteins.

Vibrational spectroscopy and conformation of peptides, polypeptides, and proteins.

1.1. Protein Dynamics and Allostery


1.1.1. Dynamic Equilibrium between Pre-existing Conformations 
The ability of macromolecules to sample an ensemble of conformations has been evident for decades, starting from the statistical mechanical theory and simulations of polymers.1–3 A polymer chain of N atoms enjoys 3N – 6 internal degrees of freedom, which gives rise to infinitely many conformations. Even a simple model of N = 100 atoms where bond lengths and bond angles are fixed, and dihedral angles are restricted to discrete isomeric states—say three states per bond—has access to 3N–3 = 1.9 × 1046 conformations. Proteins, too, are polymers, and have access to ensembles of conformations. The main structural difference between proteins and other chain molecules is that, under physiological conditions, proteins sample a significantly narrower distribution of conformations compared to disordered polymers. Their conformational variations are confined to the neighborhood of a global energy minimum that defines their “native state”.

While the native state has been traditionally viewed as a “unique structure” selected or encoded by the particular amino acid sequence, it is now established by theory, computations, and experiments, after the work of pioneering scientists in the field,4–15 that the native state actually represents an ensemble of microstates: these microstates maintain the overall “fold” and usually share common secondary structure, but they differ in their detailed atomic coordinates. Differences are manifested by variations in bond lengths, bond angles, dihedral angles, loop conformations, substructure packing, or even entire domain or subunit positions and orientations.

Importantly, these microstates are not static: there is a dynamic equilibrium which allows for continual interconversions between them while maintaining their probability distribution. These “jigglings and wigglings of atoms” as expressed by Feynman,16 and clearly observed in molecular dynamics (MD) simulations, were originally viewed as random events, or stochastic properties, hardly relevant to biological function. They essentially account for local relaxation phenomena in the nanoseconds regime, which may facilitate, for example, the diffusion of oxygen into the heme cavity of myoglobin17 or the permeation of ions across selectivity filters in ion channels.18–20 However, recent studies indicate that these thermal fluctuations may not only passively facilitate but also actively drive concerted domain movements and/or allosteric interactions, such as those required for substrate binding, ion channel gating, or catalytic function.15,21–34 Figure 1 provides an overview of the broad range of equilibrium motions accessible under native state conditions, ranging from bond length vibrations, of the order of femtoseconds, to coupled movements of multimeric substructures, of the order of milliseconds or seconds.



Figure 1

Equilibrium motions of proteins. Motions accessible near native state conditions range from femtoseconds (bond length vibrations) to milliseconds or slower (concerted movements of multiple subunits; passages between equilibrium substates). X-ray crystallographic ...






1.1.2. Functional Significance of Collective Motions 
In the last two decades, there has been a surge in the number of studies based on principal components analysis (PCA)36 of biomolecular structures and dynamics. These studies have proven useful in unraveling the collective modes, and in particular those at the low frequency end of the mode spectrum, that underlie the equilibrium dynamics of proteins.37 Normal mode analysis (NMA) of equilibrium structures,38,39 essential dynamics analysis (EDA) of the covariance matrices retrieved from MD runs,40 and singular value decomposition (SVD) of MD or Monte Carlo (MC) trajectories41–43 all fall in this category of PCA-based methods. Recently, a server has been developed to efficiently perform such calculations using a variety of input structures.44

PCA-based studies provide increasing support to the view that the apparently random fluctuations of proteins under native state conditions conceal contributions from highly cooperative movements (e.g., concerted opening and closing of domains) that are directly relevant to biological function. Functional movements indeed involve passages between collections of microstates or substates that coexist in a dynamic equilibrium (Figure 2). The most cooperative motions usually occur at the low frequency end of the mode spectrum. These modes engage large substructures, if not the entire structure, hence their designation as global or essential modes. They are intrinsically accessible to biomolecules, arising solely from structure. In a sense, in the same way as sequence encodes structure, structure encodes the equilibrium dynamics. We refer to these global movements that are collectively encoded by the 3-dimensional (3D) structure as intrinsic motions of the examined protein, intrinsic to the protein fold or topology of native contacts. Biomolecular structures conceivably evolved to favor the global modes that help them achieve their biological or allosteric functions.21 Briefly, the emerging paradigm is structure-encodes-dynamics-encodes-function, and an evolutionary pressure originating from functional dynamics requirements may have selected the relatively small space of functional structures.



Figure 2

Energy profile of the native state modeled at different resolutions. N denotes the native state, modeled at a coarse-grained scale as a single energy minimum. A more detailed examination of the structure and energetics reveals two or more substates (S1, ...



The predisposition of proteins to undergo functional changes in structure is now supported by numerous experimental and computational studies, and an increasing amount of data demonstrates that allosteric responses are driven by intrinsically accessible motions.15,23,24,45–51 These studies have brought a new understanding to the role of collective dynamics in protein functions, demonstrating in particular how the functions of membrane proteins such as signal transduction, pore opening, ion gating, or substrate translocation are enabled by the cooperative movements of symmetrically arranged subunits. These findings are in support of the original Monod–Wyman–Changeux (MWC) view of allosteric effects,52,53 the main tenets of which are predisposition of the structure to access alternative conformations via cooperative changes in structure (simultaneously engaging all subunits) and selection from this pool of accessible conformation to achieve biological function in the presence of ligand/substrate binding. Recent findings on the relevance of global modes to functional dynamics are presented below for select, widely studied membrane proteins. The goal here is to review NMA-based computational methods and their applications to membrane proteins. We will also discuss recent developments for improving the methodology and its implementation in structure refinement and drug discovery methods.

/pdf/normal-mode-analysis-of-biomolecular-structures-functional-3ewv6tb33x.pdf

Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins

The conformational space of the 10-55 fragment of the B-domain of staphylococcal protein A has been investigated by using the electrostatically driven Monte Carlo (EDMC) method. The ECEPP/3 (empirical conformational energy program for peptides) force-field plus two different continuum solvation models, namely SRFOPT (Solvent Radii Fixed with atomic solvation parameters OPTimized) and OONS (Ooi, Oobatake, Nemethy, and Scheraga solvation model), were used to describe the conformational energy of the chain. After an exhaustive search, starting from two different random conformations, three of four runs led to native-like conformations. Boltzmann-averaged root-mean-square deviations (RMSD) for all of the backbone heavy atoms with respect to the native structure of 3.35 A and 4.54 A were obtained with SRFOPT and OONS, respectively. These results show that the protein-folding problem can be solved at the atomic detail level by an ab initio procedure, starting from random conformations, with no knowledge except the amino acid sequence. To our knowledge, the results reported here correspond to the largest protein ever folded from a random conformation by an initial-value formulation with a full atomic potential, without resort to knowledge-based information.

Atomically detailed folding simulation of the B domain of staphylococcal protein A from random structures

Vibrational analysis of the structure of gramicidin A. I. Normal mode analysis.

Along the allostery stream: Recent advances in computational methods for allosteric drug discovery

Normal mode calculations have been carried out on three low-energy structures of gramicidin S obtained from conformational energy calculations. When the results on the amide modes are compared with observed bands in the infrared and Raman spectra of crystalline gramicidin S and its N-deuterated derivative, one of the structures is clearly disfavored. Of the other two, one is slightly favored, and it corresponds to the lowestenergy structure obtained from the energy calculations. Spectra from solutions in DMSO and CH3 OH suggest that the molecular conformation is essentially retained in these solvents.

/pdf/vibrational-analysis-of-peptides-polypeptides-and-proteins-5dzmi47tsv.pdf

Vibrational analysis of peptides, polypeptides and proteins XXVII. Structure of gramicidin S from normal mode analyses of low-energy conformations.

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Vibrational analysis of peptides, polypeptides and proteins XXVII. Structure of gramicidin S from normal mode analyses of low-energy conformations.