Molecular theory of the helix-coli transition in polyamino acids. II. Numerical evaluation of s and sigma for polyglycine and poly-L-alaine in the absence (for s and sigma) and presence (for sigma) of solvent

The effect of epigenetic modifications on the secondary structures and possible binding positions of the N-terminal tail of histone H3 in the nucleosome: a computational study

The roles of histone tails as substrates for reversible chemical modifications and dynamic cognate surfaces for the binding of regulatory proteins are well established. Despite these crucial roles, experimentally derived knowledge of the structure and possible binding sites of histone tails in chromatin is limited. In this study, we utilized molecular dynamics of isolated histone H3 N-terminal peptides to investigate its structure as a function of post-translational modifications that are known to be associated with defined chromatin states. We observed a structural preference for α-helices in isoforms associated with an inactive chromatin state, while isoforms associated with active chromatin states lacked α-helical content. The physicochemical effect of the post-translational modifications was highlighted by the interaction of arginine side-chains with the phosphorylated serine residues in the inactive isoform. We also showed that the isoforms exhibit different tail lengths, and, using molecular docking of the first 15 N-terminal residues of an H3 isoform, identified potential binding sites between the superhelical gyres on the octamer surface, close to the site of DNA entry/exit in the nucleosome. We discuss the possible functional role of the binding of the H3 tail within the nucleosome on both nucleosome and chromatin structure and stability.

My 65 years in protein chemistry

This is a tour of a physical chemist through 65 years of protein chemistry from the time when emphasis was placed on the determination of the size and shape of the protein molecule as a colloidal particle, with an early breakthrough by James Sumner, followed by Linus Pauling and Fred Sanger, that a protein was a real molecule, albeit a macromolecule. It deals with the recognition of the nature and importance of hydrogen bonds and hydrophobic interactions in determining the structure, properties, and biological function of proteins until the present acquisition of an understanding of the structure, thermodynamics, and folding pathways from a linear array of amino acids to a biological entity. Along the way, with a combination of experiment and theoretical interpretation, a mechanism was elucidated for the thrombin-induced conversion of fibrinogen to a fibrin blood clot and for the oxidative-folding pathways of ribonuclease A. Before the atomic structure of a protein molecule was determined by x-ray diffraction or nuclear magnetic resonance spectroscopy, experimental studies of the fundamental interactions underlying protein structure led to several distance constraints which motivated the theoretical approach to determine protein structure, and culminated in the Empirical Conformational Energy Program for Peptides (ECEPP), an all-atom force field, with which the structures of fibrous collagen-like proteins and the 46-residue globular staphylococcal protein A were determined. To undertake the study of larger globular proteins, a physics-based coarse-grained UNited-RESidue (UNRES) force field was developed, and applied to the protein-folding problem in terms of structure, thermodynamics, dynamics, and folding pathways. Initially, single-chain and, ultimately, multiple-chain proteins were examined, and the methodology was extended to protein-protein interactions and to nucleic acids and to protein-nucleic acid interactions. The ultimate results led to an understanding of a variety of biological processes underlying natural and disease phenomena.

Are Peptides Good Two-State Folders?

The folding kinetics of proteins is frequently single-exponential, as basins of folded and unfolded conformations are well separated by a high barrier. However, for relatively short peptides, a two-state character of folding is rather the exception than the rule. In this work, we use a Zwanzig-type model of protein conformational dynamics to study the dependence of folding kinetics on the protein chain length, M. The analysis is focused on the gap in the eigenvalue spectrum of the rate matrix that describes the protein's conformational dynamics. When there is a large gap between the two smallest in magnitude nonzero eigenvalues, the corresponding relaxation times have qualitatively different physical interpretations. The longest of these two times characterizes the interbasin equilibration (i.e., folding), whereas the second time characterizes the intrabasin relaxation. We derive approximate analytical solutions for the two eigenvalues that show how they depend on M. From these solutions, we infer that there is a large gap between the two, and thus, the kinetics is essentially single-exponential when M is large enough such that 2(M+1) is much larger than M(2).

From helix-coil transitions to protein folding

An evolution of procedures to simulate protein structure and folding pathways is described. From an initial focus on the helix-coil transition and on hydrogen-bonding and hydrophobic interactions, our original attempts to determine protein structure and folding pathways were based on an experimental approach. Experiments on the oxidative folding of reduced bovine pancreatic ribonuclease A (RNase A) led to a mechanism by which the molecule folded to the native structure by a minimum of four different pathways. The experiments with RNase A were followed by development of a molecular mechanics approach, first, making use of global optimization procedures and then with molecular dynamics (MD), evolving from an all-atom to a united-residue model. This hierarchical MD approach facilitated probing of the folding trajectory to longer time scales than with all-atom MD, and hence led to the determination of complete folding trajectories, thus far for a protein containing as many as 75 amino acid residues. With increasing refinement of the computational procedures, the computed results are coming closer to experimental observations, providing an understanding as to how physics directs the folding process.

Helices and Sheets in vacuo

The structures and properties of unsolvated peptides large enough to possess secondary structure have been examined by experiments and simulations. Some of the factors that stabilize unsolvated helices and sheets have been identified. The charge, in particular, plays a critical role in stabilizing alpha-helices and destabilizing beta-sheets. Some helices are much more stable in vacuum than in aqueous solution. Factors like helix propensity, context, and the incorporation of specific stabilizing interactions have been examined. The helix propensities in vacuum differ from those found in solution. Studies of the hydration of unsolvated peptides can be performed one water molecule at a time. The first few water molecules only bind weakly to unsolvated peptides, and they bind much more strongly to some conformations than to others. The most favorable binding locations are not the protonation sites, but clefts or pockets where a water molecule can establish a network of hydrogen bonds. Non-covalent interactions between secondary structure elements leads to the formation of tertiary structure. Helical peptides assemble into complexes with a variety of intriguing structures. The intramolecular coupling of helices to make antiparallel coiled-coil geometries has also been investigated with model peptides.

Helix-coil transitions re-visited

The thermally-induced helix-coil transition in polyamino acids is a good model for determining the helix-forming propensities of amino acids but not for the two-state folding/unfolding transition in globular proteins. The equilibrium and kinetic treatments of the helix-coil transition are summarized here together with a description of applications to various types of homopolymers and copolymers. Attention is then focused on the helix-coil transition in poly-L-alanine as an example of a non-polar polyamino acid. To render such a non-polar polymer water soluble, it is necessary to introduce polar amino acids such as lysines, but care must be taken as to the location of such polar residues. If they are attached as end groups, as in a triblock copolymer, they do not perturb the helix-forming tendency of the central poly-L-alanine block significantly, but if they are introduced within the sequence of alanine residues, then the hydration properties of the lysines dominate the behavior of the resulting copolymer, thereby leading to erroneous values of the parameters characterizing the helix-forming tendency of the alanines. Neutral but polar residues, such as glutamines, also exhibit hydration-dominating properties but less so than charged lysines. Some details of the calculations for an alanine/glutamine copolymer are presented here. It is concluded that random copolymers based on a neutral water-soluble host provide reliable information about the helix-forming tendencies of amino acid residues that are introduced as guests among such neutral host residues.

Evolution of physics-based methodology for exploring the conformational energy landscape of proteins

The evolution of our physics-based computational methods for determining protein conformation without the introduction of secondary-structure predictions, homology modeling, threading, or fragment coupling is described. Initial use of a hard-sphere potential captured much of the structural properties of polypeptide chains, and subsequent more refined force fields, together with efficient methods of global optimization provide indications that progress is being made toward an understanding of the interresidue interactions that underlie protein folding.

The low-temperature heat capacity of solid proteins

Several harmonic models of protein fluctuations are used to calculate the heat capacity. They get the spectral density of conformational modes from inelastic neutron scattering, normal mode calculations, or macroscopic elasticity (Debye model). It is assumed that the low-frequency spectral density depends only weakly on temperature and protein species. The Debye model predicts temperatures below which modes are primarily in their ground states: 10 and 80 K for the lattice and conformational modes, respectively. The models differ most below 100 K. The mode calculations yield the most accurate predictions, though all three models are within twofold of the data. The heat capacity has the power law form aTb for T less than 30 K. The experimental b's of proteins are 1.6-1.8, and the theoretical, 1.1-1.3. One possible explanation for the discrepancy is the occurrence of transitions between discrete conformations. All of the models approach the measured data in the range 100-200 K. They are very similar above 200 K, where the heat capacity includes significant contributions from bond stretching and bending. This masks the possible anharmonic behavior of the conformational modes. Hydration substantially increases the heat capacity above 200 K. This effect seems to be a consequence of conformational transitions that have higher energy than the ones seen with low hydration. The analysis also predicts that denaturation with constant hydration produces a negligible increase of heat capacity. The larger increment in solution arises from the different hydration of the folded and unfolded states, and is responsible for the existence of cold denaturation. This phenomenon is thus predicted not to occur when the hydration is constant.

Protein folding

This review describes recent advances in studies on the stabilities of the three-dimensional structures of proteins and on the processes leading to the formation of these structures. The term ‘protein folding’ will be used here to denote the process of the conversion of an open polypeptide chain into the unique three-dimensional conformation of the native protein. Experimental and theoretical aspects of protein folding have been reviewed by anfinsen & Scheraga (1975). In the present article, we emphasize advances made since the writing of that review, together with a brief summary of the background of recent studies.