On the relative strengths of amide…amide and amide…water hydrogen bonds

Reframing the Protein Folding Problem: Entropy as Organizer

It has been a long-standing conviction that a protein's native fold is selected from a vast number of conformers by the optimal constellation of enthalpically favorable interactions. In marked contrast, this Perspective introduces a different mechanism, one that emphasizes conformational entropy as the principal organizer in protein folding while proposing that the conventional view is incomplete. This mechanism stems from the realization that hydrogen bond satisfaction is a thermodynamic necessity. In particular, a backbone hydrogen bond may add little to the stability of the native state, but a completely unsatisfied backbone hydrogen bond would be dramatically destabilizing, shifting the U(nfolded) ⇌ N(ative) equilibrium far to the left. If even a single backbone polar group is satisfied by solvent when unfolded but buried and unsatisfied when folded, that energy penalty alone, approximately +5 kcal/mol, would rival almost the entire free energy of protein stabilization, typically between -5 and -15 kcal/mol under physiological conditions. Consequently, upon folding, buried backbone polar groups must form hydrogen bonds, and they do so by assembling scaffolds of α-helices and/or strands of β-sheet, the only conformers in which, with rare exception, hydrogen bond donors and acceptors are exactly balanced. In addition, only a few thousand viable scaffold topologies are possible for a typical protein domain. This thermodynamic imperative winnows the folding population by culling conformers with unsatisfied hydrogen bonds, thereby reducing the entropy cost of folding. Importantly, conformational restrictions imposed by backbone···backbone hydrogen bonding in the scaffold are sequence-independent, enabling mutation─and thus evolution─without sacrificing the structure.

Theoretical identification of thermostabilizing amino acid mutations for G-protein-coupled receptors

Thermostabilization of a membrane proteins, especially G-protein-coupled receptors (GPCRs), is often necessary for biochemical applications and pharmaceutical studies involving structure-based drug design. Here we review our theoretical, physics-based method for identifying thermostabilizing amino acid mutations. Its novel aspects are the following: The entropic effect originating from the translational displacement of hydrocarbon groups within the lipid bilayer is treated as a pivotal factor; a reliable measure of thermostability is introduced and a mutation which enlarges the measure to a significant extent is chosen; and all the possible mutations can be examined with moderate computational effort. It was shown that mutating the residue at a position of N_BW = 3.39 (N_BW is the Ballesteros-Weinstein number) to Arg or Lys leads to the stabilization of significantly many different GPCRs of class A in the inactive state. Up to now, we have been successful in stabilizing several GPCRs and newly solving three-dimensional structures for the muscarinic acetylcholine receptor 2 (M2R), prostaglandin E receptor 4 (EP4), and serotonin 2A receptor (5-HT_2AR) using X-ray crystallography. The subjects to be pursued in future studies are also discussed.

A comprehensive study of the molecular vibrations in solid-state benzylic amide [2]catenane

The interpretation of vibrational spectra is often complex but a detailed knowledge of the normal modes responsible for the experimental bands provides valuable information about the molecular structure of the sample. In this work we record and assign in detail the infrared (IR) spectrum of the benzylic amide [2]catenane, a complex molecular solid displaying crimped mechanical bonds like the links of a chain. In spite of the large size of the unit cell, we calculate all the vibrational modes of the catenane crystal using quantum first-principles calculations. The activity of each mode is also evaluated using the Born effective charges approach and a theoretical spectrum is constructed for comparison purposes. We find a remarkable agreement between the calculations and the experimental results without the need to apply any further empirical correction or fitting to the eigenfrequencies. A detailed description in terms of the usual internal coordinates is provided for over 1000 normal modes. This thorough analysis allows us to perform the complete assignment of the spectrum, revealing the nature of the most active modes responsible for the IR features. Finally, we compare the obtained results with those of Raman spectroscopy, studying the effects of the rule of mutual exclusion in vibrational spectroscopy according to the different levels of molecular symmetry embedded in this mechanically interlocked molecular compound.

Universal effects of solvent species on the stabilized structure of a protein

We investigate the effects of solvent specificities on the stability of the native structure (NS) of a protein on the basis of our free-energy function (FEF). We use CPB-bromodomain (CBP-BD) and apoplastocyanin (apoPC) as representatives of the protein universe and water, methanol, ethanol, and cyclohexane as solvents. The NSs of CBP-BD and apoPC consist of 66% α-helices and of 35% β-sheets and 4% α-helices, respectively. In order to assess the structural stability of a given protein immersed in each solvent, we contrast the FEF of its NS against that of a number of artificially created, misfolded decoys possessing the same amino-acid sequence but significantly different topology and α-helix and β-sheet contents. In the FEF, we compute the solvation entropy using the morphometric approach combined with the integral equation theories, and the change in electrostatic (ES) energy upon the folding is obtained by an explicit atomistic but simplified calculation. The ES energy change is represented by the break of protein-solvent hydrogen bonds (HBs), formation of protein intramolecular HBs, and recovery of solvent-solvent HBs. Protein-solvent and solvent-solvent HBs are absent in cyclohexane. We are thus able to separately evaluate the contributions to the structural stability from the entropic and energetic components. We find that for both CBP-BD and apoPC, the energetic component dominates in methanol, ethanol, and cyclohexane, with the most stable structures in these solvents sharing the same characteristics described as an association of α-helices. In particular, those in the two alcohols are identical. In water, the entropic component is as strong as or even stronger than the energetic one, with a large gain of translational, configurational entropy of water becoming crucially important so that the relative contents of α-helix and β-sheet and the content of total secondary structures are carefully selected to achieve sufficiently close packing of side chains. If the energetic component is excluded for a protein in water, the priority is given to closest side-chain packing, giving rise to the formation of a structure with very low α-helix and β-sheet contents. Our analysis, which requires minimal computational effort, can be applied to any protein immersed in any solvent and provides robust predictions that are quite consistent with the experimental observations for proteins in different solvent environments, thus paving the way toward a more detailed understanding of the folding process.

Cryoprotectant Toxicity: Facts, Issues, and Questions

High levels of penetrating cryoprotectants (CPAs) can eliminate ice formation during cryopreservation of cells, tissues, and organs to cryogenic temperatures. But CPAs become increasingly toxic as concentration increases. Many strategies have been attempted to overcome the problem of eliminating ice while minimizing toxicity, such as attempting to optimize cooling and warming rates, or attempting to optimize time of adding individual CPAs during cooling. Because strategies currently used are not adequate, CPA toxicity remains the greatest obstacle to cryopreservation. CPA toxicity stands in the way of cryogenic cryopreservation of human organs, a procedure that has the potential to save many lives. This review attempts to describe what is known about CPA toxicity, theories of CPA toxicity, and strategies to reduce CPA toxicity. Critical analysis and suggestions are also included.

Estimation of Hydrogen-Exchange Protection Factors from MD Simulation Based on Amide Hydrogen Bonding Analysis

Hydrogen exchange (HX) studies have provided critical insight into our understanding of protein folding, structure, and dynamics. More recently, hydrogen exchange mass spectrometry (HX-MS) has become a widely applicable tool for HX studies. The interpretation of the wealth of data generated by HX-MS experiments as well as other HX methods would greatly benefit from the availability of exchange predictions derived from structures or models for comparison with experiment. Most reported computational HX modeling studies have employed solvent-accessible-surface-area based metrics in attempts to interpret HX data on the basis of structures or models. In this study, a computational HX-MS prediction method based on classification of the amide hydrogen bonding modes mimicking the local unfolding model is demonstrated. Analysis of the NH bonding configurations from molecular dynamics (MD) simulation snapshots is used to determine partitioning over bonded and nonbonded NH states and is directly mapped into a protection factor (PF) using a logistics growth function. Predicted PFs are then used for calculating deuteration values of peptides and compared with experimental data. Hydrogen exchange MS data for fatty acid synthase thioesterase (FAS-TE) collected for a range of pHs and temperatures was used for detailed evaluation of the approach. High correlation between prediction and experiment for observable fragment peptides is observed in the FAS-TE and additional benchmarking systems that included various apo/holo proteins for which literature data were available. In addition, it is shown that HX modeling can improve experimental resolution through decomposition of in-exchange curves into rate classes, which correlate with prediction from MD. Successful rate class decompositions provide further evidence that the presented approach captures the underlying physical processes correctly at the single residue level. This assessment is further strengthened in a comparison of residue resolved protection factor predictions for staphylococcal nuclease with NMR data, which was also used to compare prediction performance with other algorithms described in the literature. The demonstrated transferable and scalable MD based HX prediction approach adds significantly to the available tools for HX-MS data interpretation based on available structures and models.

H-Bonding network in fully deuterated N-methylformamide-water mixtures as studied by neutron scattering. Complementarity to X-ray study

In complementarity with X-ray scattering and as extension of our previous publication, neutron scattering measurements are combined to DFT calculation to investigate the structural features of N-methylformamide-water mixtures (NMF-water) for three water molar fractions x w = 0.5 , 0.66 and x w = 0.75 . The recorded data at atmospheric pressure and room temperature are analyzed to yield the structure factor, the molecular form factor and the pair correlation function. Neutron investigations corroborate the X-ray ones and clearly show that liquid order in solutions is well accounted for by a tetramer. In this cluster, an NMF molecule is connected to three water molecules by one N-D···O and two O-D···O hydrogen bonds.

Forces stabilizing proteins

The goal of this article is to summarize what has been learned about the major forces stabilizing proteins since the late 1980s when site-directed mutagenesis became possible. The following conclusions are derived from experimental studies of hydrophobic and hydrogen bonding variants. (1) Based on studies of 138 hydrophobic interaction variants in 11 proteins, burying a -CH2- group on folding contributes 1.1±0.5 kcal/mol to protein stability. (2) The burial of non-polar side chains contributes to protein stability in two ways: first, a term that depends on the removal of the side chains from water and, more importantly, the enhanced London dispersion forces that result from the tight packing in the protein interior. (3) Based on studies of 151 hydrogen bonding variants in 15 proteins, forming a hydrogen bond on folding contributes 1.1±0.8 kcal/mol to protein stability. (4) The contribution of hydrogen bonds to protein stability is strongly context dependent. (5) Hydrogen bonds by side chains and peptide groups make similar contributions to protein stability. (6) Polar group burial can make a favorable contribution to protein stability even if the polar group is not hydrogen bonded. (7) Hydrophobic interactions and hydrogen bonds both make large contributions to protein stability.

Contribution of hydrogen bonds to protein stability

Our goal was to gain a better understanding of the contribution of the burial of polar groups and their hydrogen bonds to the conformational stability of proteins. We measured the change in stability, Δ(ΔG), for a series of hydrogen bonding mutants in four proteins: villin headpiece subdomain (VHP) containing 36 residues, a surface protein from Borrelia burgdorferi (VlsE) containing 341 residues, and two proteins previously studied in our laboratory, ribonucleases Sa (RNase Sa) and T1 (RNase T1). Crystal structures were determined for three of the hydrogen bonding mutants of RNase Sa: S24A, Y51F, and T95A. The structures are very similar to wild type RNase Sa and the hydrogen bonding partners form intermolecular hydrogen bonds to water in all three mutants. We compare our results with previous studies of similar mutants in other proteins and reach the following conclusions. (1) Hydrogen bonds contribute favorably to protein stability. (2) The contribution of hydrogen bonds to protein stability is strongly context dependent. (3) Hydrogen bonds by side chains and peptide groups make similar contributions to protein stability. (4) Polar group burial can make a favorable contribution to protein stability even if the polar groups are not hydrogen bonded. (5) The contribution of hydrogen bonds to protein stability is similar for VHP, a small protein, and VlsE, a large protein.

Role of unsatisfied hydrogen bond acceptors in RNA energetics and specificity

RNA plays essential roles in much of biology. These functions are dictated by structures mediated by hydrogen bonding, stacking, electrostatics, and steric interactions. Roles of unsatisfied hydrogen bond functionalities in these structures are less well understood. Herein, we evaluated the energetic contributions of unsatisfied hydrogen bonding groups by placing chemically modified substituents in select internal positions in RNA helices and conducting thermodynamic studies. We find that unsatisfied carbonyl groups make exceptional contributions to structure formation (approximately 3 kcal/mol in free energy), most likely due to a combination of strain and dehydration effects. Thus, unsatisfied hydrogen bonding groups are likely key determinants in the folding energetics and specificity of many RNA and DNA molecules and may be especially important in tertiary structure interactions.

Modeling of folding and unfolding mechanisms in alanine-based alpha-helical polypeptides

alpha-Helix formation is known to be opposed by the entropy loss due to the folding and favored by the energy of molecular interactions. However, the underlying mechanism of these factors is still being discussed. Here we have used the experimental and calculation data for short alanine-based peptides embedded in water to model the mechanism of helix folding and unfolding and to calculate microscopically the free energy factors of alanine in the frame of helix coil conformational integrals. Classical helix-coil transition theories take into account the interactions in a peptide chain only if the i, i + 3 peptide bond participates in hydrogen bonding. But quantum mechanical calculations showed that interactions of the i, i + 2 peptide bond play an important role in helix folding too. We also included the short-range repulsive interactions due to molecular steric clashes and the end effects due to polar/hydrogen-bonding interactions at the N and C termini. The helix and coil regions of peptide conformational space were defined using an experimental steric criterion for hydrogen bonding. Arginine helix propensity was discussed and estimated. Monte Carlo numerical simulations of thermodynamics and kinetics for the 21 amino acid alpha-helical polypeptide Ac-A5(AAARA)3A-NMe were carried out and found to be in an agreement with the experimental results.

Energetics of protein folding

The energetics of protein folding determine the 3D structure of a folded protein. Knowledge of the energetics is needed to predict the 3D structure from the amino acid sequence or to modify the structure by protein engineering. Recent developments are discussed: major factors are reviewed and auxiliary factors are discussed briefly. Major factors include the hydrophobic factor (burial of non-polar surface area) and van der Waals interactions together with peptide hydrogen bonds and peptide solvation. The long-standing model for the hydrophobic factor (free energy change proportional to buried non-polar surface area) is contrasted with the packing-desolvation model and the approximate nature of the proportionality between free energy and apolar surface area is discussed. Recent energetic studies of forming peptide hydrogen bonds (gas phase) are reviewed together with studies of peptide solvation in solution. Closer agreement is achieved between the 1995 values for protein unfolding enthalpies in vacuum given by Lazaridis-Archontis-Karplus and Makhatadze-Privalov when the solvation enthalpy of the peptide group is taken from electrostatic calculations. Auxiliary factors in folding energetics include salt bridges and side-chain hydrogen bonds, disulfide bridges, and propensities to form alpha-helices and beta-structure. Backbone conformational entropy is a major energetic factor which is discussed only briefly for lack of knowledge.

A backbone-based theory of protein folding

Under physiological conditions, a protein undergoes a spontaneous disorder order transition called "folding." The protein polymer is highly flexible when unfolded but adopts its unique native, three-dimensional structure when folded. Current experimental knowledge comes primarily from thermodynamic measurements in solution or the structures of individual molecules, elucidated by either x-ray crystallography or NMR spectroscopy. From the former, we know the enthalpy, entropy, and free energy differences between the folded and unfolded forms of hundreds of proteins under a variety of solvent/cosolvent conditions. From the latter, we know the structures of approximately 35,000 proteins, which are built on scaffolds of hydrogen-bonded structural elements, alpha-helix and beta-sheet. Anfinsen showed that the amino acid sequence alone is sufficient to determine a protein's structure, but the molecular mechanism responsible for self-assembly remains an open question, probably the most fundamental open question in biochemistry. This perspective is a hybrid: partly review, partly proposal. First, we summarize key ideas regarding protein folding developed over the past half-century and culminating in the current mindset. In this view, the energetics of side-chain interactions dominate the folding process, driving the chain to self-organize under folding conditions. Next, having taken stock, we propose an alternative model that inverts the prevailing side-chain/backbone paradigm. Here, the energetics of backbone hydrogen bonds dominate the folding process, with preorganization in the unfolded state. Then, under folding conditions, the resultant fold is selected from a limited repertoire of structural possibilities, each corresponding to a distinct hydrogen-bonded arrangement of alpha-helices and/or strands of beta-sheet.

Limited validity of group additivity for the folding energetics of the peptide group

The principle of group additivity is a standard feature of analyses of the energetics of protein folding, but it is known that it may not always be valid for the polar peptide group. The neighboring residue effect shows that group additivity is not strictly valid for a heteropeptide. We show here that group additivity fails seriously for peptide groups close to either peptide end, even for a homopeptide that has blocked end groups with no formal charges involved. The failure of group additivity is caused by the electrostatic character of the solvation of peptide polar groups and is illustrated with values of the electrostatic solvation free energy (ESF) calculated by DelPhi. Solvation free energies and enthalpies are known experimentally for monoamides and are often used to model the solvation of peptide groups, but ESF results show that monoamide values are very different from those of peptide groups. A main cause of the difference is that peptide solvation depends on the dipole-dipole interactions made between adjacent peptide groups, which vary with peptide conformation. Ligands that interact with the peptide backbone by an electrostatic mechanism could show a similar peptide end effect, and hydrogen exchange results from the literature confirm that exchange rates are position-dependent close to peptide ends.

Translational-entropy gain of solvent upon protein folding

We show that even in the complete absence of potential energies among the atoms in a protein-aqueous solution system, there is a physical factor that favors the folded state of the protein. It is a gain in the translational entropy (TE) of water originating from the translational movement of water molecules. An elaborate statistical-mechanical theory is employed to analyze the TE of water in which a protein or peptide with a prescribed conformation is immersed. It is shown that if the number of residues is sufficiently large, the TE gain is powerful enough to compete with the conformational-entropy loss upon folding. For protein G we have tested over 100 compact conformations generated by a computer simulation with the all-atom potentials as well as the native structure. A significant finding is that the largest TE is attained in the native structure. The translational movement of water molecules is quite effective in achieving the tight packing in the interior of a natural protein. These results are true only when the solvent is water whose molecular size is the smallest among the ordinary liquids in nature.

Do all backbone polar groups in proteins form hydrogen bonds?

Evidence from proteins and peptides supports the conclusion that intrapeptide hydrogen bonds stabilize the folded form of proteins. Paradoxically, evidence from small molecules supports the opposite conclusion, that intrapeptide hydrogen bonds are less favorable than peptide-water hydrogen bonds. A related issue-often lost in this debate about comparing peptide-peptide to peptide- water hydrogen bonds-involves the energetic cost of an unsatisfied hydrogen bond. Here, experiment and theory agree that breaking a hydrogen bond costs between 5 and 6 kcal/mol. Accordingly, the likelihood of finding an unsatisfied hydrogen bond in a protein is insignificant. This realization establishes a powerful rule for evaluating protein conformations.

Effect of Temperature and Concentration on the Structure of N-Methylacetamide−Water Complexes: Near-Infrared Spectroscopic Study

Generalized two-dimensional (2D) FT-NIR correlation spectroscopy and chemometric methods have been used to study temperature-dependent spectral changes in pure N-methylacetamide (NMA) and NMA-water mixtures. We also examined the effect of varying water content on the structure of the mixture. It has been found that the extent of self-association of NMA in CCl4 is very high; the association occurs even at concentration of 0.001 M. In the pure liquid NMA, the population of the monomers is negligible and the structure is dominated by the linear associates. An increase in temperature reduces the number of hydrogen bonds, but in contrast to alcohols their strength remains nearly the same. This reflects a difference in the mechanism of thermal breaking of the associates of NMA and alcohols. The present results reveal that the interaction between NMA and water in the NMA-rich region (X(H2O) < 0.1) does not have a significant effect on the intrinsic structure of NMA. The structure of NMA is dominant, and the molecules of water do not form separate clusters but are dispersed and incorporated into the structure of NMA. We did not observe the presence of the free OH groups in the mixture. This led to the suggestion that each molecule of water forms two hydrogen bonds to two different molecules of NMA. An analysis of the asynchronous spectra reveals that most of the peaks observed in the asynchronous spectra, constructed from the temperature-dependent data, simply result from the frequency shift. This assumption is supported by the simulation studies.

Relation between peptide backbone solvation and the energetics of peptide hydrogen bonds

The H-bond inventory approach is used commonly to interpret data involving changes in the number or types of protein hydrogen bonds. I point out here that this approach gives an incorrect answer either for the standard free energy or enthalpy of the reaction between simple amides and water. On the other hand, an electrostatic solvation approach fits almost within error the polar solvation free energies of small molecules, including amides. The electrostatic solvation approach is used here to discuss the relation between peptide backbone solvation and the enthalpy change for forming an alanine helix.

Energetics of the interaction between water and the helical peptide group and its role in determining helix propensities

The alanine helix provides a model system for studying the energetics of interaction between water and the helical peptide group, a possible major factor in the energetics of protein folding. Helix formation is enthalpy-driven (-1.0 kcal/mol per residue). Experimental transfer data (vapor phase to aqueous) for amides give the enthalpy of interaction with water of the amide group as approximately -11.5 kcal/mol. The enthalpy of the helical peptide hydrogen bond, computed for the gas phase by quantum mechanics, is -4.9 kcal/mol. These numbers give an enthalpy deficit for helix formation of -7.6 kcal/mol. To study this problem, we calculate the electrostatic solvation free energy (ESF) of the peptide groups in the helical and beta-strand conformations, by using the delphi program and parse parameter set. Experimental data show that the ESF values of amides are almost entirely enthalpic. Two key results are: in the beta-strand conformation, the ESF value of an interior alanine peptide group is -7.9 kcal/mol, substantially less than that of N-methylacetamide (-12.2 kcal/mol), and the helical peptide group is solvated with an ESF of -2.5 kcal/mol. These results reduce the enthalpy deficit to -1.5 kcal/mol, and desolvation of peptide groups through partial burial in the random coil may account for the remainder. Mutant peptides in the helical conformation show ESF differences among nonpolar amino acids that are comparable to observed helix propensity differences, but the ESF differences in the random coil conformation still must be subtracted.

Development and validation of a genetic algorithm for flexible docking

Prediction of small molecule binding modes to macromolecules of known three-dimensional structure is a problem of paramount importance in rational drug design (the "docking" problem). We report the development and validation of the program GOLD (Genetic Optimisation for Ligand Docking). GOLD is an automated ligand docking program that uses a genetic algorithm to explore the full range of ligand conformational flexibility with partial flexibility of the protein, and satisfies the fundamental requirement that the ligand must displace loosely bound water on binding. Numerous enhancements and modifications have been applied to the original technique resulting in a substantial increase in the reliability and the applicability of the algorithm. The advanced algorithm has been tested on a dataset of 100 complexes extracted from the Brookhaven Protein DataBank. When used to dock the ligand back into the binding site, GOLD achieved a 71% success rate in identifying the experimental binding mode.

SCF-MO study of the polyhydration of N,N'-dimethylmalonamide

The effect of hydration on the conformation of the N,3 nylons has been studied using AM1 SCF-MO on the model molecule N,N'-dimethylmalonamide (NNMA). The polyhydration model has been used, so that only the water molecules directly bonded to solute molecule are considered. The study reveals that, although hydration induces dramatic changes in the torsional angles of the molecule, the new conformation still remains in the helical region of the Ramachandran map.