From propensities to patterns to principles in protein folding.

As proposed here, ß-turns play an essential role in protein self-assembly. This compact, four-residue motif affects protein conformation dramatically by reversing the overall chain direction. Turns are the "hinges" in globular proteins. This new proposal broadens a previous hypothesis that globular proteins solve the folding problem in part by filtering conformers with unsatisfied backbone hydrogen bonds, thereby preorganizing the folding population. Recapitulating that hypothesis: unsatisfied conformers 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 at room temperature. Consequently, globular proteins are built on scaffolds of hydrogen-bonded α-helices and/or strands of ß-sheet, motifs that can be extended indefinitely, with intra-segment hydrogen bond partners for their backbone polar groups and without steric clash. Scaffolds foster a protein-wide hydrogen-bonded network, and, of thermodynamic necessity, they self-assemble cooperatively. Unlike elements of repetitive secondary structure, α-helices and ß-sheet, a four-residue ß-turn has only a single hydrogen bond (from i + 3 → i), not a cooperatively formed assembly of hydrogen bonds. As such, turns can form autonomously and are poised to initiate assembly of scaffold elements by bringing them together in an orientation and registration that promotes cooperative "zipping". The overall effect of this self-assembly mechanism is to induce substantial preorganization in the thermodynamically accessible folding population and, concomitantly, to reduce the folding entropy.

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 ß-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.

Building blocks of protein structures: Physics meets biology.

The native state structures of globular proteins are stable and well packed indicating that self-interactions are favored over protein-solvent interactions under folding conditions. We use this as a guiding principle to derive the geometry of the building blocks of protein structures-α helices and strands assembled into ß sheets-with no adjustable parameters, no amino acid sequence information, and no chemistry. There is an almost perfect fit between the dictates of mathematics and physics and the rules of quantum chemistry. Protein evolution is facilitated by sequence-independent platforms, which can elaborate sequence-dependent functional diversity. Our work highlights the vital role of discreteness in life and may have implications for the creation of artificial life and on the nature of life elsewhere in the cosmos.

Protein folding - seeing is deceiving.

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical-chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α-helices and strands of ß-sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen-bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of "frustration" is largely eliminated and the Levinthal paradox is resolved. Putting the "bottom line" at the top: it is likely that hydrogen-bond satisfaction represents a largely under-appreciated parameter in protein folding models.

Ramachandran maps for side chains in globular proteins.

The Ramachandran plot for backbone ϕ,ψ-angles in a blocked monopeptide has played a central role in understanding protein structure. Curiously, a similar analysis for side chain χ-angles has been comparatively neglected. Instead, efforts have focused on compiling various types of side chain libraries extracted from proteins of known structure. Departing from this trend, the following analysis presents backbone-based maps of side chains in blocked monopeptides. As in the original ϕ,ψ-plot, these maps are derived solely from hard-sphere steric repulsion. Remarkably, the side chain biases exhibit marked similarities to corresponding biases seen in high-resolution protein structures. Consequently, some of the entropic cost for side chain localization in proteins is prepaid prior to the onset of folding events because conformational bias is built into the chain at the covalent level. Furthermore, side chain conformations are seen to experience fewer steric restrictions for backbone conformations in either the α or ß basins, those map regions where repetitive ϕ,ψ-angles result in α-helices or strands of ß-sheet, respectively. Here, these α and ß basins are entropically favored for steric reasons alone; a blocked monopeptide is too short to accommodate the peptide hydrogen bonds that stabilize repetitive secondary structure. Thus, despite differing energetics, α/ß-basins are favored for both monopeptides and repetitive secondary structure, underpinning an energetically unfrustrated compatibility between these two levels of protein structure.

How the hydrophobic factor drives protein folding.

How hydrophobicity (HY) drives protein folding is studied. The 1971 Nozaki-Tanford method of measuring HY is modified to use gases as solutes, not crystals, and this makes the method easy to use. Alkanes are found to be much more hydrophobic than rare gases, and the two different kinds of HY are termed intrinsic (rare gases) and extrinsic (alkanes). The HY values of rare gases are proportional to solvent-accessible surface area (ASA), whereas the HY values of alkanes depend on special hydration shells. Earlier work showed that hydration shells produce the hydration energetics of alkanes. Evidence is given here that the transfer energetics of alkanes to cyclohexane [Wolfenden R, Lewis CA, Jr, Yuan Y, Carter CW, Jr (2015) Proc Natl Acad Sci USA 112(24):7484-7488] measure the release of these shells. Alkane shells are stabilized importantly by van der Waals interactions between alkane carbon and water oxygen atoms. Thus, rare gases cannot form this type of shell. The very short (approximately picoseconds) lifetime of the van der Waals interaction probably explains why NMR efforts to detect alkane hydration shells have failed. The close similarity between the sizes of the opposing energetics for forming or releasing alkane shells confirms the presence of these shells on alkanes and supports Kauzmann's 1959 mechanism of protein folding. A space-filling model is given for the hydration shells on linear alkanes. The model reproduces the n values of Jorgensen et al. [Jorgensen WL, Gao J, Ravimohan C (1985) J Phys Chem 89:3470-3473] for the number of waters in alkane hydration shells.

On interpretation of protein X-ray structures: Planarity of the peptide unit.

Pauling's mastery of peptide stereochemistry-based on small molecule crystal structures and the theory of chemical bonding-led to his realization that the peptide unit is planar and then to the Pauling-Corey-Branson model of the α-helix. Similarly, contemporary protein structure refinement is based on experimentally determined diffraction data together with stereochemical restraints. However, even an X-ray structure at ultra-high resolution is still an under-determined model in which the linkage among refinement parameters is complex. Consequently, restrictions imposed on any given parameter can affect the entire structure. Here, we examine recent studies of high resolution protein X-ray structures, where substantial distortions of the peptide plane are found to be commonplace. Planarity is assessed by the ω-angle, a dihedral angle determined by the peptide bond (C-N) and its flanking covalent neighbors; for an ideally planar trans peptide, ω = 180°. By using a freely available refinement package, Phenix [Afonine et al. (2012) Acta Cryst. D, 68:352-367], we demonstrate that tightening default restrictions on the ω-angle can significantly reduce apparent deviations from peptide unit planarity without consequent reduction in reported evaluation metrics (e.g., R-factors). To be clear, our result does not show that substantial non-planarity is absent, only that an equivalent alternative model is possible. Resolving this disparity will ultimately require improved understanding of the deformation energy. Meanwhile, we urge inclusion of ω-angle statistics in new structure reports in order to focus critical attention on the usual practice of assigning default values to ω-angle constraints during structure refinement.

Molten globules, entropy-driven conformational change and protein folding.

The exquisite side chain close-packing in the protein core and at binding interfaces has prompted a conviction that packing selectivity is the primary mechanism for molecular recognition in folding and/or binding reactions. Contrary to this view, molten globule proteins can adopt native topology and bind targets tightly and specifically in the absence of side chain close-packing. The molten globule is a highly dynamic form with native-like secondary structure and a loose protein core that admits solvent. The related (but still controversial) dry molten globule is an expanded form of the native protein with largely intact topology but a tighter protein core that excludes solvent. Neither form retains side chain close-packing, and therefore both structure and function must result from other factors, assuming that the reality of the dry molten globule is accepted. This simplifying realization calls for a re-evaluation of established models.

Reducing the dimensionality of the protein-folding search problem.

How does a folding protein negotiate a vast, featureless conformational landscape and adopt its native structure in biological real time? Motivated by this search problem, we developed a novel algorithm to compare protein structures. Procedures to identify structural analogs are typically conducted in three-dimensional space: the tertiary structure of a target protein is matched against each candidate in a database of structures, and goodness of fit is evaluated by a distance-based measure, such as the root-mean-square distance between target and candidate. This is an expensive approach because three-dimensional space is complex. Here, we transform the problem into a simpler one-dimensional procedure. Specifically, we identify and label the 11 most populated residue basins in a database of high-resolution protein structures. Using this 11-letter alphabet, any protein's three-dimensional structure can be transformed into a one-dimensional string by mapping each residue onto its corresponding basin. Similarity between the resultant basin strings can then be evaluated by conventional sequence-based comparison. The disorder → order folding transition is abridged on both sides. At the onset, folding conditions necessitate formation of hydrogen-bonded scaffold elements on which proteins are assembled, severely restricting the magnitude of accessible conformational space. Near the end, chain topology is established prior to emergence of the close-packed native state. At this latter stage of folding, the chain remains molten, and residues populate natural basins that are approximated by the 11 basins derived here. In essence, our algorithm reduces the protein-folding search problem to mapping the amino acid sequence onto a restricted basin string.

A thermodynamic definition of protein domains.

Protein domains are conspicuous structural units in globular proteins, and their identification has been a topic of intense biochemical interest dating back to the earliest crystal structures. Numerous disparate domain identification algorithms have been proposed, all involving some combination of visual intuition and/or structure-based decomposition. Instead, we present a rigorous, thermodynamically-based approach that redefines domains as cooperative chain segments. In greater detail, most small proteins fold with high cooperativity, meaning that the equilibrium population is dominated by completely folded and completely unfolded molecules, with a negligible subpopulation of partially folded intermediates. Here, we redefine structural domains in thermodynamic terms as cooperative folding units, based on m-values, which measure the cooperativity of a protein or its substructures. In our analysis, a domain is equated to a contiguous segment of the folded protein whose m-value is largely unaffected when that segment is excised from its parent structure. Defined in this way, a domain is a self-contained cooperative unit; i.e., its cooperativity depends primarily upon intrasegment interactions, not intersegment interactions. Implementing this concept computationally, the domains in a large representative set of proteins were identified; all exhibit consistency with experimental findings. Specifically, our domain divisions correspond to the experimentally determined equilibrium folding intermediates in a set of nine proteins. The approach was also proofed against a representative set of 71 additional proteins, again with confirmatory results. Our reframed interpretation of a protein domain transforms an indeterminate structural phenomenon into a quantifiable molecular property grounded in solution thermodynamics.

The Levinthal paradox of the interactome.

The central biological question of the 21st century is: how does a viable cell emerge from the bewildering combinatorial complexity of its molecular components? Here, we estimate the combinatorics of self-assembling the protein constituents of a yeast cell, a number so vast that the functional interactome could only have emerged by iterative hierarchic assembly of its component sub-assemblies. A protein can undergo both reversible denaturation and hierarchic self-assembly spontaneously, but a functioning interactome must expend energy to achieve viability. Consequently, it is implausible that a completely "denatured" cell could be reversibly renatured spontaneously, like a protein. Instead, new cells are generated by the division of pre-existing cells, an unbroken chain of renewal tracking back through contingent conditions and evolving responses to the origin of life on the prebiotic earth. We surmise that this non-deterministic temporal continuum could not be reconstructed de novo under present conditions.

Counting peptide-water hydrogen bonds in unfolded proteins.

It is often assumed that the peptide backbone forms a substantial number of additional hydrogen bonds when a protein unfolds. We challenge that assumption in this article. Early surveys of hydrogen bonding in proteins of known structure typically found that most, but not all, backbone polar groups are satisfied, either by intramolecular partners or by water. When the protein is folded, these groups form approximately two hydrogen bonds per peptide unit, one donor or acceptor for each carbonyl oxygen or amide hydrogen, respectively. But when unfolded, the backbone chain is often believed to form three hydrogen bonds per peptide unit, one partner for each oxygen lone pair or amide hydrogen. This assumption is based on the properties of small model compounds, like N-methylacetamide, or simply accepted as self-evident fact. If valid, a chain of N residues would have approximately 2N backbone hydrogen bonds when folded but 3N backbone hydrogen bonds when unfolded, a sufficient difference to overshadow any uncertainties involved in calculating these per-residue averages. Here, we use exhaustive conformational sampling to monitor the number of H-bonds in a statistically adequate population of blocked polyalanyl-six-mers as the solvent quality ranges from good to poor. Solvent quality is represented by a scalar parameter used to Boltzmann-weight the population energy. Recent experimental studies show that a repeating (Gly-Ser) polypeptide undergoes a denaturant-induced expansion accompanied by breaking intramolecular peptide H-bonds. Results from our simulations augment this experimental finding by showing that the number of H-bonds is approximately conserved during such expansion⇋compaction transitions.

Redrawing the Ramachandran plot after inclusion of hydrogen-bonding constraints.

A protein backbone has two degrees of conformational freedom per residue, described by its ϕ,ψ-angles. Accordingly, the energy landscape of a blocked peptide unit can be mapped in two dimensions, as shown by Ramachandran, Sasisekharan, and Ramakrishnan almost half a century ago. With atoms approximated as hard spheres, the eponymous Ramachandran plot demonstrated that steric clashes alone eliminate 3/4 of ϕ,ψ-space, a result that has guided all subsequent work. Here, we show that adding hydrogen-bonding constraints to these steric criteria eliminates another substantial region of ϕ,ψ-space for a blocked peptide; for conformers within this region, an amide hydrogen is solvent-inaccessible, depriving it of a hydrogen-bonding partner. Yet, this "forbidden" region is well populated in folded proteins, which can provide longer-range intramolecular hydrogen-bond partners for these otherwise unsatisfied polar groups. Consequently, conformational space expands under folding conditions, a paradigm-shifting realization that prompts an experimentally verifiable conjecture about likely folding pathways.

Dry molten globule intermediates and the mechanism of protein unfolding.

New experimental results show that either gain or loss of close packing can be observed as a discrete step in protein folding or unfolding reactions. This finding poses a significant challenge to the conventional two-state model of protein folding. Results of interest involve dry molten globule (DMG) intermediates, an expanded form of the protein that lacks appreciable solvent. When an unfolding protein expands to the DMG state, side chains unlock and gain conformational entropy, while liquid-like van der Waals interactions persist. Four unrelated proteins are now known to form DMGs as the first step of unfolding, suggesting that such an intermediate may well be commonplace in both folding and unfolding. Data from the literature show that peptide amide protons are protected in the DMG, indicating that backbone structure is intact despite loss of side-chain close packing. Other complementary evidence shows that secondary structure formation provides a major source of compaction during folding. In our model, the major free-energy barrier separating unfolded from native states usually occurs during the transition between the unfolded state and the DMG. The absence of close packing at this barrier provides an explanation for why phi-values, derived from a Brønsted-Leffler plot, depend primarily on structure at the mutational site and not on specific side-chain interactions. The conventional two-state folding model breaks down when there are DMG intermediates, a realization that has major implications for future experimental work on the mechanism of protein folding.

Physical-chemical determinants of coil conformations in globular proteins.

We present a method with the potential to generate a library of coil segments from first principles. Proteins are built from alpha-helices and/or beta-strands interconnected by these coil segments. Here, we investigate the conformational determinants of short coil segments, with particular emphasis on chain turns. Toward this goal, we extracted a comprehensive set of two-, three-, and four-residue turns from X-ray-elucidated proteins and classified them by conformation. A remarkably small number of unique conformers account for most of this experimentally determined set, whereas remaining members span a large number of rare conformers, many occurring only once in the entire protein database. Factors determining conformation were identified via Metropolis Monte Carlo simulations devised to test the effectiveness of various energy terms. Simulated structures were validated by comparison to experimental counterparts. After filtering rare conformers, we found that 98% of the remaining experimentally determined turn population could be reproduced by applying a hydrogen bond energy term to an exhaustively generated ensemble of clash-free conformers in which no backbone polar group lacks a hydrogen-bond partner. Further, at least 90% of longer coil segments, ranging from 5- to 20 residues, were found to be structural composites of these shorter primitives. These results are pertinent to protein structure prediction, where approaches can be divided into either empirical or ab initio methods. Empirical methods use database-derived information; ab initio methods rely on physical-chemical principles exclusively. Replacing the database-derived coil library with one generated from first principles would transform any empirically based method into its corresponding ab initio homologue.