Theory of protein folding

Protein folding should be complex. Proteins organize themselves into specific three-dimensional structures, through a myriad of conformational changes. The classical view of protein folding describes this process as a nearly sequential series of discrete intermediates. In contrast, the energy landscape theory of folding considers folding as the progressive organization of an ensemble of partially folded structures through which the protein passes on its way to the natively folded structure. As a result of evolution, proteins have a rugged funnel-like landscape biased toward the native structure. Connecting theory and simulations of minimalist models with experiments has completely revolutionized our understanding of the underlying mechanisms that control protein folding.     

An analysis of protein folding pathways

We have developed a model of the protein folding process based on three primary assumptions: that burying of hydrophobic area is the dominant contribution to the relative free energy of a conformation, that a record of the folding process is largely preserved in the final structure, and that the denatured state is a random coil. Detailed folding pathways are identified for 19 protein structures. The picture of the folding process that emerges from this analysis is one of nucleation by regions of 8-16 residues. Nucleation sites then lead to larger structures by two mechanisms: propagation and diffusion/collision. A Monte Carlo simulation is used to follow the folding pathway when propagation is the dominant mechanism. Because detailed pathways are derived for each protein, the models are susceptible to experimental verification.     

Reduced alphabet for protein folding prediction

What are the key building blocks that would have been needed to construct complex protein folds? This is an important issue for understanding protein folding mechanism and guiding de novo protein design. Twenty naturally occurring amino acids and eight secondary structures consist of a 28‐letter alphabet to determine folding kinetics and mechanism. Here we predict folding kinetic rates of proteins from many reduced alphabets. We find that a reduced alphabet of 10 letters achieves good correlation with folding rates, close to the one achieved by full 28‐letter alphabet. Many other reduced alphabets are not significantly correlated to folding rates. The finding suggests that not all amino acids and secondary structures are equally important for protein folding. The foldable sequence of a protein could be designed using at least 10 folding units, which can either promote or inhibit protein folding. Reducing alphabet cardinality without losing key folding kinetic information opens the door to potentially faster machine learning and data mining applications in protein structure prediction, sequence alignment and protein design. Proteins 2015; 83:631–639. © 2015 Wiley Periodicals, Inc.     

Pressure provides new insights into protein folding, dynamics and structure

Hydrostatic pressure is a powerful tool for studying protein folding, and the dynamics and structure of folding intermediates. Recently, pressure techniques have opened two important fronts to aid our understanding of how polypeptides fold into highly structured conformations. The first advance is the stabilization of folding intermediates, making it possible to characterize their structures and dynamics by different methodologies. Kinetic studies under pressure constitute the second advance, promising detailed appraisal and understanding of protein folding landscapes. The combination of these two approaches enables dissection of the roles of packing and cavities in folding, and in assembly of multimolecular structures such as protein-DNA complexes and viruses. The study of aggregates and amyloids, derived from partially folded intermediates at the junction between productive and off-pathway folding, have also been studied, promising better understanding of diseases associated with protein misfolding.     

Machinery of protein folding and unfolding

During the past two years, a large amount of biochemical, biophysical and low- to high-resolution structural data have provided mechanistic insights into the machinery of protein folding and unfolding. It has emerged that dual functionality in terms of folding and unfolding might exist for some systems. The majority of folding/unfolding machines adopt oligomeric ring structures in a cooperative fashion and utilise the conformational changes induced by ATP binding/hydrolysis for their specific functions.     

The protein folding 'speed limit'

How fast can a protein possibly fold? This question has stimulated experimentalists to seek fast folding proteins and to engineer them to fold even faster. Proteins folding at or near the speed limit are prime candidates for all-atom molecular dynamics simulations. They may also have no free energy barrier, allowing the direct observation of intermediate structures on the pathways from the unfolded to the folded state. Both experimental and theoretical approaches predict a speed limit of approximately N/100micros for a generic N-residue single-domain protein, with alpha proteins folding faster than beta or alphabeta. The predicted limits suggest that most known ultrafast folding proteins can be engineered to fold more than ten times faster.     

Principles of protein folding--a perspective from simple exact models.

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.     

The relation between mRNA folding and protein structure

About 200 mRNA sequences of Escherichia coli and human with matching protein secondary structure data were studied. The mRNA folding for each native sequence and for corresponding randomized sequences was calculated through free energy minimization. We have found that the folding energy of mRNA segments in different protein secondary structures is significantly different. The average Z score is more negative for regular secondary structure (alpha-helix and beta-strand) than that for coil. This suggests that the codon choice in native mRNA sequence coding for protein regular structure contributes more to the mRNA folding stability.     

Elementary steps in protein folding.

The mechanism of protein folding is under intense theoretical and experimental investigation. From stopped-flow mixing experiments we have detailed knowledge of processes slower than about 1 ms, but until recently little was known about folding and unfolding reactions on the microsecond to nanosecond time scale. The use of novel techniques allowed to explore the elementary steps in protein folding, such as intrachain diffusion and formation of alpha-helices, beta-hairpins and loop structures. This brief review discusses the time scales of these early elementary events which are crucial for the understanding of how proteins fold.     

Inter-residue interactions in protein folding and stability

During the process of protein folding, the amino acid residues along the polypeptide chain interact with each other in a cooperative manner to form the stable native structure. The knowledge about inter-residue interactions in protein structures is very helpful to understand the mechanism of protein folding and stability. In this review, we introduce the classification of inter-residue interactions into short, medium and long range based on a simple geometric approach. The features of these interactions in different structural classes of globular and membrane proteins, and in various folds have been delineated. The development of contact potentials and the application of inter-residue contacts for predicting the structural class and secondary structures of globular proteins, solvent accessibility, fold recognition and ab initio tertiary structure prediction have been evaluated. Further, the relationship between inter-residue contacts and protein-folding rates has been highlighted. Moreover, the importance of inter-residue interactions in protein-folding kinetics and for understanding the stability of proteins has been discussed. In essence, the information gained from the studies on inter-residue interactions provides valuable insights for understanding protein folding and de novo protein design.     

Contact order and ab initio protein structure prediction

Although much of the motivation for experimental studies of protein folding is to obtain insights for improving protein structure prediction, there has been relatively little connection between experimental protein folding studies and computational structural prediction work in recent years. In the present study, we show that the relationship between protein folding rates and the contact order (CO) of the native structure has implications for ab initio protein structure prediction. Rosetta ab initio folding simulations produce a dearth of high CO structures and an excess of low CO structures, as expected if the computer simulations mimic to some extent the actual folding process. Consistent with this, the majority of failures in ab initio prediction in the CASP4 (critical assessment of structure prediction) experiment involved high CO structures likely to fold much more slowly than the lower CO structures for which reasonable predictions were made. This bias against high CO structures can be partially alleviated by performing large numbers of additional simulations, selecting out the higher CO structures, and eliminating the very low CO structures; this leads to a modest improvement in prediction quality. More significant improvements in predictions for proteins with complex topologies may be possible following significant increases in high-performance computing power, which will be required for thoroughly sampling high CO conformations (high CO proteins can take six orders of magnitude longer to fold than low CO proteins). Importantly for such a strategy, simulations performed for high CO structures converge much less strongly than those for low CO structures, and hence, lack of simulation convergence can indicate the need for improved sampling of high CO conformations. The parallels between Rosetta simulations and folding in vivo may extend to misfolding: The very low CO structures that accumulate in Rosetta simulations consist primarily of local up-down beta-sheets that may resemble precursors to amyloid formation.     

Conformation of peptide fragments of proteins in aqueous solution: implications for initiation of protein folding

Applications of sensitive new technologies, in particular, two-dimensional NMR spectroscopy, have allowed detection of folded structures in short peptide fragments of proteins in aqueous solution under conditions where native proteins fold. These structures are in rapid dynamic exchange with unfolded states. These observations provide evidence in support of models for protein folding which postulate localized regions of folded structure as initiation sites for the folding process. Since these initiation processes are expected to be rapid, such models are consistent with kinetic evidence that the rate-determining steps of protein folding occur late in the process and probably involve rearrangement of incorrectly folded intermediates.     

Contact order revisited: influence of protein size on the folding rate

Guided by the recent success of empirical model predicting the folding rates of small two-state folding proteins from the relative contact order (CO) of their native structures, by a theoretical model of protein folding that predicts that logarithm of the folding rate decreases with the protein chain length L as L(2/3), and by the finding that the folding rates of multistate folding proteins strongly correlate with their sizes and have very bad correlation with CO, we reexamined the dependence of folding rate on CO and L in attempt to find a structural parameter that determines folding rates for the totality of proteins. We show that the Abs_CO = CO x L, is able to predict rather accurately folding rates for both two-state and multistate folding proteins, as well as short peptides, and that this Abs_CO scales with the protein chain length as L(0.70 +/- 0.07) for the totality of studied single-domain proteins and peptides.     

Contact patterns between helices and strands of sheet define protein folding patterns

Comparing and classifying protein folding patterns allows organizing the known structures and enumerating possible protein structural patterns including those not yet observed. We capture the essence of protein folding patterns in a concise tableau representation based on the order and contact patterns of secondary structures: helices and strands of sheet. The tableaux are intelligible to both humans and computers. They provide a database, derived from the Protein Data Bank, mineable in studies of protein architecture. Using this database, we have: (i) determined statistical properties of secondary structure contacts in an unbiased set of protein domains from ASTRAL, (ii) observed that in 98% of cases, the tableau is a faithful representation of the folding pattern as classified in SCOP, (iii) demonstrated that to a large extent the local structure of proteins indicates their complete folding topology, and (iv) studied the use of the representation for fold identification.     

Protein <Emphasis Type="Italic">N</Emphasis>-glycosylation,protein folding,and protein quality control

Quality control of protein folding represents a fundamental cellular activity. Early steps of protein N-glycosylation involving the removal of three glucose and some specific mannose residues in the endoplasmic reticulum have been recognized as being of importance for protein quality control. Specific oligosaccharide structures resulting from the oligosaccharide processing may represent a glycocode promoting productive protein folding, whereas others may represent glyco-codes for routing not correctly folded proteins for dislocation from the endoplasmic reticulum to the cytosol and subsequent degradation. Although quality control of protein folding is essential for the proper functioning of cells, it is also the basis for protein folding disorders since the recognition and elimination of non-native conformers can result either in loss-of-function or pathological-gain-of-function. The machinery for protein folding control represents a prime example of an intricate interactome present in a single organelle, the endoplasmic reticulum. Here, current views of mechanisms for the recognition and retention leading to productive protein folding or the eventual elimination of misfolded glycoproteins in yeast and mammalian cells are reviewed.     

Side-chain entropy effects on protein secondary structure formation

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.     

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.     

Predicting protein folding cores by empirical potential functions

Theoretical and in vitro experiments suggest that protein folding cores form early in the process of folding, and that proteins may have evolved to optimize both folding speed and native-state stability. In our previous work (Chen et al., Structure, 14 (2006) 1401), we developed a set of empirical potential functions and used them to analyze interaction energies among secondary-structure elements in two β-sandwich proteins. Our work on this group of proteins demonstrated that the predicted folding core also harbors residues that form native-like interactions early in the folding reaction. In the current work, we have tested our empirical potential functions on structurally-different proteins for which the folding cores have been revealed by protein hydrogen-deuterium exchange experiments. Using a set of 29 unrelated proteins, which have been extensively studied in the literature, we demonstrate that the average prediction result from our method is significantly better than predictions based on other computational methods. Our study is an important step towards the ultimate goal of understanding the correlation between folding cores and native structures.