Physical principles of protein structure and protein folding

Physical principles determining the protein structure and protein folding are reviewed: (i) the molecular theory of protein secondary structure and the method of its prediction based on this theory; (ii) the existence of a limited set of thermodynamically favourable folding patterns of α- and β-regions in a compact globule which does not depend on the details of the amino acid sequence; (iii) the moderns approaches to the prediction of the folding patterns of α- and β-regions in concrete proteins; (iv) experimental approaches to the mechanism of protein folding. The review reflects theoretical and experimental works of the author and his collaborators as well as those of other groups.     

Secondary structure prediction and folding of globular protein: refolding of ferredoxin

The physicochemical mechanism of protein folding has been elucidated by the island model, describing a growth type of folding. The folding pathway is closely related with nucleation on the polypeptide chain and thus the formation of small local structures or secondary structures at the earliest stage of folding is essential to all following steps. The island model is applicable to any protein, but a high precision of secondary structure prediction is indispensable to folding simulation. The secondary structures formed at the earliest stage of folding are supposed to be of standard form, but they are usually deformed during the folding process, especially at the last stage, although the degree of deformation is different for each protein. Ferredoxin is an example of a protein having this property. According to X-ray investigation (1FDX), ferredoxin is not supposed to have secondary structures. However, if we assumed that in ferredoxin all the residues are in a coil state, we could not attain the correct structure similar to the native one. Further, we found that some parts of the chain are not flexible, suggesting the presence of secondary structures, in agreement with the recent PDB data (1DUR). Assuming standard secondary structures (-helices and -strands) at the nonflexible parts at the early stage of folding, and deforming these at the final stage, a structure similar to the native one was obtained. Another peculiarity of ferredoxin is the absence of disulfide bonds, in spite of its having eight cysteines. The reason cysteines do not form disulfide bonds became clear by applying the lampshade criterion, but more importantly, the two groups of cysteines are ready to make iron complexes, respectively, at a rather later stage of folding. The reason for poor prediction accuracy of secondary structure with conventional methods is discussed.     

Alpha-hairpin stability and folding of transmembrane segments

Molecular Dynamics (MD) simulations at low dielectric constant have been carried out for peptides matching the double spanning segments of transmembrane proteins. Different folding dynamics have been observed. The peptides folded into the stable helix-turn-helix conformation-alpha-hairpin-with antiparallel-oriented strands or unstable alpha-hairpin conformation that unfolded later into the straight helical structure. The peptide having flexible residues in the TM helices often misfolded into a tangled structure that can be avoided by restricting the flexibility of these residues. General conclusions can be drawn from the observed folding dynamics. The stability and folding of some double spanning transmembrane fragments are self-assembling. The following and/or neighboring peptide chains of the protein may support the stability of the hairpin structure of other fragments. The stability of the TM helices containing flexible residues could be maintained due to contacts with neighboring TM segments.     

Probing the energy landscape of protein folding/unfolding transition states

Previous molecular dynamics (MD) simulations of the thermal denaturation of chymotrypsin inhibitor 2 (CI2) have provided atomic-resolution models of the transition state ensemble that is well supported by experimental studies. Here, we use simulations to further investigate the energy landscape around the transition state region. Nine structures within approximately 35 ps and 3 A C(alpha) RMSD of the transition state ensemble identified in a previous 498 K thermal denaturation simulation were quenched under the quasi-native conditions of 335 K and neutral pH. All of the structures underwent hydrophobically driven collapse in response to the drop in temperature. Structures less denatured than the transition state became structurally more native-like, while structures that were more denatured than the transition state tended to show additional loss of native structure. The structures in the immediate region of the transition state fluctuated between becoming more and less native-like. All of the starting structures had the same native-like topology and were quite similar (within 3.5 A C(alpha) RMSD). That the structures all shared native-like topology, yet diverged into either more or less native-like structures depending on which side of the transition state they occupied on the unfolding trajectory, indicates that topology alone does not dictate protein folding. Instead, our results suggest that a detailed interplay of packing interactions and interactions with water determine whether a partially denatured protein will become more native-like under refolding conditions.     

Mechanisms of protein folding

Understanding the mechanism by which a polypeptide chain folds into its native structure is a central problem of modern biophysics. The collaborative efforts of experimental and theoretical studies recently raised the tantalizing possibility to define a unifying mechanism for protein folding. In this review we summarize some of these intriguing advances and analyze them together with a discussion on the new findings concerning the so-called downhill folding.     

Water dynamics clue to key residues in protein folding

A computational method independent of experimental protein structure information is proposed to recognize key residues in protein folding, from the study of hydration water dynamics. Based on all-atom molecular dynamics simulation, two key residues are recognized with distinct water dynamical behavior in a folding process of the Trp-cage protein. The identified key residues are shown to play an essential role in both 3D structure and hydrophobic-induced collapse. With observations on hydration water dynamics around key residues, a dynamical pathway of folding can be interpreted.     

Protein folding: then and now

Over the past three decades the protein folding field has undergone monumental changes. Originally a purely academic question, how a protein folds has now become vital in understanding diseases and our abilities to rationally manipulate cellular life by engineering protein folding pathways. We review and contrast past and recent developments in the protein folding field. Specifically, we discuss the progress in our understanding of protein folding thermodynamics and kinetics, the properties of evasive intermediates, and unfolded states. We also discuss how some abnormalities in protein folding lead to protein aggregation and human diseases.     

Local secondary structure content predicts folding rates for simple,two-state proteins

Many single-domain proteins exhibit two-state folding kinetics, with folding rates that span more than six orders of magnitude. A quantity of much recent interest for such proteins is their contact order, the average separation in sequence between contacting residue pairs. Numerous studies have reached the surprising conclusion that contact order is well-correlated with the logarithm of the folding rate for these small, well-characterized molecules. Here, we investigate the physico-chemical basis for this finding by asking whether contact order is actually a composite number that measures the fraction of local secondary structure in the protein; viz. turns, helices, and hairpins. To pursue this question, we calculated the secondary structure content for 24 two-state proteins and obtained coefficients that predict their folding rates. The predicted rates correlate strongly with experimentally determined rates, comparable to the correlation with contact order. Further, these predicted folding rates are correlated strongly with contact order. Our results suggest that the folding rate of two-state proteins is a function of their local secondary structure content, consistent with the hierarchic model of protein folding. Accordingly, it should be possible to utilize secondary structure prediction methods to predict folding rates from sequence alone.     

The implications of gene heterozygosity for protein folding and protein turnover

The offspring of closely related parents often suffer from inbreeding depression, sometimes resulting in a slower growth rate for inbred offspring relative to non-inbred offspring. Previous research has shown that some of the slower growth rate of inbred organisms can be attributed to the inbred organisms’ increased levels of protein turnover. This paper attempts to show that the higher levels of protein turnover among inbred organisms can be attributed to accumulations of misfolded and aggregated proteins that require degradation by the inbred organisms’ protein quality control systems. The accumulation of misfolded and aggregated proteins within inbred organisms are the result of more negative free energies of folding for proteins encoded at homozygous gene loci and higher concentrations of potentially aggregating non-native protein species within the cell. The theory presented here makes several quantitative predictions that suggest a connection between protein misfolding/aggregation and polyploidy that can be tested by future research.     

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

Equilibrium amide hydrogen exchange and protein folding kinetics

The classical Linderstrøm-Lang hydrogen exchange (HX) model is extended to describe the relationship between the HX behaviors (EX1 and EX2) and protein folding kinetics for the amide protons that can only exchange by global unfolding in a three-state system including native (N), intermediate (I), and unfolded (U) states. For these slowly exchanging amide protons, it is shown that the existence of an intermediate (I) has no effect on the HX behavior in an off-pathway three-state system (IUN). On the other hand, in an on-pathway three-state system (UIN), the existence of a stable folding intermediate has profound effect on the HX behavior. It is shown that fast refolding from the unfolded state to the stable intermediate state alone does not guarantee EX2 behavior. The rate of refolding from the intermediate state to the native state also plays a crucial role in determining whether EX1 or EX2 behavior should occur. This is mainly due to the fact that only amide protons in the native state are observed in the hydrogen exchange experiment. These new concepts suggest that caution needs to be taken if one tries to derive the kinetic events of protein folding from equilibrium hydrogen exchange experiments.     

A computer model to dynamically simulate protein folding: studies with crambin

The current work describes a simplified representation of protein structure with uses in the simulation of protein folding. The model assumes that a protein can be represented by a freely rotating rigid chain with a single atom approximating the effect of each side chain. Potentials describing the attraction or repulsion between different types of amino acids are determined directly from the distribution of amino acids in the database of known protein structures. The optimization technique of simulated annealing has been used to dynamically sample the conformations available to this simple model, allowing the protein to evolve from an extended, random coil into a compact globular structure. Many characteristics expected of true proteins, such as the sequence-dependent formation of secondary structure, the partitioning of hydrophobic residues, and specific disulfide pairing, are reproduced by the simulation, suggesting the model may accurately simulate the folding process.     

Ab initio RNA folding by discrete molecular dynamics: from structure prediction to folding mechanisms

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 A deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNA(Phe), pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses.     

Probing protein folding and stability using disulfide bonds

Disulfide bonds are required to stabilize the folded conformations of many proteins. The rates and equilibria of processes involved in disulfide bond formation and breakage can be manipulated experimentally and can be used to obtain important information about protein folding and stability. A number of experimental procedures for studying these processes, and approaches to interpreting the resulting data, are described here.     

Capturing native/native like structures with a physico-chemical metric (pcSM) in protein folding

Specification of the three dimensional structure of a protein from its amino acid sequence, also called a “Grand Challenge” problem, has eluded a solution for over six decades. A modestly successful strategy has evolved over the last couple of decades based on development of scoring functions (e.g. mimicking free energy) that can capture native or native-like structures from an ensemble of decoys generated as plausible candidates for the native structure. A scoring function must be fast enough in discriminating the native from unfolded/misfolded structures, and requires validation on a large data set(s) to generate sufficient confidence in the score. Here we develop a scoring function called pcSM that detects true native structure in the top 5 with 93% accuracy from an ensemble of candidate structures. If we eliminate the native from ensemble of decoys then pcSM is able to capture near native structure (RMSD < = 5 ?) in top 10 with 86% accuracy. The parameters considered in pcSM are a C-alpha Euclidean metric, secondary structural propensity, surface areas and an intramolecular energy function. pcSM has been tested on 415 systems consisting 142,698 decoys (public and CASP—largest reported hitherto in literature). The average rank for the native is 2.38, a significant improvement over that existing in literature. In-silico protein structure prediction requires robust scoring technique(s). Therefore, pcSM is easily amenable to integration into a successful protein structure prediction strategy. The tool is freely available at http://www.scfbio-iitd.res.in/software/pcsm.jsp.     

A general model of the P2 protein of peripheral nervous system myelin based on secondary structure predictions, tertiary folding principles, and experimental observations

The amino acid sequence of the P2 protein of peripheral myelin was analyzed with regard to regions of probable alpha-helix, beta-structure, beta-turn, and unordered conformation by means of several algorithms commonly used to predict secondary structure in proteins. Because of the high beta-sheet content and virtual absence of alpha-helix shown by the circular dichroic spectra of the protein, a bias was introduced into the algorithms to favor the beta-structure over the alpha-helical conformation. In order to define those beta-sheet residues that could lie on the external hydrophilic surface of the protein and those that could lie in its hydrophobic interior, the predicted beta-strands were examined for charged and uncharged amino acids located at alternating positions in the sequence. The sequential beta-strands in the predicted secondary structure were then ordered into beta-sheets and aligned according to generally accepted tertiary folding principles and certain chemical properties peculiar to the P2 protein. The general model of the P2 protein that emerged was a "Greek key" beta-barrel, consisting of eight antiparallel beta-strands with a two-stranded ribbon of antiparallel beta-structure emerging from one end. The model has an uncharged, hydrophobic core and a highly hydrophilic surface. The two Cys residues, which form a disulfide, occur in a loop connecting two adjacent antiparallel strands. Two hydrophilic loops, each containing a cluster of acidic residues and a single Phe, protrude from one end of the molecule. The general model is consistent with many of the properties of the actual protein, including the relatively weak nature of its association with myelin lipids and the positions of amino acid substitutions. Alternative beta-strand orderings yield three specific models having different interstrand connections across the barrel ends.     

The folding mechanism of a two-domain protein: folding kinetics and domain docking of the gene-3 protein of phage fd

The gene-3 protein (G3P) of filamentous phages is essential for the infection of Escherichia coli. The carboxy-terminal domain anchors this protein in the phage coat, whereas the two amino-terminal domains N1 and N2 protrude from the phage surface. We analyzed the folding mechanism of the two-domain fragment N1-N2 of G3P (G3P(*)) and the interplay between folding and domain assembly. For this analysis, a variant of G3P(*) was used that contained four stabilizing mutations (IIHY-G3P(*)). The observed refolding kinetics extend from 10 ms to several hours. Domain N1 refolds very rapidly (with a time constant of 9.4 ms at 0.5 M guanidinium chloride, 25 degrees C) both as a part of IIHY-G3P(*) and as an isolated protein fragment. The refolding of domain N2 is slower and involves two reactions with time constants of seven seconds and 42 seconds. These folding reactions of the individual domains are followed by a very slow, spectroscopically silent docking process, which shows a time constant of 6200 seconds. This reaction was detected by a kinetic unfolding assay for native molecules. Before docking, N1 and N2 unfold fast and independently, after docking they unfold slowly in a correlated fashion. A high energy barrier is thus created by domain docking, which protects G3P kinetically against unfolding. The slow domain docking is possibly important for the infection of E.coli by the phage. Upon binding to the F pilus, the N2 domain separates from N1 and the binding site for TolA on domain N1 is exposed. Since domain reassembly is so slow, this binding site remains accessible until pilus retraction has brought N1 close to TolA on the bacterial surface.     

Evolutionary aspects of protein structure and folding

Four basic stages of evolution of protein structure are described based on recent work of the authors targeted specifically on reconstruction of the earliest events in the protein evolution. According to this reconstruction, the initial stage of short peptides of, probably, only few amino-acid residues had been followed by formation of closed loops of the size 25-30 residues, which corresponds to the polymer-statistically optimal ring closure size for mixed polypeptide chains. The next stage involved fusion of the respective small linear genes and formation of protein structures consisting of several closed loops of the nearly standard size, up to 4-6 loops (100-200 amino acid residues) in a typical protein fold. The last, modern stage began with combinatorial fusion of the presumably circular 300-600 bp DNA units and, accordingly, formation of multidomain proteins.