Flexibility and mobility in mesophilic and thermophilic homologous proteins from molecular dynamics and FoldUnfold method

To function properly protein molecules require both flexibility and rigidity, therefore fast and accurate prediction of protein rigidity/flexibility is one of the important problems in protein science. In this work we used two theoretical approaches to determine flexible regions in four homologous pairs of proteins from thermophilic and mesophilic organisms. Protein pairs chosen in this study were selected to represent four typical folding classes. Our first approach, FoldUnfold, uses amino acid sequence and statistical information on the density of contacts of amino acids in tertiary structures of known globular proteins. The main advantages of such knowledge-based methodology are its computational speed and ability to make predictions in the absence of three-dimensional (3D) structure of a protein. The second approach uses a graph theory-based rigid cluster decomposition termed FIRST, applied together with Molecular Dynamics (MD) simulations of proteins with known structure. While MD simulations are time-consuming, they are the most direct way of studying physical properties of proteins, including their rigidity/flexibility. Flexible regions predicted by both methods in this work were in good agreement with each other. We also showed that high mobility of a site is not necessarily indicative of its high flexibility and vice versa. In our simulations thermophile proteins were less flexible than their mesophilic homologues. Longer flexible loops were found in mesophilic proteins of all classes.

Library of disordered patterns in 3D protein structures

Intrinsically disordered regions serve as molecular recognition elements, which play an important role in the control of many cellular processes and signaling pathways. It is useful to be able to predict positions of disordered regions in protein chains. The statistical analysis of disordered residues was done considering 34,464 unique protein chains taken from the PDB database. In this database, 4.95% of residues are disordered (i.e. invisible in X-ray structures). The statistics were obtained separately for the N- and C-termini as well as for the central part of the protein chain. It has been shown that frequencies of occurrence of disordered residues of 20 types at the termini of protein chains differ from the ones in the middle part of the protein chain. Our systematic analysis of disordered regions in PDB revealed 109 disordered patterns of different lengths. Each of them has disordered occurrences in at least five protein chains with identity less than 20%. The vast majority of all occurrences of each disordered pattern are disordered. This allows one to use the library of disordered patterns for predicting the status of a residue of a given protein to be ordered or disordered. We analyzed the occurrence of the selected patterns in three eukaryotic and three bacterial proteomes.

Two-, three-, and four-state events occur in the mechanical unfolding of small protein L using molecular dynamics simulation

Mechanical properties of (protein L)(5) have been recently investigated by single-molecule force spectroscopy. It has been demonstrated that the unfolding of individual domains proceeds through a two-state mechanism. Here, we study mechanical properties of protein L at the atomic level under stretching at constant velocity using molecular dynamics simulations. We have found that the unfolding process of protein L can occur either in a single step or through short living and quite native like intermediate states, which was not observed in previous studies. Analysis of the 24 trajectories from molecular dynamics simulations with explicit water showed that the mechanical unfolding of protein L occurs through at least two pathways. These pathways coincide in two- and multi-state events and at different extension velocities studied (0.125, 0.0625 and 0.005 A x ps(-1)).

Is protein folding rate dependent on number of folding stages? Modeling of protein folding with ferredoxin-like fold

Statistical analysis of protein folding rates has been done for 84 proteins with available experimental data. A surprising result is that the proteins with multi-state kinetics from the size range of 50-100 amino acid residues (a.a.) fold as fast as proteins with two-state kinetics from the same size range. At the same time, the proteins with two-state kinetics from the size range 101-151 a.a. fold faster than those from the size range 50-100 a.a. Moreover, it turns out unexpectedly that usually in the group of structural homologs from the size range 50-100 a.a., proteins with multi-state kinetics fold faster than those with two-state kinetics. The protein folding for six proteins with a ferredoxin-like fold and with a similar size has been modeled using Monte Carlo simulations and dynamic programming. Good correlation between experimental folding rates, some structural parameters, and the number of Monte Carlo steps has been obtained. It is shown that a protein with multi-state kinetics actually folds three times faster than its structural homologs.

Prediction of amino acid residues protected from hydrogen-deuterium exchange in a protein chain

We have investigated the possibility to predict protection of amino acid residues from hydrogen-deuterium exchange. A database containing experimental hydrogen-deuterium exchange data for 14 proteins for which these data are known has been compiled. Different structural parameters related to flexibility of amino acid residues and their amide groups have been analyzed to answer the question whether these parameters can be used for predicting the protection of amino acid residues from hydrogen-deuterium exchange. A method for prediction of protection of amino acid residues, which uses only the amino acid sequence of a protein, has been elaborated.

Multiple Unfolding Intermediates Obtained by Molecular Dynamic Simulations under Stretching for Immunoglobulin-Binding Domain of Protein G

We have studied the mechanical properties of the immunoglobulin-binding domain of protein G at the atomic level under stretching at constant velocity using molecular dynamics simulations. We have found that the unfolding process can occur either in a single step or through intermediate states. Analysis of the trajectories from the molecular dynamic simulations showed that the mechanical unfolding of the immunoglobulin-binding domain of protein G is triggered by the separation of the terminal beta-strands and the order in which the secondary-structure elements break is practically the same in two- and multi-state events and at the different extension velocities studied. It is seen from our analysis of 24 trajectories that the theoretical pathway of mechanical unfolding for the immunoglobulin-binding domain of protein G does not coincide with that proposed in denaturant studies in the absence of force.

ComSin: database of protein structures in bound (complex) and unbound (single) states in relation to their intrinsic disorder

Most of the proteins in a cell assemble into complexes to carry out their function. In this work, we have created a new database (named ComSin) of protein structures in bound (complex) and unbound (single) states to provide a researcher with exhaustive information on structures of the same or homologous proteins in bound and unbound states. From the complete Protein Data Bank (PDB), we selected 24 910 pairs of protein structures in bound and unbound states, and identified regions of intrinsic disorder. For 2448 pairs, the proteins in bound and unbound states are identical, while 7129 pairs have sequence identity 90% or larger. The developed server enables one to search for proteins in bound and unbound states with several options including sequence similarity between the corresponding proteins in bound and unbound states, and validation of interaction interfaces of protein complexes. Besides that, through our web server, one can obtain necessary information for studying disorder-to-order and order-to-disorder transitions upon complex formation, and analyze structural differences between proteins in bound and unbound states. The database is available at http://antares.protres.ru/comsin/.

Coupling between properties of the protein shape and the rate of protein folding

There are several important questions on the coupling between properties of the protein shape and the rate of protein folding. We have studied a series of structural descriptors intended for describing protein shapes (the radius of gyration, the radius of cross-section, and the coefficient of compactness) and their possible connection with folding behavior, either rates of folding or the emergence of folding intermediates, and compared them with classical descriptors, protein chain length and contact order. It has been found that when a descriptor is normalized to eliminate the influence of the protein size (the radius of gyration normalized to the radius of gyration of a ball of equal volume, the coefficient of compactness defined as the ratio of the accessible surface area of a protein to that of an ideal ball of equal volume, and relative contact order) it completely looses its ability to predict folding rates. On the other hand, when a descriptor correlates well with protein size (the radius of cross-section and absolute contact order in our consideration) then it correlates well with the logarithm of folding rates and separates reasonably well two-state folders from multi-state ones. The critical control for the performance of new descriptors demonstrated that the radius of cross-section has a somewhat higher predictive power (the correlation coefficient is −0.74) than size alone (the correlation coefficient is −0.65). So, we have shown that the numerical descriptors of the overall shape-geometry of protein structures are one of the important determinants of the protein-folding rate and mechanism.

Amyloid-like properties of Saccharomyces cerevisiae cell wall glucantransferase Bgl2p: prediction and experimental evidences

Glucantransferase Bgl2p is a major conserved cell wall constituent described for a wide range of yeast species. In the baker's yeast Saccharomyces cerevisiae it is the only non-covalently bound cell wall protein that cannot be released from cell walls by sequential SDS and trypsin treatment. It contains seven amyloidogenic determinants. Circular dichroism analysis and fluorescence spectroscopy with thioflavin T indicate the presence of beta-sheet structures in Bgl2p isolates. Bgl2p forms fibrils, a process that is enforced in the presence of other cell wall components. Thus the data obtained is the first evidence for amyloid-like properties of yeast cell wall protein-glucantransferase Bgl2p.

Understanding the folding rates and folding nuclei of globular proteins

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" <--> "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data.

More compact protein globules exhibit slower folding rates

We have demonstrated that, among proteins of the same size, alpha/beta proteins have on the average a greater number of contacts per residue due to their more compact (more "spherical") structure, rather than due to tighter packing. We have examined the relationship between the average number of contacts per residue and folding rates in globular proteins according to general protein structural class (all-alpha, all-beta, alpha/beta, alpha+beta). Our analysis demonstrates that alpha/beta proteins have both the greatest number of contacts and the slowest folding rates in comparison to proteins from the other structural classes. Because alpha/beta proteins are also known to be the oldest proteins, it can be suggested that proteins have evolved to pack more quickly and into looser structures.

Different packing of external residues can explain differences in the thermostability of proteins from thermophilic and mesophilic organisms

MOTIVATION

Understanding the basis of protein stability in thermophilic organisms raises a general question: what structural properties of proteins are responsible for the higher thermostability of proteins from thermophilic organisms compared to proteins from mesophilic organisms?

RESULTS

A unique database of 373 structurally well-aligned protein pairs from thermophilic and mesophilic organisms is constructed. Comparison of proteins from thermophilic and mesophilic organisms has shown that the external, water-accessible residues of the first group are more closely packed than those of the second. Packing of interior parts of proteins (residues inaccessible to water molecules) is the same in both cases. The analysis of amino acid composition of external residues of proteins from thermophilic organisms revealed an increased fraction of such amino acids as Lys, Arg and Glu, and a decreased fraction of Ala, Asp, Asn, Gln, Thr, Ser and His. Our theoretical investigation of folding/unfolding behavior confirms the experimental observations that the interactions that differ in thermophilic and mesophilic proteins form only after the passing of the transition state during folding. Thus, different packing of external residues can explain differences in thermostability of proteins from thermophilic and mesophilic organisms.

AVAILABILITY

The database of 373 structurally well-aligned protein pairs is available at http://phys.protres.ru/resources/termo_meso_base.html.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Prediction of number and position of domain boundaries in multi-domain proteins by use of amino acid sequence alone

Prediction of protein domain boundaries is an important step for the prediction of three-dimensional structure. The simple method PDP has been elaborated for prediction of the number and position of domain boundaries in multi-domain proteins by use of amino acid sequence alone. The method uses an optimized scale based on the statistics of appearance of amino acid residues at domain boundaries. Our method demonstrates promising results in comparison to other methods that do not use homologous sequences. From the database of proteins that are targets from CASP6 (Critical Assessment of Techniques for Protein Structure Prediction) our program correctly assigned the number of domains for approximately 80% of one domain proteins and approximately 50% for two-domain proteins. Our method offers three main advantages: it is very simple, it is fast, and it uses a minimal number of parameters in comparison with other methods.

Prediction of amyloidogenic and disordered regions in protein chains

The determination of factors that influence protein conformational changes is very important for the identification of potentially amyloidogenic and disordered regions in polypeptide chains. In our work we introduce a new parameter, mean packing density, to detect both amyloidogenic and disordered regions in a protein sequence. It has been shown that regions with strong expected packing density are responsible for amyloid formation. Our predictions are consistent with known disease-related amyloidogenic regions for eight of 12 amyloid-forming proteins and peptides in which the positions of amyloidogenic regions have been revealed experimentally. Our findings support the concept that the mechanism of amyloid fibril formation is similar for different peptides and proteins. Moreover, we have demonstrated that regions with weak expected packing density are responsible for the appearance of disordered regions. Our method has been tested on datasets of globular proteins and long disordered protein segments, and it shows improved performance over other widely used methods. Thus, we demonstrate that the expected packing density is a useful value with which one can predict both intrinsically disordered and amyloidogenic regions of a protein based on sequence alone. Our results are important for understanding the structural characteristics of protein folding and misfolding.

FoldUnfold: web server for the prediction of disordered regions in protein chain

Identification of disordered regions in polypeptide chains is very important because such regions are essential for protein function. A new parameter, namely mean packing density of residues has been introduced to detect disordered regions in a protein sequence. We have demonstrated that regions with weak expected packing density would be responsible for the appearance of disordered regions. Our method (FoldUnfold) has been tested on datasets of globular proteins (559 proteins) and long disordered protein segments (129 proteins) and showed improved performance over some other widely used methods, such as DISOPRED, PONDR VL3H, IUPred and GlobPlot.

AVAILABILITY

The FoldUnfold server is available for users at http://skuld.protres.ru/~mlobanov/ogu/ogu.cgi. There is a link to our server through the web site of DisProt (http://www.disprot.org/predictors.php).

Is it possible to predict amyloidogenic regions from sequence alone?

Identification of potentially amyloidogenic regions in polypeptide chains is very important because the amyloid fibril formation can be induced in most normal proteins. In our work we suggest a new method to detect amyloidogenic regions in protein sequence. It is based on the assumption that packing is tight inside an amyloid and therefore regions which could potentially pack well would have a tendency to form amyloids. This means that the regions with strong expected packing of residues would be responsible for the amyloid formation. We use this property to identify potentially amyloidogenic regions in proteins basing on their amino acid sequences only. Our predictions are consistent with known disease-related amyloidogenic regions for 8 of 11 amyloid-forming proteins and peptides in which the positions of amyloidogenic regions have been revealed experimentally. Predictions of the regions which are responsible for the formation of amyloid fibrils in proteins unrelated to disease have been also done.

Trend of amino acid composition of proteins of different taxa

Archaea, bacteria and eukaryotes represent the main kingdoms of life. Is there any trend for amino acid compositions of proteins found in full genomes of species of different kingdoms? What is the percentage of totally unstructured proteins in various proteomes? We obtained amino acid frequencies for different taxa using 195 known proteomes and all annotated sequences from the Swiss-Prot data base. Investigation of the two data bases (proteomes and Swiss-Prot) shows that the amino acid compositions of proteins differ substantially for different kingdoms of life, and this difference is larger between different proteomes than between different kingdoms of life. Our data demonstrate that there is a surprisingly small selection for the amino acid composition of proteins for higher organisms (eukaryotes) and their viruses in comparison with the "random" frequency following from a uniform usage of codons of the universal genetic code. On the contrary, lower organisms (bacteria and especially archaea) demonstrate an enhanced selection of amino acids. Moreover, according to our estimates, 12%, 3% and 2% of the proteins in eukaryotic, bacterial and archaean proteomes are totally disordered, and long (> 41 residues) disordered segments are found to occur in 16% of arhaean, 20% of eubacterial and 43% of eukaryotic proteins for 19 archaean, 159 bacterial and 17 eukaryotic proteomes, respectively. A correlation between amino acid compositions of proteins of various taxa, show that the highest correlation is observed between eukaryotes and their viruses (the correlation coefficient is 0.98), and bacteria and their viruses (the correlation coefficient is 0.96), while correlation between eukaryotes and archaea is 0.85 only.

Entropy capacity determines protein folding

Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Here, based on the known experimental data and using theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue-that is, an entropy capacity-for fast protein folding. Statistical analysis of conformational entropy and number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts (class alpha/beta has the largest number of contacts) and average conformational entropy per residue (class all-alpha has the largest number of rotatable angles phi, psi, and chi per residue). These class-specific features determine the folding rates: alpha proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones. Our result is in agreement with the experimental folding rates for 60 proteins. This suggests that structural and sequence properties are important determinants of protein folding rates.

Comparison of X-ray and NMR structures: Is there a systematic difference in residue contacts between X-ray- and NMR-resolved protein structures?

We have compared structures of 78 proteins determined by both NMR and X-ray methods. It is shown that X-ray and NMR structures of the same protein have more differences than various X-ray structures obtained for the protein, and even more than various NMR structures of the protein. X-ray and NMR structures of 18 of these 78 proteins have obvious large-scale structural differences that seem to reflect a difference of crystal and solution structures. The other 60 pairs of structures have only small-scale differences comparable with differences between various X-ray or various NMR structures of a protein; we have analyzed these structures more attentively. One of the main differences between NMR and X-ray structures concerns the number of contacts per residue: (1) NMR structures presented in PDB have more contacts than X-ray structures at distances below 3.0 A and 4.5-6.5 A, and fewer contacts at distances of 3.0-4.5 A and 6.5-8.0 A; (2) this difference in the number of contacts is greater for internal residues than for external ones, and it is larger for beta-containing proteins than for all-alpha proteins. Another significant difference is that the main-chain hydrogen bonds identified in X-ray and NMR structures often differ. Their correlation is 69% only. However, analogous difference is found for refined and rerefined NMR structures, allowing us to suggest that the observed difference in interresidue contacts of X-ray and NMR structures of the same proteins is due mainly to a difference in mathematical treatment of experimental results.

To be folded or to be unfolded?

The lack of ordered structure in "natively unfolded" proteins raises a general question: Are there intrinsic properties of amino acid residues that are responsible for the absence of fixed structure at physiological conditions? In this article, we demonstrate that the competence of a protein to be folded or to be unfolded may be determined by the property of amino acid residues to form a sufficient number of contacts in a globular state. The expected average number of contacts per residue calculated from the amino acid sequence alone (using the average number of contacts for 20 amino acid residues in globular proteins) can be used as one of the simple indicators of natively unfolded proteins. The prediction accuracy for the sets of 80 folded and 90 natively unfolded proteins reaches 89% if the expected average number of contacts is used as a parameter and 83% in the case of hydrophobicity. An optimal set of artificial parameters for 20 amino acid residues obtained by Monte Carlo algorithm to maximally separate the sets of 90 natively unfolded and 80 folded proteins demonstrates the upper limit for prediction accuracy, which is 95%.

[The interaction of the GroEL chaperone with early kinetic intermediates of renaturing proteins inhibits the formation of their native structure]

The main function of the chaperone GroEL is to prevent nonspecific association of nonnative protein chains and provide their correct folding. In the present work, the renaturation kinetics of three globular proteins (human alpha-lactalbumin, bovine carbonic anhydrase, and yeast phosphoglycerate kinase) in the presence of different molar excess of GroEL (up to 10-fold) was studied. It was shown that the formation of the native structure during the refolding of these proteins is retarded with an increase in GroEL molar excess due to the interaction of kinetic protein intermediates with the chaperone. Mg(2+)-ATP and Mg(2+)-ADP weaken this interaction and decrease the retarding effect of GroEL on the protein refolding kinetics. The theoretical modeling of protein folding in the presence of GroEL showed that the experimentally observed linear increase in the protein refolding half-time with increasing molar excess of GroEL must occur only when the protein adopts its native structure outside of GroEL (i.e. in the free state), while the refolding of the protein in the complex with GroEL is inhibited. The dissociation constants of GroEL complexed with the kinetic intermediates of the proteins studied were evaluated, and a simple mechanism of the functioning of GroEL as a molecular chaperone was proposed.

General Dynamic Properties of A 12-36 Amyloid Peptide Involved in Alzheimer's Disease from Unfolding Simulation

To study the folding/unfolding properties of a beta-amyloid peptide Abeta(12-36) of Alzheimer's disease, five molecular dynamics simulations of Abeta(12-36) in explicit water were done at 450 K starting from a structure that is stable in trifluoroethanol/water at room temperature with two alpha-helices. Due to high temperature, the initial helical structure unfolded during the simulation. The observed aspects of the unfolding were as follows. 1) One helix (helix 1) had a longer life than the other (helix 2), which correlates well with the theoretically computed Phi values. 2) Temporal prolongation of helix 1 was found before unfolding. 3) Hydrophobic cores formed frequently with rearrangement of amino-acid residues in the hydrophobic cores. The formation and rearrangement of the hydrophobic cores may be a general aspect of this peptide in the unfolded state, and the structural changes accompanied by the hydrophobic-core rearrangement may lead the peptide to the most stable structure. 4) Concerted motions (collective modes) appeared to unfold helix 1. The collective modes were similar with those observed in another simulation at 300 K. The analysis implies that the conformation moves according to the collective modes when the peptide is in the initial stage of protein unfolding and in the final stage of protein folding.

Outlining folding nuclei in globular proteins

Our theoretical approach for prediction of folding/unfolding nuclei in three-dimensional protein structures is based on a search for free energy saddle points on networks of protein unfolding pathways. Under some approximations, this search is performed rapidly by dynamic programming and results in prediction of Phi values, which can be compared with those found experimentally. In this study, we optimize some details of the model (specifically, hydrogen atoms are taken into account in addition to heavy atoms), and compare the theoretically obtained and experimental Phi values (which characterize involvement of residues in folding nuclei) for all 17 proteins, where Phi values are now known for many residues. We show that the model provides good Phi value predictions for proteins whose structures have been determined by X-ray analysis (the average correlation coefficient is 0.65), with a more limited success for proteins whose structures have been determined by NMR techniques only (the average correlation coefficient is 0.34), and that the transition state free energies computed from the same model are in a good anticorrelation with logarithms of experimentally measured folding rates at mid-transition (the correlation coefficient is -0.73).

Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics

We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.

Prediction of protein domain boundaries from sequence alone

We present here a simple approach to identify domain boundaries in proteins of an unknown three-dimensional structure. Our method is based on the hypothesis that a high-side chain entropy of a region in a protein chain must be compensated by a high-residue interaction energy within the region, which could correlate with a well-structured part of the globule, that is, with a domain unit. For protein domains, this means that the domain boundary is conditioned by amino acid residues with a small value of side chain entropy, which correlates with the side chain size. On the one hand, relatively high Ala and Gly content on the domain boundary results in high conformational entropy of the backbone chain between the domains. On the other hand, the presence of Pro residues leads to the formation of hinges for a relative orientation of domains. The method was applied to 646 proteins with two contiguous domains extracted from the SCOP database with a success rate of 63%. We also report the prediction of domain boundaries for CASP5 targets obtained with the same method.

beta-Hairpins, alpha-helices, and the intermediates among the secondary structures in the energy landscape of a peptide from a distal beta-hairpin of SH3 domain

Energy landscape of a peptide, extracted from a distal beta-hairpin of src SH3 domain, in explicit water was obtained with the multicanonical molecular dynamics. A variety of beta-hairpins with various strand-strand hydrogen bonds were found in the energy landscape at 300 K. There was no energy barrier between random-coil and hairpins. Thus, the peptide conformation can easily change from the random-coil to the hairpins in the thermal fluctuations at 300 K. The landscape also included two clusters of alpha-helices, among which an energy barrier existed, and besides, these helix clusters were separated from the other conformations. Thus, the free-energy barrier exists among the helices and the other conformations. Intermediate clusters were found between the helix and the hairpin clusters. The current study showed that the isolated state of this peptide in water fluctuates among random-coil, beta-hairpin, and alpha-helix. In SH3 domain, which has a topology of mainly beta-protein, the whole-protein folding may proceed when the segment is folded in the beta-hairpin and the other parts of the protein are coupled with the beta-hairpin in an energetically or kinetically favorite way.

Alpha-helix and beta-hairpin Folding from experiment, analytical theory and molecular dynamics simulations

The alpha-helix and beta-hairpin are the minimal secondary structure elements of proteins. Identification of the factors governing the formation of these structures independently of the rest of the protein is important for understanding the determinants and rules driving the folding process to a unique native structure. It has been shown that some alpha-helices and beta-hairpins can fold autonomously into native-like structures, either in aqueous solution or in the presence of an organic co-solvent; possible mechanisms of these processes have been considered in literature. The characteristic times for folding of alpha and beta structures are estimated from experiments, simple analytical theories and more detailed computer models. Our aim is to review recent experimental and theoretical studies of folding of alpha and beta structures focusing much attention on beta-hairpins.

Folding nuclei in proteins

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed just close to the equilibrium point. Here the 'two-state' transition proceeds without any accumulation of metastable intermediates, and only the transition state ('folding nucleus') is outlined by its key influence on the folding-unfolding kinetics. Our aim is to review recent experimental and theoretical studies of the folding nuclei.

Folding nuclei in 3D protein structures

This paper presents and analyzes the results of several new approaches to the problem of finding the folding nucleus in a given 3D protein structure. Firstly, we show that the participation of residues in the hydrophobic core and the secondary structure of native protein has a rather modest correlation with the experimentally found phi values characterizing the participation of residues in the folding nuclei. Then we tried to find the nuclei as the free energy saddle points on the network of the folding/unfolding pathways using the branch-and-bound technique and dynamic programming. We also attempted to estimate the phi values from solving of kinetic equations for the network of protein folding/unfolding pathways. These approaches give a better correlation with experiment, and the estimated folding time is consistent with the experimentally observed rapid folding of small proteins.

Optimal region of average side-chain entropy for fast protein folding

Search and study the general principles that govern kinetics and thermodynamics of protein folding generates new insight into the factors that control this process. Here, we demonstrate based on the known experimental data and using theoretical modeling of protein folding that side-chain entropy is one of the general determinants of protein folding. We show for proteins belonging to the same structural family that there exists an optimal relationship between the average side-chain entropy and the average number of contacts per residue for fast folding kinetics. Analysis of side-chain entropy for proteins that fold without additional agents demonstrates that there exists an optimal region of average side-chain entropy for fast folding. Deviation of the average side-chain entropy from the optimal region results in an anomalous protein folding process (prions, alpha-lytic protease, subtilisin, some DNA-binding proteins). Proteins with high or low side-chain entropy would have extended unfolded regions and would require some additional agents for complete folding. Such proteins are common in nature, and their structure properties have biological importance.

A theoretical search for folding/unfolding nuclei in three-dimensional protein structures

When a protein folds or unfolds, it has to pass through many half-folded microstates. Only a few of them can be seen experimentally. In a two-state transition proceeding with no accumulation of metastable intermediates [Fersht, A. R. (1995) Curr. Opin. Struct. Biol. 5, 79-84], only the semifolded microstates corresponding to the transition state can be outlined; they influence the folding/unfolding kinetics. Our aim is to calculate them, provided the three-dimensional protein structure is given. The presented approach follows from the capillarity theory of protein folding and unfolding [Wolynes, P. G. (1997) Proc. Natl. Acad. Sci. USA 94, 6170-6175]. The approach is based on a search for free-energy saddle point(s) on a network of protein unfolding pathways. Under some approximations, this search is rapidly performed by dynamic programming and, despite its relative simplicity, gives a good correlation with experiment. The computed folding nuclei look like ensembles of those compact and closely packed parts of the three-dimensional native folds that contain a small number of disordered protruding loops. Their estimated free energy is consistent with the rapid (within seconds) folding and unfolding of small proteins at the point of thermodynamic equilibrium between the native fold and the coil.

Hyperphosphorylation induces structural modification of tau-protein

The effect of hyperphosphorylation on the structural properties and conformational stability of bovine tau-protein was studied by means of circular dichroism and fluorescence lifetime techniques. Normal protein contains unusual secondary structure elements: extended left-handed helices. The structure of this protein was assumed to be of a 'tadpole' type - a globular C-terminal part with a long and rigid tail included in the extended left-handed helix. Either a decrease or an increase of pH induced only minor changes of the normal tau-protein surface. Hyperphosphorylation affected the extended part of the protein molecule; the decrease of pH in this case induced considerable structural rearrangements, and the conformation of the C-terminal part of the protein molecule was transformed into a molten globule-like state.

Roughness of the globular protein surface: analysis of high resolution X-ray data

In an earlier publication [Serdyuk, I.N. et al., Biofizika, in press, 1997] we demonstrated that the asymmetry extent of globular proteins does not change with increasing their sizes, and the observed nontrivial dependence of the protein accessible surface area on the molecular mass [Miller, S., J. Mol. Biol. 196:641-656, 1987] (A(s) - M dependence) is a reflection of the protein surface relief peculiarities. To clarify these peculiarities, an analysis of the molecular surface on the basis of high-resolution x-ray data has been done for 25 globular proteins not containing prosthetic groups. The procedure was based on studying the dependence of the minimal number (N) of probe bodies (here cubes) covering the entire protein surface, both on their size (N - R dependence) and on the value of dry protein volume (N - V dependence). Two levels of protein surface organization have been detected by molecular surface analysis. On the micro scale (2-7 A), the surface is characterized by a D = 2.1 fractal dimension which is intrinsic to surfaces with weak deformations and reflects the local atomic group packing. On the macro scale, large-scale surface defects are revealed that are interpreted as the result of secondary structure elements packing. A simple model of protein surface representation reflecting large-scale irregularities has been proposed.

Geometrical factor and physical reasons for its influence on the kinetic and thermodynamic properties of RNA-like heteropolymers

BACKGROUND

It has been shown that not only the primary sequence but also the geometry of the native conformation influences the kinetic and thermodynamic properties of a protein-like model. The purpose of this paper is to elucidate the geometrical factor, which affects the kinetic and thermodynamic properties of RNA-like heteropolymers, and physical reasons for this phenomenon.

RESULTS

It is shown that increasing the strength of long-range contacts can accelerate the finding of the native secondary structure for RNA-like heteropolymers. Decreasing the strength of long-range contacts results in deceleration of this process. The physical reason for this phenomenon is the increase in the average energy of non-native structures and, as a consequence, the increase (in absolute value) of the relative value of native energy from strengthening long-range contacts under constant energy of the native state. Statistical analysis of natural RNAs has shown that the mean stability of helices formed by the pairing of regions that are remote along the chain prevails over the mean stability of helices formed by regions that are close along the chain.

CONCLUSIONS

The kinetics simulations suggest that the folding of the RNA secondary structure depends on the structural factors of the native state. One of these factors accelerating large RNA folding is the existence of strong long-range helices in the native secondary structure.

Folding of chains with random and edited sequences: similarities and differences

We have investigated the process of protein folding by Monte-Carlo simulation of folding occurring in a simple 3D lattice model of a protein globule. We have found the range of 'optimal' temperatures where the native fold is achieved by the Monte-Carlo process much faster than that by exhaustive sorting of all the chain folds. The 'optimal' temperatures are essentially the same for different random and 'edited' sequences (for the latter, the native fold energy is separated by a considerable gap from the energies of other low-energy folds; for random sequences, this gap is negligible). At the 'optimal' temperatures, the 'edited' chains attain their native fold faster than the random ones. However, the essence is that the native folds of 'edited' chains are thermodynamically stable at temperatures optimal for fast folding, while the native folds of random chains are unstable at the temperatures optimal for fast folding; also, at low temperatures where the native folds of random chains are stable, folding kinetics is very slow. Consequently, stable native folds are formed slowly by random sequences and rapidly by the 'edited' ones.