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Recent advancements in experimental and computational methods for RNA secondary structure detection have revealed the crucial role of RNA structural elements in diverse molecular processes within living cells. It has been demonstrated that the secondary structure of the entire viral genome is often responsible for performing crucial functions in the viral life cycle and also influences virus evolution. To investigate the role of viral RNA secondary structure, alongside experimental techniques, the use of bioinformatics tools is important for analyzing various secondary structure patterns, including hairpin loops, internal loops, multifurcations, external loops, bulges, stems, and pseudoknots. Here, we have introduced a Python package for analyzing RNA secondary structure elements in viral genomes, which includes the recognition of common secondary structure patterns, the generation of descriptive statistics for these structural elements, and the provision of their basic properties. We applied the developed package to analyze the secondary structures of complete viral genomes collected from the literature, aiming to gain insights into viral function and evolution. Both the package and the collection of secondary structures of viral genomes are available at http://github.com/KazanovLab/RNAsselem ., Competing Interests: Declarations Competing interests The authors declare no competing interests., (© 2024. The Author(s).)

Enhancing protein stability holds paramount significance in biotechnology, therapeutics, and the food industry. Circular permutations offer a distinctive avenue for manipulating protein stability while keeping intra-protein interactions intact. Amidst the creation of circular permutants, determining the optimal placement of the new N- and C-termini stands as a pivotal, albeit largely unexplored, endeavor. In this study, we employed PONDR-FIT's predictions of disorder propensity to guide the design of circular permutants for the GroEL apical domain (residues 191-345). Our underlying hypothesis posited that a higher predicted disorder value would correspond to reduced stability in the circular permutants, owing to the increased likelihood of fluctuations in the novel N- and C-termini. To substantiate this hypothesis, we engineered six circular permutants, positioning glycines within the loops as locations for the new N- and C-termini. We demonstrated the validity of our hypothesis along the set of the designed circular permutants, as supported by measurements of melting temperatures by circular dichroism and differential scanning microcalorimetry. Consequently, we propose a novel computational methodology that rationalizes the design of circular permutants with projected stability. Video Abstract., (© 2024. The Author(s).)

The molecular toxicity of the uranyl ion (UO 2 2+ ) in living cells is primarily determined by its high affinity to both native and potential metal-binding sites that commonly occur in the structure of biomolecules. Recent advances in computational and experimental research have shed light on the structural properties and functional impacts of uranyl binding to proteins, organic ligands, nucleic acids, and their complexes. In the present work, we report the results of the computational investigation of the uranyl-mediated loss of DNA-binding activity of PARP-1, a eukaryotic enzyme that participates in DNA repair, cell differentiation, and the induction of inflammation. The latest experimental studies have shown that the uranyl ion directly interacts with its DNA-binding subdomains, zinc fingers Zn1 and Zn2, and alters their tertiary structure. Here, we propose an atomistic mechanism underlying this process and compute the free energy change along the suggested pathway. Our Quantum Mechanics/Molecular Mechanics (QM/MM) simulations of the Zn2-UO 2 2+ complex indicate that the uranyl ion replaces zinc in its native binding site. However, the resulting state is destroyed due to the spontaneous internal hydrolysis of the U-Cys162 coordination bond. Despite the enthalpy of hydrolysis being +2.8 kcal/mol, the overall reaction free energy change is -0.6 kcal/mol, which is attributed to the loss of domain's native tertiary structure originally maintained by a zinc ion. The subsequent reorganization of the binding site includes the association of the uranyl ion with the Glu190/Asp191 acidic cluster and significant perturbations in the domain's tertiary structure driven by a further decrease in the free energy by 6.8 kcal/mol. The disruption of the DNA-binding interface revealed in our study is consistent with previous experimental findings and explains the loss of PARP-like zinc fingers' affinity for nucleic acids.

Mutations that prevent the production of proteins in the DMD gene cause Duchenne muscular dystrophy. Most frequently, these are deletions leading to reading-frame shift. The "reading-frame rule" states that deletions that preserve ORF result in a milder Becker muscular dystrophy. By removing several exons, new genome editing tools enable reading-frame restoration in DMD with the production of BMD-like dystrophins. However, not every truncated dystrophin with a significant internal loss functions properly. To determine the effectiveness of potential genome editing, each variant should be carefully studied in vitro or in vivo. In this study, we focused on the deletion of exons 8-50 as a potential reading-frame restoration option. Using the CRISPR-Cas9 tool, we created the novel mouse model DMDdel8-50, which has an in-frame deletion in the DMD gene. We compared DMDdel8-50 mice to C57Bl6/CBA background control mice and previously generated DMDdel8-34 KO mice. We discovered that the shortened protein was expressed and correctly localized on the sarcolemma. The truncated protein, on the other hand, was unable to function like a full-length dystrophin and prevent disease progression. On the basis of protein expression, histological examination, and physical assessment of the mice, we concluded that the deletion of exons 8-50 is an exception to the reading-frame rule.

AlphaFold changed the field of structural biology by achieving three-dimensional (3D) structure prediction from protein sequence at experimental quality. The astounding success even led to claims that the protein folding problem is "solved". However, protein folding problem is more than just structure prediction from sequence. Presently, it is unknown if the AlphaFold-triggered revolution could help to solve other problems related to protein folding. Here we assay the ability of AlphaFold to predict the impact of single mutations on protein stability (ΔΔG) and function. To study the question we extracted the pLDDT and metrics from AlphaFold predictions before and after single mutation in a protein and correlated the predicted change with the experimentally known ΔΔG values. Additionally, we correlated the same AlphaFold pLDDT metrics with the impact of a single mutation on structure using a large scale dataset of single mutations in GFP with the experimentally assayed levels of fluorescence. We found a very weak or no correlation between AlphaFold output metrics and change of protein stability or fluorescence. Our results imply that AlphaFold may not be immediately applied to other problems or applications in protein folding., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Pak et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The ability of protein chains to spontaneously form their three-dimensional structures is a long-standing mystery in molecular biology. The most conceptual aspect of this mystery is how the protein chain can find its native, "working" spatial structure (which, for not too big protein chains, corresponds to the global free energy minimum) in a biologically reasonable time, without exhaustive enumeration of all possible conformations, which would take billions of years. This is the so-called "Levinthal's paradox." In this review, we discuss the key ideas and discoveries leading to the current understanding of protein folding kinetics, including folding landscapes and funnels, free energy barriers at the folding/unfolding pathways, and the solution of Levinthal's paradox. A special role here is played by the "all-or-none" phase transition occurring at protein folding and unfolding and by the point of thermodynamic (and kinetic) equilibrium between the "native" and the "unfolded" phases of the protein chain (where the theory obtains the simplest form). The modern theory provides an understanding of key features of protein folding and, in good agreement with experiments, it (i) outlines the chain length-dependent range of protein folding times, (ii) predicts the observed maximal size of "foldable" proteins and domains. Besides, it predicts the maximal size of proteins and domains that fold under solely thermodynamic (rather than kinetic) control. Complementarily, a theoretical analysis of the number of possible protein folding patterns, performed at the level of formation and assembly of secondary structures, correctly outlines the upper limit of protein folding times., Competing Interests: Competing interestsThe authors declare no competing interests., (© International Union for Pure and Applied Biophysics (IUPAB) and Springer-Verlag GmbH Germany, part of Springer Nature 2022, Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.)

Motivation: Prediction of protein stability change upon mutation (ΔΔG) is crucial for facilitating protein engineering and understanding of protein folding principles. Robust prediction of protein folding free energy change requires the knowledge of protein three-dimensional (3D) structure. In case, protein 3D structure is not available, one can predict the structure from protein sequence; however, the perspectives of ΔΔG predictions for predicted protein structures are unknown. The accuracy of using 3D structures of the best templates for the ΔΔG prediction is also unclear., Results: To investigate these questions, we used a representative set of seven diverse and accurate publicly available tools (FoldX, Eris, Rosetta, DDGun, ACDC-NN, ThermoNet and DynaMut) for stability change prediction combined with AlphaFold or I-Tasser for protein 3D structure prediction. We found that best templates perform consistently better than (or similar to) homology models for all ΔΔG predictors. Our findings imply using the best template structure for the prediction of protein stability change upon mutation if the protein 3D structure is not available., Availability and Implementation: The data are available at https://github.com/ivankovlab/template-vs-model., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author(s) 2022. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Elevated plasma levels of hyaluronic acid (HA) is a disease marker in liver pathology and other inflammatory disorders. Inhibition of HA synthesis with coumarin 4-methylumbelliferone (4MU) has a beneficial effect in animal models of fibrosis, inflammation, cancer and metabolic syndrome. 4MU is an active compound of approved choleretic drug hymecromone with low bioavailability and a broad spectrum of action. New, more specific and efficient inhibitors of hyaluronan synthases (HAS) are required. We have tested several newly synthesized coumarin compounds and commercial chitin synthesis inhibitors to inhibit HA production in cell culture assay. Coumarin derivative compound VII (10'-methyl-6'-phenyl-3'H-spiro[piperidine-4,2'-pyrano[3,2-g]chromene]-4',8'-dione) demonstrated inhibition of HA secretion by NIH3T3 cells with the half-maximal inhibitory concentration (IC50) = 1.69 ± 0.75 μΜ superior to 4MU (IC50 = 8.68 ± 1.6 μΜ). Inhibitors of chitin synthesis, etoxazole, buprofezin, triflumuron, reduced HA deposition with IC50 of 4.21 ± 3.82 μΜ, 1.24 ± 0.87 μΜ and 1.48 ± 1.44 μΜ, respectively. Etoxazole reduced HA production and prevented collagen fibre formation in the CCl4 liver fibrosis model in mice similar to 4MU. Bioinformatics analysis revealed homology between chitin synthases and HAS enzymes, particularly in the pore-forming domain, containing the proposed site for etoxazole binding., (© The Author(s) 2021. Published by Oxford University Press.)

"How do proteins fold?" Researchers have been studying different aspects of this question for more than 50 years. The most conceptual aspect of the problem is how protein can find the global free energy minimum in a biologically reasonable time, without exhaustive enumeration of all possible conformations, the so-called "Levinthal's paradox." Less conceptual but still critical are aspects about factors defining folding times of particular proteins and about perspectives of machine learning for their prediction. We will discuss in this review the key ideas and discoveries leading to the current understanding of folding kinetics, including the solution of Levinthal's paradox, as well as the current state of the art in the prediction of protein folding times., Competing Interests: The authors declare no conflict of interest.

Motivation: Epistasis, the context-dependence of the contribution of an amino acid substitution to fitness, is common in evolution. To detect epistasis, fitness must be measured for at least four genotypes: the reference genotype, two different single mutants and a double mutant with both of the single mutations. For higher-order epistasis of the order n, fitness has to be measured for all 2n genotypes of an n-dimensional hypercube in genotype space forming a "combinatorially complete dataset". So far, only a handful of such datasets have been produced by manual curation. Concurrently, random mutagenesis experiments have produced measurements of fitness and other phenotypes in a high-throughput manner, potentially containing a number of combinatorially complete datasets., Results: We present an effective recursive algorithm for finding all hypercube structures in random mutagenesis experimental data. To test the algorithm, we applied it to the data from a recent HIS3 protein dataset and found all 199,847,053 unique combinatorially complete genotype combinations of dimensionality ranging from two to twelve. The algorithm may be useful for researchers looking for higher-order epistasis in their high-throughput experimental data., Availability: https://github.com/ivankovlab/HypercubeME.git., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author(s) 2019. Published by Oxford University Press.)

Characterizing the fitness landscape, a representation of fitness for a large set of genotypes, is key to understanding how genetic information is interpreted to create functional organisms. Here we determined the evolutionarily-relevant segment of the fitness landscape of His3, a gene coding for an enzyme in the histidine synthesis pathway, focusing on combinations of amino acid states found at orthologous sites of extant species. Just 15% of amino acids found in yeast His3 orthologues were always neutral while the impact on fitness of the remaining 85% depended on the genetic background. Furthermore, at 67% of sites, amino acid replacements were under sign epistasis, having both strongly positive and negative effect in different genetic backgrounds. 46% of sites were under reciprocal sign epistasis. The fitness impact of amino acid replacements was influenced by only a few genetic backgrounds but involved interaction of multiple sites, shaping a rugged fitness landscape in which many of the shortest paths between highly fit genotypes are inaccessible., Competing Interests: The authors have declared that no competing interests exist.

Motivation: Computational prediction of the effect of mutations on protein stability is used by researchers in many fields. The utility of the prediction methods is affected by their accuracy and bias. Bias, a systematic shift of the predicted change of stability, has been noted as an issue for several methods, but has not been investigated systematically. Presence of the bias may lead to misleading results especially when exploring the effects of combination of different mutations., Results: Here we use a protocol to measure the bias as a function of the number of introduced mutations. It is based on a self-consistency test of the reciprocity the effect of a mutation. An advantage of the used approach is that it relies solely on crystal structures without experimentally measured stability values. We applied the protocol to four popular algorithms predicting change of protein stability upon mutation, FoldX, Eris, Rosetta and I-Mutant, and found an inherent bias. For one program, FoldX, we manage to substantially reduce the bias using additional relaxation by Modeller. Authors using algorithms for predicting effects of mutations should be aware of the bias described here., Availability and Implementation: All calculations were implemented by in-house PERL scripts., Supplementary Information: Supplementary data are available at Bioinformatics online., Note: The article 10.1093/bioinformatics/bty348, published alongside this paper, also addresses the problem of biases in protein stability change predictions.

In the course of evolution, genes traverse the nucleotide sequence space, which translates to a trajectory of changes in the protein sequence in protein sequence space. The correspondence between regions of the nucleotide and protein sequence spaces is understood in general but not in detail. One of the unexplored questions is how many sequences a protein can reach with a certain number of nucleotide substitutions in its gene sequence. Here I propose an algorithm to calculate the volume of protein sequence space accessible to a given protein sequence as a function of the number of nucleotide substitutions made in the protein-coding sequence. The algorithm utilizes the power of the dynamic programming approach, and makes all calculations within a couple of seconds on a desktop computer. I apply the algorithm to green fluorescence protein, and get the number of sequences four times higher than estimated before. However, taking into account the astronomically huge size of the protein sequence space, the previous estimate can be considered as acceptable as an order of magnitude estimation. The proposed algorithm has practical applications in the study of evolutionary trajectories in sequence space.

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: "U-to-N" and "N-to-U". In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the "N-to-U" transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical "detailed balance" principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the "N-to-U" transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the "U-to-N" transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the "foldable" protein domains., (Copyright © 2017 Elsevier B.V. All rights reserved.)

Fitness landscapes depict how genotypes manifest at the phenotypic level and form the basis of our understanding of many areas of biology, yet their properties remain elusive. Previous studies have analysed specific genes, often using their function as a proxy for fitness, experimentally assessing the effect on function of single mutations and their combinations in a specific sequence or in different sequences. However, systematic high-throughput studies of the local fitness landscape of an entire protein have not yet been reported. Here we visualize an extensive region of the local fitness landscape of the green fluorescent protein from Aequorea victoria (avGFP) by measuring the native function (fluorescence) of tens of thousands of derivative genotypes of avGFP. We show that the fitness landscape of avGFP is narrow, with 3/4 of the derivatives with a single mutation showing reduced fluorescence and half of the derivatives with four mutations being completely non-fluorescent. The narrowness is enhanced by epistasis, which was detected in up to 30% of genotypes with multiple mutations and mostly occurred through the cumulative effect of slightly deleterious mutations causing a threshold-like decrease in protein stability and a concomitant loss of fluorescence. A model of orthologous sequence divergence spanning hundreds of millions of years predicted the extent of epistasis in our data, indicating congruence between the fitness landscape properties at the local and global scales. The characterization of the local fitness landscape of avGFP has important implications for several fields including molecular evolution, population genetics and protein design., Competing Interests: The authors declare no interests.

The prediction of protein folding rates is a necessary step towards understanding the principles of protein folding. Due to the increasing amount of experimental data, numerous protein folding models and predictors of protein folding rates have been developed in the last decade. The problem has also attracted the attention of scientists from computational fields, which led to the publication of several machine learning-based models to predict the rate of protein folding. Some of them claim to predict the logarithm of protein folding rate with an accuracy greater than 90%. However, there are reasons to believe that such claims are exaggerated due to large fluctuations and overfitting of the estimates. When we confronted three selected published models with new data, we found a much lower predictive power than reported in the original publications. Overly optimistic predictive powers appear from violations of the basic principles of machine-learning. We highlight common misconceptions in the studies claiming excessive predictive power and propose to use learning curves as a safeguard against those mistakes. As an example, we show that the current amount of experimental data is insufficient to build a linear predictor of logarithms of folding rates based on protein amino acid composition.

The study of molecular evolution is important because it reveals how protein functions emerge and evolve. Recently, several types of studies indicated that substitutions in molecular evolution occur in a compensatory manner, whereby the occurrence of a substitution depends on the amino acid residues at other sites. However, a molecular or structural basis behind the compensation often remains obscure. Here, we review studies on the interface of structural biology and molecular evolution that revealed novel aspects of compensatory evolution. In many cases structural studies benefit from evolutionary data while structural data often add a functional dimension to the study of molecular evolution., (Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Regulated intramembrane proteolysis (RIP) is a critical mechanism for intercellular communication and regulates the function of membrane proteins through sequential proteolysis. RIP typically starts with ectodomain shedding of membrane proteins by extracellular membrane-bound proteases followed by intramembrane proteolysis of the resulting membrane-tethered fragment. However, for the majority of RIP proteases the corresponding substrates and thus, their functions, remain unknown. Proteome-wide identification of RIP protease substrates is possible by mass spectrometry-based quantitative comparison of RIP substrates or their cleavage products between different biological states. However, this requires quantification of peptides from only the ectodomain or cytoplasmic domain. Current analysis software does not allow matching peptides to either domain. Here we present the QARIP (Quantitative Analysis of Regulated Intramembrane Proteolysis) web server which matches identified peptides to the protein transmembrane topology. QARIP allows determination of quantitative ratios separately for the topological domains (cytoplasmic, ectodomain) of a given protein and is thus a powerful tool for quality control, improvement of quantitative ratios and identification of novel substrates in proteomic RIP datasets. To our knowledge, the QARIP web server is the first tool directly addressing the phenomenon of RIP. The web server is available at http://webclu.bio.wzw.tum.de/qarip/. This website is free and open to all users and there is no login requirement.

Over the last 5 years proteogenomics (using mass spectroscopy to identify proteins predicted from genomic sequences) has emerged as a promising approach to the high-throughput identification of protein N-termini, which remains a problem in genome annotation. Comparison of the experimentally determined N-termini with those predicted by sequence analysis tools allows identification of the signal peptides and therefore conclusions on the cytoplasmic or extracytoplasmic (periplasmic or extracellular) localization of the respective proteins. We present here the results of a proteogenomic study of the signal peptides in Escherichia coli K-12 and compare its results with the available experimental data and predictions by such software tools as SignalP and Phobius. A single proteogenomics experiment recovered more than a third of all signal peptides that had been experimentally determined during the past three decades and confirmed at least 31 additional signal peptides, mostly in the known exported proteins, which had been previously predicted but not validated. The filtering of putative signal peptides for the peptide length and the presence of an eight-residue hydrophobic patch and a typical signal peptidase cleavage site proved sufficient to eliminate the false-positive hits. Surprisingly, the results of this proteogenomics study, as well as a re-analysis of the E. coli genome with the latest version of SignalP program, show that the fraction of proteins containing signal peptides is only about 10%, or half of previous estimates., (Published 2013. This article is a U.S. Government work and is in the public domain in the USA.)

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured rates of spontaneous folding of single-domain globular proteins range from microseconds to hours: the difference (11 orders of magnitude) is akin to the difference between the life span of a mosquito and the age of the universe. Here, we show that physical theory with biological constraints outlines a "golden triangle" limiting the possible range of folding rates for single-domain globular proteins of various size and stability, and that the experimentally measured folding rates fall within this narrow triangle built without any adjustable parameters, filling it almost completely. In addition, the golden triangle predicts the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control. It also predicts the maximal allowed size of the "foldable" protein domains, and the size of domains found in known protein structures is in a good agreement with this limit.

Unlabelled: Signal peptides are a cornerstone mechanism for cellular protein localization, yet until now experimental determination of signal peptides has come from only a narrow taxonomic sampling. As a result, the dominant view is that Sec-cleaved signal peptides in prokaryotes are defined by a canonical AxA motif. Although other residues are permitted in the motif, alanine is by far the most common. Here we broadly examine proteomics data to reveal the signal peptide sequences for 32 bacterial and archaeal organisms from nine phyla and demonstrate that this alanine preference is not universal. Discoveries include fundamentally distinct signal peptide motifs from Alphaproteobacteria, Spirochaetes, Thermotogae and Euryarchaeota. In these novel motifs, alanine is no longer the dominant residue but has been replaced in a different way for each taxon. Surprisingly, divergent motifs correlate with a proteome-wide reduction in alanine. Computational analyses of ~1,500 genomes reveal numerous major evolutionary clades which have replaced the canonical signal peptide sequence with novel motifs., Importance: This article replaces a widely held general model with a more detailed model describing phylogenetically correlated variation in motifs for Sec secretion.

Prediction of protein folding rates and folding nuclei is an important problem of protein science. Most of the previously proposed models for protein folding in vitro are based on the nucleation mechanism of this process. Our model considering protein folding as a flow arising in a network of folding-unfolding pathways at a coarse-grained free-energy landscape was described a few years ago, along with an algorithm for calculation of protein folding rates. Here we extend our approach and describe in detail a mathematically strict algorithm for calculating the "folding nuclei", arising as bottlenecks of the flow. Although the proposed physical theory uses no adjustable parameters, its results are in good agreement with experiment. This paper presents (i) the general theory and (ii) the results for the simplest case, i.e., folding/unfolding at the midpoint of thermodynamic equilibrium between the native and unfolded states of a protein; results for "in-water" conditions, i.e., for the case when no denaturant is added and the native state of a protein is much more stable than the unfolded one, will be described in the next paper of the series.

This paper, second in the series, extends our analysis of networks of protein folding-unfolding pathways in vitro from the equilibrium, analytically the simplest, to "in-water" conditions, i.e., to the case when the native state of a protein is, as a rule, much more stable than the unfolded one. Protein folding rates and folding nuclei determined for such "physiological" conditions are of special biological and medical interest because of their relevance to misfolding diseases and other folding-related disorders. Given the native protein structures and their experimental in-water stabilities, the previously developed general theory (see paper 1 of this series) is applied here to compute the in-water folding and unfolding rates and outline the folding nuclei. Agreement between these calculations and experiment appears to be reasonably good.

Background: Divergence of two independently evolving sequences that originated from a common ancestor can be described by two parameters, the asymptotic level of divergence E and the rate r at which this level of divergence is approached. Constant negative selection impedes allele replacements and, therefore, is routinely assumed to decelerate sequence divergence. However, its impact on E and on r has not been formally investigated., Results: Strong selection that favors only one allele can make E arbitrarily small and r arbitrarily large. In contrast, in the case of 4 possible alleles and equal mutation rates, the lowest value of r, attained when two alleles confer equal fitnesses and the other two are strongly deleterious, is only two times lower than its value under selective neutrality., Conclusions: Constant selection can strongly constrain the level of sequence divergence, but cannot reduce substantially the rate at which this level is approached. In particular, under any constant selection the divergence of sequences that accumulated one substitution per neutral site since their origin from the common ancestor must already constitute at least one half of the asymptotic divergence at sites under such selection., Reviewers: This article was reviewed by Drs. Nicolas Galtier, Sergei Maslov, and Nick Grishin.

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.

We propose here KineticDB, a systematically compiled database of protein folding kinetics, which contains about 90 unique proteins. The main goal of the KineticDB is to provide users with a diverse set of protein folding rates determined experimentally. The search for determinants of protein folding is still in progress, aimed at obtaining a new understanding of the folding process. Comparison with experimental protein folding rates has been the main tool for validation of both theoretical models and empirical relationships during the last 10 years. It is, therefore, necessary to provide a researcher with as much data as possible in a simple and easy-to-use way. At present, the KineticDB contains the results of folding kinetics measurements of single-domain proteins and separate protein domains as well as short peptides without disulfide bonds. It includes data on about 90 unique proteins and many mutants that have been systematically accumulated over the last 10 years and is the largest collection of protein folding kinetic data presented as a database. The KineticDB is available at http://kineticdb.protres.ru/db/index.pl.

We have demonstrated here that protein compactness, which we define as the ratio of the accessible surface area of a protein to that of the ideal sphere of the same volume, is one of the factors determining the mechanism of protein folding. Proteins with multi-state kinetics, on average, are more compact (compactness is 1.49+/-0.02 for proteins within the size range of 101-151 amino acid residues) than proteins with two-state kinetics (compactness is 1.59+/-0.03 for proteins within the same size range of 101-151 amino acid residues). We have shown that compactness for homologous proteins can explain both the difference in folding rates and the difference in folding mechanisms.

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., ((c) 2007 Wiley-Liss, Inc.)

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.

We present a method for predicting folding rates of proteins from their amino acid sequences only, or rather, from their chain lengths and their helicity predicted from their sequences. The method achieves 82% correlation with experiment over all 64 "two-state" and "multistate" proteins (including two artificial peptides) studied up to now.

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&#95;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&#95;CO scales with the protein chain length as L(0.70 +/- 0.07) for the totality of studied single-domain proteins and peptides.

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., (Copyright 2003 Wiley-Liss, Inc.)