Protein unfolding rates correlate as strongly as folding rates with native structure

Although the folding rates of proteins have been studied extensively, both experimentally and theoretically, and many native state topological parameters have been proposed to correlate with or predict these rates, unfolding rates have received much less attention. Moreover, unfolding rates have generally been thought either to not relate to native topology in the same manner as folding rates, perhaps depending on different topological parameters, or to be more difficult to predict. Using a dataset of 108 proteins including two-state and multistate folders, we find that both unfolding and folding rates correlate strongly, and comparably well, with well-established measures of native topology, the absolute contact order and the long range order, with correlation coefficient values of 0.75 or higher. In addition, compared to folding rates, the absolute values of unfolding rates vary more strongly with native topology, have a larger range of values, and correlate better with thermodynamic stability. Similar trends are observed for subsets of different protein structural classes. Taken together, these results suggest that choosing a scaffold for protein engineering may require a compromise between a simple topology that will fold sufficiently quickly but also unfold quickly, and a complex topology that will unfold slowly and hence have kinetic stability, but fold slowly. These observations, together with the established role of kinetic stability in determining resistance to thermal and chemical denaturation as well as proteases, have important implications for understanding fundamental aspects of protein unfolding and folding and for protein engineering and design.     

Folding rates and low-entropy-loss routes of two-state proteins

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.     

Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction.

The contact order is believed to be an important factor for understanding protein folding mechanisms. In our earlier work, we have shown that the long-range interactions play a vital role in protein folding. In this work, we analyzed the contribution of long-range contacts to determine the folding rate of two-state proteins. We found that the residues that are close in space and are separated by at least ten to 15 residues in sequence are important determinants of folding rates, suggesting the presence of a folding nucleus at an interval of approximately 25 residues. A novel parameter "long-range order" has been proposed to predict protein folding rates. This parameter shows as good a relationship with the folding rate of two-state proteins as contact order. Further, we examined the minimum limit of residue separation to determine the long-range contacts for different structural classes. We observed an excellent correlation between long-range order and folding rate for all classes of globular proteins. We suggest that in mixed-class proteins, a larger number of residues can serve as folding nuclei compared to all-alpha and all-beta proteins. A simple statistical method has been developed to predict the folding rates of two-state proteins using the long-range order that produces an agreement with experimental results that is better or comparable to other methods in the literature.     

Locating the stabilizing residues in (alpha/beta)8 barrel proteins based on hydrophobicity, long-range interactions, and sequence conservation

In nature, 1 out of every 10 proteins has an (alpha/beta)(8) (TIM)-barrel fold, and in most cases, pairwise comparisons show no sequence similarity between them. Hence, delineating the key residues that induce very different sequences to share a common fold is important for understanding the folding and stability of TIM-barrel domains. In this work, we propose a new consensus approach for locating these stabilizing residues based on long-range interactions, hydrophobicity, and conservation of amino acid residues. We have identified 957 stabilizing residues in 63 proteins from a nonredundant set of 71 TIM-barrel domains. Most of these residues are located in the 8-stranded beta-sheet, with nearly one half of them oriented toward the interior of the barrel and the other half oriented toward the surrounding alpha-helices. Several stabilizing residues are found in the N- and C-terminal loops, whereas very few appear in the alpha-helices that surround the internal beta-sheet. Further, these 957 residues are placed in 434 stabilizing segments of various sizes, and each domain contains 1-10 of these segments. We found that 8 segments per domain is the most abundant one, and two thirds of the proteins have 7-9 stabilizing segments. Finally, we verified the identified residues with experimental temperature factors and found that these residues are among the ones with less mobility in the considered proteins. We suggest that our new protocol serves as a powerful tool to identify the stabilizing residues in TIM-barrel domains, which can be used as potential candidates for studying protein folding and stability by means of protein engineering experiments.     

Taking advantage of local structure descriptors to analyze interresidue contacts in protein structures and protein complexes

Interresidue protein contacts in proteins structures and at protein-protein interface are classically described by the amino acid types of interacting residues and the local structural context of the contact, if any, is described using secondary structures. In this study, we present an alternate analysis of interresidue contact using local structures defined by the structural alphabet introduced by Camproux et al. This structural alphabet allows to describe a 3D structure as a sequence of prototype fragments called structural letters, of 27 different types. Each residue can then be assigned to a particular local structure, even in loop regions. The analysis of interresidue contacts within protein structures defined using Vorono? tessellations reveals that pairwise contact specificity is greater in terms of structural letters than amino acids. Using a simple heuristic based on specificity score comparison, we find that 74% of the long-range contacts within protein structures are better described using structural letters than amino acid types. The investigation is extended to a set of protein-protein complexes, showing that the similar global rules apply as for intraprotein contacts, with 64% of the interprotein contacts best described by local structures. We then present an evaluation of pairing functions integrating structural letters to decoy scoring and show that some complexes could benefit from the use of structural letter-based pairing functions.     

A simple measure of native-state topology and chain connectivity predicts the folding rates of two-state proteins with and without crosslinks

The folding rates of two-state proteins have been found to correlate with simple measures of native-state topology. The most prominent among these measures is the relative contact order (CO), which is the average CO, or localness, of all contacts in the native protein structure, divided by the chain length. Here, we test whether such measures can be generalized to capture the effect of chain crosslinks on the folding rate. Crosslinks change the chain connectivity and therefore also the localness of some of the native contacts. These changes in localness can be taken into account by the graph-theoretical concept of effective contact order (ECO). The relative ECO, however, the natural extension of the relative CO for proteins with crosslinks, overestimates the changes in the folding rates caused by crosslinks. We suggest here a novel measure of native-state topology, the relative logCO, and its natural extension, the relative logECO. The relative logCO is the average value for the logarithm of the CO of all contacts, divided by the logarithm of the chain length. The relative log(E)CO reproduces the folding rates of a set of 26 two-state proteins without crosslinks with essentially the same high correlation coefficient as the relative CO. In addition, it also captures the folding rates of eight two-state proteins with crosslinks.     

Importance of hydrophobic cluster formation through long-range contacts in the folding transition state of two-state proteins

Understanding the folding pathways of proteins is a challenging task. The Phi value approach provides a detailed understanding of transition-state structures of folded proteins. In this work, we have computed the hydrophobicity associated with each residue in the folded state of 16 two-state proteins and compared the Phi values of each mutant residue. We found that most of the residues with high Phi value coincide with local maximum in surrounding hydrophobicity, or have nearby residues that show such maximum in hydrophobicity, indicating the importance of hydrophobic interactions in the transition state. We have tested our approach to different structural classes of proteins, such as alpha-helical, SH3 domains of all-beta proteins, beta-sandwich, and alpha/beta proteins, and we observed a good agreement with experimental results. Further, we have proposed a hydrophobic contact network pattern to relate the Phi values with long-range contacts, which will be helpful to understand the transition-state structures of folded proteins. The present approach could be used to identify potential hydrophobic clusters that may form through long-range contacts during the transition state.     

Identification of the configuration of neosartorin by long-range nuclear Overhauser effect measurements

The relative configuration of the two xanthene units of neosartorin, a new ergochrome biosynthesised by the soil mould Neosartorya fischeri, was determined using a 1D double-pulsed field gradient spin-echo NOESY experiment. It was found that both units have the same relative stereochemistry. Long-range nonbonding interactions between the substituents of different xanthene units stabilise the nonplanar configuration of the two aromatic rings A and A' connecting both monomer units of neosartorin.     

Local and long-range structural effects caused by the removal of the N-terminal polypeptide fragment from immunoglobulin L chain lambda

The role of the N-terminal polypeptide fragment of the immunoglobulin l-chain in V domain packing stability, and the flexibility of the whole chain was approached by molecular dynamics simulation. The observations were supported by experimental analysis. The N-terminal polypeptide fragment appeared to be the low-stability packing element in the V domain. At moderately elevated temperature it may be replaced at its packing locus by Congo red and then removed by proteolysis. After removal of Congo red by adsorption to (diethylamino)ethyl (DEAE) cellulose, the stability of complete L chain and of L chain devoid of the N-terminal polypeptide fragment were compared. The results indicated that the N-terminal polypeptide fragment plays an essential role in the stability of the V domain. Its removal makes the domain accessible for ANS and Congo red dye binding without heating. The decreased domain stability was registered in particular as increased root mean square (RMS) fluctuation and higher susceptibility to proteolytic attack. The long-range effect was most clearly manifested at 340 K as independent V and C domain fluctuation in the l-chain devoid of the N-terminal polypeptide fragment. This is likely due to the lack of direct connections between the N- and C-termini of the V domain polypeptide. In a complete V domain the connection involves residues 8-12 and 106-110 in particular. Partial or complete disruption of this connection increases the freedom of V domain rotation, while its increased cohesion strengthens the coupling of the V and C domains, making the whole L chain less flexible.     

Condensed Representations of Protein Secondary Structure Sequences and Their Application

Abstract

In this paper, we propose a nongraphical representation for protein secondary structures. By counting the frequency of occurrence of all possible four-tuples (i.e., four-letter words) of a protein secondary structure sequence, we construct a set of 3 × 3 matrices for the corresponding protein secondary structure sequence. Furthermore, the leading eigenvalues of these matrices are computed and considered as invariants for the protein secondary structure sequences. To illustrate the utility of our approach, we apply it to a set of real data to distinguish protein structural classes. The result indicates that it can be used to complement the classification of protein secondary structures.     

Influence of Paleolithic range contraction,admixture and long‐distance dispersal on genetic gradients of modern humans in Asia

Cavalli‐Sforza and coauthors originally explored the genetic variation of modern humans throughout the world and observed an overall east‐west genetic gradient in Asia. However, the specific environmental and population genetics processes causing this gradient were not formally investigated and promoted discussion in recent studies. Here we studied the influence of diverse environmental and population genetics processes on Asian genetic gradients and identified which could have produced the observed gradient. To do so, we performed extensive spatially‐explicit computer simulations of genetic data under the following scenarios: (a) variable levels of admixture between Paleolithic and Neolithic populations, (b) migration through long‐distance dispersal (LDD), (c) Paleolithic range contraction induced by the last glacial maximum (LGM), and (d) Neolithic range expansions from one or two geographic origins (the Fertile Crescent and the Yangzi and Yellow River Basins). Next, we estimated genetic gradients from the simulated data and we found that they were sensible to the analysed processes, especially to the range contraction induced by LGM and to the number of Neolithic expansions. Some scenarios were compatible with the observed east‐west genetic gradient, such as the Paleolithic expansion with a range contraction induced by the LGM or two Neolithic range expansions from both the east and the west. In general, LDD increased the variance of genetic gradients among simulations. We interpreted the obtained gradients as a consequence of both allele surfing caused by range expansions and isolation by distance along the vast east‐west geographic axis of this continent.     

Joint estimation of contemporary seed and pollen dispersal rates among plant populations

There are few statistical methods for estimating contemporary dispersal among plant populations. A maximum-likelihood procedure is introduced here that uses pre- and post-dispersal population samples of biparentally inherited genetic markers to jointly estimate contemporary seed and pollen immigration rates from a set of discrete external sources into a target population. Monte Carlo simulations indicate that accurate estimates and reliable confidence intervals can be obtained using this method for both pollen and seed migration rates at modest sample sizes (100 parents/population and 100 offspring) when population differentiation is moderate (F(ST) ≥ 0.1), or by increasing pre-dispersal samples (to about 500 parents/population) when genetic divergence is weak (F(ST) = 0.01). The method exhibited low sensitivity to the number of source populations and achieved good accuracy at affordable genetic resolution (10 loci with 10 equifrequent alleles each). Unsampled source populations introduced positive biases in migration rate estimates from sampled sources, although they were minor when the proportion of immigration from the latter was comparatively low. A practical application of the method to a metapopulation of the Australian resprouter shrub Banksia attenuata revealed comparable levels of directional seed and pollen migration among dune groups, and the estimate of seed dispersal was higher than a previous estimate based on conservative assignment tests. The method should be of interest to researchers and managers assessing broad-scale nonequilibrium seed and pollen gene flow dynamics in plants.     

A novel approach to predict active sites of enzyme molecules

Enzymes are critical in many cellular signaling cascades. With many enzyme structures being solved, there is an increasing need to develop an automated method for identifying their active sites. However, given the atomic coordinates of an enzyme molecule, how can we predict its active site? This is a vitally important problem because the core of an enzyme molecule is its active site from the viewpoints of both pure scientific research and industrial application. In this article, a topological entity was introduced to characterize the enzymatic active site. Based on such a concept, the covariant discriminant algorithm was formulated for identifying the active site. As a paradigm, the serine hydrolase family was demonstrated. The overall success rate by jackknife test for a data set of 88 enzyme molecules was 99.92%, and that for a data set of 50 independent enzyme molecules was 99.91%. Meanwhile, it was shown through an example that the prediction algorithm can also be used to find any typographic error of a PDB file in annotating the constituent amino acids of catalytic triad and to suggest a possible correction. The very high success rates are due to the introduction of a covariance matrix in the prediction algorithm that makes allowance for taking into account the coupling effects among the key constituent atoms of active site. It is anticipated that the novel approach is quite promising and may become a useful high throughput tool in enzymology, proteomics, and structural bioinformatics. Proteins 2004. © 2004 Wiley-Liss, Inc.     

Long distance dispersal and the fate of a gene from the colonization front

There is an increasing recognition that long distance dispersal (LDD) plays a key role in establishing spatial genetic structure during colonization. Recent works, focused on short distance dispersal, demonstrated that a neutral mutation arising at the colonization front can either ‘surf’ with the wave front and reach high frequencies or stay near its place of origin at low frequencies. Here, we examine how LDD, and more generally the shape of the dispersal kernel, modifies this phenomenon and how the width of the colonization corridor affects the fate of the mutation. We demonstrate that when LDD events are more frequent, the ‘surfing phenomenon’ is less frequent, probably because any alleles can get far ahead from the colonization front and preclude the invasion by others alleles, thus leading to an attenuation of the diversity loss. We also demonstrate that the width of the colonization corridor influences the fate of the mutation, wide spaces decreasing the probability of invasion. Overall, the genetic structure of diversity resulted not only from LDD but also particularly from the shape of the dispersal kernel.     

Birds on the move in the face of climate change: High species turnover in northern Europe

Species richness is predicted to increase in the northern latitudes in the warming climate due to ranges of many southern species expanding northwards. We studied changes in the composition of the whole avifauna and in bird species richness in a period of already warming climate in Finland (in northern Europe) covering 1,100 km in south–north gradient across the boreal zone (over 300,000 km²). We compared bird species richness and species‐specific changes (for all 235 bird species that occur in Finland) in range size (number of squares occupied) and range shifts (measured as median of area of occupancy) based on bird atlas studies between 1974–1989 and 2006–2010. In addition, we tested how the habitat preference and migration strategy of species explain species‐specific variation in the change of the range size. The study was carried out in 10 km squares with similar research intensity in both time periods. The species richness did not change significantly between the two time periods. The composition of the bird fauna, however, changed considerably with 37.0% of species showing an increase and 34.9% a decrease in the numbers of occupied squares, that is, about equal number of species gained and lost their range. Altogether 95.7% of all species (225/235) showed changes either in the numbers of occupied squares or they experienced a range shift (or both). The range size of archipelago birds increased and long‐distance migrants declined significantly. Range loss observed in long‐distance migrants is in line with the observed population declines of long‐distance migrants in the whole Europe. The results show that there is an ongoing considerable species turnover due to climate change and due to land use and other direct human influence. High bird species turnover observed in northern Europe may also affect the functional diversity of species communities.