Folding Rates Of Two-state Proteins Research Articles

A Simple Model of Protein Folding Kinetics Based on Native Topology

The folding rates of two-state proteins range over six orders of magnitude: from microseconds to seconds. These folding rates correlate with contact order, a simple measure of the topology of the native structure. The question we would like to answer is the following: What physical principles underlie the correlation between folding rates and contact order? To answer this question, we’re developing a simple master equation model based on native contacts and loop-closure entropies. Our hypothesis is that folding proceeds mostly through the closure of small loops, and that large loop closures are slower and less important.

Local and non-local native topologies reveal the underlying folding landscape of proteins

Due to Plaxco, Simons, Baker and others, it is now well known that the two-state single domain protein folding rate is fairly well predicted from knowledge of the topology of the native structure. Plaxco et al found that the folding rates of two-state proteins correlate with the average degree to which native contacts are ‘local’ within the chain sequence: fast-folders usually have mostly local structures. Here, we dissected the native topology further by focusing on non-local and local contacts using lower and upper bounds of allowable sequence separation in computing the average contact order. We analyzed non-local and local contacts of 82 two-state proteins whose experimental folding rates span over six orders of magnitude. We observed that both the number of non-local contacts and the average sequence separation of non-local contacts (non-local CO) are both negatively correlated with the folding rate, showing that the non-local contacts dominate the barrier-crossing process. Surprisingly, the local contact orders of the proteins also correlate with the folding rates. However, this correlation shows a strong positive trend indicating the role of a diffusive search in the denatured basin.

Analysis of Rate-limiting Long-range Contacts in the Folding Rate of Three-state and Two-state Proteins

In the past decade, when compared to models describing the folding rates of two-state proteins, models describing the folding mechanism of three-state proteins remain quite limited due to the complexity present in the folding mechanism and lack in their experimental data. In the present work, rate-limiting long-range contacts were classified into various bins based on sequence separation distance between the contacting residues and the role of these bins were analyzed for their importance in a data set of 35 three-state proteins. Predicting the folding rates of these proteins have been carried out by relating experimental folding rates and long-range contacts obtained from various sequence separation bins. For comparison, using the present model, prediction of the folding rates of 45 two-state proteins also resulted with good accuracy. Our method shows that long-range contacts observed in the final 3-D structure of proteins at various sequence separation bins are found to be an important descriptor in explaining the folding rates of three-state proteins and suggest that formation of contacts between residues present at these sequence separation distance may be a crucial factor in deciding structure formation and folding rates of these proteins. The aim of our present work is not to construct a new descriptor for the folding rates of three-state proteins, nor is to provide improved means of folding-rate prediction for these proteins. We tend to elucidate that how long-range contacts play a crucial role in the folding mechanism of three state proteins belonging to three major structural classes and implication of these observations due to rate-limiting long-range contacts has been discussed in the light of other experimental studies of protein folding.

Folding rate prediction using complex network analysis for proteins with two- and three-state folding kinetics

It is a challenging task to investigate the different in- fluence of long-range and short-range interactions on two-state and three-state folding kinetics of protein. The networks of the 30 two-state proteins and 15 three-state proteins were constructed by complex networks analysis at three length scales: Protein Contact Networks, Long-range Interaction Networks and Short-range Interaction Networks. To uncover the relationship between structural properties and folding kinetics of the proteins, the correlations of protein network parameters with protein folding rate and topology parameters contact order were analyzed. The results show that Protein Contact Networks and Short-range Interaction Networks (for both two-state and three-state proteins) exhibit the “small-world” property and Long-range Interaction networks indicate “scale-free” behavior. Our results further indicate that all Protein Contact Networks and Short- range Interaction networks are assortative type. While some of Long-range Interaction Networks are of assortative type, the others are of disassortative type. For two-state proteins, the clustering coefficients of Short-range Interaction Networks show prominent correlation with folding rate and contact order. The assortativity coefficients of Short-range Interaction Networks also show remarkable correlation with folding rate and contact order. Similar correlations exist in Protein Contact Networks of three-state proteins. For two-state proteins, the correlation between contact order and folding rate is determined by the numbers of local contacts. Short- range interactions play a key role in determining the connecting trend among amino acids and they impact the folding rate of two-state proteins directly. For three-state proteins, the folding rate is determined by short-range and long-range interactions among residues together.

On the role of structural class of a protein with two‐state folding kinetics in determining correlations between its size, topology, and folding rate

The time it takes for proteins to fold into their native states varies over several orders of magnitude depending on their native-state topology, size, and amino acid composition. In a number of previous studies, it was found that there is strong correlation between logarithmic folding rates and contact order for proteins that fold with two-state kinetics, while such correlation is absent for three-state proteins. Conversely, strong correlations between folding rates and chain length occur within three-state proteins, but not in two-state proteins. Here, we demonstrate that chain lengths and folding rates of two-state proteins are not correlated with each other only when all-alpha, all-beta, and mixed-class proteins are considered together, which is typically the case. However, when considering all-alpha and all-beta two-state proteins separately, there is significant linear correlation between folding rate and size. Moreover, the sets of data points for the all-alpha and all-beta classes define asymptotes of lower and upper limits on folding rates of mixed-class proteins. By analyzing correlation of other topological parameters with folding rates of two-state proteins, we find that only the long-range order exhibits correlation with folding rates that is uniform over all three classes. It is also the only descriptor to provide statistically significant correlations for each of the three structural classes. We give an interpretation of this observation in terms of Makarov and Plaxco's diffusion-based topomer-search model.

Accurate Prediction of the Folding Rate for Two-State Proteins Based on Amino Acid Sequences

One of the most important challenges in biology is to understand and simulate the folding behavior of some simple two-state proteins. In this work, a large pool for descriptors of proteins was developed including amino acid descriptors, topological descriptors and charged partial surface area descriptors. A heuristic method was employed to select significant features. As a result, three descriptors, total contact distance, unfolding entropy change and total charge weighted partial negative surface area were chosen. Total contact distance was proved to be the most relevant factor controlling the folding behavior. Based on these descriptors, a support vector machine method was applied to build a predictive model. Comparing the statistical results of other works and methods, support vector machine method exhibited the best whole performance. Our results demonstrate that the native-state topology is the major determinant for the folding rates of two-state proteins and that the support vector machine method is a powerful tool to build a predictive model. In turn, the method and the knowledge can be used to develop in-silico predictive models to simulate the folding process of proteins.

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.

タンパク質のフォールディング速度と構造パラメータとの相関解析

Folding rates of many globular proteins which exhibit two-state and non-two-state folding have been determined experimentally. Previous studies have focused on the two-state folding, and clarified that the folding rate of two-state proteins depends on the native backbone structure. Here, we performed a statistical analysis of the relationship between the folding rate and structure-based parameters of non-two-state proteins. As a result, we found that the formation rates of both the intermediate and the native state of non-two-state folding similarly depend on the native backbone structure. The comparison of non-two-state and two-state folding suggests that non-two-state folding is more general than two-state folding.

Role of non-covalent interactions for determining the folding rate of two-state proteins

Understanding the factors influencing the folding rate of proteins is a challenging problem. In this work, we have analyzed the role of non-covalent interactions for the folding rate of two-state proteins by free-energy approach. We have computed the free-energy terms, hydrophobic, electrostatic, hydrogen-bonding and van der Waals free energies. The hydrophobic free energy has been divided into the contributions from different atoms, carbon, neutral nitrogen and oxygen, charged nitrogen and oxygen, and sulfur. All the free-energy terms have been related with the folding rates of 28 two-state proteins with single and multiple correlation coefficients. We found that the hydrophobic free energy due to carbon atoms and hydrogen-bonding free energy play important roles to determine the folding rate in combination with other free energies. The normalized energies with total number of residues showed better results than the total energy of the protein. The comparison of amino acid properties with free-energy terms indicates that the energetic terms explain better the folding rate than amino acid properties. Further, the combination of free energies with topological parameters yielded the correlation of 0.91. The present study demonstrates the importance of topology for determining the folding rate of two-state proteins.

Importance of Native‐State Topology for Determining the Folding Rate of Two‐State Proteins.

Understanding the relationship between amino acid sequences and folding rate of proteins is a challenging task similar to protein folding problem. In this work, we have analyzed the relative importance of protein sequence and structure for predicting the protein folding rates in terms of amino acid properties and contact distances, respectively. We found that the parameters derived with protein sequence (physical-chemical, energetic, and conformational properties of amino acid residues) show very weak correlation (|r| < 0.39) with folding rates of 28 two-state proteins, indicating that the sequence information alone is not sufficient to understand the folding rates of two-state proteins. However, the maximum positive correlation obtained for the properties, number of medium-range contacts, and α-helical tendency reveals the importance of local interactions to initiate protein folding. On the other hand, a remarkable correlation (r varies from −0.74 to −0.88) has been obtained between structural parameters...

Local Secondary Structure Content Predicts Folding Rates for Simple, Two-state Proteins

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

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-α and all-β 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.