Total Contact Distance Research Articles

Assessing the effect of dynamics on the closed-loop protein-folding hypothesis

The closed-loop (loop-n-lock) hypothesis of protein folding suggests that loops of about 25 residues, closed through interactions between the loop ends (locks), play an important role in protein structure. Coarse-grain elastic network simulations, and examination of loop lengths in a diverse set of proteins, each supports a bias towards loops of close to 25 residues in length between residues of high stability. Previous studies have established a correlation between total contact distance (TCD), a metric of sequence distances between contacting residues (cf. contact order), and the log-folding rate of a protein. In a set of 43 proteins, we identify an improved correlation (r2 = 0.76), when the metric is restricted to residues contacting the locks, compared to the equivalent result when all residues are considered (r2 = 0.65). This provides qualified support for the hypothesis, albeit with an increased emphasis upon the importance of a much larger set of residues surrounding the locks. Evidence of a similar-sized protein core/extended nucleus (with significant overlap) was obtained from TCD calculations in which residues were successively eliminated according to their hydrophobicity and connectivity, and from molecular dynamics simulations. Our results suggest that while folding is determined by a subset of residues that can be predicted by application of the closed-loop hypothesis, the original hypothesis is too simplistic; efficient protein folding is dependent on a considerably larger subset of residues than those involved in lock formation.

Intrinsic Relationship of Amino Acid Composition/Occurrence with Topological Parameters and Protein Folding Rates

Understanding the relationship between amino acid sequences and folding rates of proteins is an important task in computational and molecular biology. It has been shown that topological parameters, contact order, long-range order and total contact distance relate well with protein folding rates. In this work, we have systematically analyzed the relationship between amino acid composition/occurrence and protein folding rates along with topological parameters derived from protein three-dimensional structures. We found that the classification of proteins based on their structural classes and folding types (two and three-state proteins) could explain the relationship very well. The amino acid composition showed good correlation with protein folding rates for two-state proteins whereas the correlation is high with amino acid occurrence for three-state proteins. The composition of polar amino acids, Asn, Gln and Ser directly correlated with protein folding rates and a reverse trend was observed between the occurrence of hydrophobic amino acids, Ile and Gly and protein folding rates. The amino acid occurrence showed a positive correlation with folding rates in two-state proteins and a negative correlation in three-state proteins, which reveals that the presence of more number of amino acids in three-state proteins slows down the folding process. The analysis on slow and fast folding proteins showed that the slow folding proteins have appreciable number of residues that form multiple contacts with other residues. Further, we have combined different amino acids based on their chemical properties and analyzed the relationship with protein folding rates, and set up multiple regression equations for predicting protein folding rates.

Multiple Contact Network Is a Key Determinant to Protein Folding Rates

Understanding the relationship between amino acid sequences and folding rates of proteins is an important task in computational and molecular biology. It has been shown that topological parameters, contact order, long-range order, and total contact distance relate well with protein folding rates. In this work, we have systematically analyzed the influence of amino acid residues that form multiple contacts in protein structures to folding rates of proteins. We observed an inverse relationship between the number of residues with multiple contacts and protein folding rates. Further analysis indicates that multiple contacts are influenced by hydrophobic residues, whereas the role is minimal between the residues that are capable of forming hydrogen bonds. The propensity of multiple contacts forming residues showed that aromatic and hydrophobic residues are dominant in two-state proteins, whereas the polar residues Ser and Thr are also preferred ones in three-state proteins. In addition, multiple contact forming residues are interconnected with each other through contact networks in protein structures. The comparison between slow and fast folding proteins demonstrated the presence of more multiple contact forming residues in slow folding proteins with a limit of 4-6 contacts/residue. These results have been reflected in amino acid sequences in the form of short-, medium-, and long-range contacts, which could discriminate slow and fast folding proteins with an accuracy of 96% using a 5-fold cross-validation method.

Cysteine-Cysteine Contact Preference Leads to Target-Focusing in Protein Folding

We perform a statistical analysis of amino-acid contacts to investigate possible preferences of amino-acid interactions. We include in the analysis only tertiary contacts, because they are less constrained—compared to secondary contacts—by proteins’ backbone rigidity. Using proteins from the protein data bank, our analysis reveals an unusually high frequency of cysteine pairings relative to that expected from random. To elucidate the possible effects of cysteine interactions in folding, we perform molecular simulations on three cysteine-rich proteins. In particular, we investigate the difference in folding dynamics between a Gō-like model (where attraction only occurs between amino acids forming a native contact) and a variant model (where attraction between any two cysteines is introduced to mimic the formation/dissociation of native/nonnative disulfide bonds). We find that when attraction among cysteines is nonspecific and comparable to a solvent-averaged interaction, they produce a target-focusing effect that expedites folding of cysteine-rich proteins as a result of a reduction of conformational search space. In addition, the target-focusing effect also helps reduce glassiness by lowering activation energy barriers and kinetic frustration in the system. The concept of target-focusing also provides a qualitative understanding of a correlation between the rates of protein folding and parameters such as contact order and total contact distance.

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.

Direct correlation between proteins' folding rates and their amino acid compositions: An ab initio folding rate prediction

Discovering the mechanism of protein folding, in molecular biology, is a great challenge. A key step to this end is to find factors that correlate with protein folding rates. Over the past few years, many empirical parameters, such as contact order, long-range order, total contact distance, secondary structure contents, have been developed to reflect the correlation between folding rates and protein tertiary or secondary structures. However, the correlation between proteins' folding rates and their amino acid compositions has not been explored. In the present work, we examined systematically the correlation between proteins' folding rates and their amino acid compositions for two-state and multistate folders and found that different amino acids contributed differently to the folding progress. The relation between the amino acids' molecular weight and degeneracy and the folding rates was examined, and the role of hydrophobicity in the protein folding process was also inspected. As a consequence, a new indicator called composition index was derived, which takes no structure factors into account and is merely determined by the amino acid composition of a protein. Such an indicator is found to be highly correlated with the protein's folding rate (r > 0.7). From the results of this work, three points of concluding remarks are evident. (1) Two-state folders and multistate folders have different rate-determining amino acids. (2) The main determining information of a protein's folding rate is largely reflected in its amino acid composition. (3) Composition index may be the best predictor for an ab initio protein folding rate prediction directly from protein sequence from the standpoint of practical application.

Folding rate prediction using n-order contact distance for proteins with two- and three-state folding kinetics

It is a challenging task to understand the relationship between sequences and folding rates of proteins. Previous studies are found that one of contact order (CO), long-range order (LRO), total contact distance (TCD), chain topology parameter (CTP), and effective length ( L eff) has a significant correlation with folding rate of proteins. In this paper, we introduce a new parameter called n-order contact distance ( nOCD) and use it to predict folding rate of proteins with two- and three-state folding kinetics. A good linear correlation between the folding rate logarithm ln k f and nOCD with n=1.2, α=0.6 is found for two-state folders (correlation coefficient is −0.809, P-value<0.0001) and n=2.8, α=1.5 for three-state folders (correlation coefficient is −0.816, P-value<0.0001). However, this correlation is completely absent for three-state folders with n=1.2, α=0.6 (correlation coefficient is 0.0943, P-value=0.661) and for two-state folders with n=2.8, α=1.5 (correlation coefficient is −0.235, P-value=0.2116). We also find that the average number of contacts per residue P m in the interval of m for two-state folders is smaller than that for three-state folders. The probability distribution P( γ) of residue having γ pairs of contacts fits a Gaussian distribution for both two- and three-state folders. We observe that the correlations between square radius of gyration S 2 and number of residues for two- and three-state folders are both good, and the correlation coefficient is 0.908 and 0.901, and the slope of the fitting line is 1.202 and 0.795, respectively. Maybe three-state folders are more compact than two-state folders. Comparisons with nTCD and nCTP are also made, and it is found that nOCD is the best one in folding rate prediction.

Critical nucleation size in the folding of small apparently two-state proteins.

For apparently two-state proteins, we found that the size (number of folded residues) of a transition state is mostly encoded by the topology, defined by total contact distance (TCD) of the native state, and correlates with its folding rate. This is demonstrated by using a simple procedure to reduce the native structures of the 41 two-state proteins with native TCD as a constraint, and is further supported by analyzing the results of eight proteins from protein engineering studies. These results support the hypothesis that the major rate-limiting process in the folding of small apparently two-state proteins is the search for a critical number of residues with the topology close to that of the native state.

Analysis of structural statistical properties of proteases and nonproteases

The different structural properties of proteases and nonproteases are well investigated in this paper. The average percentage P L of residues having a number of long-range contacts greater than or equal to N L(≥ N L) for the proteases is larger than that for the nonproteases. The average number of long-range contacts per residue P L,μ in four secondary structure μ ( μ=H, E, T, and N) for the proteases is also larger than that for the nonproteases. We calculate the average contact order (CO) per protein, the average long-range order (LRO) per protein, and the average total contact distance (TCD) per protein, and find that the average value of LRO for the nonproteases is smaller than that for the proteases. However, both proteases and nonproteases have the same average values of CO and TCD. The average number of long-range contacts per residue C L for the proteases is larger than that for the nonproteases, however, the average number of short-range contacts per residue C S for the proteases is smaller than that for the nonproteases. It is also shown that the square of radius of gyration for the proteases is relatively smaller than for the nonproteases. This finding implies that proteases are more compact than nonproteases. In protein molecule, each residue has a different ability to form contacts, and in general the number of residues having a small number of contacts is greater than that having a large number of contacts. Here we have concluded that the probability P( n) of amino acid residues having n pairs of contacts in all residues fits a good Gaussian distribution, and there has the same form of Gaussian distribution for 20 amino acid residues. The most probable number of contacts, n C, for the proteases is greater than that for the nonproteases for 20 amino acid residues and one has a good correlation with the Fauchere-Pliska hydrophobicity (FPH) scale. Finally we discuss the relative contribution of amino acid residues involved in cation–π interactions. The higher fraction of cation–π interactions observed in the proteases is found to be reflection of the more general, more frequent occurrence of these interactions in these proteins. All these findings would be helpful for us to understand structural differences between the proteases and other proteins.

Analysis of the amino acid effect on protein folding by atom pair contacts

New atomic pair contacts with considering the coordinates of each atom in a residue are introduced here. We analyze the ability of all the 20 amino acid residues to form long-range and short-range contacts by calculating the average numbers of short- and long-range contacts between different amino acid pairs. It is concluded that Phe-Phe, Leu-Phe and Leu-Leu have a high tendency to form contacts. The relative ability to form atom pair contact does not depend on the limiting value of R C. The average number of contacts per residue, which is the scale of the relative ability to form contacts for the 20 amino acid residue types, is also calculated. The result shows that hydrophobic residues with large numbers of long-range contacts more easily form long-range contacts, while the hydrophilic ones form long-range contacts less often. Linear regression analysis by a new method of counting contacts concludes that either contact order (CO) or total contact distance (TCD) parameter has a significant correlation with the logarithms of folding rates. The relative deviations between the experimentally observed ln k f and the two parameters CO and TCD are smaller than that with previous methods. Moreover, the values of CO λ-μ and TCD λ-μ between λ-type and μ-type amino acids are investigated. Comparisons between the Fauchere–Pliska hydrophobicity scale and the average number of contacts per residue formed are also made. The new knowledge of atomic pair contacts can help us understand the importance of amino acid residue type and its sequence in globular structure of the protein in detail.

Folding rate prediction based on neural network model

One of the most important challenges in biology is to understand the relationship between the folded structure of a protein and its primary amino acid sequence. A related and challenging task is to understand the relationship between sequences and folding rates of proteins. Previous studies found that one of contact order (CO), long-range order (LRO), and total contact distance (TCD) has a significant correlation with folding rate of protein. Although the predicted results from TCD can provide better results, the deviation is also large for some proteins. In this paper, we adopt back-propagation neural network to study the relationship between folding rate and protein structure. In our model, the input nodes are CO, LRO, and TCD, and the output node is folding rate. The number of nodes in the hidden layer is seven. Our results show that the relative errors for the predicted results are even lower than other methods in the literature. We also observe a best excellent correlation between the folding rate and contact parameters (including CO, LRO, and TCD), and find that the folding rate depends on CO, LRO and TCD simultaneously. This means that CO, LRO and TCD are similarly important in folding rate of protein. Some comparisons are made with other methods.

Folding Rate Prediction Using Total Contact Distance

Linear regression analysis found that either contact order (CO) or long-range order (LRO) parameter has a significant correlation with the logarithms of folding rates. This suggests that sequence separation per contact and total number of contacts are both important in determining the rate of folding. Here, the two factors are incorporated into a new parameter, total contact distance (TCD). Using a database of 28 two-state or weakly three-state folding proteins, TCD is found to be the most accurate among the three parameters (CO, LRO, and TCD) in terms of correlation and prediction. It provides even more accurate prediction than the best neural network results with two descriptors (contact order and stability per residue). The improvement is achieved in all three-structural classes (all α, β, and mixed). The accuracy of total contact distance in predicting folding rates is essentially unchanged if “short”-ranged contacts ( |i − j| ≤ 14 ) are not included in calculation. Thus, only long-range contacts with a sequence separation of more than 14 residues are important in determining the rate of folding. This is consistent with the results from the long-range order parameter. One of the significant outliers in prediction is found to be associated with the only protein in the database that involves nonlocal disulfide bonds. Removing the protein leads to a correlation coefficient of 0.89 between experimental observed and predicted folding rates in jackknife cross validation. The corresponding values for CO and LRO are 0.71 and 0.80, respectively.