Application of long-range order to predict unfolding rates of two-state proteins.

Predicting the experimental unfolding rates of two-state proteins and models describing the unfolding rates of these proteins is quite limited because of the complexity present in the unfolding mechanism and the lack of experimental unfolding data compared with folding data. In this work, 25 two-state proteins characterized by Maxwell et al. (Protein Sci 2005;14:602­616) using a consensus set of experimental conditions were taken, and the parameter long-range order (LRO) derived from their three-dimensional structures were related with their experimental unfolding rates ln(k(u)). From the total data set of 30 proteins used by Maxwell et al. (Protein Sci 2005;14:602­616), five slow-unfolding proteins with very low unfolding rates were considered to be outliers and were not included in our data set. Except all beta structural class, LRO of both the all-alpha and mixed-class proteins showed a strong inverse correlation of r = -0.99 and -0.88, respectively, with experimental ln(k(u)). LRO shows a correlation of -0.62 with experimental ln(k(u)) for all-beta proteins. For predicting the unfolding rates, a simple statistical method has been used and linear regression equations were developed for individual structural classes of proteins using LRO, and the results obtained showed a better agreement with experimental results.

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.

Refinement of the long-range order parameter in predicting folding rates of two-state proteins.

Long-range order (LRO) is one of the most successful descriptors in relating the three-dimensional structures of proteins with their folding rates. LRO highlights the importance of long-range contacts (residues that are far in sequence and closer in the 3D structure) in determining the folding rates of proteins across all structural classes of proteins. In this work, we have updated the data set of two-state folding proteins to examine the robustness of LRO parameter and to assess whether any refinements are required in defining the computation of LRO. LRO shows a better correlation (r = -0.85) for the increased dataset with a very small difference in distance cut-off compared to the old data set and reinforces the robustness of the parameter. When the dataset was grouped into three major structural classes, slight refinement of the parameter (distance of separation in space and sequence) gave better correlations. The corresponding correlation for the three structural classes are r = -0.92; sequence separation 23; spatial distance cut-off 5.5 A for all alpha structural class, r = -0.84; sequence separation 43; spatial distance cut-off 7 A for all beta structural class and r = -0.82; sequence separation 8; spatial distance cut-off 8 A for mixed class proteins. It is envisaged that during the process of protein folding, formation of long-range contacts beyond the above sequence separation limits may play a key role in determining the folding rates of proteins, and this aspect is discussed in the light of experimental studies on the formation of interresidue contacts and end-to-end loops in unfolded polypeptide chains.