Local packing density is the main structural determinant of the rate of protein sequence evolution at site level.

Functional and biophysical constraints result in site-dependent patterns of protein sequence variability. It is commonly assumed that the key structural determinant of site-specific rates of evolution is the Relative Solvent Accessibility (RSA). However, a recent study found that amino acid substitution rates correlate better with two Local Packing Density (LPD) measures, the Weighted Contact Number (WCN) and the Contact Number (CN), than with RSA. This work aims at a more thorough assessment. To this end, in addition to substitution rates, we considered four other sequence variability scores, four measures of solvent accessibility (SA), and other CN measures. We compared all properties for each protein of a structurally and functionally diverse representative dataset of monomeric enzymes. We show that the best sequence variability measures take into account phylogenetic tree topology. More importantly, we show that both LPD measures (WCN and CN) correlate better than all of the SA measures, regardless of the sequence variability score used. Moreover, the independent contribution of the best LPD measure is approximately four times larger than that of the best SA measure. This study strongly supports the conclusion that a site's packing density rather than its solvent accessibility is the main structural determinant of its rate of evolution.

Site-specific structural constraints on protein sequence evolutionary divergence: local packing density versus solvent exposure.

Protein sequences evolve under selection pressures imposed by functional and biophysical requirements, resulting in site-dependent rates of amino acid substitution. Relative solvent accessibility (RSA) and local packing density (LPD) have emerged as the best candidates to quantify structural constraint. Recent research assumes that RSA is the main determinant of sequence divergence. However, it is not yet clear which is the best predictor of substitution rates. To address this issue, we compared RSA and LPD with site-specific rates of evolution for a diverse data set of enzymes. In contrast with recent studies, we found that LPD measures correlate better than RSA with evolutionary rate. Moreover, the independent contribution of RSA is minor. Taking into account that LPD is related to backbone flexibility, we put forward the possibility that the rate of evolution of a site is determined by the ease with which the backbone deforms to accommodate mutations.

On the relationship between the sequence conservation and the packing density profiles of the protein complexes.

We have recently showed that the weighted contact number profiles (or the packing density profiles) of proteins are well correlated with those of the corresponding sequence conservation profiles. The results suggest that a protein structure may contain sufficient information about sequence conservation comparable to that derived from multiple homologous sequences. However, there are ambiguities concerning how to compute the packing density of the subunit of a protein complex. For the subunits of a complex, there are different ways to compute its packing density--one including the packing contributions of the other subunits and the other one excluding their contributions. Here we selected two sets of enzyme complexes. Set A contains complexes with the active sites comprising residues from multiple subunits, while set B contains those with the active sites residing on single subunits. In Set A, if the packing density profile of a subunit is computed considering the contributions of the other subunits of the complex, it will agree better with the sequence conservation profile. But in Set B the situations are reversed. The results may be due to the stronger functional and structural constraints on the evolution processes on the complexes of Set A than those of Set B to maintain the enzymatic functions of the complexes. The comparison of the packing density and the sequence conservation profiles may provide a simple yet potentially useful way to understanding the structural and evolutionary couplings between the subunits of protein complexes.

Deriving correlated motions in proteins from X-ray structure refinement by using TLS parameters.

Dynamic information in proteins may provide valuable information for understanding allosteric regulation of protein complexes or long-range effects of the mutations on enzyme activity. Experimental data such as X-ray B-factors or NMR order parameters provide a convenient estimate of atomic fluctuations (or atomic auto-correlated motions) in proteins. However, it is not as straightforward to obtain atomic cross-correlated motions in proteins - one usually resorts to more sophisticated computational methods such as Molecular Dynamics, normal mode analysis or atomic network models. In this report, we show that atomic cross-correlations can be reliably obtained directly from protein structure using X-ray refinement data. We have derived an analytic form of atomic correlated motions in terms of the original TLS parameters used to refine the B-factors of X-ray structures. The correlated maps computed using this equation are well correlated with those of the method based on a mechanical model (the correlation coefficient is 0.75) for a non-homologous dataset comprising 100 structures. We have developed an approach to compute atomic cross-correlations directly from X-ray protein structure. Being in analytic form, it is fast and provides a feasible way to compute correlated motions in proteins in a high throughput way. In addition, avoiding sophisticated computational operations; it provides a quick, reliable way, especially for non-computational biologists, to obtain dynamics information directly from protein structure relevant to its function.

Evolutionary information hidden in a single protein structure.

The knowledge of conserved sequences in proteins is valuable in identifying functionally or structurally important residues. Generating the conservation profile of a sequence requires aligning families of homologous sequences and having knowledge of their evolutionary relationships. Here, we report that the conservation profile at the residue level can be quantitatively derived from a single protein structure with only backbone information. We found that the reciprocal packing density profiles of protein structures closely resemble their sequence conservation profiles. For a set of 554 nonhomologous enzymes, 74% (408/554) of the proteins have a correlation coefficient > 0.5 between these two profiles. Our results indicate that the three-dimensional structure, instead of being a mere scaffold for positioning amino acid residues, exerts such strong evolutionary constraints on the residues of the protein that its profile of sequence conservation essentially reflects that of its structural characteristics.

On the relationship between catalytic residues and their protein contact number.

Due to advances in structural biology, an increasing number of protein structures of unknown function have been deposited in Protein Data Bank (PDB). These proteins are usually characterized by novel structures and sequences. Conventional comparative methodology (such as sequence alignment, structure comparison, or template search) is unable to determine their function. Thus, it is important to identify protein's function directly from its structure, but this is not an easy task. One of the strategies used is to analyze whether there are distinctive structure-derived features associated with functional residues. If so, one may be able to identify the functional residues directly from a single structure. Recently, we have shown that protein weighted contact number is related to atomic thermal fluctuations and can be used to derive motional correlations in proteins. In this report, we analyze the weighted contact-number profiles of both catalytic residues and non-catalytic residues for a dataset of 760 structures. We found that catalytic residues have distinct distributions of weighted contact numbers from those of non-catalytic residues. Using this feature, we are able to effectively differentiate catalytic residues from other residues with a single optimized threshold value. Our method is simple to implement and compares favourably with other more sophisticated methods. In addition, we discuss the physics behind the relationship between catalytic residues and their contact numbers as well as other features (such as residue centrality or B-factors) associated with catalytic residues.

On the relationship between the protein structure and protein dynamics.

Recently, we have developed a method (Shih et al., Proteins: Structure, Function, and Bioinformatics 2007;68: 34-38) to compute correlation of fluctuations of proteins. This method, referred to as the protein fixed-point (PFP) model, is based on the positional vectors of atoms issuing from the fixed point, which is the point of the least fluctuations in proteins. One corollary from this model is that atoms lying on the same shell centered at the fixed point will have the same thermal fluctuations. In practice, this model provides a convenient way to compute the average dynamical properties of proteins directly from the geometrical shapes of proteins without the need of any mechanical models, and hence no trajectory integration or sophisticated matrix operations are needed. As a result, it is more efficient than molecular dynamics simulation or normal mode analysis. Though in the previous study the PFP model has been successfully applied to a number of proteins of various folds, it is not clear to what extent this model will be applied. In this article, we have carried out the comprehensive analysis of the PFP model for a dataset comprising 972 high-resolution X-ray structures with pairwise sequence identity or=0.5. Our result shows that the fixed-point model is indeed quite general and will be a useful tool for high throughput analysis of dynamical properties of proteins.

Deriving protein dynamical properties from weighted protein contact number.

It has recently been shown that in proteins the atomic mean-square displacement (or B-factor) can be related to the number of the neighboring atoms (or protein contact number), and that this relationship allows one to compute the B-factor profiles directly from protein contact number. This method, referred to as the protein contact model, is appealing, since it requires neither trajectory integration nor matrix diagonalization. As a result, the protein contact model can be applied to very large proteins and can be implemented as a high-throughput computational tool to compute atomic fluctuations in proteins. Here, we show that this relationship can be further refined to that between the atomic mean-square displacement and the weighted protein contact-number, the weight being the square of the reciprocal distance between the contacting pair. In addition, we show that this relationship can be utilized to compute the cross-correlation of atomic motion (the B-factor is essentially the auto-correlation of atomic motion). For a nonhomologous dataset comprising 972 high-resolution X-ray protein structures (resolution <2.0 A and sequence identity <25%), the mean correlation coefficient between the X-ray and computed B-factors based on the weighted protein contact-number model is 0.61, which is better than those of the original contact-number model (0.51) and other methods. We also show that the computed correlation maps based on the weighted contact-number model are globally similar to those computed through normal model analysis for some selected cases. Our results underscore the relationship between protein dynamics and protein packing. We believe that our method will be useful in the study of the protein structure-dynamics relationship.

A simple way to compute protein dynamics without a mechanical model.

We found that in proteins the average atomic fluctuation is linearly related to the square of the atomic distance from the center of mass of the protein. Using this simple relation, we can accurately compute the temperature factors of proteins of a wide range of sizes and folds, and the correlation of the fluctuations in proteins. This simple relation provides a direct link between protein dynamics and the static protein's geometrical shape and offers a simple way to compute protein dynamics without either long time trajectory integration or any matrix operations.

Structure-stability-activity relationship in covalently cross-linked N-carbamoyl D-amino acid amidohydrolase and N-acylamino acid racemase.

N-Acylamino acid racemase (NAAAR) and N-carbamoyl-D-amino-acid amidohydrolase (D-NCAase) are important biocatalysts for producing enantiopure alpha-amino acids. NAAAR forms an octameric assembly and displays induced fit movements upon substrate binding, while D-NCAase is a tetramer that does not change conformation in the presence of a ligand. To investigate the effects of introducing potentially stabilizing S-S bridges in these different multimeric enzymes, cysteine residues predicted to form inter or intra-subunit disulfide bonds were introduced by site-directed mutagenesis. Inter-subunit S-S bonds were formed in two NAAAR variants (A68C-D72C and P60C-Y100C) and two d-NCAase variants (A302C and P295C-F304C). Intra-subunit S-S bonds were formed in two additional NAAAR variants (E149C-A182C and V265C). Crystal structures of NAAARs variants show limited deviations from the wild-type overall tertiary structure. An apo A68C-D72C subunit differs from the wild-type enzyme, in which it has an ordered lid loop, resembling ligand-bound NAAAR. The structures of A222C and A302C D-NCAases are nearly identical to the wild-type enzyme. All mutants with inter-subunit bridges had increases in thermostability. Compared with the wild-type enzyme, A68C-D72C NAAAR showed similar kcat/Km ratios, whereas mutant D-NCAases demonstrated increased kcat/Km ratios at high temperatures (A302C: 4.2-fold at 65 degrees C). Furthermore, molecular dynamic simulations reveal that A302C substantially sustains the fine-tuned catalytic site as temperature increases, achieving enhanced activity.