Allosteric Communication Occurs via Networks of Tertiary and Quaternary Motions in Proteins

Allosteric proteins bind an effector molecule at one site resulting in a functional change at a second site. We hypothesize that allosteric communication in proteins relies upon networks of quaternary (collective, rigid-body) and tertiary (residue–residue contact) motions. We argue that cyclic topology of these networks is necessary for allosteric communication. An automated algorithm identifies rigid bodies from the displacement between the inactive and the active structures and constructs “quaternary networks” from these rigid bodies and the substrate and effector ligands. We then integrate quaternary networks with a coarse-grained representation of contact rearrangements to form “global communication networks” (GCNs). The GCN reveals allosteric communication among all substrate and effector sites in 15 of 18 multidomain and multimeric proteins, while tertiary and quaternary networks exhibit such communication in only 4 and 3 of these proteins, respectively. Furthermore, in 7 of the 15 proteins connected by the GCN, 50% or more of the substrate-effector paths via the GCN are “interdependent” paths that do not exist via either the tertiary or the quaternary network. Substrate-effector “pathways” typically are not linear but rather consist of polycyclic networks of rigid bodies and clusters of rearranging residue contacts. These results argue for broad applicability of allosteric communication based on structural changes and demonstrate the utility of the GCN. Global communication networks may inform a variety of experiments on allosteric proteins as well as the design of allostery into non-allosteric proteins.     

Local motions in a benchmark of allosteric proteins

Allosteric proteins have been studied extensively in the last 40 years, but so far, no systematic analysis of conformational changes between allosteric structures has been carried out. Here, we compile a set of 51 pairs of known inactive and active allosteric protein structures from the Protein Data Bank. We calculate local conformational differences between the two structures of each protein using simple metrics, such as backbone and side-chain Cartesian displacement, and torsion angle change and rearrangement in residue-residue contacts. Thresholds for each metric arise from distributions of motions in two control sets of pairs of protein structures in the same biochemical state. Statistical analysis of motions in allosteric proteins quantifies the magnitude of allosteric effects and reveals simple structural principles about allostery. For example, allosteric proteins exhibit substantial conformational changes comprising about 20% of the residues. In addition, motions in allosteric proteins show strong bias toward weakly constrained regions such as loops and the protein surface. Correlation functions show that motions communicate through protein structures over distances averaging 10-20 residues in sequence space and 10-20 A in Cartesian space. Comparison of motions in the allosteric set and a set of 21 nonallosteric ligand-binding proteins shows that nonallosteric proteins also exhibit bias of motion toward weakly constrained regions and local correlation of motion. However, allosteric proteins exhibit twice as much percent motion on average as nonallosteric proteins with ligand-induced motion. These observations may guide efforts to design flexibility and allostery into proteins.     

Correlating allostery with rigidity

Allosteric proteins demonstrate the phenomenon of a ligand binding to a protein at a regulatory or effector site and thereby changing the chemical affinity of the catalytic site. As such, allostery is extremely important biologically as a regulatory mechanism for molecular concentrations in many cellular processes. One particularly interesting feature of allostery is that often the catalytic and effector sites are separated by a large distance. Structural comparisons of allosteric proteins resolved in both inactive and active states indicate that a variety of structural rearrangement and changes in motions may contribute to general allosteric behavior. In general it is expected that the coupling of catalytic and regulatory sites is responsible for allosteric behavior. We utilize a novel examination of allostery using rigidity analysis of the underlying graph of the protein structures. Our results indicate a general global change in rigidity associated with allosteric transitions where the R state is more rigid than the T state. A set of allosteric proteins with heterotropic interactions is used to test the hypothesis that catalytic and effector sites are structurally coupled. Observation of a rigid path connecting the effector and catalytic sites in 68.75% of the structures points to rigidity as a means by which the distal sites communicate with each other and so contribute to allosteric regulation. Thus structural rigidity is shown to be a fundamental underlying property that promotes cooperativity and non-locality seen in allostery.     

From Principal Component to Direct Coupling Analysis of Coevolution in Proteins: Low-Eigenvalue Modes are Needed for Structure Prediction

Various approaches have explored the covariation of residues in multiple-sequence alignments of homologous proteins to extract functional and structural information. Among those are principal component analysis (PCA), which identifies the most correlated groups of residues, and direct coupling analysis (DCA), a global inference method based on the maximum entropy principle, which aims at predicting residue-residue contacts. In this paper, inspired by the statistical physics of disordered systems, we introduce the Hopfield-Potts model to naturally interpolate between these two approaches. The Hopfield-Potts model allows us to identify relevant ‘patterns’ of residues from the knowledge of the eigenmodes and eigenvalues of the residue-residue correlation matrix. We show how the computation of such statistical patterns makes it possible to accurately predict residue-residue contacts with a much smaller number of parameters than DCA. This dimensional reduction allows us to avoid overfitting and to extract contact information from multiple-sequence alignments of reduced size. In addition, we show that low-eigenvalue correlation modes, discarded by PCA, are important to recover structural information: the corresponding patterns are highly localized, that is, they are concentrated in few sites, which we find to be in close contact in the three-dimensional protein fold.     

The difference between protein structures that are obtained by X-ray analysis and magnetic resonance spectroscopy

We have analyzed the proteins whose structures were determined both by X-ray analysis (X-ray) and nuclear magnetic resonance (NMR) on condition that these structures do not differ greatly when spatially superimposed on each other (61 pairs of protein structures). Atom-atomic contacts (contact distances varied from 2 to 8 A) have been analyzed and it has been found that NMR structures (in comparison with X-ray ones) have more contacts in the range below 3.5 A and above 5.5 A. In the case of residue-residue contacts NMR structures have more contacts below 3 A and between 4.5 and 6.5 A. At all the other contact distances analyzed the X-ray structures have more contacts. The difference in the number of atom-atomic and residue-residue contacts is greater for internal residues, that are concealed from water, as compared to the surface residues. The other, not less important difference deals with the number of hydrogen bonds in the main chain: it is larger for the X-ray structures. The correlation between the hydrogen bonds identified in the structures obtained by both methods is no more than 32%. The consideration of a complete set of protein structures obtained by NMR results in the fact that the number of hydrogen bonds grows 1.2 times as compared to those obtained with the X-ray analysis, whereas the correlation increases only by 65%. We have also demonstrated that alpha-helices in the NMR structures are more distorted in comparison with the ideal alpha-helix, than alpha-helices in the X-ray structures.     

RankViaContact: ranking and visualization of amino acid contacts

SUMMARY: RankViaContact is a web service for calculation of residue-residue contact energies in proteins based on a coarse-grained model, and for visualization of interactions. The service provides information about ranked contact energies of residues, coordination numbers and the relative solvent accessibility of selected residues, as well as sequence and structure information. The program can be used to design stabilizing mutations, to analyze residue-residue contacts and to study the consequences of mutations. AVAILABILITY: http://bioinf.uta.fi/Rank.htm.     

Distribution of amino acid residues and residue-residue contacts in molecular chaperones.

The amino acid distribution and residue-residue contacts in molecular chaperones are different when compared to normal globular proteins. The study of molecular chaperones reveals a different surrounding environment to exist for the residues Cys, Trp, and His which may play an important role in determining the chaperone structures. Unlike globular proteins, it has been observed that a one-to-one correspondence between the amino acid distribution in a sequence and the structures of molecular chaperones. The preference of amino acid residues surrounding all 20 types of residues in secondary structures and their accessible surface areas have been analysed.     

Inversion of the allosteric response of Escherichia coli glucosamine-6-P deaminase to N-acetylglucosamine 6-P, by single amino acid replacements

Amino acid replacements in the active site of glucosamine-6-P deaminase from Escherichia coli (GlcN6P deaminase, EC 3.5.99.6) involving the residues D141 and E148 produce atypical allosteric kinetics. These residues are located in the chain segment 139-156 which is part of the active site and which also forms several intersubunit contacts close to the allosteric site. In the D141N and E148Q mutant forms of this deaminase, there is an inversion of the effect of its physiological allosteric effector, N-acetylglucosamine 6-P, which becomes an inhibitor at substrate concentrations above a critical value. For both mutants, this particular point appears at low substrate concentration and the inhibition by the allosteric activator is the dominant effect in velocity versus substrate curves. These effects are analyzed as a particular case of the concerted allosteric model, assuming that the R state, the conformer displaying the higher affinity for the substrate, is the less catalytic state, thus producing an inverted allosteric response.     

Identification of amino acids involved in protein structural uniqueness: implication for de novo protein design

Structural uniqueness is characteristic of native proteins and is essential to express their biological functions. The major factors that bring about the uniqueness are specific interactions between hydrophobic residues and their unique packing in the protein core. To find the origin of the uniqueness in their amino acid sequences, we analyzed the distribution of the side chain rotational isomers (rotamers) of hydrophobic amino acids in protein tertiary structures and derived deltaS(contact), the conformational-entropy changes of side chains by residue-residue contacts in each secondary structure. The deltaS(contact) values indicate distinct tendencies of the residue pairs to restrict side chain conformation by inter-residue contacts. Of the hydrophobic residues in alpha-helices, aliphatic residues (Leu, Val, Ile) strongly restrict the side chain conformations of each other. In beta-sheets, Met is most strongly restricted by contact with Ile, whereas Leu, Val and Ile are less affected by other residues in contact than those in alpha-helices. In designed and native protein variants, deltaS(contact) was found to correlate with the folding-unfolding cooperativity. Thus, it can be used as a specificity parameter for designing artificial proteins with a unique structure.     

Computation of Conformational Coupling in Allosteric Proteins

In allosteric regulation, an effector molecule binding a protein at one site induces conformational changes, which alter structure and function at a distant active site. Two key challenges in the computational modeling of allostery are the prediction of the structure of one allosteric state starting from the structure of the other, and elucidating the mechanisms underlying the conformational coupling of the effector and active sites. Here we approach these two challenges using the Rosetta high-resolution structure prediction methodology. We find that the method can recapitulate the relaxation of effector-bound forms of single domain allosteric proteins into the corresponding ligand-free states, particularly when sampling is focused on regions known to change conformation most significantly. Analysis of the coupling between contacting pairs of residues in large ensembles of conformations spread throughout the landscape between and around the two allosteric states suggests that the transitions are built up from blocks of tightly coupled interacting sets of residues that are more loosely coupled to one another.     

Influence of medium and long range interactions in protein folding.

Protein structures are stabilized by both local and long range interactions. In this work, we analyze the residue-residue contacts and the role of medium- and long-range interactions in globular proteins belonging to different structural classes. The results show that while medium range interactions predominate in all-alpha class proteins, long-range interactions predominate in all-beta class. Based on this, we analyze the performance of several structure prediction methods in different structural classes of globular proteins and found that all the methods predict the secondary structures of all-alpha proteins more accurately than other classes. Also, we observed that the residues occurring in the range of 21-30 residues apart contributes more towards long-range contacts and about 85% of residues are involved in long-range contacts. Further, the preference of residue pairs to the folding and stability of globular proteins is discussed.     

Inter-residue and solvent-residue interactions in proteins: a statistical study on experimental structures

A large set of protein structures resolved by X-ray or NMR techniques has been extracted from the Protein Data Bank and analyzed using statistical methods. In particular, we investigate the interactions between side chains and the interactions between solvent and side chains, pointing out on the possibility of including the solvent as part of a knowledge-based potential. The solvent-residue contacts are accounted for on the basis of the Voronoi's polyhedron analysis. Our investigation confirms the importance of hydrophobic residues in determining the protein stability. We observe that in general hydrophobic-hydrophobic interactions and, more specifically, aromatic-aromatic contacts tend to be increasingly distally separated in the primary sequence of proteins, thus connecting distinct secondary structure elements. A simple relation expressing the dependence of the protein free energy by the number of residues is proposed. Such a relation includes both the residue-residue and the solvent-residue contributions. The former is dominant for large size proteins, whereas for small sizes (number of residues less than 100) the two terms are comparable. Gapless threading experiments show that the solvent-residue knowledge-based potential yields a significant contribution with respect to discriminating the native structure of proteins. Such contribution is important especially for proteins of small size and is similar to that given by the most favorable residue-residue knowledge-based potential referring to hydrophobic-hydrophobic interactions such as isoleucine-leucine. In general, the inclusion of the solvent-residue interaction produces a relevant increase of the free energy gap between the native structures and decoys.     

Distinct allosteric pathways in imidazole glycerol phosphate synthase from yeast and bacteria

Understanding the relationship between protein structures and their function is still an open question that becomes very challenging when allostery plays an important functional role. Allosteric proteins, in fact, exploit different ranges of motions (from sidechain local fluctuations to long-range collective motions) to effectively couple distant binding sites, and of particular interest is whether allosteric proteins of the same families with similar functions and structures also necessarily share the same allosteric mechanisms. Here, we compared the early dynamics initiating the allosteric communication of a prototypical allosteric enzyme from two different organisms, i.e., the imidazole glycerol phosphate synthase (IGPS) enzymes from the thermophilic bacteria and the yeast, working at high and room temperatures, respectively. By combining molecular dynamics simulations and network models derived from graph theory, we found rather distinct early allosteric dynamics in the IGPS from the two organisms, involving significatively different allosteric pathways in terms of both local and collective motions. Given the successful prediction of key allosteric residues in the bacterial IGPS, whose mutation disrupts its allosteric communication, the outcome of this study paves the way for future experimental studies on the yeast IGPS that could foster therapeutic applications by exploiting the control of IGPS enzyme allostery.     

Residue-residue contact substitution probabilities derived from aligned three-dimensional structures and the identification of common folds.

We report the derivation of scores that are based on the analysis of residue-residue contact matrices from 443 3-dimensional structures aligned structurally as 96 families, which can be used to evaluate sequence-structure matches. Residue-residue contacts and the more than 3 x 10(6) amino acid substitutions that take place between pairs of these contacts at aligned positions within each family of structures have been tabulated and segregated according to the solvent accessibility of the residues involved. Contact maps within a family of structures are shown to be highly conserved (approximately 75%) even when the sequence identity is approaching 10%. In a comparison involving a globin structure and the search of a sequence databank (> 21,000 sequences), the contact probability scores are shown to provide a very powerful secondary screen for the top scoring sequence-structure matches, where between 69% and 84% of the unrelated matches are eliminated. The search of an aligned set of 2 globins against a sequence databank and the subsequent residue contact-based evaluation of matches locates all 618 globin sequences before the first non-globin match. From a single bacterial serine proteinase structure, the structural template approach coupled with residue-residue contact substitution data lead to the detection of the mammalian serine proteinase family among the top matches in the search of a sequence databank.     

Identifying folding nucleus based on residue contact networks of proteins

In the native structure of a protein, all the residues are tightly parked together in a specific order following its folding and every residue contacts with some spatially neighbor residues. A residue contact network can be constructed by defining the residues as nodes and the native contacts as edges. During the folding of small single-domain proteins, there is a set of contacts (or bonds), defined as the folding nucleus (FN), which is formed around the transition state, i.e., a rate-limiting barrier located at about the middle between the unfolded states and the native state on the free energy landscape. Such a FN plays an essential role in the folding dynamics and the residues, which form the related contacts called as folding nucleus residues (FNRs). In this work, the FNRs in proteins are identified by using quantities which characterize the topology of residue contact networks of proteins. By comparing the specificities of residues with the network quantities K(R), L(R), and D(R), up to 90% FNRs of six typical proteins found experimentally are identified. It is found that the FNRs behave the full-closeness centrals rather than degree or closeness centers in the residue contact network, implying that they are important to the folding cooperativity of proteins. Our study shows that the FNRs can be identified solely from the native structures of proteins based on the analysis of residue contact network without any knowledge of the transition state ensemble.     

The β structure: Inter-strand correlations

β structures in 19 proteins have been analysed for pairwise residue-residue correlations. The results show that hydrophobic residues tend to go together mainly as inter-strand nearest-neighbours, a non-local sequence correlation. This suggests that hydrophobic residues in different parts of the protein molecule might “recognize” each other when a β sheet is formed.     

Influence of Medium and Long Range Interactions in (α/β)8 Barrel Proteins

The residue-residue contacts and the role of medium and long rangeinteractions in 36 (/)₈ barrel proteins have beenanalysed. The influence of long range contacts in the formation ofphysico-chemically similar clusters, and the preference of amino acidresidues towards long range contacts have also been studied. Theresults reveal a nearly uniform level of medium and long rangecontacts in most of the proteins. The residues Gln and Ala havehighest medium range contacts and the residue Pro has the lowestmedium range contacts. The residue Cys has the highest long rangecontact followed by other hydrophobic residues namely Val, Ile andLeu. In the physico-chemically similar clusters identified in theseproteins, 25–40 percent residues are influenced by long rangecontacts, and the residues Cys, Ile, Val and Met are the mostpreferred ones.     

Hill coefficient ratios give binding ratios of allosteric enzyme effectors; inhibition, activation, and squatting in deoxycytidylate aminohydrolase (EC 3.5.4.12)

The ratio of the steady-state kinetic Hill coefficients of two different effectors equals (under some rather weak general assumptions) the ratio in which the effectors displace each other from an enzyme. This principle can make implications of experimental allosteric enzyme kinetic data immediately apparent. We can use it to find that one molecule of the allosteric inhibitor of dCMP aminohydrolase, at moderately high effector concentrations, displaces one molecule of substrate, or one molecule of activator, whereas at very high concentrations, one molecule of inhibitor displaces two of substrate. Further use of the principle suggests that substrate, at high concentrations, binds binds to activator sites. However, ratios of substrate, activator, and inhibitor Hill coefficients are incompatible with a simple model of activation in which substrate and activator are bound to the same conformation.     

Pump-probe molecular dynamics as a tool for studying protein motion and long range coupling

A new method for analyzing the dynamics of proteins is developed and tested. The method, pump-probe molecular dynamics, excites selected atoms or residues with a set of oscillating forces, and the transmission of the impulse to other parts of the protein is probed using Fourier transform of the atomic motions. From this analysis, a coupling profile can be determined which quantifies the degree of interaction between pump and probe residues. Various physical properties of the method such as reciprocity and speed of transmission are examined to establish the soundness of the method. The coupling strength can be used to address questions such as the degree of interaction between different residues at the level of dynamics, and identify propagation of influence of one part of the protein on another via "pathways" through the protein. The method is illustrated by analysis of coupling between different secondary structure elements in the allosteric protein calmodulin, and by analysis of pathways of residue-residue interaction in the PDZ domain protein previously elucidated by genomics and mutational studies.     

The structure of pyruvate kinase from Leishmania mexicana reveals details of the allosteric transition and unusual effector specificity.

Glycolysis occupies a central role in cellular metabolism, and is of particular importance for the catabolic production of ATP in protozoan parasites such as Leishmania and Trypanosoma. In these organisms pyruvate kinase plays a key regulatory role, and is unique in responding to fructose 2,6-bisphosphate as allosteric activator. The determination of the first eukaryotic pyruvate kinase crystal structure in the T-state is reported. A comparison of the leishmania and yeast R-state enzymes reveals fewer differences than the previous comparison of Escherichia coli T-state and rabbit muscle non-allosteric enzymes. Structural changes related to the allosteric transition can therefore be distinguished from those that are a consequence of the inherent wide structural divergence between bacterial and mammalian proteins. The allosteric transition involves significant changes in a tightly packed array of eight alpha helices at the interface near the catalytic site. At the other interface the allosteric transition appears to be accompanied by the bending of a ten-stranded intersubunit beta sheet adjacent to the effector site. Helix Calpha1 makes contacts to the N-terminal helical domain and bridges both interfaces. A comparison of the effector sites of the leishmania and yeast enzymes reveals the structural basis for the different effector specificity. Two loops comprising residues 443-453 and 480-489 adopt very different conformations in the two enzymes, and Lys453 and His480 that are a feature of trypanosomatid enzymes provide probable ligands for the 2-phospho group of the effector molecule. These differences offer an opportunity for the design of drugs that would bind to the trypanosomatid enzymes but not to those of the mammalian host.