Geometric cooperativity and anticooperativity of three-body interactions in native proteins

Characterizing multibody interactions of hydrophobic, polar, and ionizable residues in protein is important for understanding the stability of protein structures. We introduce a geometric model for quantifying 3-body interactions in native proteins. With this model, empirical propensity values for many types of 3-body interactions can be reliably estimated from a database of native protein structures, despite the overwhelming presence of pairwise contacts. In addition, we define a nonadditive coefficient that characterizes cooperativity and anticooperativity of residue interactions in native proteins by measuring the deviation of 3-body interactions from 3 independent pairwise interactions. It compares the 3-body propensity value from what would be expected if only pairwise interactions were considered, and highlights the distinction of propensity and cooperativity of 3-body interaction. Based on the geometric model, and what can be inferred from statistical analysis of such a model, we find that hydrophobic interactions and hydrogen-bonding interactions make nonadditive contributions to protein stability, but the nonadditive nature depends on whether such interactions are located in the protein interior or on the protein surface. When located in the interior, many hydrophobic interactions such as those involving alkyl residues are anticooperative. Salt-bridge and regular hydrogen-bonding interactions, such as those involving ionizable residues and polar residues, are cooperative. When located on the protein surface, these salt-bridge and regular hydrogen-bonding interactions are anticooperative, and hydrophobic interactions involving alkyl residues become cooperative. We show with examples that incorporating 3-body interactions improves discrimination of protein native structures against decoy conformations. In addition, analysis of cooperative 3-body interaction may reveal spatial motifs that can suggest specific protein functions.     

Thermodynamic model of cooperativity in a dimeric protein: unique and independent parameters formulation.

A model of the cooperative interaction of ligand binding to a dimeric protein is presented based upon the unique and independent parameters (UIP) thermodynamic formulation (Gutheil and McKenna, Biophys. Chem. 45 (1992) 171-179). The analysis is developed from an initial model which includes coupled conformational and ligand binding equilibria. This completely general model is then restricted to focus on conformationally mediated cooperative interactions between the ligands and the expressions for the apparent ligand binding constant and the apparent ligand-ligand interaction constant are derived. The conditions under which there is no cooperative interaction between the ligands are found as roots to a polynomial equation. Consideration of the distribution of species among the various conformational states in this general model leads to a set of inequalities which can be represented as a two dimensional plot of boundaries. By superimposing a contour plot of the value of the apparent ligand-ligand interaction constant over the plot of boundaries a complete graphical representation of this system is achieved similar to a phase diagram. It is found that the parameter space homologous to Koshland-Nemethy-Filmer type of model is most consistent with both positive and negative cooperativity in this model. The maximal amount of positive and negative cooperativity are found to be simple functions of Kc, the equilibrium constant associated with the change of a subunit and ligand from the unligated to ligated conformation. It is shown that under certain limiting conditions the apparent allosteric interaction between ligands is equal to the conformational interaction between subunits. The methods presented are generally applicable to the theoretical analysis of thermodynamic interactions in complex systems.     

Cooperative stabilization of the SIR complex provides robust epigenetic memory in a model of SIR silencing in Saccharomyces cerevisiae

How alternative chromatin-based regulatory states can be made stable and heritable in order to provide robust epigenetic memory is poorly understood. Here, we develop a stochastic model of the silencing system in Saccharomyces cerevisiae that incorporates cooperative binding of the repressive SIR complex and antisilencing histone modifications, in addition to positive feedback in Sir2 recruitment. The model was able to reproduce key features of SIR regulation of an HM locus, including heritable bistability, dependence on the silencer elements, and sensitivity to SIR dosage. We found that antisilencing methylation of H3K79 by Dot1 was not needed to generate these features, but acted to reduce spreading of SIR binding, consistent with its proposed role in containment of silencing. In contrast, cooperative inter-nucleosome interactions mediated by the SIR complex were critical for concentrating SIR binding around the silencers in the absence of barriers, and for providing bistability in SIR binding. SIR-SIR interactions magnify the cooperativity in the Sir2-histone deacetylation positive feedback reaction and complete a double-negative feedback circuit involving antisilencing modifications. Thus, our modeling underscores the potential importance of cooperative interactions between nucleosome-bound complexes both in the SIR system and in other chromatin-based complexes in epigenetic regulation.     

Unraveling Subunit Cooperativity in Homotetrameric HCN2 Channels

In a multimeric receptor protein, the binding of a ligand can modulate the binding of a succeeding ligand. This phenomenon, called cooperativity, is caused by the interaction of the receptor subunits. By using a complex Markovian model and a set of parameters determined previously, we analyzed how the successive binding of four ligands leads to a complex cooperative interaction of the subunits in homotetrameric HCN2 pacemaker channels. The individual steps in the model were characterized by Gibbs free energies for the equilibria and activation energies, specifying the affinity of the binding sites and the transition rates, respectively. Moreover, cooperative free energies were calculated for each binding step in both the closed and the open channel. We show that the cooperativity sequence positive-negative-positive determined for the binding affinity is generated by the combined effect of very different cooperativity sequences determined for the binding and unbinding rates, which are negative-negative-positive and no-negative-no, respectively. It is concluded that in the ligand-induced activation of HCN2 channels, the sequence of cooperativity based on the binding affinity is caused by two even qualitatively different sequences of cooperativity that are based on the rates of ligand binding and unbinding.     

A protein complex network of Drosophila melanogaster

Determining the composition of protein complexes is an essential step toward understanding the cell as an integrated system. Using coaffinity purification coupled to mass spectrometry analysis, we examined protein associations involving nearly 5,000 individual, FLAG-HA epitope-tagged Drosophila proteins. Stringent analysis of these data, based on a statistical framework designed to define individual protein-protein interactions, led to the generation of a Drosophila protein interaction map (DPiM) encompassing 556 protein complexes. The high quality of the DPiM and its usefulness as a paradigm for metazoan proteomes are apparent from the recovery of many known complexes, significant enrichment for shared functional attributes, and validation in human cells. The DPiM defines potential novel members for several important protein complexes and assigns functional links to 586 protein-coding genes lacking previous experimental annotation. The DPiM represents, to our knowledge, the largest metazoan protein complex map and provides a valuable resource for analysis of protein complex evolution.     

Structural basis of affinity maturation and intramolecular cooperativity in a protein-protein interaction

Although protein-protein interactions are involved in nearly all cellular processes, general rules for describing affinity and selectivity in protein-protein complexes are lacking, primarily because correlations between changes in protein structure and binding energetics have not been well determined. Here, we establish the structural basis of affinity maturation for a protein-protein interaction system that we had previously characterized energetically. This model system exhibits a 1500-fold affinity increase. Also, its affinity maturation is restricted by negative intramolecular cooperativity. With three complex and six unliganded variant X-ray crystal structures, we provide molecular snapshots of protein interface remodeling events that span the breadth of the affinity maturation process and present a comprehensive structural view of affinity maturation. Correlating crystallographically observed structural changes with measured energetic changes reveals molecular bases for affinity maturation, intramolecular cooperativity, and context-dependent binding.     

Studying multisite binary and ternary protein interactions by global analysis of isothermal titration calorimetry data in SEDPHAT: application to adaptor protein complexes in cell signaling

Multisite interactions and the formation of ternary or higher-order protein complexes are ubiquitous features of protein interactions. Cooperativity between different ligands is a hallmark for information transfer, and is frequently critical for the biological function. We describe a new computational platform for the global analysis of isothermal titration calorimetry (ITC) data for the study of binary and ternary multisite interactions, implemented as part of the public domain multimethod analysis software SEDPHAT. The global analysis of titrations performed in different orientations was explored, and the potential for unraveling cooperativity parameters in multisite interactions was assessed in theory and experiment. To demonstrate the practical potential and limitations of global analyses of ITC titrations for the study of cooperative multiprotein interactions, we have examined the interactions of three proteins that are critical for signal transduction after T-cell activation, LAT, Grb2, and Sos1. We have shown previously that multivalent interactions between these three molecules promote the assembly of large multiprotein complexes important for T-cell receptor activation. By global analysis of the heats of binding observed in sets of ITC injections in different orientations, which allowed us to follow the formation of binary and ternary complexes, we observed negative and positive cooperativity that may be important to control the pathway of assembly and disassembly of adaptor protein particles.     

Dissecting cooperative and additive binding energetics in the affinity maturation pathway of a protein-protein interface

When two proteins associate they form a molecular interface that is a structural and energetic mosaic. Within such interfaces, individual amino acid residues contribute distinct binding energies to the complex. In combination, these energies are not necessarily additive, and significant positive or negative cooperative effects often exist. The basis of reliable algorithms to predict the specificities and energies of protein-protein interactions depends critically on a quantitative understanding of this cooperativity. We have used a model protein-protein system defined by an affinity maturation pathway, comprising variants of a T cell receptor Vbeta domain that exhibit an overall affinity range of approximately 1500-fold for binding to the superantigen staphylococcal enterotoxin C3, in order to dissect the cooperative and additive energetic contributions of residues within an interface. This molecular interaction has been well characterized previously both structurally, by x-ray crystallographic analysis, and energetically, by scanning alanine mutagenesis. Through analysis of group and individual maturation and reversion mutations using surface plasmon resonance spectroscopy, we have identified energetically important interfacial residues, determined their cooperative and additive energetic properties, and elucidated the kinetic and thermodynamic bases for molecular evolution in this system. The summation of the binding free energy changes associated with the individual mutations that define this affinity maturation pathway is greater than that of the fully matured variant, even though the affinity gap between the end point variants is relatively large. Two mutations in particular, both located in the complementarity determining region 2 loop of the Vbeta domain, exhibit negative cooperativity.     

Are protein complexes made of cores,modules and attachments?

It has recently been proposed by Gavin et al. (Nature 2006, 440, 631-636) that protein complexes in the cell exist in different forms. The proteins within each complex were proposed to exist as three different classes, being core, module or attachment proteins. This study investigates whether the core-module-attachment classification of proteins within each complex is supported by other high-throughput protein data. Core proteins were found to have lower abundance, and shorter half-life as compared to attachment proteins, whilst the abundance and half-life of core and module proteins were similar. When the cell was perturbed, core proteins had smaller changes in abundance as compared to module and attachment proteins. Comparisons between six different pairwise interaction types of core, module and attachment proteins within a complex showed interaction types involving core or module proteins were more likely to be mediated by domain-domain interactions (DDIs) than interaction types involving attachment proteins. Interaction types that involve attachment proteins had a relatively higher ratio of abundance and ratio of half-life. So we conclude that, the core, module and attachment model of protein complexes is supported by data from these proteomic scale datasets, and describe a model for a typical protein complex that considers the above results.     

Competitive cooperative bindings of a small ligand to a linear polymer. II. Investigations on the mechanisms of proflavine binding to poly (A) and DNA.

Experimental binding isotherms relative to the interactions between proflavine and poly(A) or DNA are analyzed by comparison with theoretical models dealing with competitive cooperative bindings. In the case of poly(A), there are apparently no specific binding sites for the positive co-operative binding (complex I) leading to dye aggregation along the polyanionic chain. The second complex (complex II) seems to involve specific base-dye interactions, but it cannot be said whether this binding displays negative cooperativity or noncooperativity. None of the two simpler theoretical models agree quantitatively with all experimental data. A plausible interpretation can be given if it is assumed that (i) the electrostatic binding of one isolated bound dye molecule (nucleus of complex I) involves a definite interaction between a phosphate group and the positive charge of the dye; (ii) the structure of complex II is such that a dye–phosphate ionic interaction is maintained. In the case of DNA, our model of monoexclusive interactions fits the data more closely than does the model of biexclusive interactions. This gives experimental support for structural models in which the intercalated molecule interacts preferentially with one strand of the double helix and blocks only one phosphate for electrostatic binding. In order to propose a mechanism consistent with equilibrium and relaxation kinetic data, a modified reaction scheme is considered which takes account of the cooperativity effects in external binding and extends previous models.     

Cooperativity during the formation of peptide/MHC class II complexes

To generate an effective immune response, class II major histocompatibility complex molecules (MHCII) must present a diverse array of peptide ligands for recognition by T lymphocytes. Peptide/MHCII complexes are stabilized by hydrophobic anchoring of peptide side chains to pockets in the MHCII protein and the formation of hydrogen bonds to the peptide backbone. Many current models of peptide/MHCII association assume an additive and independent contribution of the interactions between major MHCII pockets and corresponding side chains in the peptide. However, significant conformational rearrangements occur in both the peptide and MHCII during binding. Therefore, we hypothesize that peptide binding to MHCII could be viewed as a folding process in which both molecules cooperate to produce the final conformation. To directly test this hypothesis, we adapt a serial mutagenesis strategy to study cooperativity in the interaction of the human MHCII HLA-DR1 and a peptide derived from influenza hemagglutinin. Substitutions in either the peptide or HLA-DR1 that are predicted to interfere with hydrogen bond formation show cooperative effects on complex stability and affinity. Substitution of a peptide side chain that provides a hydrophobic contact also contributes to the cooperative effect, suggesting a role for all energetic sources in the folding process. We propose that cooperativity throughout the peptide-binding groove reflects the folding of segments of the MHCII molecule into helices around the peptide with a concomitant folding of the peptide into a polyproline helix. The implications of cooperativity for peptide/MHCII structure and epitope selection are discussed.     

Interactions of the Integrase Protein of the Conjugative Transposon Tn916 with Its Specific DNA Binding Sites

The binding of two chimeric proteins, consisting of the N-terminal or C-terminal DNA binding domain of Tn916 Int fused to maltose binding protein, to specific oligonucleotide substrates was analyzed by gel mobility shift assay. The chimeric protein with the N-terminal domain formed two complexes of different electrophoretic mobilities. The faster-moving complex, whose formation displayed no cooperativity, contained two protein monomers bound to a single DNA molecule. The slower-moving complex, whose formation involved cooperative binding (Hill coefficient > 1.0), contained four protein monomers bound to a single DNA molecule. Methylation interference experiments coupled with the analysis of protein binding to mutant oligonucleotide substrates showed that formation of the faster-moving complex containing two protein monomers required the presence of two 11-bp direct repeats (called DR2) in direct orientation. Formation of the slower-moving complex required only a single DR2 repeat. Binding of the N-terminal domains in vivo could serve to position two Int monomers on the DNA near each end of the transposon and assist in bringing together the ends of the transposon so that excision can occur. The chimeric protein with the C-terminal domain of Int also formed two complexes of different electrophoretic mobilities. The major, slower-moving complex, whose formation involved cooperative binding, contained two protein molecules bound to one DNA molecule. This finding suggested that while the C-terminal domain of Int can bind DNA as a monomer, a cooperative interaction between two monomers of the C-terminal domain may help to bring the ends of the transposon together during excision.     

Cooperative charge fluctuations by migrating protons in globular proteins

A review of the hydrogen bonded network on the protein surface shows the presence of a charged complex system with parallel and competitive interactions, including ionizable side-chains, migrating protons, bound water and nearby backbone peptides. This system displays cooperative effects of dynamical nature, reviewed for lysozyme as a case. By increasing the water coverage of the protein powder, the bound water cluster exhibits a percolative transition, detectable by the onset of large water-assisted displacements of migrating protons, with a parallel emergence of protein mobility and biological function. By lowering the temperature, migrating protons exhibit a glassy dielectric relaxation in the low frequency range, pointing to a frustration by competing interactions similar to that observed in spin glasses and fragile glass forming liquids. The observation of these dissipative processes implies the occurrence of spontaneous charge fluctuations. A simplified model of the protein surface, where conformational and ionizable side-chain fluctuations are averaged out, is used to discuss the statistical physics of these cooperative effects. Some biological implications of this dynamical cooperativity for enzymatic activity are briefly suggested at the end.     

Molecular cooperativity of drebrin(1-300) binding and structural remodeling of f-actin

Drebrin A, an actin-binding protein, is a key regulatory element in synaptic plasticity of neuronal dendrites. Understanding how drebrin binds and remodels F-actin is important for a functional analysis of their interactions. Conventionally, molecular models for protein-protein interactions use binding parameters derived from bulk solution measurements with limited spatial resolution, and the inherent assumption of homogeneous binding sites. In the case of actin filaments, their structural and dynamic states—as well as local changes in those states—may influence their binding parameters and interaction cooperativity. Here, we probed the structural remodeling of single actin filaments and the binding cooperativity of DrebrinA_1-300 –F–actin using AFM imaging. We show direct evidence of DrebrinA_1-300-induced cooperative changes in the helical structure of F-actin and observe the binding cooperativity of drebrin to F-actin with nanometer resolution. The data confirm at the in vitro molecular level that variations in the F-actin helical structure can be modulated by cooperative binding of actin-binding proteins.     

Mathematical modeling suggests cooperative interactions between a disordered polyvalent ligand and a single receptor site

BACKGROUND: The CDK inhibitor Sic1 must be phosphorylated on at least six sites in order to allow its recognition by the SCF ubiquitin ligase subunit Cdc4. However, because Cdc4 appears to have only a single phospho-epitope binding site, the apparent cooperative dependence on the number of phosphorylation sites in Sic1 cannot be accounted for by traditional thermodynamic models of cooperativity. RESULTS: We develop a general kinetic model, which predicts an unexpected multiplicative increase in affinity as a function of ligand sites. This effect, termed allovalency, derives from a high local concentration of interaction sites moving independently of each other. Modeling of this interaction by a first exit time approach indicates that the probability of ligand rebinding increases exponentially with the number of sites. This type of interaction is relatively immune to loss of any one site and may be easily tuned to any given threshold by adjusting the properties of individual sites. CONCLUSIONS: The allovalency model suggests that a previously undescribed mechanism may underlie certain cooperative interactions. The widespread occurrence of flexible polyvalent ligands in biological systems suggests that this principle may be broadly applicable.     

Evaluation of direct and cooperative contributions towards the strength of buried hydrogen bonds and salt bridges

An experimental approach to evaluate the net binding free energy of buried hydrogen bonds and salt bridges is presented. The approach, which involves a modified multiple-mutant cycle protocol, was applied to selected interactions between TEM-1-beta-lactamase and its protein inhibitor, BLIP. The selected interactions (two salt bridges and two hydrogen bonds) all involving BLIP-D49, define a distinct binding unit. The penta mutant, where all side-chains constructing the binding unit were mutated to Ala, was used as a reference state to which combinations of side-chains were introduced. At first, pairs of interacting residues were added allowing the determination of interaction energies in the absence of neighbors, using double mutant cycles. Addition of neighboring residues allowed the evaluation of their cooperative effects on the interaction. The two isolated salt bridges were either neutral or repulsive whereas the two hydrogen bonds contribute 0.3 kcal mol(-1 )each. Conversely, a double mutant cycle analysis of these interactions in their native environment showed that they all stabilize the complex by 1-1.5 kcal mol(-1). Examination of the effects of neighboring residues on each of the interactions revealed that the formation of a salt bridge triad, which involves two connected salt bridges, had a strong cooperative effect on stabilizing the complex independent of the presence or absence of additional neighbors. These results demonstrate the importance of forming net-works of buried salt bridges. We present theoretical electrostatic calculations which predict the observed mode of cooperativity, and suggest that the cooperative networking effect results from the favorable contribution of the protein to the interaction. Furthermore, a good correlation between calculated and experimentally determined interaction energies for the two salt bridges, and to a lesser extent for the two hydrogen bonds, is shown. The data analysis was performed on values of DeltaDeltaG(double dagger)K(d) which reflect the strength of short range interactions, while DeltaDeltaG(o)K(D) values which include the effects of long range electrostatic forces that alter specifically DeltaDeltaG(double dagger)k(a) were treated separately.     

Probing possible downhill folding: native contact topology likely places a significant constraint on the folding cooperativity of proteins with approximately 40 residues

Experiments point to appreciable variations in folding cooperativity among natural proteins with approximately 40 residues, indicating that the behaviors of these proteins are valuable for delineating the contributing factors to cooperative folding. To explore the role of native topology in a protein's propensity to fold cooperatively and how native topology might constrain the degree of cooperativity achievable by a given set of physical interactions, we compared folding/unfolding kinetics simulated using three classes of native-centric C^α chain models with different interaction schemes. The approach was applied to two homologous 45-residue fragments from the peripheral subunit-binding domain family and a 39-residue fragment of the N-terminal domain of ribosomal protein L9. Free-energy profiles as functions of native contact number were computed to assess the heights of thermodynamic barriers to folding. In addition, chevron plots of folding/unfolding rates were constructed as functions of native stability to facilitate comparison with available experimental data. Although common Gō-like models with pairwise Lennard-Jones-type interactions generally fold less cooperatively than real proteins, the rank ordering of cooperativity predicted by these models is consistent with experiment for the proteins investigated, showing increasing folding cooperativity with increasing nonlocality of a protein's native contacts. Models that account for water-expulsion (desolvation) barriers and models with many-body (nonadditive) interactions generally entail higher degrees of folding cooperativity indicated by more linear model chevron plots, but the rank ordering of cooperativity remains unchanged. A robust, experimentally valid rank ordering of model folding cooperativity independent of the multiple native-centric interaction schemes tested here argues that native topology places significant constraints on how cooperatively a protein can fold.     

Structural requirements for cooperativity in ileal bile acid-binding proteins

Ileal bile acid-binding proteins (I-BABP), belonging to the family of intracellular lipid-binding proteins, control bile acid trafficking in enterocytes and participate in regulating the homeostasis of these cholesterol-derived metabolites. I-BABP orthologues share the same structural fold and are able to host up to two ligands in their large internal cavities. However variations in the primary sequences determine differences in binding properties such as the degree of binding cooperativity. To investigate the molecular requirements for cooperativity we adopted a gain-of-function approach, exploring the possibility to turn the noncooperative chicken I-BABP (cI-BABP) into a cooperative mutant protein. To this aim we first solved the solution structure of cI-BABP in complex with two molecules of the physiological ligand glycochenodeoxycholate. A comparative structural analysis with closely related members of the same protein family provided the basis to design a double mutant (H99Q/A101S cI-BABP) capable of establishing a cooperative binding mechanism. Molecular dynamics simulation studies of the wild type and mutant complexes and essential dynamics analysis of the trajectories supported the role of the identified amino acid residues as hot spot mediators of communication between binding sites. The emerging picture is consistent with a binding mechanism that can be described as an extended conformational selection model.