Prediction of protein-protein association rates from a transition-state theory

We recently developed a theory for the rates of protein-protein association. The theory is based on the concept of a transition state, which separates the bound state, with numerous short-range interactions but restricted translational and rotational freedom, and the unbound state, with, at most, a small number of interactions but expanded configurational freedom. When not accompanied by large-scale conformational changes, protein-protein association becomes diffusion limited. The association rate is then predicted as k(a)=k(a)(0)exp(-DeltaG(el)(double dagger)/k(B)T), where DeltaG(el)(double dagger) is the electrostatic interaction free energy in the transition state, k(a)(0) is the rate in the absence of electrostatic interactions, and k(B)T is thermal energy. Here, this transition-state theory is used to predict the association rates of four protein complexes. The predictions for the wild-type complexes and 23 mutants are found to agree closely with experimental data over wide ranges of ionic strength.     

Binding hot spots in the TEM1-BLIP interface in light of its modular architecture

Proteins bind one another in aqua's solution to form tight and specific complexes. Previously we have shown that this is achieved through the modular architecture of the interaction network formed by the interface residues, where tight cooperative interactions are found within modules but not between them. Here we extend this study to cover the entire interface of TEM1 beta-lactamase and its protein inhibitor BLIP using an improved method for deriving interaction maps based on REDUCE to add hydrogen atoms and then by evaluating the interactions using modifications of the programs PROBE, NCI and PARE. An extensive mutagenesis study of the interface residues indeed showed that each module is energetically independent on other modules, and that cooperativity is found only within a module. By solving the X-ray structure of two interface mutations affecting two different modules, we demonstrated that protein-protein binding occur via the structural reorganization of the binding modules, either by a "lock and key" or an induced fit mechanism. To explain the cooperativity within a module, we performed multiple-mutant cycle analysis of cluster 2 resulting in a high-resolution energy map of this module. Mutant studies are usually done in reference to alanine, which can be regarded as a deletion of a side-chain. However, from a biological perspective, there is a major interest to understand non-Ala substitutions, as they are most common. Using X-ray crystallography and multiple-mutant cycle analysis we demonstrated the added complexity in understanding non-Ala mutations. Here, a double mutation replacing the wild-type Glu,Tyr to Tyr,Asn on TEM1 (res id 104,105) caused a major backbone structural rearrangement of BLIP, changing the composition of two modules but not of other modules within the interface. This shows the robustness of the modular approach, yet demonstrates the complexity of in silico protein design.     

Variations in the unstructured C-terminal tail of interferons contribute to differential receptor binding and biological activity

Type I interferons (IFNs) elicit antiviral, antiproliferative and immunomodulatory properties in cells. All of them bind to the same receptor proteins, IFNAR1 and IFNAR2, with different affinities. While the 13 known IFNalphas are highly conserved, the C-terminal unstructured tail was found to have large variation in its net charge, from neutral to +4. This led us to speculate that the tail may have a role in modulation of the IFN biological activity, through fine-tuning the binding to IFNAR2. To evaluate this hypothesis, we replaced the tail of IFNalpha2 with that of IFNalpha8 and IFNbeta tails, or deleted the last five residues of this segment. Mutations to the more positively charged tail of IFNalpha8 resulted in a 20-fold higher affinity to IFNAR2, which results in a higher antiviral and antiproliferative activity. Double and multiple mutant cycle analysis placed the tail near a negatively charged loop on IFNAR2, comprising of residues Glu 132-134. Deleting the tail resulted in only twofold reduction in binding compared to the wild-type. Next, we modeled the location of the tail using a two-step procedure: first we generated 200 models of the tail docked on IFNAR2 using HADDOCK, second the models were scored according to the fit between experimentally determined rates of association of nine mutant complexes, and their calculated rates using the PARE software. From the results we suggest that the unstructured tail of IFNalpha is gaining a specific structure in the bound state, binding to a groove below the 132-134 loop in IFNAR2.     

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.     

The Effect of Different Force Applications on the Protein-Protein Complex Barnase-Barstar

Steered molecular dynamics simulations are a tool to examine the energy landscape of protein-protein complexes by applying external forces. Here, we analyze the influence of the velocity and geometry of the probing forces on a protein complex using this tool. With steered molecular dynamics, we probe the stability of the protein-protein complex Barnase-Barstar. The individual proteins are mechanically labile. The Barnase-Barstar binding site is more stable than the folds of the individual proteins. By using different force protocols, we observe a variety of responses of the system to the applied tension.     

Thermodynamic stability of the bacteriorhodopsin lattice as measured by lipid dilution

To determine the strength of noncovalent interactions that stabilize a membrane protein complex, we have developed an in vitro method for quantifying the dissociation of the bacteriorhodopsin (BR) lattice, a naturally occurring two-dimensional crystal. A lattice suspension was titrated with a short- and long-chain phosphatidylcholine mixture to dilute BR within the lipid bilayer. The fraction of BR in the lattice form as a function of added lipid was determined by visible circular dichroism spectroscopy and fit with a cooperative self-assembly model to obtain a critical concentration for lattice assembly. Critical concentration values of wild-type and mutant proteins were used to calculate the change in lattice stability upon mutation (DeltaDeltaG). By using this method, a series of mutant proteins was examined in which residues at the BR-BR interface were replaced with smaller amino acids, either Ala or Gly. Most of the mutant lattices were destabilized, with DeltaDeltaG values of 0.2-1.1 kcal/mol at 30 degrees C, consistent with favorable packing of apolar residues in the membrane. One mutant, I45A, was stabilized by approximately 1.0 kcal/mol, possibly due to increased lipid entropy. The DeltaDeltaG values agreed well with previous in vivo measurements, except in the case of I45A. The ability to measure the change in stability of mutant protein complexes in a lipid bilayer may provide a means of determining the contributions of specific protein-protein and protein-lipid interactions to membrane protein structure.     

New insights into the mechanism of protein-protein association

Association of a protein complex follows a two-step mechanism, with the first step being the formation of an encounter complex that evolves into the final complex. Here, we analyze recent experimental data of the association of TEM1-beta-lactamase with BLIP using theoretical calculations and simulation. We show that the calculated Debye-Hückel energy of interaction for a pair of proteins during association resembles an energy funnel, with the final complex at the minima. All attraction is lost at inter-protein distances of 20 A, or rotation angles of >60 degrees from the orientation of the final complex. For faster-associating protein complexes, the energy funnel deepens and its volume increases. Mutations with the largest impact on association (hotspots for association) have the largest effect on the size and depth of the energy funnel. Analyzing existing evidence, we suggest that the transition state along the association pathway is the formation of the final complex from the encounter complex. Consequently, pairs of proteins forming an encounter complex will tend to dissociate more readily than to evolve into the final complex. Increasing directional diffusion by increasing favorable electrostatic attraction results in a faster forming and slower dissociating encounter complex. The possible applicability of electrostatic calculations for protein-protein docking is discussed.     

Increasing the net charge and decreasing the hydrophobicity of bovine carbonic anhydrase decreases the rate of denaturation with sodium dodecyl sulfate

This study compares the rate of denaturation with sodium dodecyl sulfate (SDS) of the individual rungs of protein charge ladders generated by acylation of the lysine epsilon-NH3+ groups of bovine carbonic anhydrase II (BCA). Each acylation decreases the number of positively charged groups, increases the net negative charge, and increases the hydrophobic surface area of BCA. This study reports the kinetics of denaturation in solutions containing SDS of the protein charge ladders generated with acetic and hexanoic anhydrides; plotting these rates of denaturation as a function of the number of modifications yields a U-shaped curve. The proteins with an intermediate number of modifications are the most stable to denaturation by SDS. There are four competing interactions-two resulting from the change in electrostatics and two resulting from the change in exposed hydrophobic surface area-that determine how a modification affects the stability of a rung of a charge ladder of BCA to denaturation with SDS. A model based on assumptions about how these interactions affect the folded and transition states has been developed and fits the experimental results. Modeling indicates that for each additional acylation, the magnitude of the change in the activation energy of denaturation (DeltaDeltaG(double dagger)) due to changes in the electrostatics is much larger than the change in DeltaDeltaG(double dagger) due to changes in the hydrophobicity, but the intermolecular and intramolecular electrostatic effects are opposite in sign. At the high numbers of acylations, hydrophobic interactions cause the hexanoyl-modified BCA to denature nearly three orders of magnitude more rapidly than the acetyl-modified BCA.     

Common Crowding Agents Have Only a Small Effect on Protein-Protein Interactions

Studies of protein-protein interactions, carried out in polymer solutions, are designed to mimic the crowded environment inside living cells. It was shown that crowding enhances oligomerization and polymerization of macromolecules. Conversely, we have shown that crowding has only a small effect on the rate of association of protein complexes. Here, we investigated the equilibrium effects of crowding on protein heterodimerization of TEM1-β-lactamase with β-lactamase inhibitor protein (BLIP) and barnase with barstar. We also contrasted these with the effect of crowding on the weak binding pair CyPet-YPet. We measured the association and dissociation rates as well as the affinities and thermodynamic parameters of these interactions in polyethylene glycol and dextran solutions. For TEM1-BLIP and for barnase-barstar, only a minor reduction in association rate constants compared to that expected based on solution viscosity was found. Dissociation rate constants showed similar levels of reduction. Overall, this resulted in a binding affinity that is quite similar to that in aqueous solutions. On the other hand, for the CyPet-YPet pair, aggregation, and not enhanced dimerization, was detected in polyethylene glycol solutions. The results suggest that typical crowding agents have only a small effect on specific protein-protein dimerization reactions. Although crowding in the cell results from proteins and other macromolecules, one may still speculate that binding in vivo is not very different from that measured in dilute solutions.     

An early transition state for folding of the P4-P6 RNA domain

Tertiary folding of the 160-nt P4-P6 domain of the Tetrahymena group I intron RNA involves burying of substantial surface area, providing a model for the folding of other large RNA domains involved in catalysis. Stopped-flow fluorescence was used to monitor the Mg2+-induced tertiary folding of pyrene-labeled P4-P6. At 35 degrees C with [Mg2+] approximately 10 mM, P4-P6 folds on the tens of milliseconds timescale with k(obs) = 15-31 s(-1). From these values, an activation free energy deltaG(double dagger) of approximately 8-16 kcal/mol is calculated, where the large range for deltaG(double dagger) arises from uncertainty in the pre-exponential factor relating k(obs) and delta G(double dagger). The folding rates of six mutant P4-P6 RNAs were measured and found to be similar to that of the wild-type RNA, in spite of significant thermodynamic destabilization or stabilization. The ratios of the kinetic and thermodynamic free energy changes phi = delta deltaG(double dagger)/delta deltaG(o') are approximately 0, implying a folding transition state in which most of the native-state tertiary contacts are not yet formed (an early folding transition state). The k(obs) depends on the Mg2+ concentration, and the initial slope of k(obs) versus [Mg2+] suggests that only approximately 1 Mg2+ ion is bound in the rate-limiting folding step. This is consistent with an early folding transition state, because folded P4-P6 binds many Mg2+ ions. The observation of a substantial deltaG(double dagger) despite an early folding transition state suggests that a simple two-state folding diagram for Mg2+-induced P4-P6 folding is incomplete. Our kinetic data are some of the first to provide quantitative values for an activation barrier and location of a transition state for tertiary folding of an RNA domain.     

Energy landscape and transition state of protein-protein association

Formation of a stereospecific protein complex is favored by specific interactions between two proteins but disfavored by the loss of translational and rotational freedom. Echoing the protein folding process, we have previously proposed a transition state for protein-protein association. Here we clarify the specification of the transition state by working with two types of toy models for protein association. A “hemisphere” model consists of two matching hemispheres as associating proteins, and a “crater” model consists of a spherical protein with a crater to which another spherical protein fits snugly. Short-range pairwise interactions between sites across the interface hold together the bound complex. Small relative translation and rotation between the subunits quickly destroy the interactions, leading to a sharp transition between the bound state with numerous short-range interactions but restricted translation and rotational freedom and the unbound state with, at most, a small number of interactions but expanded configurational freedom. This transition sets the outer boundary of the bound state as well as the transition state for association. The energy landscape is funnel-like, with the deep well of the bound state surrounded by a broad shallow basin. Calculations with the toy models suggest that mutational change in the interaction energy in the x-ray structure of a protein-protein complex, commonly used to approximate the effect on the association constant, overestimates the effect of mutation by 10–20%. With an eye toward specifying the transition states of actual protein complexes, we find that the total number of contacts between the subunits serves as a good surrogate of the interaction energy. This formalism of protein-protein association is applied to the barnase-barstar complex, reproducing the experimental results for the association rate over a wide range of ionic strength.     

Determination of the two-dimensional interaction rate constants of a cytokine receptor complex

Ligand-receptor interactions within the plane of the plasma membrane play a pivotal role for transmembrane signaling. The biophysical principles of protein-protein interactions on lipid bilayers, though, have hardly been experimentally addressed. We have dissected the interactions involved in ternary complex formation by ligand-induced cross-linking of the subunits of the type I interferon (IFN) receptors ifnar1 and ifnar2 in vitro. The extracellular domains ifnar1-ectodomain (EC) and ifnar2-EC were tethered in an oriented manner on solid-supported lipid bilayers. The interactions of IFNalpha2 and several mutants, which exhibit different association and dissociation rate constants toward ifnar1-EC and ifnar2-EC, were monitored by simultaneous label-free detection and surface-sensitive fluorescence spectroscopy. Surface dissociation rate constants were determined by measuring ligand exchange kinetics, and by measuring receptor exchange on the surface by fluorescence resonance energy transfer. Strikingly, approximately three-times lower dissociation rate constants were observed for both receptor subunits compared to the dissociation in solution. Based on these directly determined surface-dissociation rate constants, the surface-association rate constants were assessed by probing ligand dissociation at different relative surface concentrations of the receptor subunits. In contrast to the interaction in solution, the association rate constants depended on the orientation of the receptor components. Furthermore, the large differences in association kinetics observed in solution were not detectable on the surface. Based on these results, the key roles of orientation and lateral diffusion on the kinetics of protein interactions in plane of the membrane are discussed.     

Free energies of protein-protein association determined by electrospray ionization mass spectrometry correlate accurately with values obtained by solution methods

The advantages of electrospray ionization mass spectrometry (ESIMS) to measure relative solution-phase affinities of tightly bound protein-protein complexes are demonstrated with selected variants of the Bacillus amyloliquefaciens protein barstar (b*) and the RNAase barnase (bn), which form protein-protein complexes with a range of picomolar to nanomolar dissociation constants. A novel chemical annealing procedure rapidly establishes equilibrium in solutions containing competing b* variants with limiting bn. The relative ion abundances of the complexes and those of the competing unbound monomers are shown to reflect the relative solution-phase concentrations of those respective species. No measurable dissociation of the complexes occurs either during ESI or mass detection, nor is there any evidence for nonspecific binding at protein concentrations < 25 microM. Differences in DeltaDeltaG of dissociation between variants were determined with precisions < 0.1 kcal/mol. The DeltaDeltaG values obtained deviate on average by 0.26 kcal/mol from those measured with a solution-phase enzyme assay. It is demonstrated that information about the protein conformation and covalent modifications can be obtained from differences in mass and charge state distributions. This method serves as a rapid and precise means to interrogate protein-protein-binding surfaces for complexes that have affinities in the picomolar to nanomolar range.     

Probing the influence on folding behavior of structurally conserved core residues in P. aeruginosa apo-azurin

The effects on folding kinetics and equilibrium stability of core mutations in the apo-mutant C112S of azurin from Pseudomonas aeruginosa were studied. A number of conserved residues within the cupredoxin family were recognized by sequential alignment as constituting a common hydrophobic core: I7, F15, L33, W48, F110, L50, V95, and V31. Of these, I7, V31, L33, and L50 were mutated for the purpose of obtaining information on the transition state and a potential folding nucleus. In addition, residue V5 in the immediate vicinity of the common core, as well as T52, separate from the core, were mutated as controls. All mutants exhibited a nonlinear dependence of activation free energy of folding on denaturant concentration, although the refolding kinetics of the V31A/C112S mutant indicated that the V31A mutation destabilizes the transition state enough to allow folding via a parallel transition state ensemble. Phi-values could be calculated for three of the six mutants, V31A/C112S, L33A/C112S, and L50A/C112S, and the fractional values of 0.63, 0.33, and 0.50 (respectively) obtained at 0.5 M GdmCl suggest that these residues are important for stabilizing the transition state. Furthermore, a linear dependence of ln k(obs)(H2O) on DeltaG(U-N)(H2O) of the core mutations and the putative involvement of ground-state effects suggest the presence of native-like residual interactions in the denatured state that bias this ensemble toward a folding-competent state.     

A binding free energy hot spot in the ankyrin repeat protein GABPbeta mediated protein-protein interaction

The frequently observed ankyrin repeat motif represents a structural scaffold evolved for mediating protein-protein interactions. As such, these repeats modulate a diverse range of cellular functions. We thermodynamically characterized the heterodimeric GA-binding protein (GABP) alphabeta complex and focused specifically on the interaction mediated by the ankyrin repeat domain of the GABPbeta. Our isothermal titration calorimetric analysis of the interaction between the GABP subunits determined an association constant (K(A)) of 6.0 x 10(8) M(-1) and that the association is favorably driven by a significant change in enthalpy (DeltaH) and a minor change in entropy (-TDeltaS). A total of 16 GABPbeta interface residues were chosen for alanine scanning mutagenesis. The calorimetrically measured differences in the free energy of binding were compared to computationally calculated values resulting in a correlation coefficient r = 0.71. We identified three spatially contiguous hydrophobic and aromatic residues that form a binding free energy hot spot (DeltaDeltaG > 2.0 kcal/mol). One residue provides structural support to the hot spot residues. Three non-hot spot residues are intermediate contributors (DeltaDeltaG approximately 1.0 kcal/mol) and create a canopy-like structure over the hot spot residues to possibly occlude solvent and orientate the subunits. The remaining interface residues are located peripherally and have weak contributions. Finally, our mutational analysis revealed a significant entropy-enthalpy compensation for this interaction.     

Apo-azurin folds via an intermediate that resembles the molten-globule

The folding of Pseudomonas aeruginosa apo-azurin was investigated with the intent of identifying putative intermediates. Two apo-mutants were constructed by replacing the main metal-binding ligand C112 with a serine (C112S) and an alanine (C112A). The guanidinium-induced unfolding free energies (DeltaG(U-N)(H2O)) of the C112S and C112A mutants were measured to 36.8 +/- 1 kJ mole(-1) and 26.1 +/- 1 kJ mole(-1), respectively, and the m-value of the transition to 23.5 +/- 0.7 kJ mole(-1) M(-1). The difference in folding free energy (DeltaDeltaG(U-N)(H2O)) is largely attributed to the intramolecular hydrogen bonding properties of the serine Ogamma in the C112S mutant, which is lacking in the C112A structure. Furthermore, only the unfolding rates differ between the two mutants, thus pointing to the energy of the native state as the source of the observed Delta DeltaG(U-N)(H2O). This also indicates that the formation of the hydrogen bonds present in C112S but absent in C112A is a late event in the folding of the apo-protein, thus suggesting that formation of the metal-binding site occurs after the rate-limiting formation of the transition state. In both mutants we also noted a burst-phase intermediate. Because this intermediate was capable of binding 1-anilinonaphtalene-8-sulfonate (ANS), as were an acid-induced species at pH 2.6, we ascribe it molten globule-like status. However, despite the presence of an intermediate, the folding of apo-azurin C112S is well approximated by a two-state kinetic mechanism.     

Crystal structure of Escherichia coli TEM1 β-lactamase at 1.8 Å resolution

The X-ray structure of Escherichia coli TEM1β-lactamase has been refined to a crystallorgphic R-factor of 16.4% for 22,510 reflections between 5.0 and 1.8 Å resolution; 199 water molecules and 1 sulphate ion were included in refinement. Except for the tips of a few solvent-exposed side chains, all protein atoms have clear electron density and refined to an average atomic temperature factor of 11 Ų. The estimated coordinates error is 0.17 Å. The substrate binding site is located at the interface of the two domains of the protein and contains 4 water molecules and the sulphate anion. One of these solvent molecules is found at hydrogen bond distance from S70 and E166. S70 and S130 are hydrogen bonded to K73 and K234, respectively. It was found that the E. coli TEM1 and Staphylococcus aureus PC1 β-lactamases crystal structures differ in the relative orientations of the two domains composing the enzymes, which result in a narrowed substrate binding cavity in the TEM1 enzyme. Local but significant differences in the vicinity of this site may explain the occurrence of TEM1 natural mutants with extended substrate specificities. © 1993 Wiley-Liss, Inc.