Protein-protein binding is often associated with changes in protonation state

pK(a) values of ionizable residues have been calculated using the PROPKA method and structures of 75 protein-protein complexes and their corresponding free forms. These pK(a) values were used to compute changes in protonation state of individual residues, net changes in protonation state of the complex relative to the uncomplexed proteins, and the correction to a binding energy calculated assuming standard protonation states at pH 7. For each complex, two different structures for the uncomplexed form of the proteins were used: the X-ray structures determined for the proteins in the absence of the other protein and the individual protein structures taken from the structure of the complex (referred to as unbound and bound structures, respectively). In 28 and 77% of the cases considered here, protein-protein binding is accompanied by a complete (>95%) or significant (>50%) change in protonation state of at least one residue using unbound structures. Furthermore, in 36 and 61% of the cases, protein-protein binding is accompanied by a complete or significant net change in protonation state of the complex relative to the separated monomers. Using bound structures, the corresponding values are 12, 51, 20, and 48%. Comparison to experimental data suggest that using unbound and bound structures lead to over- and underestimation of binding-induced protonation state changes, respectively. Thus, we conclude that protein-protein binding is often associated with changes in protonation state of amino acid residues and with changes in the net protonation state of the proteins. The pH-dependent correction to the binding energy contributes at least one order of magnitude to the binding constant in 45 and 23%, using unbound and bound structures, respectively.     

A fast and accurate computational approach to protein ionization

We report a very fast and accurate physics-based method to calculate pH-dependent electrostatic effects in protein molecules and to predict the pK values of individual sites of titration. In addition, a CHARMm-based algorithm is included to construct and refine the spatial coordinates of all hydrogen atoms at a given pH. The present method combines electrostatic energy calculations based on the Generalized Born approximation with an iterative mobile clustering approach to calculate the equilibria of proton binding to multiple titration sites in protein molecules. The use of the GBIM (Generalized Born with Implicit Membrane) CHARMm module makes it possible to model not only water-soluble proteins but membrane proteins as well. The method includes a novel algorithm for preliminary refinement of hydrogen coordinates. Another difference from existing approaches is that, instead of monopeptides, a set of relaxed pentapeptide structures are used as model compounds. Tests on a set of 24 proteins demonstrate the high accuracy of the method. On average, the RMSD between predicted and experimental pK values is close to 0.5 pK units on this data set, and the accuracy is achieved at very low computational cost. The pH-dependent assignment of hydrogen atoms also shows very good agreement with protonation states and hydrogen-bond network observed in neutron-diffraction structures. The method is implemented as a computational protocol in Accelrys Discovery Studio and provides a fast and easy way to study the effect of pH on many important mechanisms such as enzyme catalysis, ligand binding, protein-protein interactions, and protein stability.     

pH-dependent stability of sperm whale myoglobin in water-guanidine hydrochloride solutions

An experimental-theoretical approach for the elucidation of protein stability is proposed. The theoretical prediction of pH-dependent protein stability is based on the macroscopic electrostatic model for calculation of the pH-dependent electrostatic free energy of proteins. As a test of the method we have considered the pH-dependent stability of sperm whale metmyoglobin. Two theoretical methods for evaluation of the electrostatic free energy and p K values are applied: the finite-difference Poisson-Boltzmann method and the semiempirical approach based on the modified Tanford-Kirkwood theory. The theoretical results for electrostatic free energy of unfolding are compared with the experimental data for guanidine hydrochloride unfolding under equilibrium conditions over a wide pH range. Using the optical parameters of the Soret absorbance to monitor conformational equilibrium and Tanford's method to estimate the resulting data, it was found that the conformational free energy of unfolding of metmyoglobin is 16.3 kcal mol(-1) at neutral pH values. The total unfolding free energies were calculated on the basis of the theoretically predicted electrostatic unfolding free energies and the experimentally measured midpoints (pH(1/2)) of acidic and alkaline denaturation transitions. Experimental data for alkaline denaturation were used for the first time in theoretical analysis of the pH-dependent unfolding of myoglobin. The present results demonstrate that the simultaneous application of appropriate theoretical and experimental methods permits a more complete analysis of the pH-dependent and pH-independent properties and stability of globular proteins.     

Thermodynamics of denaturation of hisactophilin, a beta-trefoil protein

Hisactophilin is a histidine-rich pH-dependent actin-binding protein from Dictyostelium discoideum. The structure of hisactophilin is typical of the beta-trefoil fold, a common structure adopted by diverse proteins with unrelated primary sequences and functions. The thermodynamics of denaturation of hisactophilin have been measured using fluorescence- and CD-monitored equilibrium urea denaturation curves, pH-denaturation, and thermal denaturation curves, as well as differential scanning calorimetry. Urea denaturation is reversible from pH 5.7 to pH 9.7; however, thermal denaturation is highly reversible only below pH approximately 6.2. Reversible denaturation by urea and heat is well fit using a two-state transition between the native and the denatured states. Urea denaturation curves are best fit using a quadratic dependence of the Gibbs free energy of unfolding upon urea concentration. Hisactophilin has moderate, roughly constant stability from pH 7.7 to pH 9.7; however, below pH 7.7, stability decreases markedly, most likely due to protonation of histidine residues. Enthalpic effects of histidine ionization upon unfolding also appear to be involved in the occurrence of cold unfolding of hisactophilin under relatively mild solution conditions. The stability data for hisactophilin are compared with data on hisactophilin function, and with data for two other beta-trefoil proteins, human interleukin-1beta, and basic fibroblast growth factor.     

How many ionizable groups can sit on a protein hydrophobic core?

Full or partial burial of ionizable groups in the hydrophobic interior of proteins underlies the large modulation in group properties (modified pK value, high nucleophilicity, enhanced capability of interaction with chemical moieties of the substrate, etc.) linked to biological function. Indeed, the few internal ionizable residues found in proteins are known to play important functional roles in catalysis and, in general, in energy transduction processes. However, ionizable‐group burial is expected to be seriously disruptive and, it is important to note, most functional sites contain not just one, but several ionizable residues. Hence, the adaptations involved in the development of function in proteins (through in vitro engineering or during the course of natural evolution) are not fully understood. Here, we explore experimentally how proteins respond to the accumulation of hydrophobic‐to‐ionizable residue substitutions. For this purpose, we have constructed a combinatorial library targeting a hydrophobic cluster in a consensus‐engineered, stabilized form of a small model protein. Contrary to naïve expectation, half of the variants randomly selected from the library are soluble, folded, and active, despite including up to four mutations. Furthermore, for these variants, the dependence of stability with the number of mutations is not synergistic and catastrophic, but smooth and approximately linear. Clearly, stabilized protein scaffolds may be robust enough to withstand many disruptive hydrophobic‐to‐ionizable residue mutations, even when they are introduced in the same region of the structure. These results should be relevant for protein engineering and may have implications for the understanding of the early evolution of enzymes. Proteins 2012; © 2011 Wiley Periodicals, Inc.     

Simulating proteins at constant pH: An approach combining molecular dynamics and Monte Carlo simulation

For the structure and function of proteins, the pH of the solution is one of the determining parameters. Current molecular dynamics (MD) simulations account for the solution pH only in a limited way by keeping each titratable site in a chosen protonation state. We present an algorithm that generates trajectories at a Boltzmann distributed ensemble of protonation states by a combination of MD and Monte Carlo (MC) simulation. The algorithm is useful for pH-dependent structural studies and to investigate in detail the titration behavior of proteins. The method is tested on the acidic residues of the protein hen egg white lysozyme. It is shown that small structural changes may have a big effect on the pK(A) values of titratable residues.     

Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries

Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson-Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pKas and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye-Huckel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pKa calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pKa estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large deltapKas of a subset of ionizable groups with the overall robustness of the DH model.     

Simulation of protein conformational freedom as a function of pH: constant-pH molecular dynamics using implicit titration

Solution pH is a determinant parameter on protein function and stability, and its inclusion in molecular dynamics simulations is attractive for studies at the molecular level. Current molecular dynamics simulations can consider pH only in a very limited way, through a somewhat arbitrary choice of a set of fixed charges on the titrable sites. Conversely, continuum electrostatic methods that explicitly treat pH effects assume a single protein conformation whose choice is not clearly defined. In this paper we describe a general method that combines both titration and conformational freedom. The method is based on a potential of mean force for implicit titration and combines both usual molecular dynamics and pH-dependent calculations based on continuum methods. A simple implementation of the method, using a mean field approximation, is presented and applied to the bovine pancreatic trypsin inhibitor. We believe that this constant-pH molecular dynamics method, by correctly sampling both charges and conformation, can become a valuable help in the understanding of the dependence of protein function and stability on pH. © 1997 Wiley-Liss Inc.     

Calbindin D(9k): a protein optimized for calcium binding at neutral pH.

The binding of calcium ions by EF-hand proteins depends strongly on the electrostatic interactions between Ca(2+) ions and negatively charged residues of these proteins. We have investigated the pH dependence of the binding of Ca(2+) ions by calbindin D(9k). This protein offers a unique possibility for interpretation of such data since the pK(a) values of all ionizable groups are known. The binding is independent of pH between 7 and 9, where maximum calcium affinity is observed. An abrupt decrease in the binding affinity is observed at pH values below 7. This decrease is due to protonation of acidic groups, leading to modification of protein charges. The pH dependence of the product of the two macroscopic Ca(2+)-binding constants can be formally described by the involvement of two acidic groups with pK(a) = 6.6. Monte Carlo calculations show that the reduction of Ca(2+) binding is strictly determined by variable electrostatic interactions due to pH-dependent changes not only in the binding sites, but also of the overall charge of the protein.     

Electrostatic interactions in the acid denaturation of alpha-lactalbumin determined by NMR.

alpha-Lactalbumin (alpha-LA) undergoes a pH-dependent unfolding from the native state to a partially unfolded state (the molten globule state). To understand the role of electrostatic interactions in protein denaturation, NMR and CD pH titration experiments are performed on guinea pig alpha-LA. Variation of pH over the range of 7.0 to 2.0 simultaneously leads to the acid denaturation of the protein and the titration of individual ionizable groups. The pH titrations are interpreted in the context of these coupled events, and indicate that acid denaturation in alpha-LA is a cooperative event that is triggered by the protonation of two ionizable residues. Our NMR results suggest that the critical electrostatic interactions that contribute to the denaturation of alpha-LA are concentrated in the calcium binding region of the protein.     

Computational protein design with side-chain conformational entropy

Recent advances in modeling protein structures at the atomic level have made it possible to tackle "de novo" computational protein design. Most procedures are based on combinatorial optimization using a scoring function that estimates the folding free energy of a protein sequence on a given main-chain structure. However, the computation of the conformational entropy in the folded state is generally an intractable problem, and its contribution to the free energy is not properly evaluated. In this article, we propose a new automated protein design methodology that incorporates such conformational entropy based on statistical mechanics principles. We define the free energy of a protein sequence by the corresponding partition function over rotamer states. The free energy is written in variational form in a pairwise approximation and minimized using the Belief Propagation algorithm. In this way, a free energy is associated to each amino acid sequence: we use this insight to rescore the results obtained with a standard minimization method, with the energy as the cost function. Then, we set up a design method that directly uses the free energy as a cost function in combination with a stochastic search in the sequence space. We validate the methods on the design of three superficial sites of a small SH3 domain, and then apply them to the complete redesign of 27 proteins. Our results indicate that accounting for entropic contribution in the score function affects the outcome in a highly nontrivial way, and might improve current computational design techniques based on protein stability.     

Protein-Protein Docking with Dynamic Residue Protonation States

Protein-protein interactions depend on a host of environmental factors. Local pH conditions influence the interactions through the protonation states of the ionizable residues that can change upon binding. In this work, we present a pH-sensitive docking approach, pHDock, that can sample side-chain protonation states of five ionizable residues (Asp, Glu, His, Tyr, Lys) on-the-fly during the docking simulation. pHDock produces successful local docking funnels in approximately half (79/161) the protein complexes, including 19 cases where standard RosettaDock fails. pHDock also performs better than the two control cases comprising docking at pH 7.0 or using fixed, predetermined protonation states. On average, the top-ranked pHDock structures have lower interface RMSDs and recover more native interface residue-residue contacts and hydrogen bonds compared to RosettaDock. Addition of backbone flexibility using a computationally-generated conformational ensemble further improves native contact and hydrogen bond recovery in the top-ranked structures. Although pHDock is designed to improve docking, it also successfully predicts a large pH-dependent binding affinity change in the Fc–FcRn complex, suggesting that it can be exploited to improve affinity predictions. The approaches in the study contribute to the goal of structural simulations of whole-cell protein-protein interactions including all the environmental factors, and they can be further expanded for pH-sensitive protein design.     

Stability and stabilization of globular proteins in solution

Proteins are multifunctional: their amino acid sequences simultaneously determine folding, function and turnover. Correspondingly, evolution selected for compromises between rigidity (stability) and flexibility (folding/function/degradation), to the result that generally the free energy of stabilization of globular proteins in solution is the equivalent to only a few weak intermolecular interactions. Additional increments may come from extrinsic factors such as ligands or specific compatible solutes. Apart from the enthalpic effects, entropy may play a role by reducing the flexibility (cystine bridges, increased proline content), or by water release from residues buried upon folding and association. Additional quaternary interactions and closer packing are typical characteristics of proteins from thermophiles. In halophiles, protein stability and function are maintained by increased ion binding and glutamic acid content, both allowing the protein inventory to compete for water at high salt. Acidophiles and alkalophiles show neutral intracellular pH; proteins facing the outside extremes of pH possess anomalously high contents in ionizable amino acids. Global comparisons of the amino acid compositions and sequences of proteins from mesophiles and extremophiles did not result in general rules of protein stabilization, even after including complete genome sequences into the search. Obviously, proteins are individuals that optimize internal packing and external solvent interactions by very different mechanisms, each protein in its own way. Strategies deduced from specific ultrastable proteins allow stabilizing point mutations to be predicted.     

Protonation free energy levels in complex molecular systems

All proteins, nucleic acids, and other biomolecules contain residues capable of exchanging protons with their environment. These proton transfer phenomena lead to pH sensitivity of many molecular processes underlying biological phenomena. In the course of biological evolution, Nature has invented some mechanisms to use pH gradients to regulate biomolecular processes inside cells or in interstitial fluids. Therefore, an ability to model protonation equilibria in molecular systems accurately would be of enormous value for our understanding of biological processes and for possible rational influence on them, like in developing pH dependent drugs to treat particular diseases. This work presents a derivation, by thermodynamic and statistical mechanical methods, of an expression for the free energy of a complex molecular system at arbitrary ionization state of its titratable residues. This constitutes one of the elements of modeling protonation equilibria. Starting from a consideration of a simple acid-base equilibrium of a model compound with a single tritratable group, we arrive at an expression which is of general validity for complex systems. The only approximation used in this derivation is the postulating that the interaction energy between any pair of titratable sites does not depend on the protonation states of all the remaining ionizable groups.     

Numerical calculations of the pH of maximal protein stability. The effect of the sequence composition and three-dimensional structure.

A large number of proteins, found experimentally to have different optimum pH of maximal stability, were studied to reveal the basic principles of their preference for a particular pH. The pH-dependent free energy of folding was modeled numerically as a function of pH as well as the net charge of the protein. The optimum pH was determined in the numerical calculations as the pH of the minimum free energy of folding. The experimental data for the pH of maximal stability (experimental optimum pH) was reproducible (rmsd = 0.73). It was shown that the optimum pH results from two factors - amino acid composition and the organization of the titratable groups with the 3D structure. It was demonstrated that the optimum pH and isoelectric point could be quite different. In many cases, the optimum pH was found at a pH corresponding to a large net charge of the protein. At the same time, there was a tendency for proteins having acidic optimum pHs to have a base/acid ratio smaller than one and vice versa. The correlation between the optimum pH and base/acid ratio is significant if only buried groups are taken into account. It was shown that a protein that provides a favorable electrostatic environment for acids and disfavors the bases tends to have high optimum pH and vice versa.     

Protein stabilization by salt bridges: concepts, experimental approaches and clarification of some misunderstandings

Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each other to experience electrostatic attraction. They contribute to protein structure and to the specificity of interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein's free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three components: charge-charge interactions, interactions of charges with permanent dipoles, and desolvation of charges. Energetically favorable Coulombic charge-charge interaction is opposed by often unfavorable desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pK(a) approach and the mutation approach. In the pK(a) approach, the contribution of charges to the free energy of unfolding of a protein is obtained from the change of pK(a) of ionizable groups caused by altered electrostatic interactions upon folding of the protein. The pK(a) approach provides the relative free energy gained or lost when ionizable groups are being charged. In the mutation approach, the coupling free energy between interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and approximate measure of the free energy of charge-charge interaction. Neither the pK(a) approach nor the mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on concepts and on the assessment of experimental methods and does not cover the vast literature.     

Do salt bridges stabilize proteins? A continuum electrostatic analysis

The electrostatic contribution to the free energy of folding was calculated for 21 salt bridges in 9 protein X-ray crystal structures using a continuum electrostatic approach with the DELPHI computer-program package. The majority (17) were found to be electrostatically destabilizing; the average free energy change, which is analogous to mutation of salt bridging side chains to hydrophobic isosteres, was calculated to be 3.5 kcal/mol. This is fundamentally different from stability measurements using pKa shifts, which effectively measure the strength of a salt bridge relative to 1 or more charged hydrogen bonds. The calculated effect was due to a large, unfavorable desolvation contribution that was not fully compensated by favorable interactions within the salt bridge and between salt-bridge partners and other polar and charged groups in the folded protein. Some of the salt bridges were studied in further detail to determine the effect of the choice of values for atomic radii, internal protein dielectric constant, and ionic strength used in the calculations. Increased ionic strength resulted in little or no change in calculated stability for 3 of 4 salt bridges over a range of 0.1-0.9 M. The results suggest that mutation of salt bridges, particularly those that are buried, to "hydrophobic bridges" (that pack at least as well as wild type) can result in proteins with increased stability. Due to the large penalty for burying uncompensated ionizable groups, salt bridges could help to limit the number of low free energy conformations of a molecule or complex and thus play a role in determining specificity (i.e., the uniqueness of a protein fold or protein-ligand binding geometry).     

Redox properties of the [2Fe-2S] center in the 24 kDa (NQO2) subunit of NADH:ubiquinone oxidoreductase (complex I)

The redox properties of the [2Fe-2S] cluster in the 24 kDa subunit of bovine heart mitochondrial NADH:ubiquinone oxidoreductase (complex I) and three of its homologues have been defined using protein-film voltammetry. The clusters in all four examples display characteristic, pH-dependent redox transitions, which, unusually, can be masked by high ionic strength conditions. At low ionic strength (10 mM NaCl) the reduction potential varies by approximately 100 mV between high and low pH limits (pH 5 and 9); thus the redox process is not strongly coupled and is unlikely to form part of the mechanism of energy transduction in complex I. The pH dependence was shown to result from pH-linked changes in protein charge, due to nonspecific protonation events, rather than from the coupling of a specific ionizable residue, and the ionic strength dependence at high and low pH was modeled using extended Debye-Hückel theory. The low potential of the 24 kDa subunit [2Fe-2S] cluster, out of line with the potentials of the other iron-sulfur clusters in complex I, is suggested to play a role in coupling reducing equivalents at the catalytic active site. Finally, the validity of using the [2Fe-2S] cluster in an isolated subunit, as a mechanistic basis for coupled proton-electron transfer in intact complex I, is evaluated.