Determination of the pKa values of titratable groups of an antigen-antibody complex, HyHEL-5-hen egg lysozyme

Protonation and pK changes in protein-ligand binding

Formation of protein-ligand complexes causes various changes in both the receptor and the ligand. This review focuses on changes in pK and protonation states of ionizable groups that accompany protein-ligand binding. Physical origins of these effects are outlined, followed by a brief overview of the computational methods to predict them and the associated corrections to receptor-ligand binding affinities. Statistical prevalence, magnitude and spatial distribution of the pK and protonation state changes in protein-ligand binding are discussed in detail, based on both experimental and theoretical studies. While there is no doubt that these changes occur, they do not occur all the time; the estimated prevalence varies, both between individual complexes and by method. The changes occur not only in the immediate vicinity of the interface but also sometimes far away. When receptor-ligand binding is associated with protonation state change at particular pH, the binding becomes pH dependent: we review the interplay between sub-cellular characteristic pH and optimum pH of receptor-ligand binding. It is pointed out that there is a tendency for protonation state changes upon binding to be minimal at physiologically relevant pH for each complex (no net proton uptake/release), suggesting that native receptor-ligand interactions have evolved to reduce the energy cost associated with ionization changes. As a result, previously reported statistical prevalence of these changes - typically computed at the same pH for all complexes - may be higher than what may be expected at optimum pH specific to each complex. We also discuss whether proper account of protonation state changes appears to improve practical docking and scoring outcomes relevant to structure-based drug design. An overview of some of the existing challenges in the field is provided in conclusion.

Chemical frustration in the protein folding landscape: grand canonical ensemble simulations of cytochrome c

A grand canonical formalism is developed to combine discrete simulations for chemically distinct species in equilibrium. Each simulation is based on a perturbed funneled landscape. The formalism is illustrated using the alkaline-induced transitions of cytochrome c as observed by FTIR spectroscopy and with various other experimental approaches. The grand canonical simulation method accounts for the acid/base chemistry of deprotonation, the inorganic chemistry of heme ligation and misligation, and the minimally frustrated folding energy landscape, thus elucidating the physics of protein folding involved with an acid/base titration of a protein. The formalism combines simulations for each of the relevant chemical species, varying by protonation and ligation states. In contrast to models based on perfectly funneled energy landscapes that contain only contacts found in the native structure, this study introduces "chemical frustration" from deprotonation and misligation that gives rise to many intermediates at alkaline pH. While the nature of these intermediates cannot be easily inferred from available experimental data, this study provides specific structural details of these intermediates, thus extending our understanding of how cytochrome c changes with an increase in pH. The results demonstrate the importance of chemical frustration for understanding biomolecular energy landscapes.

pH-dependent association of proteins. The test case of monoclonal antibody HyHEL-5 and its antigen hen egg white lysozyme

We describe a method for determining diffusion-controlled rate constants for protein-protein association that explicitly includes the solution pH. The method combines the transient-complex theory for computing electrostatically enhanced association rates with an approach based on a rigorous thermodynamic cycle and partition functions for energy levels characterizing protonation states of associating proteins and their complexes. To test our method, we determine the pH-dependent kinetics of association of the HyHEL-5 antibody with its antigen hen egg white lysozyme. It was shown experimentally that their association rate constant depends on pH, increasing linearly in the pH range 6-8 and saturating or even exhibiting a flat maximum in the pH range 8-10. The presented methodology leads to a qualitative agreement with the experimental data. Our approach allows one to study diffusion-controlled protein-protein association under different pH conditions by taking into account the ensembles of protonation states rather than just the most probable protonation state of each protein.

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.

Calculation of weak protein-protein interactions: the pH dependence of the second virial coefficient

Interactions between proteins are often sufficiently weak that their study through the use of conventional structural techniques becomes problematic. Of the few techniques capable of providing experimental measures of weak protein-protein interactions, perhaps the most useful is the second virial coefficient, B(22), which quantifies a protein solution's deviations from ideal behavior. It has long been known that B(22) can in principle be computed, but only very recently has it been demonstrated that such calculations can be performed using protein models of true atomic detail (Biophys. J. 1998, 75:2469-2477). The work reported here extends these previous efforts in an attempt to develop a transferable energetic model capable of reproducing the experimental trends obtained for two different proteins over a range of pH and ionic strengths. We describe protein-protein interaction energies by a combination of three separate terms: (i) an electrostatic interaction term based on the use of effective charges, (ii) a term describing the electrostatic desolvation that occurs when charged groups are buried by an approaching protein partner, and (iii) a solvent-accessible surface area term that is used to describe contributions from van der Waals and hydrophobic interactions. The magnitude of the third term is governed by an adjustable, empirical parameter, gamma, that is altered to optimize agreement between calculated and experimental values of B(22). The model is applied separately to the proteins lysozyme and chymotrypsinogen, yielding optimal values of gamma that are almost identical. There are, however, clear difficulties in reproducing B(22) values at the extremes of pH. Explicit calculation of the protonation states of ionizable amino acids in the 200 most energetically favorable protein-protein structures suggest that these difficulties are due to a neglect of the protonation state changes that can accompany complexation. Proper reproduction of the pH dependence of B(22) will, therefore, almost certainly require that account be taken of these protonation state changes. Despite this problem, the fact that almost identical gamma values are obtained from two different proteins suggests that the basic energetic formulation used here, which can be evaluated very rapidly, might find use in dynamical simulations of weak protein-protein interactions at intermediate pH values.

Salt links dominate affinity of antibody HyHEL-5 for lysozyme through enthalpic contributions

The binding of murine monoclonal antibody HyHEL-5 to lysozyme has been the subject of extensive crystallographic, computational, and experimental investigations. The complex of HyHEL-5 with hen egg lysozyme (HEL) features salt bridges between Fab heavy chain residue Glu(50), and Arg(45) and Arg(68) of HEL. This interaction has been predicted to play a dominant role in the association on the basis of molecular electrostatics calculations. The association of aspartic acid and glutamine mutants at position 50(H) of the cloned HyHEL-5 Fab with HEL and bobwhite quail lysozyme (BQL), an avian variant bearing an Arg(68) --> Lys substitution in the epitope, was characterized by isothermal titration calorimetry and sedimentation equilibrium. Affinities for HEL were reduced by 400-fold (E50(H)D) and 40,000-fold (E50(H)Q) (DeltaDeltaG degrees estimated at 4.0 and 6.4 kcal mol(-1), respectively). The same mutations reduce affinity for BQL by only 7- and 55-fold, respectively, indicating a reduced specificity for HEL. The loss of affinity upon mutation is in each case primarily due to an unfavorable change in the enthalpy of the interaction; the entropic contribution is virtually unchanged. An enthalpy-entropy compensation exists for each interaction; DeltaH degrees decreases, while DeltaS degrees increases with temperature. The DeltaCp for each mutant interaction is less negative than the wild-type. Mutant-cycle analysis suggests the mutations present in the HyHEL-5 Fab mutants are linked to those present in the BQL with coupling energies between 3 and 4 kcal mol(-1).

Cloning, expression, and characterization of the Fab fragment of the anti-lysozyme antibody HyHEL-5

Hybridoma cDNAs encoding the individual chains of the Fab fragment of the well characterized murine monoclonal antibody HyHEL-5 were cloned and sequenced. The recombinant Fab fragment was produced by expressing each chain in a separate Escherichia coli pET vector, denaturing inclusion bodies and co-refolding. Characterization of the purified Fab by MALDI-TOF mass spectrometry and N-terminal amino acid sequencing demonstrated proper processing of the individual chains. The association of the recombinant Fab fragment with hen egg lysozyme and the avian epitope variant bobwhite quail lysozyme was found by isothermal titration calorimetry to have energetics very similar to that of the HyHEL-5 IgG. Heterologous expression of the HyHEL-5 Fab fragment opens the way to structure/function studies in this well-known system.

Association and dissociation kinetics of bobwhite quail lysozyme with monoclonal antibody HyHEL-5

The anti-hen egg lysozyme monoclonal antibody HyHEL-5 and its complexes with various species-variant and mutant lysozymes have been the subject of considerable experimental and theoretical investigation. The affinity of HyHEL-5 for bobwhite quail lysozyme (BWQL) is over 1000-fold lower than its affinity for the original antigen, hen egg lysozyme (HEL). This difference is believed to arise almost entirely from the replacement in BWQL of the structural and energetic epitope residue Arg68 by lysine. In this study, the association and dissociation kinetics of BWQL with HyHEL-5 were investigated under a variety of conditions and compared with previous results for HEL. HyHEL-5-BWQL association follows a bimolecular mechanism and the dissociation of the antibody-antigen complex is a first-order process. Changes in ionic strength (from 27 to 500 mM) and pH (from 6.0 to 10.0) produced about a 2-fold change in the association and dissociation rates. The effect of viscosity modifiers on the association reaction was also studied. The large difference in the HEL and BWQL affinities for HyHEL-5 is essentially due to differences in the dissociation rate constant.

Association and dissociation kinetics of anti-hen egg lysozyme monoclonal antibodies HyHEL-5 and HyHEL-10

The immunoglobulin G1 (IgG1) kappa antibodies HyHEL-5 and HyHEL-10 interact with nonoverlapping epitopes on hen egg lysozyme (HEL); the HyHEL-5/HEL interface has two energetically and structurally important salt links, whereas the HyHEL-10/HEL interface involves predominantly hydrogen bonds and van der Waals interactions. The kinetics of association and dissociation of antibodies HyHEL-5 and HyHEL-10 with HEL under a variety of conditions were investigated in this study. The association of each antibody with HEL follows second-order kinetics. The association process is significantly diffusion-limited, as indicated by the viscosity dependence of the interaction of both antibodies with HEL, although detailed energetics suggest that the association process may be more complex. The association rate constant for the HyHEL-5/HEL system is within a factor of 2 of the modified Smoluchowski estimate for proteins of this size, whereas HyHEL-10 interacts with HEL with an association rate an order of magnitude lower. The association reactions are insensitive to ionic strength, showing only a twofold decrease in the association rate constant when the ionic strength was increased from 27 mM to 500 mM. Interestingly, the association rate constant for the interaction of HyHEL-5 with HEL varies with pH in the range 6.0-10.0, whereas HyHEL-10/HEL association is not affected by pH in the same range. The dissociation of the HyHEL-5/HEL and HyHEL-10/HEL complexes follow first-order kinetics with half-lives at 25 degrees C of approximately 3,150 s and approximately 21,660 s, respectively.

pH dependence of antibody/lysozyme complexation

Association between proteins often depends on the pH and ionic strength conditions of the medium in which it takes place. This is especially true in complexation involving titratable residues at the complex interface. Continuum electrostatics methods were used to calculate the pH-dependent energetics of association of hen egg lysozyme with two closely related monoclonal antibodies raised against it and the association of these antibodies against an avian species variant. A detailed analysis of the energetic contributions reveals that even though the hallmark of association in the two complexes is the presence of conserved charged-residue interactions, the environment of these interactions significantly influences the titration behavior and concomitantly the energetics. The contributing factors include minor structural rearrangements, buried interfacial area, dielectric environment of the key titratable residues, and geometry of the residue dispositions. Modeled structures of several mutant complexes were also studied so as to further delineate the contribution of individual factors to the titration behavior.

Modeling of protein conformational fluctuations in pKa predictions

A method is presented to account for conformational fluctuations of a protein in predicting the pK(a) values of its titrating groups. Conformations of the protein are generated by conventional molecular dynamics or Monte Carlo simulations, in which the protonations of the titrating groups are fixed. For each protein conformation, the electrostatic free energies required to add a proton charge to a titrating group while other groups are either unprotonated or protonated are calculated within a dielectric continuum model. These are used to determine the mean protonations of the titrating groups in the conformation at a series of pH values. The mean protonations are then used to determine the relative weight of the particular conformation with the titrating groups having all possible protonations. A conformationally averaged mean protonation for each titrating group is finally obtained by the weighted sum of the group's mean protonations in all the conformations. This method is applied to yeast iso-1-ferricytochrome c. The predicted pK(a) values are in general agreement with experimental results.