Coupling between conformation and proton binding in proteins

Interest centers here on whether the use of a fixed charge distribution of a protein solute, or a treatment that considers proton-binding equilibria by solving the Poisson equation, is a better approach to discriminate native from non-native conformations of proteins. In this analysis of the charge distribution of 7 proteins, we estimate the solvation free energy contribution to the total free energy by exploring the 2(zeta) possible ionization states of the whole molecule, with zeta being the number of ionizable groups in the amino acid sequence, for every conformation in the ensembles of 7 proteins. As an additional consideration of the role of electrostatic interactions in determining the charge distribution of native folds, we carried out a comparison of alternative charge assignment models for the ionizable residues in a set of 21 native-like proteins. The results of this work indicate that (1) for 6 out of 7 proteins, estimation of solvent polarization based on the Generalized Born model with a fixed charge distribution provides the optimal trade-off between accuracy, with respect to the Poisson equation, and speed when compared to the accessible surface area model; for the seventh protein, consideration of all possible ionization states of the whole molecule appears to be crucial to discriminate the native from non-native conformations; (2) significant differences in the degree of ionization and hence the charge distribution for native folds are found between the different charge models examined; (3) the stability of the native state is determined by a delicate balance of all the energy components, and (4) conformational entropy, and hence the dynamics of folding, may play a crucial role for a successful ab initio protein folding prediction.     

Protein-binding polynomials

Using a new method recently published for analyzing the binding isotherms of biopolymers (Poland, 2000a), we calculate the complete binding polynomials for lysozyme, insulin, and serum albumin from published titration data. These three proteins have, respectively, 22, 32, and 184 dissociable protons and hence are represented by series in powers of the hydrogen ion concentration with the highest powers in the series being the numbers just indicated. Given the complete binding polynomial, the distribution function giving the concentration of all states of proton binding can then be calculated at any pH.     

The binding of physiologically significant protons to 2,3-diphosphoglycerate

The intrinsic pKa values of protons of 2,3-diphosphoglycerate (DPG) which titrate in the physiologically significant range (i.e., pH 6.8-7.8) have been determined by measuring the changes in chemical shifts of the two phosphate resonances of the molecule as a function of pH using 31P-NMR spectroscopy. While conventional acid-base titration techniques resulted in apparent pKa values of 6.39 and 7.39 for these protons, analysis of the 31P-NMR data by statistical thermodynamic methods yielded intrinsic pKa values of 6.99 +/- 0.07 and 7.28 +/- 0.04, for protons associated with the phosphates bound to carbon-3 (C-3) and carbon-2 (C-2), respectively, with an interaction energy of +0.77 kcal/mol. The free energies for the binding of protons to the C-2 and C-3 phosphates and the associated interaction energies determined by 31P-NMR were used to generate a theoretical titration curve which was essentially identical to that determined by conventional acid-base titration. The physiological implications of this work are briefly discussed.     

Ligand binding distributions in nucleic acids

We illustrate a new method for the determination of the complete binding polynomial for nucleic acids based on experimental titration data with respect to ligand concentration. From the binding polynomial, one can then calculate the distribution function for the number of ligands bound at any ligand concentration. The method is based on the use of a finite set of moments of the binding distribution function, which are obtained from the titration curve. Using the maximum-entropy method, the moments are then used to construct good approximations to the binding distribution function. Given the distribution functions at different ligand concentrations, one can calculate all of the coefficients in the binding polynomial no matter how many binding sites a molecule has. Knowledge of the complete binding polynomial in turn yields the thermodynamics of binding. This method gives all of the information that can be obtained from binding isotherms without the assumption of any specific molecular model for the nature of the binding. Examples are given for the binding of Mn(2+) and Mg(2+) to t-RNA and for the binding of Mg(2+) and I(6) to poly-C using literature data.     

Protein denaturant binding polynomials

We show how moments of the denaturant binding distribution function can be extracted from experimental data on the denaturation of a protein as a function of the concentration of denaturant and how in turn these moments can be used to construct the denaturant binding distribution function. This approach is similar to our recent work on using the maximum-entropy method to construct ligand-binding distributions from moments obtained from titration curves for nucleic acids and proteins. As an example we take literature data on the denaturation of ferro- and ferricytochrome c by guanidine hydrochloride and from it construct the denaturant binding polynomial and binding distribution function for the unfolded protein.     

Protein-Binding Polynomials

Using a new method recently published for analyzing the binding isotherms of biopolymers (Poland, 2000a), we calculate the complete binding polynomials for lysozyme, insulin, and serum albumin from published titration data. These three proteins have, respectively, 22, 32, and 184 dissociable protons and hence are represented by series in powers of the hydrogen ion concentration with the highest powers in the series being the numbers just indicated. Given the complete binding polynomial, the distribution function giving the concentration of all states of proton binding can then be calculated at any pH.     

A mathematical view on the decoupled sites representation

The decoupled sites representation (DSR) is a theoretical instrument which allows to regard complex pH titration curves of biomolecules with several interacting proton binding sites as composition of isolated, non-interacting sites, each with a standard Henderson–Hasselbalch titration curve. In this work, we present the mathematical framework in which the DSR is embedded and give mathematical proofs for several statements in the periphery of the DSR. These proofs also identify exceptions. To apply the DSR to any molecule, it is necessary to extend the set of binding energies from ${\mathbb{R}}$ to a stripe within ${\mathbb{C}}$ . An important observation in this context is that even positive interaction energies (repulsion) between the binding sites will not guarantee real binding energies in the decoupled system, at least if the molecule has more than four proton binding sites. Moreover, we show that for a given overall titration curve it is not only possible to find a corresponding system with an interaction energy of zero but with any arbitrary fix interaction energy. This result also effects practical work as it shows that for any given titration curve, there is an infinite number of corresponding hypothetical molecules. Furthermore, this implies that—using a common definition of cooperative binding on the level of interaction energies—a meaningful measure of cooperativity between the binding sites cannot be defined solely on the basis of the overall titration. Consequently, all measures of cooperativity based on the overall binding curve do not measure the type of cooperativity commonly defined on the basis of interaction energies. Understanding the DSR mathematically provides the basis of transferring the DSR to biomolecules with different types of interacting ligands, such as protons and electrons, which play an important role within electron transport chains like in photosynthesis.     

Dimensions,energetics, and denaturant effects of the protein unstructured state

Determining the energetics of the unfolded state of a protein is essential for understanding the folding mechanics of ordered proteins and the structure–function relation of intrinsically disordered proteins. Here, we adopt a coil‐globule transition theory to develop a general scheme to extract interaction and free energy information from single‐molecule fluorescence resonance energy transfer spectroscopy. By combining protein stability data, we have determined the free energy difference between the native state and the maximally collapsed denatured state in a number of systems, providing insight on the specific/nonspecific interactions in protein folding. Both the transfer and binding models of the denaturant effects are demonstrated to account for the revealed linear dependence of inter‐residue interactions on the denaturant concentration, and are thus compatible under the coil‐globule transition theory to further determine the dimension and free energy of the conformational ensemble of the unfolded state. The scaling behaviors and the effective θ‐state are also discussed.     

Free energy distributions in proteins.

Protein molecules in solution have a broad distribution of enthalpy states. A good approximation to the distribution function for enthalpy states can be calculated, using the maximum-entropy method, from the moments of the distribution that, in turn, are obtained from the experimental temperature dependence of the heat capacity. In the present paper, we show that the enthalpy probability distribution can then be formulated in terms of a free energy function that gives the free energy of the protein corresponding to a particular value of the enthalpy. By the location of the minima in this function, the free energy distribution graphically indicates the most probable values of the enthalpy for the protein. We find that the behavior of the free energy functions for proteins falls somewhere between two different cases: a two-state like function with two minima, the relative levels of the two states changing with temperature; and, a single-minimum function where the position of the minimum shifts to higher enthalpy values as the temperature is increased. We show that the temperature dependence of the free energy function can be expressed in terms of a central free energy distribution for a given, fixed temperature (which is most conveniently chosen as the temperature of the maximum in the heat capacity). The nature of this central free energy function for a given protein thus yields all of the thermodynamic behavior of that protein over the temperature range of the denaturation process.     

Correlation between membrane-localized protons and flash-driven ATP formation in chloroplast thylakoids

Flash-driven ATP formation by spinach chloroplast thylakoids, using the luciferin luminescence assay to detect ATP formed in single turnover flashes, was studied under conditions where a membrane protein amine buffering pool was either protonated or deprotonated before the beginning of the flash trains. The flash number for the onset of ATP formation was delayed by about 10 flashes (from 15 to about 25) when the amine pool was deprotonated as compared to the protonated state. The delay was substantially reversed again by reprotonating the pool upon application of 20–30 single-turnover flashes and 8 min of dark before addition of ADP, P_i, and the luciferin system. In the case of deprotonation by desaspidin, the uncoupler was removed by binding to BSA before the reprotonating flashes were given. Reprotonation was carried out before addition of ADP and P_i, to avoid a possible interference by the ATP-ase, which can energize the system by pumping protons. The reprotonated state, as indicated by an onset lag of about 15 flashes rather than 25 for the deprotonated state, was stable in the dark over extended dark times. The number of protons released by 10 flashes is approximately 30 nmol H⁺ (mg chl)^–1, an amount similar to the size of the reversibly protonated amine group buffering pool. The data are consistent with the hypothesis that the amine buffering groups must be in the protonated state before any protons proceed to the coupling complex and energize ATP formation. Other work has suggested that the amine buffering pool is sequestered within membrane proteins rather than being exposed directly to the inner aqueous bulk phase. Therefore, it is possible that the sequested amine group array may provide localized association-dissociation sites for proton movement to the coupling complex.     

Salt dependent binding of T4 gene 32 protein to single and double-stranded DNA: single molecule force spectroscopy measurements

Bacteriophage T4 gene 32 protein (gp32) is a well-studied representative of the large family of single-stranded DNA (ssDNA) binding proteins, which are essential for DNA replication, recombination and repair. Surprisingly, gp32 has not previously been observed to melt natural dsDNA. At the same time, *I, a truncated version of gp32 lacking its C-terminal domain (CTD), was shown to decrease the melting temperature of natural DNA by about 50 deg. C. This profound difference in the duplex destabilizing ability of gp32 and *I is especially puzzling given that the previously measured binding of both proteins to ssDNA was similar. Here, we resolve this apparent contradiction by studying the effect of gp32 and *I on the thermodynamics and kinetics of duplex DNA melting. We use a previously developed single molecule technique for measuring the non-cooperative association constants (K(ds)) to double-stranded DNA to determine K(ds) as a function of salt concentration for gp32 and *I. We then develop a new single molecule method for measuring K(ss), the association constant of these proteins to ssDNA. Comparing our measured binding constants to ssDNA for gp32 and *I we see that while they are very similar in high salt, they strongly diverge at [Na+] < 0.2 M. These results suggest that intact protein must undergo a conformational rearrangement involving the CTD that is in pre-equilibrium to its non-cooperative binding to both dsDNA and ssDNA. This lowers the effective concentration of protein available for binding, which in turn lowers the rate at which it can destabilize dsDNA. For the first time, we quantify the free energy of this CTD unfolding, and show it to be strongly salt dependent and associated with sodium counter-ion condensation on the CTD.     

Hidden partners: Using cross‐docking calculations to predict binding sites for proteins with multiple interactions

Protein‐protein interactions control a large range of biological processes and their identification is essential to understand the underlying biological mechanisms. To complement experimental approaches, in silico methods are available to investigate protein‐protein interactions. Cross‐docking methods, in particular, can be used to predict protein binding sites. However, proteins can interact with numerous partners and can present multiple binding sites on their surface, which may alter the binding site prediction quality. We evaluate the binding site predictions obtained using complete cross‐docking simulations of 358 proteins with 2 different scoring schemes accounting for multiple binding sites. Despite overall good binding site prediction performances, 68 cases were still associated with very low prediction quality, presenting individual area under the specificity‐sensitivity ROC curve (AUC) values below the random AUC threshold of 0.5, since cross‐docking calculations can lead to the identification of alternate protein binding sites (that are different from the reference experimental sites). For the large majority of these proteins, we show that the predicted alternate binding sites correspond to interaction sites with hidden partners, that is, partners not included in the original cross‐docking dataset. Among those new partners, we find proteins, but also nucleic acid molecules. Finally, for proteins with multiple binding sites on their surface, we investigated the structural determinants associated with the binding sites the most targeted by the docking partners.     

Interplay between binding affinity and kinetics in protein–protein interactions

To clarify the interplay between the binding affinity and kinetics of protein–protein interactions, and the possible role of intrinsically disordered proteins in such interactions, molecular simulations were carried out on 20 protein complexes. With bias potential and reweighting techniques, the free energy profiles were obtained under physiological affinities, which showed that the bound‐state valley is deep with a barrier height of 12 ? 33 RT. From the dependence of the affinity on interface interactions, the entropic contribution to the binding affinity is approximated to be proportional to the interface area. The extracted dissociation rates based on the Arrhenius law correlate reasonably well with the experimental values (Pearson correlation coefficient R = 0.79). For each protein complex, a linear free energy relationship between binding affinity and the dissociation rate was confirmed, but the distribution of the slopes for intrinsically disordered proteins showed no essential difference with that observed for ordered proteins. A comparison with protein folding was also performed. Proteins 2016; 84:920–933. © 2016 Wiley Periodicals, Inc.     

The effect of multiple binding modes on empirical modeling of ligand docking to proteins.

A popular approach to the computational modeling of ligand/receptor interactions is to use an empirical free energy like model with adjustable parameters. Parameters are learned from one set of complexes, then used to predict another set. To improve these empirical methods requires an independent way to study their inherent errors. We introduce a toy model of ligand/receptor binding as a workbench for testing such errors. We study the errors incurred from the two state binding assumption--the assumption that a ligand is either bound in one orientation, or unbound. We find that the two state assumption can cause large errors in free energy predictions, but it does not affect rank order predictions significantly. We show that fitting parameters using data from high affinity ligands can reduce two state errors; so can using more physical models that do not use the two state assumption. We also find that when using two state models to predict free energies, errors are more severe on high affinity ligands than low affinity ligands. And we show that two state errors can be diagnosed by systematically adding new binding modes when predicting free energies: if predictions worsen as the modes are added, then the two state assumption in the fitting step may be at fault.     

Anion modulation of the 1H/2H exchange rates in backbone amide protons monitored by NMR spectroscopy

The ability of three anionic cosolutes (sulfate, thiocyanate, and chloride) in modulating the (1)H/(2)H exchange rates for backbone amide protons has been investigated using nuclear magnetic resonance (NMR) for two different proteins: the IGg-binding domain of protein L (ProtL) and the glucose-galactose-binding protein (GGBP). Our results show that moderate anion concentrations (0.2 M-1 M) regulate the exchange rate following the Hofmeister series: Addition of thiocyanate increases the exchange rates for both proteins, while sulfate and chloride (to a less extent) slow down the exchange reaction. In the presence of the salt, no alteration of the protein structure and minimal variations in the number of measurable peaks are observed. Experiments with model compounds revealed that the unfolded state is modulated in an equivalent way by these cosolutes. For ProtL, the estimated values for the local free energy change upon salt addition (m (3,DeltaG )) are consistent with the previously reported free energy contribution from the cosolute's preferential interaction/exclusion term indicating that nonspecific weak interactions between the anion and the amide groups constitute the dominant mechanism for the exchange-rate modulation. The same trend is also found for GGBP in the presence of thiocyanate, underlining the generality of the exchange-rate modulation mechanism, complementary to more investigated effects like the electrostatic interactions or specific anion binding to protein sites.     

Charge effects on folded and unfolded proteins

We develop a theory for the effects of charge on the stabilization of globular proteins. The folding process is modeled as occurring through a fictitious intermediate state along a two-part thermodynamic pathway in which the molecule (i) increases its density and then (ii) rearranges its ionic groups to the protein surface. The equilibrium for the binding of protons in salt solutions is assumed to be driven by the electrical potential due to the charge distribution, in addition to the intrinsic binding affinity and bulk proton concentration. The potential is calculated for inside and outside a porous sphere model of the protein using the Poisson-Boltzmann relation, wherein the interior dielectric constant is taken to be a linear function of the chain density. The model predicts the slope of the titration curves for native myoglobin in agreement with experiments by Breslow and Gurd (1962). From the similar experiments on the unfolded state, and from the experiments of Privalov et al. (1986) on the intrinsic viscosity of the unfolded molecules, the theory shows that the unfolded state has a much higher density than a chain in a theta solvent and that the density increases with ionic strength. In addition, from the free energy of proton binding to the protein, we also calculate the electrostatic contributions to protein stability, a major contribution deriving from changes in ionization. We consider the example of the stability of myoglobin as a function of pH, ionic strength, and ionic groups buried in the native protein structure. We show that although maximum stability of most proteins should occur at their isoelectric point, the burial of nontitratable groups should lead to maximum stabilities at pH values other than the isoelectric point.     

Different combinations of atomic interactions predict protein‐small molecule and protein‐DNA/RNA affinities with similar accuracy

Interactions between proteins and other molecules play essential roles in all biological processes. Although it is widely held that a protein's ligand specificity is determined primarily by its three‐dimensional structure, the general principles by which structure determines ligand binding remain poorly understood. Here we use statistical analyses of a large number of protein?ligand complexes with associated binding‐affinity measurements to quantitatively characterize how combinations of atomic interactions contribute to ligand affinity. We find that there are significant differences in how atomic interactions determine ligand affinity for proteins that bind small chemical ligands, those that bind DNA/RNA and those that interact with other proteins. Although protein‐small molecule and protein‐DNA/RNA binding affinities can be accurately predicted from structural data, models predicting one type of interaction perform poorly on the others. Additionally, the particular combinations of atomic interactions required to predict binding affinity differed between small‐molecule and DNA/RNA data sets, consistent with the conclusion that the structural bases determining ligand affinity differ among interaction types. In contrast to what we observed for small‐molecule and DNA/RNA interactions, no statistical models were capable of predicting protein?protein affinity with >60% correlation. We demonstrate the potential usefulness of protein‐DNA/RNA binding prediction as a possible tool for high‐throughput virtual screening to guide laboratory investigations, suggesting that quantitative characterization of diverse molecular interactions may have practical applications as well as fundamentally advancing our understanding of how molecular structure translates into function. Proteins 2015; 83:2100–2114. © 2015 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.