Probing structural and physical basis of protein energetics linked to protons and salt

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.

Fast coarse-grained model for RNA titration

A new numerical scheme for RNA (ribonucleic acid) titration based on the Debye-Hückel framework for the salt description is proposed in an effort to reduce the computational costs for further applications to study protein-RNA systems. By means of different sets of Monte Carlo simulations, we demonstrated that this new scheme is able to correctly reproduce the experimental titration behavior and salt pK_a shifts. In comparison with other theoretical approaches, similar or even better outcomes are achieved at much lower computational costs. The model was tested on the lead-dependent ribozyme, the branch-point helix, and the domain 5 from Azotobacter vinelandii Intron 5.

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 R to a stripe within 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.

Ligand-binding interactions and stability

The reversible interaction or binding of ligands to biological macromolecules is fundamental to nearly every aspect of biochemistry and cell biology. Binding events typically do not occur in isolation in biochemistry, and are almost always coupled or linked to other reactions such as protonation changes, other ligand-binding interactions, structural transitions, and folding. It is rarely sufficient to simply state that something binds. An understanding of binding requires a measure of affinity, stoichiometry, and the contributions of linked reactions. Emphasis is placed here on defining binding and the influence of linkage on binding and stability using both spectroscopic and calorimetric data.

Carboxyl pK(a) values, ion pairs, hydrogen bonding, and the pH-dependence of folding the hyperthermophile proteins Sac7d and Sso7d

Sac7d and Sso7d are homologous, hyperthermophile proteins with a high density of charged surface residues and potential ion pairs. To determine the relative importance of specific amino acid side-chains in defining the stability and function of these Archaeal chromatin proteins, pK(a) values were measured for the acidic residues in both proteins using (13)C NMR chemical shifts. The stability of Sso7d enabled titrations to pH 1 under low-salt conditions. Two aspartate residues in Sso7d (D16 and D35) and a single glutamate residue (G54) showed significantly perturbed pK(a) values in low salt, indicating that the observed pH-dependence of stability was primarily due to these three residues. The pH-dependence of backbone amide NMR resonances demonstrated that perturbation of all three pK(a) values was primarily the result of side-chain to backbone amide hydrogen bonds. Few of the significantly perturbed acidic pK(a) values in Sac7d and Sso7d could be attributed to primarily ion pair or electrostatic interactions. A smaller perturbation of E48 (E47 in Sac7d) was ascribed to an ion pair interaction that may be important in defining the DNA binding surface. The small number (three) of significantly altered pK(a) values was in good agreement with a linkage analysis of the temperature, pH, and salt-dependence of folding. The linkage of the ionization of two or more side-chains to protein folding led to apparent cooperativity in the pH-dependence of folding, although each group titrated independently with a Hill coefficient near unity. These results demonstrate that the acid pH-dependence of protein stability in these hyperthermophile proteins is due to independent titration of acidic residues with pK(a) values perturbed primarily by hydrogen bonding of the side-chain to the backbone. This work demonstrates the need for caution in using structural data alone to argue the importance of ion pairs in stabilizing hyperthermophile proteins.

Hofmeister effects in protein unfolding kinetics: Estimation of changes in surface area upon formation of the transition state

We studied the effect of three electrolytes (LiCl, Na(2)SO(4), GuHCl) on the unfolding reaction of chymopapain, a two-domain protein belonging in the papain family of cysteine proteinases. Due to methodological reasons, these studies were carried out at pH 1.5 where the protein unfolds following biphasic kinetics. We have observed the presence of two different effects of electrolyte concentration on the unfolding reactions. At low ionic strength, the ionic atmosphere brought about an increase in reaction rates, regardless of the type of ions being present; this effect is attributed to a general "electrostatic screening" of charge-charge interactions in the macromolecule. At high ionic strength, each electrolyte exerted a distinctively different effect: both rate constants were largely increased by GuHCl (a well-known protein denaturant), but only slightly by LiCl; in contrast, Na(2)SO(4) (a good precipitant) decreased the value of both unfolding rates. These ion-specific (Hofmeister) effects were further used to estimate changes in accessible surface area (DeltaASA) upon formation of the transition states (TS) for unfolding. Results obtained with LiCl and Na(2)SO(4), which we analyzed by means of a parameterization derived from published solubility data of amino acid derivatives, are consistent with DeltaASA increments (for each phase) of about 8.0% of the total theoretical DeltaASA for complete unfolding of the chymopapain molecule. Results in the presence of GuHCl, which were analyzed by using a previous parameterization of protein unfolding data, gave larger DeltaASAs of activation, equivalent to 13 and 16% of the total unfolding DeltaASA.

Effect of linker segments on the stability of epithelial cadherin domain 2

Epithelial cadherin is a transmembrane protein that is essential in calcium-dependent cell-cell recognition and adhesion. It contains five independently folded globular domains in its extracellular region. Each domain has a seven-strand beta-sheet immunoglobulin fold. Short seven-residue peptide segments connect the globular domains and provide oxygens to chelate calcium ions at the interface between the domains (Nagar et al., Nature 1995;380:360-364). Recently, stability studies of ECAD2 (Prasad et al., Biochemistry 2004;43:8055-8066) were undertaken with the motivation that Domain 2 is a representative domain for this family of proteins. The definition of a domain boundary is somewhat arbitrary; hence, it was important to examine the effect of the adjoining linker regions that connect Domain 2 to the adjacent domains. Present studies employ temperature-denaturation and proteolytic susceptibility to provide insight into the impact of these linkers on Domain 2. The significant findings of our present study are threefold. First, the linker segments destabilize the core domain in the absence of calcium. Second, the destabilization due to addition of the linker segments can be partially reversed by the addition of calcium. Third, sodium chloride stabilizes all constructs. This result implies that electrostatic repulsion is a contributor to destabilization of the core domain by addition of the linkers. Thus, the context of Domain 2 within the whole molecule affects its thermodynamic characteristics.

Communication Between Noncontacting Macromolecules

Molecular interactions are the language that molecules use to communicate recognition, binding, and regulation, events central to biological control mechanisms. Traditionally, such interactions involve direct, atom-to-atom, noncovalent contacts, or indirect contacts bridged by relatively fixed solvent molecules. Here we discuss a third class of molecular communication that, to date, has received less experimental attention, namely solvent-mediated communication between noncontacting macromolecules. This form of communication can be understood in terms of fundamental, well-established principles (coupled equilibria and linkage thermodynamics) that govern interactions between individual polymers and their solutions. In contrast to simple solutions used in laboratory studies, biological systems contain a multitude of nominally noninteracting biopolymers within the same solution environment. The exquisite control of biological function requires some form of communication between many of these solution components, even in the absence of direct and/or indirect contacts. Such communication must be considered when describing potential mechanisms of biological regulation.

The salt-dependence of a protein-ligand interaction: ion-protein binding energetics

Using the binding of a nucleotide inhibitor (guanosine-3'-monophosphate) to a ribonuclease (ribonuclease Sa) as a model system, we show that the salt-dependence of the interaction arises due to specific ion binding at the site of nucleotide binding. The presence of specific ion-protein binding is concluded from a combination of differential scanning calorimetry and NMR data. Isothermal titration calorimetry data are then fit to determine the energetic profile (enthalpy, entropy, and heat capacity) for both the ion-protein and nucleotide-protein interactions. The results provide insight into the energetics of charge-charge interactions, and have implications for the interpretation of an observed salt-dependence. Further, the presence of specific ion-binding leads to a system behavior as a function of temperature that is drastically different from that predicted from Poisson-Boltzmann calculations.

Ligand-linked stability of mutants of the C-domain of calmodulin

There is a necessary energetic linkage between ligand binding and stability in biological molecules. The critical glutamate in Site 4 was mutated to create two mutants of the C-domain of calmodulin yielding E140D and E140Q. These proteins were stably folded in the absence of calcium, but had dramatically impaired binding of calcium. We determined the stability of the mutant proteins in the absence and presence of calcium using urea-induced unfolding monitored by circular dichroism (CD) spectroscopy. These calcium-dependent unfolding curves were fit to models that allowed for linkage of stability to binding of a single calcium ion to the native and unfolded states. Simultaneous analysis of the unfolding profiles for each mutant yielded estimates for calcium-binding constants that were consistent with results from direct titrations monitored by fluorescence. Binding to the unfolded state was not an important energetic contributor to the ligand-linked stability of these mutants.

Effect of pH on the stability and structure of yeast hexokinase A. Acidic amino acid residues in the cleft region are critical for the opening and the closing of the structure

pH and salts have a marked effect on the stability, structure, and function of many globular proteins due to their ability to influence the electrostatic interactions. In this work, calorimetry, CD, and fluorescence studies have been carried out to understand the pH-dependent conformational changes of the two-domain protein yeast hexokinase A. In conjunction with the crystal structural data available, the present results have enabled the complete characterization and analysis of the pH-dependent conformational changes of the enzyme that have strong implications in understanding its structure-function relationship. The calorimetric profiles show a single thermal transition in the acidic pH range, whereas two independent transitions were observed in the alkaline pH range, suggesting the structural merger of the domains at the acidic pH. Comparison of the thermal transitions at pH 8.5 studied by different techniques suggests that the first transition corresponds to the smaller domain, and the second transition corresponds to the larger domain. The acid-denatured state of hexokinase A has high secondary structure content with little or no tertiary interactions and binds to the hydrophobic dye 8-anilinonaphthalene-1-sulfonic acid, suggesting that it is a molten globule-like state, whereas the alkali-denatured state is less structured than the acid-denatured state but more structured than the urea-denatured state, suggestive of a premolten globule-like state. Structural analysis using the published hexokinase B structure as well as the hexokinase A structure with the revised amino acid sequence in conjunction with the results obtained by us suggests that the ionization state of the acidic residues at the active site could regulate domain movements that are responsible for the opening and the closure of the cleft between the two domains and in turn affect the structure and function of the enzyme.

Allosteric effects of chloride ions at the intradimeric alpha1beta1 and alpha2beta2 interfaces of human hemoglobin

The structural transition induced by ligand binding in human hemoglobin encompasses quaternary structure changes at the interfaces between the two alphabeta dimers. In contrast, the interfaces between alpha and beta subunits within the same dimer (i.e., alpha1beta1 and alpha2beta2 interfaces) are structurally invariant. Previous work from this laboratory using NMR spectroscopy has identified four sites at the intradimeric alpha1beta1 and alpha2beta2 interfaces that, although structurally invariant, experience significant changes in the rates of proton exchange upon ligand binding. These sites are Hisalpha103(G10) and Hisalpha122(H5) in each alpha subunit of the hemoglobin tetramer. In the present work, we show that the proton exchange at the Hisalpha103(G10) sites is affected by the interactions of hemoglobin with chloride ions. Increasing concentrations of chloride ions at pH 6.45 and at 37 degrees C enhance the exchange rate of the Hisalpha103(G10) N(epsilon 2) proton. The enhancement is greater in deoxygenated than in ligated hemoglobin. In the framework of the local unfolding model for proton exchange, these results suggest that the structural free energy and/or the proton transfer reactions at the Hisalpha103(G10) sites depend on the concentration of chloride ions. Therefore, the ligand-induced changes at the Hisalpha103(G10) sites are modulated by the allosteric effect of chloride ions on hemoglobin.

Thermodynamic consequences of burial of polar and non-polar amino acid residues in the protein interior

Effects of amino acid substitutions at four fully buried sites of the ubiquitin molecule on the thermodynamic parameters (enthalpy, Gibbs energy) of unfolding were evaluated experimentally using differential scanning calorimetry. The same set of substitutions has been incorporated at each of four sites. These substitutions have been designed to perturb packing (van der Waals) interactions, hydration, and/or hydrogen bonding. From the analysis of the thermodynamic parameters for these ubiquitin variants we conclude that: (i) packing of non-polar groups in the protein interior is favorable and is largely defined by a favorable enthalpy of van der Waals interactions. The removal of one methylene group from the protein interior will destabilize a protein by approximately 5 kJ/mol, and will decrease the enthalpy of a protein by 12 kJ/mol. (ii) Burial of polar groups in the non-polar interior of a protein is highly destabilizing, and the degree of destabilization depends on the relative polarity of this group. For example, burial of Thr side-chain in the non-polar interior will be less destabilizing than burial of Asn side-chain. This decrease in stability is defined by a large enthalpy of dehydration of polar groups upon burial. (iii) The destabilizing effect of dehydration of polar groups upon burial can be compensated if these buried polar groups form hydrogen bonding. The enthalpy of this hydrogen bonding will compensate for the unfavorable dehydration energy and as a result the effect will be energetically neutral or even slightly stabilizing.

Salt-induced stabilization of apoflavodoxin at neutral pH is mediated through cation-specific effects

Electrostatic contributions to the conformational stability of apoflavodoxin were studied by measurement of the proton and salt-linked stability of this highly acidic protein with urea and temperature denaturation. Structure-based calculations of electrostatic Gibbs free energy were performed in parallel over a range of pH values and salt concentrations with an empirical continuum method. The stability of apoflavodoxin was higher near the isoelectric point (pH 4) than at neutral pH. This behavior was captured quantitatively by the structure-based calculations. In addition, the calculations showed that increasing salt concentration in the range of 0 to 500 mM stabilized the protein, which was confirmed experimentally. The effects of salts on stability were strongly dependent on cationic species: K(+), Na(+), Ca(2+), and Mg(2+) exerted similar effects, much different from the effect measured in the presence of the bulky choline cation. Thus cations bind weakly to the negatively charged surface of apoflavodoxin. The similar magnitude of the effects exerted by different cations indicates that their hydration shells are not disrupted significantly by interactions with the protein. Site-directed mutagenesis of selected residues and the analysis of truncation variants indicate that cation binding is not site-specific and that the cation-binding regions are located in the central region of the protein sequence. Three-state analysis of the thermal denaturation indicates that the equilibrium intermediate populated during thermal unfolding is competent to bind cations. The unusual increase in the stability of apoflavodoxin at neutral pH affected by salts is likely to be a common property among highly acidic proteins.

The acid-induced folded state of Sac7d is the native state

Sac7d unfolds at low pH in the absence of salt, with the greatest extent of unfolding obtained at pH 2. We have previously shown that the acid unfolded protein is induced to refold by decreasing the pH to 0 or by addition of salt (McCrary BS, Bedell J. Edmondson SP, Shriver JW, 1998, J Mol Biol 276:203-224). Both near-ultraviolet circular dichroism spectra and ANS fluorescence enhancements indicate that the acid- and salt-induced folded states have a native fold and are not molten globular. 1H,15N heteronuclear single quantum coherence NMR spectra confirm that the native, acid-, and salt-induced folded states are essentially identical. The most significant differences in amide 1H and 15N chemical shifts are attributed to hydrogen bonding to titrating carboxyl side chains and through-bond inductive effects. The 1H NMR chemical shifts of protons affected by ring currents in the hydrophobic core of the acid- and salt-induced folded states are identical to those observed in the native. The radius of gyration of the acid-induced folded state at pH 0 is shown to be identical to that of the native state at pH 7 by small angle X-ray scattering. We conclude that acid-induced collapse of Sac7d does not lead to a molten globule but proceeds directly to the native state. The folding of Sac7d as a function of pH and anion concentration is summarized with a phase diagram that is similar to those observed for other proteins that undergo acid-induced folding except that the A-state is encompassed by the native state. These results demonstrate that formation of a molten globule is not a general property of proteins that are refolded by acid.

Linkage of protonation and anion binding to the folding of Sac7d

The temperature, pH, and salt dependence of the folding of recombinant Sac7d from the hyperthermophile Sulfolobus acidocaldarius is mapped using multi-dimensional differential scanning calorimetry (DSC) and folding progress surfaces followed by circular dichroism. Linkage relations are derived to explain the observed dependencies, and it is shown that the data can be explained by the linkage of at least two protonation reactions and two anion binding sites to a two-state unfolding process. Circular dichroism spectra indicate that a native-like fold is stabilized at acid pH by anion binding. An apparent binding isotherm surface (folding progress versus pH and salt) is used to obtain intrinsic chloride binding constants as a function of pH for both sites. A saddle is predicted in the folding progress surface (progress versus temperature and pH) at low salt with a minimum near pH 2 and 20 degrees C with approximately 25% of the protein folded. The position of the saddle is sensitive to the intrinsic delta C degrees of unfolding and provides a third measure of delta C degrees independent of that obtained by a Kirchoff plot of DSC data and chemical denaturation. The observed enthalpy of unfolding approaches zero near the saddle making the unfolding largely invisible to DSC under these conditions. The linkage analysis demonstrates that the delta C degrees for unfolding obtained from a Kirchoff plot of DSC data should be distinguished from the intrinsic delta C degrees of unfolding. It is shown that the discrepancy between the free energy of unfolding for Sac7d obtained by DSC and that obtained by chemical denaturation may be explained by the linkage of protonation and anion binding to protein folding. The linkage analysis demonstrates the limitations of using the delta Hcal/ delta Hvh ratio an indication of two-state unfolding.

Structure-based statistical thermodynamic analysis of T4 lysozyme mutants: structural mapping of cooperative interactions

The recent development of a structural parameterization of the energetics of protein folding has permitted the incorporation of the functions that describe the enthalpy, entropy and heat capacity changes, i.e. the individual components of the Gibbs energy, into a statistical thermodynamic formalism that describes the distribution of conformational states under equilibrium conditions. The goal of this approach is to construct with the computer a large ensemble of conformational states, and then to derive the most probable population distribution, i.e. the distribution of states that best accounts for a wide array of experimental observables. This analysis has been applied to four different mutants of T4 lysozyme (S44A, S44G, V131A, V131G). It is shown that the structural parameterization predicts well the stability of the protein and the effects of the mutations. The entire set of folding constants per residue has been calculated for the four mutants. In all cases, the effect of the mutations propagates beyond the mutation site itself through sequence and three-dimensional space. This phenomenon occurs despite the fact that the mutations are at solvent-exposed locations and do not directly affect other interactions in the protein. These results suggest that single amino acid mutations at solvent-exposed locations, or other locations that cause a minimal perturbation, can be used to identify the extent of cooperative interactions. The magnitude and extent of these effects and the accuracy of the algorithm can be tested by means of NMR-detected hydrogen exchange.