Molecular mechanisms of pH-driven conformational transitions of proteins: Insights from continuum electrostatics calculations of acid unfolding

Ultra-sensitive, rapid detection of dried bloodstains by surface enhanced Raman scattering on Ag substrates

A simple water extraction and transfer procedure is found to result in reproducible and highly sensitive 785 nm excited SERS spectra of 24 h dried bloodstains on Ag nanoparticle substrates. This protocol allows confirmatory detection and identification of dried stains of blood that have been diluted by up to 10⁵ in water on Ag substrates. While previous SERS results demonstrated similar performance on Au substrates when a 50% acetic acid extraction and transfer procedure was used, the water/Ag methodology avoids any potential DNA damage when the sample size is extremely small (≤∼1 μL) due to low pH exposure. The water only procedure is not effective on Au SERS substrates. This metal substrate difference results from the efficient red blood cell lysis and hemoglobin denaturation effects of the Ag nanoparticle surfaces as compare to that of Au nanoparticles. Consequently, the 50% acetic acid exposure is required for the acquisition of 785 nm SERS spectra of dried bloodstains on Au substrates.

Quantifying charge state heterogeneity for proteins with multiple ionizable residues

Ionizable residues can release and take up protons and this has an influence on protein structure and function. The extent of protonation is linked to the overall pH of the solution and the local environments of ionizable residues. Binding or unbinding of a single proton generates a distinct charge microstate defined by a specific pattern of charges. Accordingly, the overall partition function is a sum over all charge microstates and Boltzmann weights of all conformations associated with each of the charge microstates. This ensemble-of-ensembles description recast as a q-canonical ensemble allows us to analyze and interpret potentiometric titrations that provide information regarding net charge as a function of pH. In the q-canonical ensemble, charge microstates are grouped into mesostates where each mesostate is a collection of microstates of the same net charge. Here, we show that leveraging the structure of the q-canonical ensemble allows us to decouple contributions of net proton binding and release from proton arrangement and conformational considerations. Through application of the q-canonical formalism to analyze potentiometric measurements of net charge in proteins with repetitive patterns of Lys and Glu residues, we determine the underlying mesostate pKa values and, more importantly, we estimate relative mesostate populations as a function of pH. This is a strength of using the q-canonical approach that cannot be replicated using purely site-specific analyses. Overall, our work shows how measurements of charge equilibria, decoupled from measurements of conformational equilibria, and analyzed using the framework of the q-canonical ensemble, provide protein-specific quantitative descriptions of pH-dependent populations of mesostates. This method is of direct relevance for measuring and understanding how different charge states contribute to conformational, binding, and phase equilibria of proteins.

A pH-dependent protein stability switch coupled to the perturbed pKa of a single ionizable residue

The contribution of electrostatic interactions in protein stability has not been fully understood. Burial of an ionizable amino acid inside the hydrophobic protein core can affect its ionization equilibrium and shift its pKa differentially in the native (N) and unfolded (U) states of a protein and this coupling between the folding/unfolding cycle and the ionization equilibria of the ionizable residue can substantially influence the protein stability. Here, we studied the coupling of the folding/unfolding cycle with the ionization of a buried ionizable residue in a multi-domain protein, Human Serum Albumin (HSA) using fluorescence spectroscopy. A pH-dependent change in the stability of HSA was observed in the near native pH range (pH 6.0-9.0). The protonation-deprotonation equilibrium of a single thiol residue that is buried in the protein structure was identified to give rise to the pH-dependent protein stability. We quantified the pKa of the thiol residue in the N and the U states. The mean pKa of the thiol in the N state was upshifted by 0.5 units to 8.7 due to the burial of the thiol in the protein structure. Surprisingly, the mean pKa of the thiol in the U state was observed to be downshifted by 1.3 units to 6.9. These results indicate that some charged residues are spatially proximal to the thiol group in the U state. Our results suggest that, in addition to the N state, electrostatic interactions in the U state are important determinants of protein stability.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

Low-pH induced structural changes, allergenicity and in vitro digestibility of lectin from black turtle bean (Phaseolus vulgaris L.)

Lectin was incubated in corresponding acidic buffers (pH 1.0-3.5) for a certain period (0.5, 1, 2, 4, 8, 12 and 24 h) at 25 °C. Low-pH induced changes in structure, allergenicity and in vitro digestibility of lectin from black turtle bean (Phaseolus vulgaris L.) were investigated in the present study. Results indicated that the alteration in structure was a progressive unfolding process mainly depending on pH environment, and the treated lectin attained a stable state at 8 h. Electrophoretic, dynamic light scattering (DLS) and size exclusion chromatography (SEC) analyses suggested that lectin monomers appeared in the solutions of pH < 2.0. Differential scanning calorimetry (DSC) confirmed that thermal stability of lectin weakened in low pH environments. Furthermore, ELISA and in vitro digestion assay showed allergenicity and digestibility significantly decreased with the structural alterations. These results showed low-pH treatments have great potential to reduce the damage of legumes protein consumption.

Switching Protein Conformational Substates by Protonation and Mutation

Protein modules that regulate the availability and conformational status of transcription factors determine the rapidity, duration, and magnitude of cellular response to changing conditions. One such system is the single-gene product Cnu, a four-helix bundle transcription co-repressor, which acts as a molecular thermosensor regulating the expression of virulence genes in enterobacteriaceae through modulation of its native conformational ensemble. Cnu and related genes have also been implicated in pH-dependent expression of virulence genes. We hypothesize that protonation of a conserved buried histidine (H45) in Cnu promotes large electrostatic frustration, thus disturbing the H-NS, a transcription factor, binding face. Spectroscopic and calorimetric methods reveal that H45 exhibits a suppressed p K_a of ∼5.1, the protonation of which switches the conformation to an alternate native ensemble in which the fourth helix is disordered. The population redistribution can also be achieved through a mutation H45V, which does not display any switching behavior at pH values greater than 4. The Wako-Saitô-Muñoz-Eaton (WSME) statistical mechanical model predicts specific differences in the conformations and fluctuations of the fourth and first helices of Cnu determining the observed pH response. We validate these predictions through fluorescence lifetime measurements of a sole tryptophan, highlighting the presence of both native and non-native interactions in the regions adjoining the binding face of Cnu. Our combined experimental-computational study thus shows that Cnu acts both as a thermo- and pH-sensor orchestrated via a subtle but quantifiable balance between the weak packing of a structural element and protonation of a buried histidine that promotes electrostatic frustration.

Microscopic mechanisms that govern the titration response and pKa values of buried residues in staphylococcal nuclease mutants

To probe the microscopic mechanisms that govern the titration behavior of buried ionizable groups, microsecond explicit solvent molecular dynamics simulations are carried out for several mutants of Staphylococcal nuclease using both fixed charge and polarizable force fields. While the ionization of Asp 66, Glu 66, and Lys 125 lead to enhanced structural fluctuations and partial unfolding of adjacent α-helical regions, the ionization of Lys 25 causes local unfolding of adjacent β sheets. Using the sampled conformational ensembles, good agreement with experimental pK_a values is obtained with Poisson-Boltzmann calculations using a protein dielectric constant of 2-4 for V66D/E; slightly larger dielectric constants are needed for Lys mutants especially L25K, suggesting that structural responses beyond microseconds are involved in ionization of Lys 25. Overall, the set of unbiased simulations provides insights into the spatial and temporal scales of protein and solvent motions that dictate the diverse titration behaviors of buried protein residues. Proteins 2017; 85:268-281. © 2016 Wiley Periodicals, Inc.

Conformational Reorganization Coupled to the Ionization of Internal Lys Residues in Proteins

Ionizable groups buried in the hydrophobic interior of proteins are essential for energy transduction and catalysis. Because the protein interior is usually neither as polar nor as polarizable as water, these groups tend to have anomalous pKa values, and their ionization tends to be coupled to conformational reorganization. To elucidate mechanisms of energy transduction in proteins, it is necessary to understand the structural determinants of the pKa values of these buried groups, including the range and character of the conformational reorganization that the ionization of these buried groups can elicit. The L25K and L125K variants of staphylococcal nuclease (SNase) were used to characterize the diverse types of structural reorganization that can be promoted by the ionization of buried groups. NMR relaxation dispersion and ZZ-exchange experiments were used to identify the locations and measure the time scales and extent of pH-dependent conformational exchange in these two proteins. The buried Lys-25 and Lys-125 residues titrate with pKa of 6.3 and 6.2, respectively. The L25K protein fluctuates between the native state and an ensemble of locally unfolded states on the 400 μs to 7 ms time scale. On the 100 to 500 ms time scale the native state exchanges with a subglobally unfolded state in which the β-barrel is partially reorganized. The equilibrium between the native state and this alternative state is highly pH dependent; at pH values below the pKa of Lys-25 the state with the partially reorganized β-barrel is the dominant state. In contrast, the L125K protein only exhibited pH-independent fluctuation in the microsecond to millisecond time scale in the region near Lys-125. The study illustrates how diverse and how localized the coupling between conformational reorganization and ionization of buried groups can be. The pH-sensitive exchange between the fully native and subglobally or locally unfolded states in time scales well into hundreds of milliseconds will challenge all computational methods for structure-based calculations of pKa values.

pH dependence of conformational fluctuations of the protein backbone

Proton binding equilibria (pK(a) values) of ionizable groups in proteins are exquisitely sensitive to their microenvironments. Apparent pK(a) values measured for individual ionizable residues with NMR spectroscopy are actually population-weighted averages of the pK(a) in different conformational microstates. NMR spectroscopy experiments with staphylococcal nuclease were used to test the hypothesis that pK(a) values of surface Glu and Asp residues are affected by pH-sensitive fluctuations of the backbone between folded and locally unfolded conformations. (15)N spin relaxation studies showed that as the pH decreases from the neutral into the acidic range the amplitudes of backbone fluctuations in the ps-ns timescale increase near carboxylic residues. Hydrogen exchange experiments suggested that backbone conformational fluctuations promoted by decreasing pH also reflect slower local or sub-global unfolding near carboxylic groups. This study has implications for structure-based pKa calculations: (1) The timescale of the backbone's response to ionization events in proteins can range from ps to ms, and even longer; (2) pH-sensitive fluctuations of the backbone can be localized to both the segment the ionizable residue is attached to or the one that occludes the ionizable group; (3) Structural perturbations are not necessarily propagated through Coulomb interactions; instead, local fluctuations appear to be coupled through the co-operativity inherent to elements of secondary structure and to networks of hydrogen bonds. These results are consistent with the idea that local conformational fluctuations and stabilities are important determinants of apparent pK(a) values of ionizable residues in proteins.

Predicting extreme pKa shifts in staphylococcal nuclease mutants with constant pH molecular dynamics

Accurate computational methods of determining protein and nucleic acid pK(a) values are vital to understanding pH-dependent processes in biological systems. In this article, we use the recently developed method constant pH molecular dynamics (CPHMD) to explore the calculation of highly perturbed pK(a) values in variants of staphylococcal nuclease (SNase). Simulations were performed using the replica exchange (REX) protocol for improved conformational sampling with eight temperature windows, and yielded converged proton populations in a total sampling time of 4 ns. Our REX-CPHMD simulations resulted in calculated pK(a) values with an average unsigned error (AUE) of 0.75 pK units for the acidic residues in Δ + PHS, a hyperstable variant of SNase. For highly pK(a)-perturbed SNase mutants with known crystal structures, our calculations yielded an AUE of 1.5 pK units and for those mutants based on modeled structures an AUE of 1.4 pK units was found. Although a systematic underestimate of pK shifts was observed in most of the cases for the highly perturbed pK mutants, correlations between conformational rearrangement and plasticity associated with the mutation and error in pK(a) prediction was not evident in the data. This study further extends the scope of electrostatic environments explored using the REX-CPHMD methodology and suggests that it is a reliable tool for rapidly characterizing ionizable amino acids within proteins even when modeled structures are employed.

Measuring the successes and deficiencies of constant pH molecular dynamics: a blind prediction study

A constant pH molecular dynamics method has been used in the blind prediction of pK_a values of titratable residues in wild type and mutated structures of the Staphylococcal nuclease (SNase) protein. The predicted values have been subsequently compared to experimental values provided by the laboratory of García-Moreno. CpHMD performs well in predicting the pK_a of solvent-exposed residues. For residues in the protein interior, the CpHMD method encounters some difficulties in reaching convergence and predicting the pK_a values for residues having strong interactions with neighboring residues. These results show the need to accurately and sufficiently sample conformational space in order to obtain pK_a values consistent with experimental results.

Thermodynamic principles for the engineering of pH-driven conformational switches and acid insensitive proteins

The general thermodynamic principles behind pH driven conformational transitions of biological macromolecules are well understood. What is less obvious is how they can be used to engineer pH switches in proteins. The acid unfolding of staphylococcal nuclease (SNase) was used to illustrate different factors that can affect pH-driven conformational transitions. Acid unfolding is a structural transition driven by preferential H(+) binding to the acid unfolded state (U) over the native (N) state of a protein. It is the result of carboxylic groups that titrate with more normal pK(a) values in the U state than in the N state. Acid unfolding profiles of proteins reflect a balance between electrostatic and non-electrostatic contributions to stability. Several strategies were used in attempts to turn SNase into an acid insensitive protein: (1) enhancing global stability of the protein with mutagenesis or with osmolytes, (2) use of high salt concentrations to screen Coulomb interactions, (3) stabilizing the N state through specific anion effects, (4) removing Asp or Glu residues that titrate with depressed pK(a) values in the N state, and (5) removing basic residues that might have strong repulsive interactions in the N state at low pH. The only effective way to engineer acid resistance in SNase is not through modulation of pK(a) values of Asp/Glu but by enhancing the global stability of the protein. Modulation of pH-driven conformational transitions by selective manipulation of the electrostatic component of the switch is an extremely difficult undertaking.

Analysis and modeling of the variable region of camelid single-domain antibodies

Camelids have a special type of Ab, known as heavy chain Abs, which are devoid of classical Ab light chains. Relative to classical Abs, camelid heavy chain Abs (cAbs) have comparable immunogenicity, Ag recognition diversity and binding affinities, higher stability and solubility, and better manufacturability, making them promising candidates for alternate therapeutic scaffolds. Rational engineering of cAbs to improve therapeutic function requires knowledge of the differences of sequence and structural features between cAbs and classical Abs. In this study, amino acid sequences of 27 cAb variable regions (V(H)H) were aligned with the respective regions of 54 classical Abs to detect amino acid differences, enabling automatic identification of cAb V(H)H CDRs. CDR analysis revealed that the H1 often (and sometimes the H2) adopts diverse conformations not classifiable by established canonical rules. Also, although the cAb H3 is much longer than classical H3 loops, it often contains common structural motifs and sometimes a disulfide bond to the H1. Leveraging these observations, we created a Monte Carlo-based cAb V(H)H structural modeling tool, where the CDR H1 and H2 loops exhibited a median root-mean-square deviation to natives of 3.1 and 1.5 Å, respectively. The protocol generated 8-12, 14-16, and 16-24 residue H3 loops with a median root-mean-square deviation to natives of 5.7, 4.5, and 6.8 Å, respectively. The large deviation of the predicted loops underscores the challenge in modeling such long loops. cAb V(H)H homology models can provide structural insights into interaction mechanisms to enable development of novel Abs for therapeutic and biotechnological use.

A Study of Ion-Neutral Collision Cross Section Values for Low Charge States of Peptides, Proteins, and Peptide/Protein Complexes

Here, we report ion-helium collision cross sections (CCS) for a number of peptide, small protein, and peptide/protein ionic complexes. The CCS values reported here are compared to previously reported results.[1, 2] We also compare values for low charge state species, i.e., [M + H](+) and [M + 2H](2+), formed by MALDI with values for high charge state species formed by ESI, and the measured CCSs are compared with predicted CCS for solid-state and solution phase structures and calculated structures obtained by using a protein-protein structure algorithm generator, based on a combined Biomolecular complex Generation with Global Evaluation and Ranking[3] and Multi Dimensional Scaling[4].

One-microsecond molecular dynamics simulation of channel gating in a nicotinic receptor homologue

Recently discovered bacterial homologues of eukaryotic pentameric ligand-gated ion channels, such as the Gloeobacter violaceus receptor (GLIC), are increasingly used as structural and functional models of signal transduction in the nervous system. Here we present a one-microsecond-long molecular dynamics simulation of the GLIC channel pH stimulated gating mechanism. The crystal structure of GLIC obtained at acidic pH in an open-channel form is equilibrated in a membrane environment and then instantly set to neutral pH. The simulation shows a channel closure that rapidly takes place at the level of the hydrophobic furrow and a progressively increasing quaternary twist. Two major events are captured during the simulation. They are initiated by local but large fluctuations in the pore, taking place at the top of the M2 helix, followed by a global tertiary relaxation. The two-step transition of the first subunit starts within the first 50 ns of the simulation and is followed at 450 ns by its immediate neighbor in the pentamer, which proceeds with a similar scenario. This observation suggests a possible two-step domino-like tertiary mechanism that takes place between adjacent subunits. In addition, the dynamical properties of GLIC described here offer an interpretation of the paradoxical properties of a permeable A13'F mutant whose crystal structure determined at 3.15 A shows a pore too narrow to conduct ions.

Molecular determinants of the pKa values of Asp and Glu residues in staphylococcal nuclease

Prior computational studies of the acid-unfolding behavior of staphylococcal nuclease (SNase) suggest that the pK(a) values of its carboxylic groups are difficult to reproduce with electrostatics calculations with continuum methods. To examine the molecular determinants of the pK(a) values of carboxylic groups in SNase, the pK(a) values of all 20 Asp and Glu residues were measured with multidimensional and multinuclear NMR spectroscopy in an acid insensitive variant of SNase. The crystal structure of the protein was obtained to describe the microenvironments of the carboxylic groups. Fourteen Asp and Glu residues titrate with relatively normal pK(a) values that are depressed by less than 1.1 units relative to the normal pK(a) of Asp and Glu in water. Only six residues have pK(a) values shifted by more than 1.5 units. Asp-21 has an unusually high pK(a) of 6.5, which is probably the result of interactions with other carboxylic groups at the active site. The most perturbed pK(a) values appear to be governed by hydrogen bonding and not by Coulomb interactions. The pK(a) values calculated with standard continuum electrostatics methods applied to static structures are more depressed than the measured values because Coulomb effects are exaggerated in the calculations. The problems persist even when the protein is treated with the dielectric constant of water. This can be interpreted to imply that structural relaxation is an important determinant of the pK(a) values; however, no major pH-sensitive conformational reorganization of the backbone was detected using NMR spectroscopy.

Evidence for conformational heterogeneity of fission protein Fis1 from Saccharomyces cerevisiae

Fission 1 (Fis1) is an evolutionarily conserved, type II integral membrane protein implicated in maintaining the proper morphology of mitochondria and peroxisomes. A concave surface on the cytosolic domain of Fis1 from Saccharomyces cerevisiae is implicated in binding other fission proteins, yet structural studies reveal that this surface is sterically occluded by its N-terminal arm. Here we address the question of whether the N-terminal arm of yeast Fis1 exists in a dynamic equilibrium that would allow access to this functionally important surface. NMR measurements sensitive to dynamics occurring on a wide range of time scales (picoseconds to minutes) were used to assess whether the Fis1 arm is dynamic. Hydrogen-deuterium exchange experiments revealed that the Fis1 arm, alpha-helix 6, and proximal loops were not protected from solvent exchange, consistent with motions on the second to minute time scale. An engineered cysteine, I85C, located on the concave surface that lies underneath the Fis1 arm, was readily modified by a fluorescent probe, revealing more solvent accessibility of this position than would be predicted from the structure. Chemical denaturation, NMR chemical shift perturbation, and residual dipolar coupling experiments support the idea that the dynamic equilibrium can be shifted on the basis of changing pH and temperature, with the changes primarily localizing to the Fis1 arm and proximal regions. The data as a whole are consistent with the Fis1 arm adopting a primarily "closed" conformational state able to undergo dynamic excursions that reveal the concave surface and therefore may be important for binding other fission factors and for Fis1 function.

The pK(a) values of acidic and basic residues buried at the same internal location in a protein are governed by different factors

The pK(a) values of internal ionizable groups are usually very different from the normal pK(a) values of ionizable groups in water. To examine the molecular determinants of pK(a) values of internal groups, we compared the properties of Lys, Asp, and Glu at internal position 38 in staphylococcal nuclease. Lys38 titrates with a normal or elevated pK(a), whereas Asp38 and Glu38 titrate with elevated pK(a) values of 7.0 and 7.2, respectively. In the structure of the L38K variant, the buried amino group of the Lys38 side chain makes an ion pair with Glu122, whereas in the structure of the L38E variant, the buried carboxyl group of Glu38 interacts with two backbone amides and has several nearby carboxyl oxygen atoms. Previously, we showed that the pK(a) of Lys38 is normal owing to structural reorganization and water penetration concomitant with ionization of the Lys side chain. In contrast, the pK(a) values of Asp38 and Glu38 are perturbed significantly owing to an imbalance between favorable polar interactions and unfavorable contributions from dehydration and from Coulomb interactions with surface carboxylic groups. Their ionization is also coupled to subtle structural reorganization. These results illustrate the complex interplay between local polarity, Coulomb interactions, and structural reorganization as determinants of pK(a) values of internal groups in proteins. This study suggests that improvements to computational methods for pK(a) calculations will require explicit treatment of the conformational reorganization that can occur when internal groups ionize.

Toward high-resolution homology modeling of antibody Fv regions and application to antibody-antigen docking

High-resolution homology models are useful in structure-based protein engineering applications, especially when a crystallographic structure is unavailable. Here, we report the development and implementation of RosettaAntibody, a protocol for homology modeling of antibody variable regions. The protocol combines comparative modeling of canonical complementarity determining region (CDR) loop conformations and de novo loop modeling of CDR H3 conformation with simultaneous optimization of V(L)-V(H) rigid-body orientation and CDR backbone and side-chain conformations. The protocol was tested on a benchmark of 54 antibody crystal structures. The median root mean square deviation (rmsd) of the antigen binding pocket comprised of all the CDR residues was 1.5 A with 80% of the targets having an rmsd lower than 2.0 A. The median backbone heavy atom global rmsd of the CDR H3 loop prediction was 1.6, 1.9, 2.4, 3.1, and 6.0 A for very short (4-6 residues), short (7-9), medium (10-11), long (12-14) and very long (17-22) loops, respectively. When the set of ten top-scoring antibody homology models are used in local ensemble docking to antigen, a moderate-to-high accuracy docking prediction was achieved in seven of fifteen targets. This success in computational docking with high-resolution homology models is encouraging, but challenges still remain in modeling antibody structures for sequences with long H3 loops. This first large-scale antibody-antigen docking study using homology models reveals the level of "functional accuracy" of these structural models toward protein engineering applications.

Structure-based pKa calculations using continuum electrostatics methods

Electrostatic free energy is useful for correlating structure with function in proteins in which ionizable groups play essential functional roles. To this end, the pK(a) values of ionizable groups must be known and their molecular determinants must be understood. Structure-based calculations of electrostatic energies and pK(a) values are necessary for this purpose. This unit describes protocols for pK(a) calculations with continuum electrostatics methods based on the numerical solution of the linearized Poisson-Boltzmann equation by the method of finite differences. Critical discussion of key parameters, approximations, and shortcomings of these methods is included. Two protocols are described for calculations with methods modified empirically to maximize agreement between measured and calculated pK(a) values. Applied judiciously, these methods can contribute useful and novel insight into properties of surface ionizable groups in proteins.

Electrostatic effects in a network of polar and ionizable groups in staphylococcal nuclease

His121 and His124 are embedded in a network of polar and ionizable groups on the surface of staphylococcal nuclease. To examine how membership in a network affects the electrostatic properties of ionizable groups, the tautomeric state and the pK(a) values of these histidines were measured with NMR spectroscopy in the wild-type nuclease and in 13 variants designed to disrupt the network. In the background protein, His121 and His124 titrate with pK(a) values of 5.2 and 5.6, respectively. In the variants, where the network was disrupted, the pK(a) values range from 4.03 to 6.46 for His121, and 5.04 to 5.99 for His124. The largest decrease in a pK(a) was observed when the favorable Coulomb interaction between His121 and Glu75 was eliminated; the largest increase was observed when Tyr91 or Tyr93 was substituted with Ala or Phe. In all variants, the dominant tautomeric state at neutral pH was the N(epsilon2) state. At one level the network behaves as a rigid unit that does not readily reorganize when disrupted: crystal structures of the E75A or E75Q variants show that even when the pivotal Glu75 is removed, the overall configuration of the network was unaffected. On the other hand, a few key hydrogen bonds appear to govern the conformation of the network, and when these bonds are disrupted the network reorganizes. Coulomb interactions within the network report an effective dielectric constant of 20, whereas a dielectric constant of 80 is more consistent with the magnitude of medium to long-range Coulomb interactions in this protein. The data demonstrate that when structures are treated as static, rigid bodies, structure-based pK(a) calculations with continuum electrostatics method are not useful to treat ionizable groups in cases where pK(a) values are governed by short-range polar and Coulomb interactions.

A buried lysine that titrates with a normal pKa: role of conformational flexibility at the protein-water interface as a determinant of pKa values

Previously we reported that Lys, Asp, and Glu residues at positions 66 and 92 in staphylococcal nuclease (SNase) titrate with pK(a) values shifted by up to 5 pK(a) units in the direction that promotes the neutral state. In contrast, the internal Lys-38 in SNase titrates with a normal pK(a). The crystal structure of the L38K variant shows that the side chain of Lys-38 is buried. The ionizable moiety is approximately 7 A from solvent and ion paired with Glu-122. This suggests that the pK(a) value of Lys-38 is normal because the energetic penalty for dehydration is offset by a favorable Coulomb interaction. However, the pK(a) of Lys-38 was also normal when Glu-122 was replaced with Gln or with Ala. Continuum electrostatics calculations were unable to reproduce the pK(a) of Lys-38 unless the protein was treated with an artificially high dielectric constant, consistent with structural reorganization being responsible for the normal pK(a) value of Lys-38. This reorganization must be local because circular dichroism and NMR spectroscopy indicate that the L38K protein is native-like under all conditions studied. In molecular dynamics simulations, the ion pair between Lys-38 and Glu-122 is unstable. The simulations show that a minor rearrangement of a loop is sufficient to allow penetration of water to the amino moiety of Lys-38. This illustrates both the important roles of local flexibility and water penetration as determinants of pK(a) values of ionizable groups buried near the protein-water interface, and the challenges faced by structure-based pK(a) calculations in reproducing these effects.

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.

Kinetic folding of Haloferax volcanii and Escherichia coli dihydrofolate reductases: haloadaptation by unfolded state destabilization at high ionic strength

Salts affect protein stability by multiple mechanisms (e.g., the Hofmeister effect, preferential hydration, electrostatic effects and weak ion binding). These mechanisms can affect the stability of both the native state and the unfolded state. Previous equilibrium stability studies demonstrated that KCl stabilizes dihydrofolate reductases (DHFRs) from Escherichia coli (ecDHFR, E. coli DHFR) and Haloferax volcanii (hvDHFR1, H. volcanii DHFR encoded by the hdrA gene) with similar efficacies, despite adaptation to disparate physiological ionic strengths (0.2 M versus 2 M). Kinetic studies can provide insights on whether equilibrium effects reflect native state stabilization or unfolded state destabilization. Similar kinetic mechanisms describe the folding of urea-denatured ecDHFR and hvDHFR1: a 5-ms stopped-flow burst-phase species that folds to the native state through two sequential intermediates with relaxation times of 0.1-3 s and 25-100 s. The latter kinetic step is very similar to that observed for the refolding of hvDHFR1 from low ionic strength. The unfolding of hvDHFR1 at low ionic strength is relatively slow, suggesting kinetic stabilization as observed for some thermophilic enzymes. Increased KCl concentrations slow the urea-induced unfolding of ecDHFR and hvDHFR1, but much less than expected from equilibrium studies. Unfolding rates extrapolated to 0 M denaturant, k(unf)(H(2)O), are relatively independent of ionic strength, demonstrating that the KCl-induced stabilization of ecDHFR and hvDHFR1 results predominantly from destabilization of the unfolded state. This supports the hypothesis from previous equilibrium studies that haloadaptation harnesses the effects of elevated salt concentrations on the properties of the aqueous solvent to enhance protein stability.

Ligand effects on the protein ensemble: unifying the descriptions of ligand binding, local conformational fluctuations, and protein stability

Detailed description of the structural and physical basis of allostery, cooperativity, and other manifestations of long-range communication between binding sites in proteins remains elusive. Here we describe an ensemble-based structural-thermodynamic model capable of treating explicitly the coupling between ligand binding reactions, local fluctuations in structure, and global conformational transitions. The H(+) binding reactions of staphylococcal nuclease and the effects of pH on its stability were used to illustrate the properties of proteins that can be described quantitatively with this model. Each microstate in the native ensemble was modeled to have dual structural character; some regions were treated as folded and retained the same atomic geometry as in the crystallographic structure while other regions were treated thermodynamically as if they were unfolded. Two sets of pK(a) values were used to describe the affinity of each H(+) binding site. One set, calculated with a standard continuum electrostatics method, describes H(+) binding to sites in folded parts of the protein. A second set of pK(a) values, obtained from model compounds in water, was used to describe H(+) binding to sites in unfolded regions. An empirical free energy function, parameterized to reproduce folding thermodynamics measured by differential scanning calorimetry, was used to calculate the probability of each microstate. The effects of pH on the distribution of microstates were determined by the H(+) binding properties of each microstate. The validity of the calculations was established by comparison with a number of different experimental observables.

Electrostatic contributions to the stability of the GCN4 leucine zipper structure

Ion pairs are ubiquitous in X-ray structures of coiled coils, and mutagenesis of charged residues can result in large stability losses. By contrast, pK(a) values determined by NMR in solution often predict only small contributions to stability from charge interactions. To help reconcile these results we used triple-resonance NMR to determine pK(a) values for all groups that ionize between pH 1 and 13 in the 33 residue leucine zipper fragment, GCN4p. In addition to the native state we also determined comprehensive pK(a) values for two models of the GCN4p denatured state: the protein in 6 M urea, and unfolded peptide fragments of the protein in water. Only residues that form ion pairs in multiple X-ray structures of GCN4p gave large pK(a) differences between the native and denatured states. Moreover, electrostatic contributions to stability were not equivalent for oppositely charged partners in ion pairs, suggesting that the interactions between a charge and its environment are as important as those within the ion pair. The pH dependence of protein stability calculated from NMR-derived pK(a) values agreed with the stability profile measured from equilibrium urea-unfolding experiments as a function of pH. The stability profile was also reproduced with structure-based continuum electrostatic calculations, although contributions to stability were overestimated at the extremes of pH. We consider potential sources of errors in the calculations, and how pK(a) predictions could be improved. Our results show that although hydrophobic packing and hydrogen bonding have dominant roles, electrostatic interactions also make significant contributions to the stability of the coiled coil.

On the application of CZE to the study of protein denaturation

Experimental mobilities obtained from CZE are used to study protein denaturation through a model based on known physicochemical theories. This model is able to provide additional information concerning the folded and unfolded protein states from mobility data. Its use comprises first the evaluation of relevant parameters of the protein microstates like the electrostatic free energy, apart from the classical conformational free energy, and second the expression of raw experimental data concerning the folding-unfolding transition into more specific physicochemical parameters like protein hydrodynamic radius, net charge number, and hydration. Spurious effects that are intrinsic to the experimental evaluation of the mobility of protein states, like BGE viscosity, pH, and ionic strength variations accompanying the changes of the denaturant agent intensity are eliminated. In order to illustrate the proposal of this work, two case studies are considered here. The first one concerns thermal and urea denaturations of horse heart ferricytochrome c and the second one involves thermal denaturation of hen egg-white lysozyme. Thus, relevant theoretical thermodynamic considerations of the folded-unfolded protein transition are presented, where the electrostatic free energy is included explicitly in the effective free energy. It is found that this transition involves sharp increases of hydrodynamic radius and protein hydration.

On the NMR analysis of pKa values in the unfolded state of proteins by extrapolation to zero denaturant

Detailed knowledge of the pH-dependence in both folded and unfolded states of proteins is essential to understand the role of electrostatics in protein stability. The increasing number of natively disordered proteins constitutes an excellent source for the NMR analysis of pKa values in the unfolded state of proteins. However, the tendency of many natively disordered proteins to aggregate via intermolecular hydrophobic clusters limits their NMR analysis over a wide pH range. To assess whether the pKa values in natively disordered polypeptides can be extrapolated from NMR measurements in the presence of denaturants, the natively disordered backbone of the C-terminal fragment 75 to 105 of Human Thioredoxin was studied. First, assignments using triple resonance experiments were performed to confirm lack of secondary structure. Then the pH-dependence of the amides and carboxylate side chains of Glu residues (Glu88, Glu95, Glu98, and Glu103) in the pH range from 2.0 to 7.0 was monitored using 2D 1H15N HSQC and 3D C(CO)NH experiments, and the behavior of their amides and corresponding carboxyl groups was compared to confirm the absence of nonlocal interactions. Lastly, the effect of increasing dimethyl urea concentration on the pKa values of these Glu residues was monitored. The results indicate that: (i) the dispersion in the pKa of carboxyl groups and the pH midpoints of amides in Glu residues is about 0.5 pH units and 0.6 pH units, respectively; (ii) the backbone amides of the Glu residues exhibit pH midpoints which are within 0.2 pH units from those of their carboxylates; (iii) the addition of denaturant produces upshifts in the pKa values of Glu residues that are nearly independent of their position in the sequence; and (iv) these upshifts show a nonlinear behavior in denaturant concentration, complicating the extrapolation to zero denaturant. Nevertheless, the relative ordering of the pKa values of Glu residues is preserved over the whole range of denaturant concentrations indicating that measurements at high denaturant concentration (e.g. 4 M dimethyl urea) can yield a qualitatively correct ranking of the pKa of these residues in natively disordered proteins whose pH-dependence cannot be monitored directly by NMR.

Intracellular pH sensors: design principles and functional significance

Changes in intracellular pH regulate many cell behaviors, including proliferation, migration, and transformation. However, our understanding of how physiological changes in pH affect protein conformations and macromolecular assemblies is limited. We present design principles, current modeling predictions, and examples of pH sensors or proteins that have activities or ligand-binding affinities that are regulated by changes in intracellular pH.

The N-terminal domain of Bcl-xL reversibly binds membranes in a pH-dependent manner

Bcl-xL regulates apoptosis by maintaining the integrity of the mitochondrial outer membrane by adopting both soluble and membrane-associated forms. The membrane-associated conformation does not require a conserved, C-terminal transmembrane domain and appears to be inserted into the bilayer of synthetic membranes as assessed by membrane permeabilization and critical surface pressure measurements. Membrane association is reversible and is regulated by the cooperative binding of approximately two protons to the protein. Two acidic residues, Glu153 and Asp156, that lie in a conserved hairpin of Bcl-xLDeltaTM appear to be important in this process on the basis of a 16% increase in the level of membrane association of the double mutant E153Q/D156N. Contrary to that for the wild type, membrane permeabilization for the mutant is not correlated with membrane association. Monolayer surface pressure measurements suggest that this effect is primarily due to less membrane penetration. These results suggest that E153 and D156 are important for the Bcl-xLDeltaTM conformational change and that membrane binding can be distinct from membrane permeabilization. Taken together, these studies support a model in which Bcl-xL activity is controlled by reversible insertion of its N-terminal domain into the mitochondrial outer membrane. Future studies with Bcl-xL mutants such as E153Q/D156N should allow determination of the relative contributions of membrane binding, insertion, and permeabilization to the regulation of apoptosis.