Realistic modeling of the denatured states of proteins allows accurate calculations of the pH dependence of protein stability

Charge Regulation during Amyloid Formation of α-Synuclein

Electrostatic interactions play crucial roles in protein function. Measuring pKa value perturbations upon complex formation or self-assembly of e.g. amyloid fibrils gives valuable information about the effect of electrostatic interactions in those processes. Site-specific pKa value determination by solution NMR spectroscopy is challenged by the high molecular weight of amyloid fibrils. Here we report a pH increase during fibril formation of α-synuclein, observed using three complementary experimental methods: pH electrode measurements in water; colorimetric changes of a fluorescent indicator; and chemical shift changes for histidine residues using solution state NMR spectroscopy. A significant pH increase was detected during fibril formation in water, on average by 0.9 pH units from 5.6 to 6.5, showing that protons are taken up during fibril formation. The pH upshift was used to calculate the average change in the apparent pKaave value of the acidic residues, which was found to increase by at least 1.1 unit due to fibril formation. Metropolis Monte Carlo simulations were performed on a comparable system that also showed a proton uptake due to fibril formation. Fibril formation moreover leads to a significant change in proton binding capacitance. Parallel studies of a mutant with five charge deletions in the C-terminal tail revealed a smaller pH increase due to fibril formation, and a smaller change (0.5 units on average) in the apparent pKaave values of the acidic residues. We conclude that the proton uptake during the fibril formation is connected to the high density of acidic residues in the C-terminal tail of α-synuclein.

Modeling pKas of unfolded proteins to probe structural models of unfolded state

Modeling unfolded states of proteins has implications for protein folding and stability. Since in unfolded state proteins adopt multiple conformations, any experimentally measured quantity is ensemble averaged, therefore the computed quantity should be ensemble averaged as well. Here, we investigate the possibility that one can model an unfolded state ensemble with the coil model approach, algorithm such as “flexible-meccano” [Ozenne V et al., Flexible-meccano: A tool for the generation of explicit ensemle descriptions of intrinsically disordered proteins and their associated experimental observables, Bioinformatics 28:1463–1470, 2012], developed to generate structures for intrinsically disordered proteins. We probe such a possibility by using generated structures to calculate pKas of titratable groups and compare with experimental data. It is demonstrated that even with a small number of representative structures of unfolded state, the average calculated pKas are in very good agreement with experimentally measured pKas. Also, predictions are made for titratable groups for which there is no experimental data available. This suggests that the coil model approach is suitable for generating 3D structures of unfolded state of proteins. To make the approach suitable for large-scale modeling, which requires limited number of structures, we ranked the structures according to their solvent accessible surface area (SASA). It is shown that in the majority of cases, the top structures with smallest SASA are enough to represent unfolded state.

Sequence charge decoration dictates coil-globule transition in intrinsically disordered proteins

We present an analytical theory to compute conformations of heteropolymers-applicable to describe disordered proteins-as a function of temperature and charge sequence. The theory describes coil-globule transition for a given protein sequence when temperature is varied and has been benchmarked against the all-atom Monte Carlo simulation (using CAMPARI) of intrinsically disordered proteins (IDPs). In addition, the model quantitatively shows how subtle alterations of charge placement in the primary sequence-while maintaining the same charge composition-can lead to significant changes in conformation, even as drastic as a coil (swelled above a purely random coil) to globule (collapsed below a random coil) and vice versa. The theory provides insights on how to control (enhance or suppress) these changes by tuning the temperature (or solution condition) and charge decoration. As an application, we predict the distribution of conformations (at room temperature) of all naturally occurring IDPs in the DisProt database and notice significant size variation even among IDPs with a similar composition of positive and negative charges. Based on this, we provide a new diagram-of-states delineating the sequence-conformation relation for proteins in the DisProt database. Next, we study the effect of post-translational modification, e.g., phosphorylation, on IDP conformations. Modifications as little as two-site phosphorylation can significantly alter the size of an IDP with everything else being constant (temperature, salt concentration, etc.). However, not all possible modification sites have the same effect on protein conformations; there are certain "hot spots" that can cause maximal change in conformation. The location of these "hot spots" in the parent sequence can readily be identified by using a sequence charge decoration metric originally introduced by Sawle and Ghosh. The ability of our model to predict conformations (both expanded and collapsed states) of IDPs at a high-throughput level can provide valuable insights into the different mechanisms by which phosphorylation/charge mutation controls IDP function.

Modulating charge patterning and ionic strength as a strategy to induce conformational changes in intrinsically disordered proteins

We present an analytical theory to describe conformational changes as a function of salt for polymers with a given sequence of charges. We apply this model to describe Intrinsically Disordered Proteins (IDPs) by explicitly accounting for charged residues and their exact placement in the primary sequence while approximating the effect of non-electrostatic interactions at a mean-field level by effective short-range (two body and three-body) interaction parameters. The effect of ions is introduced by treating electrostatic interactions within Debye-Huckle approximation. Using typical values of the short-range mean-field parameters derived from all-atom Monte Carlo simulations (at zero salt), we predict the conformational changes as a function of salt concentration. We notice that conformational transitions in response to changes in ionic strength strongly depend on sequence specific charge patterning. For example, globule to coil transition can be observed upon increasing salt concentration, in stark contrast to uniformly charged polyelectrolyte theories based on net charge only. In addition, it is possible to observe non-monotonic behavior with salt as well. Drastic differences in salt-induced conformational transitions is also evident between two doubly phosphorylated sequences-derived from the same wild type sequence-that only differ in the site of phosphorylation. Similar effects are also predicted between two sequences derived from the same parent sequence differing by a single site mutation where a negative charge is replaced by a positive charge. These effects are purely a result of charge decoration and can only be understood in terms of metrics based on specific placement of charges, and cannot be explained by models based on charge composition alone. Identifying sequences and hot spots within sequences-for post translational modification or charge mutation-using our high-throughput theory will yield fundamental insights into design and biological regulation mediated by phosphorylation and/or local changes in salt concentration.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

A pH-dependent computational approach to the effect of mutations on protein stability

This article describes a novel software implementation for high-throughput scanning mutagenesis with a focus on protein stability. The approach combines molecular mechanics calculations with calculations of protein ionization and a Gaussian-chain model of electrostatic interactions in unfolded state. Comprehensive testing demonstrates a state-of-the-art accuracy for predicted free energy differences on single, double, and triple mutations with a correlation coefficient R above 0.7, which takes about 1.5 min per mutation on a single CPU. Unlike most of existing in silico methods for fast mutagenesis, the stability changes are reported as a continuous function of solution pH for wide pH intervals. We also propose a novel in silico strategy for searching stabilized protein variants that is based on combinatorial scanning mutagenesis using representative amino acid types. Our in silico predictions are in excellent agreement with the hyper-stabilized variants of mesophilic cold shock protein found using the Proside method of direct evolution. © 2016 Wiley Periodicals, Inc.

Studying the role of cooperative hydration in stabilizing folded protein states

Understanding and modelling protein folding remains a key scientific and engineering challenge. Two key questions in protein folding are (1) why many proteins adopt a folded state and (2) how these proteins transition from the random coil ensemble to a folded state. In this paper we employ molecular dynamics simulations to address the first of these questions. Computational methods are well-placed to address this issue due to their ability to analyze systems at atomic-level resolution. Traditionally, the stability of folded proteins has been ascribed to the balance of two types of intermolecular interactions: hydrogen-bonding interactions and hydrophobic contacts. In this study, we explore a third type of intermolecular interaction: cooperative hydration of protein surface residues. To achieve this, we consider multiple independent simulations of the villin headpiece domain to quantify the contributions of different interactions to the energy of the native and fully extended states. In addition, we consider whether these findings are robust with respect to the protein forcefield, the water model, and the presence of salt. In all cases, we identify many cooperatively hydrated interactions that are transient but energetically favor the native state. Whilst further work on additional protein structures, forcefields, and water models is necessary, these results suggest a role for cooperative hydration in protein folding that should be explored further. Rational design of cooperative hydration on the protein surface could be a viable strategy for increasing protein stability.

Statistical Mechanical Model for pH-Induced Protein Folding: Application to Apomyoglobin

Despite the major role of pH in protein folding and stability, a quantitative understanding of the pH-induced protein folding mechanism remains elusive. Two conventional models, the Monod-Wyman-Changeux and Linderstrøm-Lang smeared charge models, respectively, have been used to analyze the formation/disruption of specific native structures and fluctuating non-native states. However, there are only a few models that can represent the overall kinetic events of folding/unfolding independent of the properties of relevant molecular species, which has hampered the efforts to systematically analyze pH-induced folding. Here, we constructed a statistical mechanical model that incorporates the protonation mechanism of conventional models along with a combined manual search and least-squares fitting procedure, which was used to investigate the folding of horse apomyoglobin over a wide pH range (2.2-6.7), with a time window ranging from ∼40 μs to ∼100 s, using continuous-/stopped-flow fluorescence at 8 °C. Quantitative analysis assuming a five-state sequential scheme indicated that (1) pH-induced folding/unfolding is represented by both specific binding and Coulombic interactions; (2) kinetic folding/unfolding intermediates share kinetic mechanisms with the equilibrium intermediate, indicating their equivalence; and (3) native-like properties are acquired successively during folding by intermediates and in transition states. This model could also be applied to a variety of association/dissociation processes.

Electrostatic effects on the folding stability of FKBP12

The roles of electrostatic interactions in protein folding stability have been a matter of debate, largely due to the complexity in the theoretical treatment of these interactions. We have developed computational methods for calculating electrostatic effects on protein folding stability. To rigorously test and further refine these methods, here we carried out experimental studies into electrostatic effects on the folding stability of the human 12-kD FK506 binding protein (FKBP12). This protein has a close homologue, FKBP12.6, with amino acid substitutions in only 18 of their 107 residues. Of the 18 substitutions, 8 involve charged residues. Upon mutating FKBP12 residues at these 8 positions individually into the counterparts in FKBP12.6, the unfolding free energy (ΔGu) of FKBP12 changed by -0.3 to 0.7 kcal/mol. Accumulating stabilizing substitutions resulted in a mutant with a 0.9 kcal/mol increase in stability. Additional charge mutations were grafted from a thermophilic homologue, MtFKBP17, which aligns to FKBP12 with 31% sequence identity over 89 positions. Eleven such charge mutations were studied, with ΔΔGu varying from -2.9 to 0.1 kcal/mol. The predicted electrostatic effects by our computational methods with refinements herein had a root-mean-square deviation of 0.9 kcal/mol from the experimental ΔΔGu values on 16 single mutations of FKBP12. The difference in ΔΔGu between mutations grafted from FKBP12.6 and those from MtFKBP17 suggests that more distant homologues are less able to provide guidance for enhancing folding stability.

Tri-peptide reference structures for the calculation of relative solvent accessible surface area in protein amino acid residues

Relative amino acid residue solvent accessibility values allow the quantitative comparison of atomic solvent-accessible surface areas in different residue types and physical environments in proteins and in protein structural alignments. Geometry-optimised tri-peptide structures in extended solvent-exposed reference conformations have been obtained for 43 amino acid residue types at a high level of quantum chemical theory. Significant increases in side-chain solvent accessibility, offset by reductions in main-chain atom solvent exposure, were observed for standard residue types in partially geometry-optimised structures when compared to non-minimised models built from identical sets of proper dihedral angles abstracted from the literature. Optimisation of proper dihedral angles led most notably to marked increases of up to 54% in proline main-chain atom solvent accessibility compared to literature values. Similar effects were observed for fully-optimised tri-peptides in implicit solvent. The relief of internal strain energy was associated with systematic variation in N, C(α) and C(β) atom solvent accessibility across all standard residue types. The results underline the importance of optimisation of 'hard' degrees of freedom (bond lengths and valence bond angles) and improper dihedral angle values from force field or other context-independent reference values, and impact on the use of standardised fixed internal co-ordinate geometry in sampling approaches to the determination of absolute values of protein amino acid residue solvent accessibility. Quantum chemical methods provide a useful and accurate alternative to molecular mechanics methods to perform energy minimisation of peptides containing non-standard (chemically modified) amino acid residues frequently present in experimental protein structure data sets, for which force field parameters may not be available. Reference tri-peptide atomic co-ordinate sets including hydrogen atoms are made freely available.

Simplicity within the complexity: bilateral impact of DMSO on the functional and unfolding patterns of α-chymotrypsin

New understanding of the fundamental links between protein stability, conformational flexibility and function, can be gained through synergic studies on their catalytic and folding/unfolding properties under the influence of stabilizing/destabilizing additives. We explored an impact of dimethyl sulfoxide (DMSO), the moderate effector of multilateral action, on the kinetic (functional) and thermodynamic (thermal unfolding) patterns of a hydrolytic enzyme, α-chymotrypsin (α-CT), over a wide range of additive concentrations, 0-70% (v/v). Both the calorimetric and kinetic data exhibited rich behavior pointing to the complex interplay of global/local stability (and flexibility) patterns. The complex action of DMSO is explained through the negative and positive preferential solvation motifs that prevail for the extreme opposite, native-like and unfolded states, respectively, implying essential stabilization of compact domains by enhancement of interfacial water networks and destabilization of a flexible active site by direct binding of DMSO to the unoccupied specific positions intended for elongated polypeptide substrates.

pH-selective mutagenesis of protein-protein interfaces: in silico design of therapeutic antibodies with prolonged half-life

Understanding the effects of mutation on pH-dependent protein binding affinity is important in protein design, especially in the area of protein therapeutics. We propose a novel method for fast in silico mutagenesis of protein–protein complexes to calculate the effect of mutation as a function of pH. The free energy differences between the wild type and mutants are evaluated from a molecular mechanics model, combined with calculations of the equilibria of proton binding. The predicted pH-dependent energy profiles demonstrate excellent agreement with experimentally measured pH-dependency of the effect of mutations on the dissociation constants for the complex of turkey ovomucoid third domain (OMTKY3) and proteinase B. The virtual scanning mutagenesis identifies all hotspots responsible for pH-dependent binding of immunoglobulin G (IgG) to neonatal Fc receptor (FcRn) and the results support the current understanding of the salvage mechanism of the antibody by FcRn based on pH-selective binding. The method can be used to select mutations that change the pH-dependent binding profiles of proteins and guide the time consuming and expensive protein engineering experiments. As an application of this method, we propose a computational strategy to search for mutations that can alter the pH-dependent binding behavior of IgG to FcRn with the aim of improving the half-life of therapeutic antibodies in the target organism.

Highly perturbed pKa values in the unfolded state of hen egg white lysozyme

The majority of pK(a) values in protein unfolded states are close to the amino acid model pK(a) values, thus reflecting the weak intramolecular interactions present in the unfolded ensemble of most proteins. We have carried out thermal denaturation measurements on the WT and eight mutants of HEWL from pH 1.5 to pH 11.0 to examine the unfolded state pK(a) values and the pH dependence of protein stability for this enzyme. The availability of accurate pK(a) values for the folded state of HEWL and separate measurements of mutant-induced effects on the folded state pK(a) values, allows us to estimate the pK(a) values of seven acidic residues in the unfolded state of HEWL. Asp-48 and Asp-66 display pK(a) values of 2.9 and 3.1 in our analysis, thus representing the most depressed unfolded state pK(a) values observed to date. We observe a strong correlation between the folded state pK(a) values and the unfolded state pK(a) values of HEWL, thus suggesting that the unfolded state of HEWL possesses a large degree of native state characteristics.

Effects of pH on proteins: predictions for ensemble and single-molecule pulling experiments

Protein conformations change among distinct thermodynamic states as solution conditions (temperature, denaturants, pH) are altered or when they are subjected to mechanical forces. A quantitative description of the changes in the relative stabilities of the various thermodynamic states is needed to interpret and predict experimental outcomes. We provide a framework based on the Molecular Transfer Model (MTM) to account for pH effects on the properties of globular proteins. The MTM utilizes the partition function of a protein calculated from molecular simulations at one set of solution conditions to predict protein properties at another set of solution conditions. To take pH effects into account, we utilized experimentally measured pK(a) values in the native and unfolded states to calculate the free energy of transferring a protein from a reference pH to the pH of interest. We validate our approach by demonstrating that the native-state stability as a function of pH is accurately predicted for chymotrypsin inhibitor 2 (CI2) and protein G. We use the MTM to predict the response of CI2 and protein G subjected to a constant force (f) and varying pH. The phase diagrams of CI2 and protein G as a function of f and pH are dramatically different and reflect the underlying pH-dependent stability changes in the absence of force. The calculated equilibrium free energy profiles as functions of the end-to-end distance of the two proteins show that, at various pH values, CI2 unfolds via an intermediate when subjected to f. The locations of the two transition states move toward the more unstable state as f is changed, which is in accord with the Hammond-Leffler postulate. In sharp contrast, force-induced unfolding of protein G occurs in a single step. Remarkably, the location of the transition state with respect to the folded state is independent of f, which suggests that protein G is mechanically brittle. The MTM provides a natural framework for predicting the outcomes of ensemble and single-molecule experiments for a wide range of solution conditions.

Analysis of electrostatic interactions in the denatured state ensemble of the N-terminal domain of L9 under native conditions

The pH dependence of protein stability is defined by the difference in the number of protons bound to the folded state and to the denatured state ensemble (DSE) as a function of pH. In many cases, the protonation behavior can be described as the sum of a set of independently titrating residues; in this case, the pH dependence of stability reflects differences in folded and DSE pK(a)'s. pH dependent stability studies have shown that there are energetically important interactions involving charged residues in the DSE of the N-terminal domain of L9 (NTL9), which affect significantly the stability of the protein. The DSE of wild type NTL9 cannot be directly characterized under native conditions because of its high stability. A destabilized double mutant of NTL9, V3AI4A, significantly populates the folded state and the DSE in the absence of denaturant. The two states are in slow exchange on the nuclear magnetic resonance time scale, and diffusion measurements indicate that the DSE is compact. The DSE pK(a)'s of all of the acidic residues were directly determined. The DSE pK(a) of Asp8 and Asp23 are depressed relative to model compounds values. Use of the mutant DSE pK(a)'s together with known native state pK(a)'s leads to a significantly improved agreement between the measured pH dependent stability and that predicted by the Tanford-Wyman linkage relationship. An analysis of the literature suggests that DSE interactions involving charged residues are relatively common and should be considered in discussions of protein stability.

NMR determination of pKa values in α-synuclein

The intrinsically unfolded protein α-synuclein has an N-terminal domain with seven imperfect KTKEGV sequence repeats and a C-terminal domain with a large proportion of acidic residues. We characterized pK(a) values for all 26 sites in the protein that ionize below pH 7 using 2D (1) H-(15) N HSQC and 3D C(CO)NH NMR experiments. The N-terminal domain shows systematically lowered pK(a) values, suggesting weak electrostatic interactions between acidic and basic residues in the KTKEGV repeats. By contrast, the C-terminal domain shows elevated pK(a) values due to electrostatic repulsion between like charges. The effects are smaller but persist at physiological salt concentrations. For α-synuclein in the membrane-like environment of sodium dodecylsulfate (SDS) micelles, we characterized the pK(a) of His50, a residue of particular interest since it is flanked within one turn of the α-helix structure by the Parkinson's disease-linked mutants E46K and A53T. The pK(a) of His50 is raised by 1.4 pH units in the micelle-bound state. Titrations of His50 in the micelle-bound states of the E46K and A53T mutants show that the pK(a) shift is primarily due to interactions between the histidine and the sulfate groups of SDS, with electrostatic interactions between His50 and Glu46 playing a much smaller role. Our results indicate that the pK(a) values of uncomplexed α-synuclein differ significantly from random coil model peptides even though the protein is intrinsically unfolded. Due to the long-range nature of electrostatic interactions, charged residues in the α-synuclein sequence may help nucleate the folding of the protein into an α-helical structure and confer protection from misfolding.

Uncovering specific electrostatic interactions in the denatured states of proteins

The stability and folding of proteins are modulated by energetically significant interactions in the denatured state that is in equilibrium with the native state. These interactions remain largely invisible to current experimental techniques, however, due to the sparse population and conformational heterogeneity of the denatured-state ensemble under folding conditions. Molecular dynamics simulations using physics-based force fields can in principle offer atomistic details of the denatured state. However, practical applications are plagued with the lack of rigorous means to validate microscopic information and deficiencies in force fields and solvent models. This study presents a method based on coupled titration and molecular dynamics sampling of the denatured state starting from the extended sequence under native conditions. The resulting denatured-state pK(a)s allow for the prediction of experimental observables such as pH- and mutation-induced stability changes. I show the capability and use of the method by investigating the electrostatic interactions in the denatured states of wild-type and K12M mutant of NTL9 protein. This study shows that the major errors in electrostatics can be identified by validating the titration properties of the fragment peptides derived from the sequence of the intact protein. Consistent with experimental evidence, our simulations show a significantly depressed pK(a) for Asp(8) in the denatured state of wild-type, which is due to a nonnative interaction between Asp(8) and Lys(12). Interestingly, the simulation also shows a nonnative interaction between Asp(8) and Glu(48) in the denatured state of the mutant. I believe the presented method is general and can be applied to extract and validate microscopic electrostatics of the entire folding energy landscape.

Defining the role of salt bridges in protein stability

Although the energetic balance of forces stabilizing proteins has been established qualitatively over the last decades, quantification of the energetic contribution of particular interactions still poses serious problems. The reasons are the strong cooperativity and the interdependence ofnoncovalent interactions. Salt bridges are a typical example. One expects that ionizable side chains frequently form ion pairs in innumerable crystal structures. Since electrostatic attraction between opposite charges is strong per se, salt bridges can intuitively be regarded as an important factor stabilizing the native structure. Is that really so? In this chapter we critically reassess the available methods to delineate the role ofelectrostatic interactions and salt bridges to protein stability, and discuss the progress and the obstacles in this endeavor. The basic problem is that formation of salt bridges depends on the ionization properties of the participating groups, which is significantly influenced by the protein environment. Furthermore, salt bridges experience thermal fluctuations, continuously break and re-form, and their lifespan in solution is governed by the flexibility of the protein. Finally, electrostatic interactions are long-range and might be significant in the unfolded state, thus seriously influencing the energetic profile. Elimination of salt bridges by protonation/deprotonation at extreme pH or by mutation provides only rough energetic estimates, since there is no way to account for the nonadditive response of the protein moiety. From what we know so far, the strength of electrostatic interactions is strongly context-dependent, yet it is unlikely that salt bridges are dominant factors governing protein stability. Nevertheless, proteins from thermophiles and hyperthermophiles exhibit more, and frequently networked, salt bridges than proteins from the mesophilic counterparts. Increasing the thermal (not the thermodynamic) stability of proteins by optimization of charge-charge interactions is a good example for an evolutionary solution utilizing physical factors.

A fast and accurate computational approach to protein ionization

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

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 contribution to the thermodynamic and kinetic stability of the homotrimeric coiled coil Lpp-56: A computational study

The protein moiety of the Braun's E. coli outer membrane lipoprotein (Lpp-56) is an attractive object of biophysical investigation in several aspects. It is a homotrimeric, parallel coiled coil, a class of coiled coils whose stability and folding have been studied only occasionally. Lpp-56 possesses unique structural properties and exhibits extremely low rates of folding and unfolding. It is natural to ask how the specificity of the structure determines the extraordinary physical chemical properties of this protein. Recently, a seemingly controversial data on the stability and unfolding rate of Lpp-56 have been published (Dragan et al., Biochemistry 2004;43: 14891-14900; Bjelic et al., Biochemistry 2006;45:8931-8939). The unfolding rate constant measured using GdmCl as the denaturing agent, though extremely low, was substantially higher than that obtained on the basis of thermal unfolding. If this large difference arises from the effect of screening of electrostatic interactions induced by GdmCl, electrostatic interactions would appear to be an important factor determining the unusual properties of Lpp-56. We present here a computational analysis of the electrostatic properties of Lpp-56 combining molecular dynamics simulations and continuum pK calculations. The pH-dependence of the unfolding free energy is predicted in good agreement with the experimental data: the change in DeltaG between pH 3 and pH 7 is approximately 60 kJ mol(-1). The results suggest that the difference in the stability of the protein observed using different experimental methods is mainly because of the effect of the reduction of electrostatic interactions when the salt (GdmCl) concentration increases. We also find that the occupancy of the interhelical salt bridges is unusually high. We hypothesize that electrostatic interactions, and the interhelical salt bridges in particular, are an important factor determining the low unfolding rate of Lpp-56.

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.

Thermodynamic and kinetic stability of penicillin acylase from Escherichia coli

Thermal denaturation of penicillin acylase (PA) from Escherichia coli has been studied by high-sensitivity differential scanning calorimetry as a function of heating rate, pH and urea concentration. It is shown to be irreversible and kinetically controlled. Upon decrease in the heating rate from 2 to 0.1 K min(-1) the denaturation temperature of PA at pH 6.0 decreases by about 6 degrees C, while the denaturation enthalpy does not change notably giving an average value of 31.6+/-2.1 J g(-1). The denaturation temperature of PA reaches a maximum value of 64.5 degrees C at pH 6.0 and decreases by about of 15 degrees C at pH 3.0 and 9.5. The pH induced changes in the denaturation enthalpy follow changes in the denaturation temperature. Increasing the urea concentration causes a decrease in both denaturation temperature and enthalpy of PA, where denaturation temperature obeys a linear relation. The heat capacity increment of PA is not sensitive to the heating rate, nor to pH, and neither to urea. Its average value is of 0.58+/-0.02 J g(-1) K(-1). The denaturation transition of PA is approximated by the Lumry-Eyring model. The first stage of the process is assumed to be a reversible unfolding of the alpha-subunit. It activates the second stage involving dissociation of two subunits and subsequent denaturation of the beta-subunit. This stage is irreversible and kinetically controlled. Using this model the temperature, enthalpy and free energy of unfolding of the alpha-subunit, and a rate constant of the irreversible stage are determined as a function of pH and urea concentration. Structural features of the folded and unfolded conformation of the alpha-subunit as well as of the transition state of the PA denaturation in aqueous and urea solutions are discussed.

A statistical approach to the prediction of pK(a) values in proteins

We propose a simple model for the calculation of pK(a) values of ionizable residues in proteins. It is based on the premise that the pK(a) shift of ionizable residues is linearly correlated to the interaction between a particular residue and the local environment created by the surrounding residues. Despite its simplicity, the model displays good prediction performance. Under the sixfold cross test prediction over a data set of 405 experimental pK(a) values in 73 protein chains with known structures, the root-mean-square deviation (RMSD) between the experimental and calculated pK(a) was found to be 0.77. The accuracy of this model increases with increasing size of the data set: the RMSD is 0.609 for glutamate (the largest data set with 141 sites) and approximately 1 pH unit for lysine, with a data set containing 45 sites.

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.

Why are proteins charged? Networks of charge-charge interactions in proteins measured by charge ladders and capillary electrophoresis

Almost all proteins contain charged amino acids. While the function in catalysis or binding of individual charges in the active site can often be identified, it is less clear how to assign function to charges beyond this region. Are they necessary for solubility? For reasons other than solubility? Can manipulating these charges change the properties of proteins? A combination of capillary electrophoresis (CE) and protein charge ladders makes it possible to study the roles of charged residues on the surface of proteins outside the active site. This method involves chemical modification of those residues to generate a large number of derivatives of the protein that differ in charge. CE separates those derivatives into groups with the same number of modified charged groups. By studying the influence of charge on the properties of proteins using charge ladders, it is possible to estimate the net charge and hydrodynamic radius and to infer the role of charged residues in ligand binding and protein folding.

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.

Mechanisms for stabilisation and the maintenance of solubility in proteins from thermophiles

Background

The database of protein structures contains representatives from organisms with a range of growth temperatures. Various properties have been studied in a search for the molecular basis of protein adaptation to higher growth temperature. Charged groups have emerged as key distinguishing factors for proteins from thermophiles and mesophiles.

Results

A dataset of 291 thermophile-derived protein structures is compared with mesophile proteins. Calculations of electrostatic interactions support the importance of charges, but indicate that increases in charge contribution to folded state stabilisation do not generally correlate with the numbers of charged groups. Relative propensities of charged groups vary, such as the substitution of glutamic for aspartic acid sidechains. Calculations suggest an energetic basis, with less dehydration for longer sidechains. Most other properties studied show weak or insignificant separation of proteins from moderate thermophiles or hyperthermophiles and mesophiles, including an estimate of the difference in sidechain rotameric entropy upon protein folding. An exception is increased burial of alanine and proline residues and decreased burial of phenylalanine, methionine, tyrosine and tryptophan in hyperthermophile proteins compared to those from mesophiles.

Conclusion

Since an increase in the number of charged groups for hyperthermophile proteins is separable from charged group contribution to folded state stability, we hypothesise that charged group propensity is important in the context of protein solubility and the prevention of aggregation. Accordingly we find some separation between mesophile and hyperthermophile proteins when looking at the largest surface patch that does not contain a charged sidechain. With regard to our observation that aromatic sidechains are less buried in hyperthermophile proteins, further analysis indicates that the placement of some of these groups may facilitate the reduction of folding fluctuations in proteins of the higher growth temperature organisms.

A molecular dynamics study of the correlations between solvent-accessible surface, molecular volume, and folding state

We analyzed the correlations between molecular volume, solvent-accessible surface, and folding state (secondary structure content) for unfolded conformers of alpha (holo- and apomyoglobin) and beta (retinal-binding protein) proteins and a small water-soluble alanine-rich alpha-helical peptide. Conformers with different degrees of folding were obtained using molecular dynamics at constant temperature and pressure with implicit solvent (dielectric constant adjustment) for all four systems and with explicit solvent for the single helix peptide. Our results support the view that unfolded conformations are not necessary extended, that volume variation is not a good indication of folding state and that the simple model of water penetrating the interior of the protein does not explain the increase in volume upon unfolding.

Role of the Charge–Charge Interactions in Defining Stability and Halophilicity of the CspB Proteins

Charge-charge interactions on the surface of native proteins are important for protein stability and can be computationally redesigned in a rational way to modulate protein stability. Such computational effort led to an engineered protein, CspB-TB that has the same core as the mesophilic cold shock protein CspB-Bs from Bacillus subtilis, but optimized distribution of charge-charge interactions on the surface. The CspB-TB protein shows an increase in the transition temperature by 20 degrees C relative to the unfolding temperature of CspB-Bs. The CspB-TB and CspB-Bs protein pair offers a unique opportunity to further explore the energetics of charge-charge interactions as the substitutions at the same sequence positions are done in largely similar structural but different electrostatic environments. In particular we addressed two questions. What is the contribution of charge-charge interactions in the unfolded state to the protein stability and how amino acid substitutions modulate the effect of increase in ionic strength on protein stability (i.e. protein halophilicity). To this end, we experimentally measured the stabilities of over 100 variants of CspB-TB and CspB-Bs proteins with substitutions at charged residues. We also performed computational modeling of these protein variants. Analysis of the experimental and computational data allowed us to conclude that the charge-charge interactions in the unfolded state of two model proteins CspB-Bs and CspB-TB are not very significant and computational models that are based only on the native state structure can adequately, i.e. qualitatively (stabilizing versus destabilizing) and semi-quantitatively (relative rank order), predict the effects of surface charge neutralization or reversal on protein stability. We also show that the effect of ionic strength on protein stability (protein halophilicity) appears to be mainly due to the screening of the long-range charge-charge interactions.

The dominant role of side-chain backbone interactions in structural realization of amino acid code. ChiRotor: a side-chain prediction algorithm based on side-chain backbone interactions

The basic differences between the 20 natural amino acid residues are due to differences in their side-chain structures. This characteristic design of protein building blocks implies that side-chain-side-chain interactions play an important, even dominant role in 3D-structural realization of amino acid codes. Here we present the results of a comparative analysis of the contributions of side-chain-side-chain (s-s) and side-chain-backbone (s-b) interactions to the stabilization of folded protein structures within the framework of the CHARMm molecular data model. Contrary to intuition, our results suggest that side-chain-backbone interactions play the major role in side-chain packing, in stabilizing the folded structures, and in differentiating the folded structures from the unfolded or misfolded structures, while the interactions between side chains have a secondary effect. An additional analysis of electrostatic energies suggests that combinatorial dominance of the interactions between opposite charges makes the electrostatic interactions act as an unspecific folding force that stabilizes not only native structure, but also compact random conformations. This observation is in agreement with experimental findings that, in the denatured state, the charge-charge interactions stabilize more compact conformations. Taking advantage of the dominant role of side-chain-backbone interactions in side-chain packing to reduce the combinatorial problem, we developed a new algorithm, ChiRotor, for rapid prediction of side-chain conformations. We present the results of a validation study of the method based on a set of high resolution X-ray structures.

pK(a) values for side-chain carboxyl groups of a PGB1 variant explain salt and pH-dependent stability

Determination of pK(a) values of titrating residues in proteins provides a direct means of studying electrostatic coupling as well as pH-dependent stability. The B1 domain of protein G provides an excellent model system for such investigations. In this work, we analyze the observed pK(a) values of all carboxyl groups in a variant of PGB1 (T2Q, N8D, N37D) at low and high ionic strength as determined using (1)H-(13)C heteronuclear NMR in a structural context. The pK(a) values are used to calculate the pH-dependent stability in low and high salt and to investigate electrostatic coupling in the system. The observed pK(a) values can explain the pH dependence of protein stability but require pK(a) shifts relative to model values in the unfolded state, consistent with persistent residual structure in the denatured state. In particular, we find that most of the deviations from the expected random coil values can be explained by a significantly upshifted pK(a) value. We show also that (13)C backbone carbonyl data can be used to study electrostatic coupling in proteins and provide specific information on hydrogen bonding and electrostatic potential at nontitrating sites.

pH-Dependent Conformational Stability of the Ribotoxin α-Sarcin and Four Active Site Charge Substitution Variants

Alpha-sarcin is an exquisitely specific ribonuclease that binds and cleaves a single phosphodiester bond in the large rRNA of the eukaryotic ribosome, inactivating it. To better understand this remarkable activity, the contributions of the active site residues (His 50, Glu 96, and His 137) to the conformational stability have been determined as a function of pH using variant proteins containing uncharged substitutes. Wild-type alpha-sarcin and the variants are maximally stable near pH 5.5, coinciding with the pH of optimal activity. A comparison of the stability vs pH profiles determined by thermal denaturation experiments to those calculated on the basis of pKa values shows that the charged forms of Glu 96 and His 137 compromise the enzyme's stability, lowering it. In contrast to barnase, there is little evidence for significant electrostatic interactions in the denatured states of alpha-sarcin or its active site variants between pH 3.5 and pH 8.5. Alpha-sarcin contains a long beta-hairpin and surface loops which are highly positively charged and which play key roles in membrane translocation and in ribosome binding. These positive charges decrease the stability of alpha-sarcin, particularly below pH 5. Hydrogen exchange measurements have been performed at pH 5.5 and reveal that the catalytic residues are firmly anchored in highly stable elements of secondary structure. Significant, though lower, levels of protection are observed for many amide protons in the positively charged beta-hairpin and long loops.

Similarity and difference in the unfolding of thermophilic and mesophilic cold shock proteins studied by molecular dynamics simulations

Molecular dynamics simulations were performed to unfold a homologous pair of thermophilic and mesophilic cold shock proteins at high temperatures. The two proteins differ in just 11 of 66 residues and have very similar structures with a closed five-stranded antiparallel beta-barrel. A long flexible loop connects the N-terminal side of the barrel, formed by three strands (beta1-beta3), with the C-terminal side, formed by two strands (beta4-beta5). The two proteins were found to follow the same unfolding pathway, but with the thermophilic protein showing much slower unfolding. Unfolding started with the melting of C-terminal strands, leading to exposure of the hydrophobic core. Subsequent melting of beta3 and the beta-hairpin formed by the first two strands then resulted in unfolding of the whole protein. The slower unfolding of the thermophilic protein could be attributed to ion pair formation of Arg-3 with Glu-46, Glu-21, and the C-terminal. These ion pairs were also found to be important for the difference in folding stability between the pair of proteins. Thus electrostatic interactions appear to play similar roles in the difference in folding stability and kinetics between the pair of proteins.

Subcellular pH and predicted pH-dependent features of proteins

A characteristic of two-dimensional proteomics gels is a general bimodal distribution of isoelectric (pI) values. Discussion of this feature has focussed on the balance of acidic and basic ionisable residues, and potential relationships between pI distributions and organism classification or protein subcellular location. Electrostatics calculations on a set of protein structures with known subcellular location show that predicted folded state pI are similar to those calculated from sequence alone, but adjusted according to a general stabilising effect from interactions between ionisable groups. Bimodal distributions dominate both pI and the predicted pH of maximal stability. However, there are significant differences between these features. The average pH of maximal stability generally follows organelle pH. Average pI values are well removed from organelle pH in most subcellular environments, consistent with the view that proteins have evolved to carry (on average) net charge in a given subcellular location, and relevant to discussion of solubility in crowded environments. Correlation of the predicted pH of maximum stability with subcellular pH suggests an evolutionary pressure to adjust folded state interactions according to environment. Finally, our analysis of ionisable group contributions to stability suggests that Golgi proteins have the largest such term, although this dataset is small.

Analysing the pH-dependent properties of proteins using pKa calculations

The results of protein pKa calculations are routinely being analysed to understand the pH-dependence of protein characteristics such as stability and catalysis. Systems of functionally important titratable groups are identified from protein from pKa calculations, but the rationalisation of the behaviour of such systems is inherently problematic due to a lack of theoretical tools and methods. I present a number of novel methods for analysing the results of protein pKa calculations which have been embedded in a graphical user interface (pKaTool). In the present paper I present novel methods for assessing the reliability of protein pKa calculations and for analysing the roles of individual residues in determining active site pKa values and the pH-dependence of protein stability. The methods presented are freely available to academic researchers at http://enzyme.ucd.ie/Science/pKa/pKaTool .

pK values of the ionizable groups of proteins

We have used potentiometric titrations to measure the pK values of the ionizable groups of proteins in alanine pentapeptides with appropriately blocked termini. These pentapeptides provide an improved model for the pK values of the ionizable groups in proteins. Our pK values determined in 0.1 M KCl at 25 degrees C are: 3.67+/-0.03 (alpha-carboxyl), 3.67+/-0.04 (Asp), 4.25+/-0.05 (Glu), 6.54+/-0.04 (His), 8.00+/-0.03 (alpha-amino), 8.55+/-0.03 (Cys), 9.84+/-0.11 (Tyr), and 10.40+/-0.08 (Lys). The pK values of some groups differ from the Nozaki and Tanford (N & T) pK values often used in the literature: Asp (3.67 this work vs. 4.0 N & T); His (6.54 this work vs. 6.3 N & T); alpha-amino (8.00 this work vs. 7.5 N & T); Cys (8.55 this work vs. 9.5 N & T); and Tyr (9.84 this work vs. 9.6 N & T). Our pK values will be useful to those who study pK perturbations in folded and unfolded proteins, and to those who use theory to gain a better understanding of the factors that determine the pK values of the ionizable groups of proteins.

Conserved quantitative stability/flexibility relationships (QSFR) in an orthologous RNase H pair

Many reports qualitatively describe conserved stability and flexibility profiles across protein families, but biophysical modeling schemes have not been available to robustly quantify both. Here we investigate an orthologous RNase H pair by using a minimal distance constraint model (DCM). The DCM is an all atom microscopic model [Jacobs and Dallakyan, Biophys J 2005;88(2):903-915] that accurately reproduces heat capacity measurements [Livesay et al., FEBS Lett 2004;576(3):468-476], and is unique in its ability to harmoniously calculate thermodynamic stability and flexibility in practical computing times. Consequently, quantified stability/flexibility relationships (QSFR) can be determined using the DCM. For the first time, a comparative QSFR analysis is performed, serving as a paradigm study to illustrate the utility of a QSFR analysis for elucidating evolutionarily conserved stability and flexibility profiles. Despite global conservation of QSFR profiles, distinct enthalpy-entropy compensation mechanisms are identified between the RNase H pair. In both cases, local flexibility metrics parallel H/D exchange experiments by correctly identifying the folding core and several flexible regions. Remarkably, at appropriately shifted temperatures (e.g., melting temperature), these differences lead to a global conservation in Landau free energy landscapes, which directly relate thermodynamic stability to global flexibility. Using ensemble-based sampling within free energy basins, rigidly, and flexibly correlated regions are quantified through cooperativity correlation plots. Five conserved flexible regions are identified within the structures of the orthologous pair. Evolutionary conservation of these flexibly correlated regions is strongly suggestive of their catalytic importance. Conclusions made herein are demonstrated to be robust with respect to the DCM parameterization.

Protein stability and surface electrostatics: a charged relationship

Engineering proteins to withstand a broad range of conditions continues to be a coveted objective, holding the potential to advance biomedicine, industry, and our understanding of disease. One way of achieving this goal lies in elucidating the underlying interactions that define protein stability. It has been shown that the hydrophobic effect, hydrogen bonding, and packing interactions between residues in the protein interior are dominant factors that define protein stability. The role of surface residues in protein stability has received much less attention. It has been believed that surface residues are not important for protein stability particularly because their interactions with the solvent should be similar in the native and unfolded states. In the case of surface charged residues, it was sometimes argued that solvent exposure meant that the high dielectric of the solvent will further decrease the strength of the charge-charge interactions. In this paper, we challenge the notion that the surface charged residues are not important for protein stability. We computationally redesigned sequences of five different proteins to optimize the surface charge-charge interactions. All redesigned proteins exhibited a significant increase in stability relative to their parent proteins, as experimentally determined by circular dichroism spectroscopy and differential scanning calorimetry. These results suggest that surface charge-charge interactions are important for protein stability and that rational optimization of charge-charge interactions on the protein surface can be a viable strategy for enhancing protein stability.

Effects of Charge-to-Alanine Substitutions on the Stability of Ribosomal Protein L30e from Thermococcus celer

The ability to rationally engineer a protein with altered stability depends upon the detailed understanding of the role of noncovalent interactions in defining thermodynamic properties of proteins. In this paper, we used T. celer L30e as a model to address the question of the role of charge-charge interactions in defining the stability of this protein. A total of 26 single-site charge-to-alanine variants of this protein were generated, and the stability of these proteins was determined using thermal- and denaturant-induced unfolding. It was found that, although L30e is isolated from a thermophilic organism and is highly thermostable, some of the substitutions lead to a further increase in the transition temperature. Analysis of the effects of high ionic strength on the stabilities of L30e variants shows that the long-range charge-charge interactions are as important as the short-range (salt bridge) interactions. The changes in stabilities of the T. celer L30e protein variants were compared with the changes in the energy of charge-charge interactions calculated using different computational models. It was found that there is a good qualitative agreement between experimental and calculated data: for 70-80% (19-21 of 26, confidence p < 0.003) of the variants, computational models predict correctly the sign of the stability changes. In particular, computational models identify correctly those charged amino acid residue substitutions of which led to enhancement in thermostability. Thus, optimization of the charge-charge interactions might be a useful approach for the rational increase in protein stability.

Predicting Reactivities of Protein Surface Cysteines as Part of a Strategy for Selective Multiple Labeling†

A variety of biophysical methods used to study proteins requires protein modification using conjugated molecular probes. Cysteine is the main residue that can be modified without the risk of altering other residues in the protein chain. It is possible to label several cysteines in a protein using highly selective labeling reactions, if the cysteines react at very different rates. The reactivity of a cysteine residue introduced into an exposed surface site depends on the fraction of cysteine in the deprotonated state. Here, it is shown that cysteine reactivity differences can be effectively predicted by an electrostatic model that yields site-specifically the fractions of cysteinate. The model accounts for electrostatic interactions between the cysteinyl anion and side chains, the local protein backbone, and water. The energies of interaction with side chains and the main chain are calculated by using the two different dielectric constants, 40 and 22, respectively. Twenty-six mutants of Escherichia coli adenylate kinase were produced, each containing a single cysteine at the protein surface, and the rates of the reaction with 5,5'-dithiobis(2-nitrobenzoic acid) (Ellman's reagent) were measured. Cysteine residues were chosen on the basis of locations that were expected to allow modification of the protein with minimal risk of perturbing its structure. The reaction rates spanned a range of 6 orders of magnitude. The correlation between predicted fractions of cysteinate and measured reaction rates was strong (R = 92%) and especially high (R = 97%) for cysteines at the helix termini. The approach developed here allows reasonably fast, automated screening of protein surfaces to identify sites that permit efficient preparations of double- or triple-labeled protein.

Effects of pH, salt, and macromolecular crowding on the stability of FK506-binding protein: an integrated experimental and theoretical study

Environmental variables can exert significant influences on the folding stability of a protein, and elucidating these influences provides insight on the determinants of protein stability. Here, experimental data on the stability of FKBP12 are reported for the effects of three environmental variables: pH, salt, and macromolecular crowding. In the pH range of 5-9, contribution to the pH dependence of the unfolding free energy from residual charge-charge interactions in the unfolded state was found to be negligible. The negligible contribution was attributed to the lack of sequentially nearest neighboring charged residues around groups that titrate in the pH range. KCl lowered the stability of FKBP12 and the E31Q/D32N double mutant at small salt concentrations but raised stability after approximately 0.5 M salt. Such a turnover behavior was accounted for by the balance of two opposing types of protein-salt interactions: the Debye-Hückel type, modeling the response of the ions to protein charges, favors the unfolded state while the Kirkwood type, accounting for the disadvantage of the ions moving toward the low-dielectric protein cavity from the bulk solvent, disfavors the unfolded state. Ficoll 70 as a crowding agent was found to have a modest effect on protein stability, in qualitative agreement with a simple model suggesting that the folded and unfolded states are nearly equally adversely affected by macromolecular crowding. For any environmental variable, it is the balance of its effects on the folded and unfolded states that determines the outcome on the folding stability.

Energy Functions for Protein Design: Adjustment with Protein–Protein Complex Affinities, Models for the Unfolded State, and Negative Design of Solubility and Specificity

The development of the EGAD program and energy function for protein design is described. In contrast to most protein design methods, which require several empirical parameters or heuristics such as patterning of residues or rotamers, EGAD has a minimalist philosophy; it uses very few empirical factors to account for inaccuracies resulting from the use of fixed backbones and discrete rotamers in protein design calculations, and describes the unfolded state, aggregates, and alternative conformers explicitly with physical models instead of fitted parameters. This approach unveils important issues in protein design that are often camouflaged by heuristic-emphasizing methods. Inter-atom energies are modeled with the OPLS-AA all-atom forcefield, electrostatics with the generalized Born continuum model, and the hydrophobic effect with a solvent-accessible surface area-dependent term. Experimental characterization of proteins designed with an unmodified version of the energy function revealed problems with under-packing, stability, aggregation, and structural specificity. Under-packing was addressed by modifying the van der Waals function. By optimizing only three parameters, the effects of >400 mutations on protein-protein complex formation were predicted to within 1.0 kcal mol(-1). As an independent test, this modified energy function was used to predict the stabilities of >1500 mutants to within 1.0 kcal mol(-1); this required a physical model of the unfolded state that includes more interactions than traditional tripeptide-based models. Solubility and structural specificity were addressed with simple physical approximations of aggregation and conformational equilibria. The complete energy function can design protein sequences that have high levels of identity with their natural counterparts, and have predicted structural properties more consistent with soluble and uniquely folded proteins than the initial designs.

Computational protein design is a challenge for implicit solvation models

Increasingly complex schemes for representing solvent effects in an implicit fashion are being used in computational analyses of biological macromolecules. These schemes speed up the calculations by orders of magnitude and are assumed to compromise little on essential features of the solvation phenomenon. In this work we examine this assumption. Five implicit solvation models, a surface area-based empirical model, two models that approximate the generalized Born treatment and a finite difference Poisson-Boltzmann method are challenged in situations differing from those where these models were calibrated. These situations are encountered in automatic protein design procedures, whose job is to select sequences, which stabilize a given protein 3D structure, from a large number of alternatives. To this end we evaluate the energetic cost of burying amino acids in thousands of environments with different solvent exposures belonging, respectively, to decoys built with random sequences and to native protein crystal structures. In addition we perform actual sequence design calculations. Except for the crudest surface area-based procedure, all the tested models tend to favor the burial of polar amino acids in the protein interior over nonpolar ones, a behavior that leads to poor performance in protein design calculations. We show, on the other hand, that three of the examined models are nonetheless capable of discriminating between the native fold and many nonnative alternatives, a test commonly used to validate force fields. It is concluded that protein design is a particularly challenging test for implicit solvation models because it requires accurate estimates of the solvation contribution of individual residues. This contrasts with native recognition, which depends less on solvation and more on other nonbonded contributions.

Charge sequence coding in statistical modeling of unfolded proteins

Unfolded proteins recently attracted attention due to accumulation of experimental evidences for their significant role in different life processes. Modeling of electrostatic interactions (EI) in unfolded state of proteins is becoming increasingly important as well. In this paper, we stress on the importance of how the sequence of charged residues of a given protein is incorporated into the models for calculation of EI in the unfolded state. On the basis of the distributions of distances between titratable sites of charged residues calculated for polypeptide chains of various compositions, it was found that the distance distribution for a pair of residues, located close to each other along the sequence of a protein, depends on what residues constitute the pair in question. It was concluded that the consideration of these residue-specific distributions is essential for a statistical model to be accurate from the physical point of view. It was suggested that use of distance intervals in the spherical model of unfolded proteins accounts better for the charge sequence than the set of single distance values. This was illustrated by comparison of the pK values of the titratable groups of the unfolded N-terminal SH3 domain of the Drosophila protein drk to the available experimental data.