Native Topology of the Designed Protein Top7 is Not Conducive to Cooperative Folding

Many single-domain proteins with <100 residues fold cooperatively; but the recently designed 92-residue Top7 protein exhibits clearly non-two-state behaviors. In apparent agreement with experiment, we found that coarse-grained, native-centric chain models, including potentials with and without elementary desolvation barriers, predicted that Top7 has a stable intermediate state in which the C-terminal fragment is folded while the rest of the chain remains disordered. We observed noncooperative folding in Top7 models that incorporated nonnative hydrophobic interactions as well. In contrast, free energy profiles deduced from models with desolvation barriers for a set of thirteen natural proteins with similar chain lengths and secondary structure elements suggested that they fold much more cooperatively than Top7. Buttressed by related studies on smaller natural proteins with chain lengths of ∼40 residues, our findings argue that the de novo native topology of Top7 likely imposed a significant restriction on the cooperativity achievable by any design for this target structure.     

Prediction of Protein-Protein Interaction Sites Using Electrostatic Desolvation Profiles

Protein-protein complex formation involves removal of water from the interface region. Surface regions with a small free energy penalty for water removal or desolvation may correspond to preferred interaction sites. A method to calculate the electrostatic free energy of placing a neutral low-dielectric probe at various protein surface positions has been designed and applied to characterize putative interaction sites. Based on solutions of the finite-difference Poisson equation, this method also includes long-range electrostatic contributions and the protein solvent boundary shape in contrast to accessible-surface-area-based solvation energies. Calculations on a large set of proteins indicate that in many cases (>90%), the known binding site overlaps with one of the six regions of lowest electrostatic desolvation penalty (overlap with the lowest desolvation region for 48% of proteins). Since the onset of electrostatic desolvation occurs even before direct protein-protein contact formation, it may help guide proteins toward the binding region in the final stage of complex formation. It is interesting that the probe desolvation properties associated with residue types were found to depend to some degree on whether the residue was outside of or part of a binding site. The probe desolvation penalty was on average smaller if the residue was part of a binding site compared to other surface locations. Applications to several antigen-antibody complexes demonstrated that the approach might be useful not only to predict protein interaction sites in general but to map potential antigenic epitopes on protein surfaces.     

Temperature dependence of the free energy landscape of the src-SH3 protein domain

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.     

Optimal docking area: a new method for predicting protein-protein interaction sites

Understanding energetics and mechanism of protein-protein association remains one of the biggest theoretical problems in structural biology. It is assumed that desolvation must play an essential role during the association process, and indeed protein-protein interfaces in obligate complexes have been found to be highly hydrophobic. However, the identification of protein interaction sites from surface analysis of proteins involved in non-obligate protein-protein complexes is more challenging. Here we present Optimal Docking Area (ODA), a new fast and accurate method of analyzing a protein surface in search of areas with favorable energy change when buried upon protein-protein association. The method identifies continuous surface patches with optimal docking desolvation energy based on atomic solvation parameters adjusted for protein-protein docking. The procedure has been validated on the unbound structures of a total of 66 non-homologous proteins involved in non-obligate protein-protein hetero-complexes of known structure. Optimal docking areas with significant low-docking surface energy were found in around half of the proteins. The 'ODA hot spots' detected in X-ray unbound structures were correctly located in the known protein-protein binding sites in 80% of the cases. The role of these low-surface-energy areas during complex formation is discussed. Burial of these regions during protein-protein association may favor the complexed configurations with near-native interfaces but otherwise arbitrary orientations, thus driving the formation of an encounter complex. The patch prediction procedure is freely accessible at http://www.molsoft.com/oda and can be easily scaled up for predictions in structural proteomics.     

Prediction of the mutation-induced change in thermodynamic stabilities of membrane proteins from free energy simulations

Comparative protein structure modeling and free energy perturbation simulation have been applied in a consecutive manner to investigate the mutation-induced stabilization of membrane proteins (MPs) in aqueous solution without knowledge of their three-dimensional structures. The calculated difference in protein solvation free energy between the wild type and a mutant compares well with their relative thermodynamic stabilities in solution. For monomeric MPs, a mutant reveals a higher stability than the wild type if the calculated solvation free energy indicates a favorable change. On the contrary, for oligomeric MPs the stability of a mutant increases as the solvation free energy of a mutated monomer becomes less favorable, indicating that the oligomeric MP mutant would be stabilized in solution due to the reduced desolvation cost for oligomerization. The present computational strategy is expected to find its way as a useful tool for assessing the relative stability of a mutant MP with respect to its wild type in solution.     

Theoretical study of interaction of winter flounder antifreeze protein with ice

Antifreeze proteins (AFPs) are synthesized by various organisms to enable their cells to survive subzero environment. These proteins bind to small ice crystals and inhibit their growth, which if left uncontrolled would be fatal to cells. The crystal structures of a number of AFPs have been determined; however, crystallographic analysis of AFP-ice complex is nearly impossible. Molecular modeling studies of AFPs' interaction with ice surface is therefore invaluable. Early models of AFP-ice interaction suggested H-bond as the primary driving force behind such interaction. Recent experimental evidence, however, suggested that hydrophobic interactions could be the main contributor to AFP-ice association. All computational studies published to date were carried out to verify the H-bond model, and no works attempting to verify the hydrophobic interaction model have been published. In this work, we Monte Carlo-minimized complexes of several AFPs with ice taking into account nonbonded interactions, H-bonds, and the hydration potential for proteins. Parameters of the hydration potential for ice were developed with the assumption that the free energy of the water-ice association should be close to zero at equilibrium melting temperature. Our calculations demonstrate that desolvation of hydrophobic groups in the AFPs upon their binding to the grooves at the ice surface is indeed the major stabilizing contributor to the free energy of AFP-ice binding. This study is consistent with available structural and mutation data on AFPs. In particular, it explains the paradoxical finding that substitution of Thr residues with Val does not affect the potency of winter flounder AFP whereas substitution with Ser abolished its antifreeze activity.     

Study of the "molten globule" intermediate state in protein folding by a hydrophobic fluorescent probe

Binding of the hydrophobic fluorescent probe, 1-anilino-naphthalene-8-sulfonate (ANS), to synthetic polypeptides and proteins with a different structural organization has been studied. It has been shown that ANS has a much stronger affinity to the protein "molten globule" state, with a pronounced secondary structure and compactness, but without a tightly packed tertiary structure as compared with its affinity to the native and coil-like proteins, or to coil-like, alpha-helical, or beta-structural hydrophilic homopolypeptides. The possibility of using ANS for the study of equilibrium and kinetic molten globule intermediates is demonstrated, with carbonic anhydrase, beta-lactamase, and alpha-lactalbumin as examples.     

The interaction of gamma-crystallins with model surfaces.

Three biophysical techniques were employed to study the structure and thermal stability of a series of homologous bovine lens gamma-crystallins upon binding to three model surfaces. The surfaces in order of increasing hydrophobicity were silica, methyl silica, and diphenyl silica. Secondary structure was analyzed by deconvolution Fourier transform infrared spectroscopy, while tertiary structure alterations were probed by front surface fluorescence spectroscopy. The effect of surface binding on protein thermal stability was analyzed by fluorescence and differential scanning calorimetry. The comparison of free and surface-bound protein with variations in the electrostatic and hydrophobic character of both the protein and the adsorbent surface with these techniques demonstrated that: (i) destabilization on hydrophobic surfaces is greater than on a more hydrophilic interface, (ii) detectable conformational changes tend to increase as the hydrophobicity of the surface increases, and (iii) subtle structural differences among proteins can play an important role in determining differences in protein stability and structure upon surface adsorption.     

Protein stabilization by salt bridges: concepts, experimental approaches and clarification of some misunderstandings

Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each other to experience electrostatic attraction. They contribute to protein structure and to the specificity of interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein's free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three components: charge-charge interactions, interactions of charges with permanent dipoles, and desolvation of charges. Energetically favorable Coulombic charge-charge interaction is opposed by often unfavorable desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pK(a) approach and the mutation approach. In the pK(a) approach, the contribution of charges to the free energy of unfolding of a protein is obtained from the change of pK(a) of ionizable groups caused by altered electrostatic interactions upon folding of the protein. The pK(a) approach provides the relative free energy gained or lost when ionizable groups are being charged. In the mutation approach, the coupling free energy between interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and approximate measure of the free energy of charge-charge interaction. Neither the pK(a) approach nor the mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on concepts and on the assessment of experimental methods and does not cover the vast literature.     

Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.     

Helix capping in the GCN4 leucine zipper.

Capping interactions associated with specific sequences at or near the ends of alpha-helices are important determinants of the stability of protein secondary and tertiary structure. We investigate here the role of the helix-capping motif Ser-X-X-Glu, a sequence that occurs frequently at the N termini of alpha helices in proteins, on the conformation and stability of the GCN4 leucine zipper. The 1.8 A resolution crystal structure of the capped molecule reveals distinct conformations, packing geometries and hydrogen-bonding networks at the amino terminus of the two helices in the leucine zipper dimer. The free energy of helix stabilization associated with the hydrogen-bonding and hydrophobic interactions in this capping structure is -1.2 kcal/mol, evaluated from thermal unfolding experiments. A single cap thus contributes appreciably to stabilizing the terminated helix and thereby the native state. These results suggest that helix capping plays a further role in protein folding, providing a sensitive connector linking alpha-helix formation to the developing tertiary structure of a protein.     

Role of non-covalent interactions for determining the folding rate of two-state proteins

Understanding the factors influencing the folding rate of proteins is a challenging problem. In this work, we have analyzed the role of non-covalent interactions for the folding rate of two-state proteins by free-energy approach. We have computed the free-energy terms, hydrophobic, electrostatic, hydrogen-bonding and van der Waals free energies. The hydrophobic free energy has been divided into the contributions from different atoms, carbon, neutral nitrogen and oxygen, charged nitrogen and oxygen, and sulfur. All the free-energy terms have been related with the folding rates of 28 two-state proteins with single and multiple correlation coefficients. We found that the hydrophobic free energy due to carbon atoms and hydrogen-bonding free energy play important roles to determine the folding rate in combination with other free energies. The normalized energies with total number of residues showed better results than the total energy of the protein. The comparison of amino acid properties with free-energy terms indicates that the energetic terms explain better the folding rate than amino acid properties. Further, the combination of free energies with topological parameters yielded the correlation of 0.91. The present study demonstrates the importance of topology for determining the folding rate of two-state proteins.     

Exploring structures in protein folding funnels with free energy functionals: the denatured ensemble

We discuss the formulation of free energy functionals that describe the formation of structure in partially folded proteins. These free energy functionals take into account the inhomogeneous nature of contact energies, chain entropy and cooperative contributions reflecting the many body character of some folding forces like hydrophobicity, but do not directly account for non-native contacts because they assume the validity of the minimal frustration principle. We show how the free energy functionals can be used to interpret experiments on partially folded proteins that probe the fractional occupancy of specific local structures. In particular, we study the hydrogen protection factors in lysozyme studied in transient experiments by Gladwin and Evans and by Nash and Jonas using equilibrium pressure denaturation and the NMR order parameters measured by Dobson and Kim for the homologous protein alpha-lactalbumin.     

Probing the initial stage of aggregation of the Abeta(10-35)-protein: assessing the propensity for peptide dimerization

Characterization of the early stages of peptide aggregation is of fundamental importance in elucidating the mechanism of the formation of deposits associated with amyloid disease. The initial step in the pathway of aggregation of the Abeta-protein, whose monomeric NMR structure is known, was studied through the simulation of the structure and stability of the peptide dimer in aqueous solution. A protocol based on shape complementarity was used to generate an assortment of possible dimer structures. The structures generated based on shape complementarity were evaluated using rapidly computed estimates of the desolvation and electrostatic interaction energies to identify a putative stable dimer structure. The potential of mean force associated with the dimerization of the peptides in aqueous solution was computed for both the hydrophobic and the electrostatic driven forces using umbrella sampling and classical molecular dynamics simulation at constant temperature and pressure with explicit solvent and periodic boundary conditions. The comparison of the two free energy profiles suggests that the structure of the peptide dimer is determined by the favorable desolvation of the hydrophobic residues at the interface. Molecular dynamics trajectories originating from two putative dimer structures indicate that the peptide dimer is stabilized primarily through hydrophobic interactions, while the conformations of the peptide monomers undergo substantial structural reorganization in the dimerization process. The finding that the phi-dimer may constitute the ensemble of stable Abeta(10-35) dimer has important implications for fibril formation. In particular, the expulsion of water molecules at the interface might be a key event, just as in the oligomerization of Abeta(16-22) fragments. We conjecture that events prior to the nucleation process themselves might involve crossing free energy barriers which depend on the peptide-peptide and peptide-water interactions. Consistent with existing experimental studies, the peptides within the ensemble of aggregated states show no signs of formation of secondary structure.     

Rapid formation of secondary structure framework in protein folding studied by stopped-flow circular dichroism

Kinetic refolding reactions of ferricytochrome c and beta-lactoglobulin have been studied by stopped-flow circular dichroism by monitoring rapid ellipticity changes of peptide backbone and side-chain chromophores. In both proteins, a transient intermediate accumulates within the dead time of stopped-flow mixing (18 ms), and the intermediate has an appreciable amount of secondary structure but possesses an unfolded tertiary structure. It is suggested that the rapid formation of a secondary structure framework in protein folding is a common property observed in a variety of globular proteins.     

Analysis of the heat capacity dependence of protein folding.

This paper presents an analysis of plots of enthalpy versus heat capacity change at 25 degrees C for the unfolding of proteins and for the dissolution of gaseous, liquid and solid solutes, first reported by Murphy, Privalov & Gill. The negative slope in the enthalpy plot for proteins is interpreted as arising from a large penalty associated with burying polar groups in the protein interior. The small enthalpy changes that accompany protein unfolding at 25 degrees C are also discussed. It is argued that the combined effects of hydrogen bond formation and close packing predict a large positive enthalpy of unfolding. Electrostatic calculations indicate that the penalty associated with burying polar groups is large enough to effectively cancel these terms, leading to the small net enthalpy changes that are observed. The free energy changes associated with protein folding are also discussed. The free energy cost of burying polar groups largely compensates for the stabilizing contribution of the hydrophobic effect and would appear to account for the fact that proteins are marginally stable, independent of their size and of their relative hydrophobicities.     

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures

Assuming that the protein primary sequence contains all information required to fold a protein into its native tertiary structure, we propose a new computational approach to protein folding by distributing the total energy of the macromolecular system along the torsional axes.We further derive a new semiempirical equation to calculate the total energy of a macromolecular system including its free energy of solvation. The energy of solvation makes an important contribution to the stability of biological structures. The segregation of hydrophilic and hydrophobic domains is essential for the formation of micelles, lipid bilayers, and biological membranes, and it is also important for protein folding. The free energy of solvation consists of two components: one derived from interactions between the atoms of the protein, and the second resulting from interactions between the protein and the solvent. The latter component is expressed as a function of the fractional area of protein atoms accessible to the solvent.The protein-folding procedure described in this article consists of two successive steps: a theoretical transition from an ideal α helix to an ideal β sheet is first imposed on the protein conformation, in order to calculate an initial secondary structure. The most stable secondary structure is built from a combination of the lowest energy structures calculated for each amino acid during this transition. An angular molecular dynamics step is then applied to this secondary structure. In this computational step, the total energy of the system consisting of the sum of the torsional energy, the van der Waals energy, the electrostatic energy, and the solvation energy is minimized. This process yields 3-D structures of minimal total energy that are considered to be the most probable native-like structures for the protein.This method therefore requires no prior hypothesis about either the secondary or the tertiary structure of the protein and restricts the input of data to its sequence. The validity of the results is tested by comparing the crystalline and computed structures of four proteins, i.e., the avian and bovine pancreatic polypeptide (36 residues each), uteroglobin (70 residues), and the calcium-binding protein (75 residues); the C_α-C_α maps show significant homologies and the position of secondary structure domains; that of the α helices is particularly close.     

Modeling of denatured state for calculation of the electrostatic contribution to protein stability

Existing models of the denatured state of proteins consider only one possible spatial distribution of protein charges and therefore are applicable to a limited number of cases. In this article, a more general framework for the modeling of the denatured state is proposed. It is based on the assumption that the titratable groups of an unfolded protein can adopt a quasi-random distribution restricted by the protein sequence. The model was applied for the calculations of electrostatic interactions in two proteins, barnase and N-terminal domain of the ribosomal protein L9. The calculated free energy of denaturation, DeltaG(pH), reproduces the experimental data better than the commonly used null approximation (NA). It was shown that the seemingly good agreement with experimental data obtained by NA originates from the compensatory effect between the pairwise electrostatic interactions and the desolvation energy of the individual sites. It was also found that the ionization properties of denatured proteins are influenced by the protein sequence.     

Molecular theory of lipid-protein interaction and the Lalpha-HII transition.

We present a molecular-level theory for lipid-protein interaction and apply it to the study of lipid-mediated interactions between proteins and the protein-induced transition from the planar bilayer (Lalpha) to the inverse-hexagonal (HII) phase. The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different size and shape, e.g., "cylinder-like," "barrel-like," or "vase-like." We assume strong hydrophobic coupling between the protein and its neighbor lipids. This means that, if necessary, the flexible lipid chains surrounding the protein will stretch, compress, and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the unperturbed bilayer. The system free energy is expressed as an integral over local molecular contributions, the latter accounting for interheadgroup repulsion, hydrocarbon-water surface energy, and chain stretching-tilting effects. We show that the molecular interaction constants are intimately related to familiar elastic (continuum) characteristics of the membrane, such as the bending rigidity and spontaneous curvature, as well as to the less familiar tilt modulus. The equilibrium configuration of the membrane is determined by minimizing the free energy functional, subject to boundary conditions dictated by the size, shape, and spatial distribution of inclusions. A similar procedure is used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal phases. Two degrees of freedom are involved in the variational minimization procedure: the local length and local tilt angle of the lipid chains. The inclusion of chain tilt is particularly important for studying noncylindrical (for instance, barrel-like) inclusions and analyzing the structure of the HII lipid phase; e.g., we find that chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal phase. Consistent with experiment, we find that only short peptides (large negative mismatch) can induce the Lalpha --> HII transition. At the transition, a peptide-poor Lalpha phase coexists with a peptide-rich HII phase.