On the entropy of protein folding

Mechanistic Modeling of Amyloid Oligomer and Protofibril Formation in Bovine Insulin

Early phase of amyloid formation, where prefibrillar aggregates such as oligomers and protofibrils are often observed, is crucial for understanding pathogenesis. However, the detailed mechanisms of their formation have been difficult to elucidate because they tend to form transiently and heterogeneously. Here, we found that bovine insulin protofibril formation proceeds in a monodisperse manner, which allowed us to characterize the detailed early aggregation process by light scattering in combination with thioflavin T fluorescence and Fourier transform infrared spectroscopy. The protofibril formation was specific to bovine insulin, whereas no significant aggregation was observed in human insulin. The kinetic analysis combining static and dynamic light scattering data revealed that the protofibril formation process in bovine insulin can be divided into two steps based on fractal dimension. When modeling the experimental data based on Smoluchowski aggregation kinetics, an aggregation scheme consisting of initial fractal aggregation forming spherical oligomers and their subsequent end-to-end association forming protofibrils was clarified. Furthermore, the analysis of temperature and salt concentration dependencies showed that the end-to-end association is the rate-limiting step, involving dehydration. The established model for protofibril formation, wherein oligomers are incorporated as a precursor, provides insight into the molecular mechanism by which protein molecules assemble during the early stage of amyloid formation.

The "Beacon" Structural Model of Protein Folding: Application for Trp-Cage in Water

Protein folding is a process in which a polypeptide must undergo folding process to obtain its three-dimensional structure. Thermodynamically, it is a process of enthalpy to overcome the loss of conformational entropy in folding. Folding is primarily related to hydrophobic interactions and intramolecular hydrogen bondings. During folding, hydrophobic interactions are regarded to be the driving forces, especially in the initial structural collapse of a protein. Additionally, folding is guided by the strong interactions within proteins, such as intramolecular hydrogen bondings related to the α-helices and β-sheets of proteins. Therefore, a protein is divided into the folding key (FK) regions related to intramolecular hydrogen bondings and the non-folding key (non-FK) regions. Various conformations are expected for FK and non-FK regions. Different from non-FK regions, it is necessary for FK regions to form the specific conformations in folding, which are regarded as the necessary folding pathways (or "beacons"). Additionally, sequential folding is expected for the FK regions, and the intermediate state is found during folding. They are reflected on the local basins in the free energy landscape (FEL) of folding. To demonstrate the structural model, molecular dynamics (MD) simulations are conducted on the folding pathway of the TRP-cage in water.

Evolution and folding of repeat proteins

Repeat proteins are made with tandem copies of similar amino acid stretches that fold into elongated architectures. These proteins constitute excellent model systems to investigate how evolution relates to structure, folding, and function. Here, we propose a scheme to map evolutionary information at the sequence level to a coarse-grained model for repeat-protein folding and use it to investigate the folding of thousands of repeat proteins. We model the energetics by a combination of an inverse Potts-model scheme with an explicit mechanistic model of duplications and deletions of repeats to calculate the evolutionary parameters of the system at the single-residue level. These parameters are used to inform an Ising-like model that allows for the generation of folding curves, apparent domain emergence, and occupation of intermediate states that are highly compatible with experimental data in specific case studies. We analyzed the folding of thousands of natural Ankyrin repeat proteins and found that a multiplicity of folding mechanisms are possible. Fully cooperative all-or-none transitions are obtained for arrays with enough sequence-similar elements and strong interactions between them, while noncooperative element-by-element intermittent folding arose if the elements are dissimilar and the interactions between them are energetically weak. Additionally, we characterized nucleation-propagation and multidomain folding mechanisms. We show that the global stability and cooperativity of the repeating arrays can be predicted from simple sequence scores.

Entropy Perspectives of Molecular and Evolutionary Biology

Attempts to find and quantify the supposed low entropy of organisms and its preservation are revised. The absolute entropy of the mixed components of non-living biomass (approximately −1.6 × 10³ J K⁻¹ L⁻¹) is the reference to which other entropy decreases would be ascribed to life. The compartmentation of metabolites and the departure from the equilibrium of metabolic reactions account for reductions in entropy of 1 and 40–50 J K⁻¹ L⁻¹, respectively, and, though small, are distinctive features of living tissues. DNA and proteins do not supply significant decreases in thermodynamic entropy, but their low informational entropy is relevant for life and its evolution. No other living feature contributes significantly to the low entropy associated with life. The photosynthetic conversion of radiant energy to biomass energy accounts for most entropy (2.8 × 10⁵ J K⁻¹ carbon kg⁻¹) produced by living beings. The comparatively very low entropy produced in other processes (approximately 4.8 × 10² J K⁻¹ L⁻¹ day⁻¹ in the human body) must be rapidly exported outside as heat to preserve low entropy decreases due to compartmentation and non-equilibrium metabolism. Enzymes and genes are described, whose control minimizes the rate of production of entropy and could explain selective pressures in biological evolution and the rapid proliferation of cancer cells.

On the Dependence of Prion and Amyloid Structure on the Folding Environment

Currently available analyses of amyloid proteins reveal the necessity of the existence of radical structural changes in amyloid transformation processes. The analysis carried out in this paper based on the model called fuzzy oil drop (FOD) and its modified form (FOD-M) allows quantifying the role of the environment, particularly including the aquatic environment. The starting point and basis for the present presentation is the statement about the presence of two fundamentally different methods of organizing polypeptides into ordered conformations—globular proteins and amyloids. The present study shows the source of the differences between these two paths resulting from the specificity of the external force field coming from the environment, including the aquatic and hydrophobic one. The water environment expressed in the fuzzy oil drop model using the 3D Gauss function directs the folding process towards the construction of a micelle-like system with a hydrophobic core in the central part and the exposure of polarity on the surface. The hydrophobicity distribution of membrane proteins has the opposite characteristic: Exposure of hydrophobicity at the surface of the membrane protein with an often polar center (as in the case of ion channels) is expected. The structure of most proteins is influenced by a more or less modified force field generated by water through the appropriate presence of a non-polar (membrane-like) environment. The determination of the proportion of a factor different from polar water enables the assessment of the protein status by indicating factors favoring the structure it represents.

Structural Refolding and Thermal Stability of Myoglobin in the Presence of Mixture of Crowders: Importance of Various Interactions for Protein Stabilization in Crowded Conditions

The intracellular environment is overcrowded with a range of molecules (small and large), all of which influence protein conformation. As a result, understanding how proteins fold and stay functional in such crowded conditions is essential. Several in vitro experiments have looked into the effects of macromolecular crowding on different proteins. However, there are hardly any reports regarding small molecular crowders used alone and in mixtures to observe their effects on the structure and stability of the proteins, which mimics of the cellular conditions. Here we investigate the effect of different mixtures of crowders, ethylene glycol (EG) and its polymer polyethylene glycol (PEG 400 Da) on the structural and thermal stability of myoglobin (Mb). Our results show that monomer (EG) has no significant effect on the structure of Mb, while the polymer disrupts its structure and decreases its stability. Conversely, the additive effect of crowders showed structural refolding of the protein to some extent. Moreover, the calorimetric binding studies of the protein showed very weak interactions with the mixture of crowders. Usually, we can assume that soft interactions induce structural perturbations while exclusion volume effects stabilize the protein structure; therefore, we hypothesize that under in vivo crowded conditions, both phenomena occur and maintain the stability and function of proteins.

A higher flexibility at the SARS-CoV-2 main protease active site compared to SARS-CoV and its potentialities for new inhibitor virtual screening targeting multi-conformers

The main-protease (Mpro) catalyzes a crucial step for the SARS-CoV-2 life cycle. The recent SARS-CoV-2 presents the main protease (MCoV2pro) with 12 mutations compared to SARS-CoV (MCoV1pro). Recent studies point out that these subtle differences lead to mobility variances at the active site loops with functional implications. We use metadynamics simulations and a sort of computational analysis to probe the dynamic, pharmacophoric and catalytic environment differences between the monomers of both enzymes. So, we verify how much intrinsic distinctions are preserved in the functional dimer of MCoV2pro, as well as its implications for ligand accessibility and optimized drug screening. We find a significantly higher accessibility to open binding conformers in the MCoV2pro monomer compared to MCoV1pro. A higher hydration propensity for the MCoV2pro S2 loop with the A46S substitution seems to exercise a key role. Quantum calculations suggest that the wider conformations for MCoV2pro are less catalytically active in the monomer. However, the statistics for contacts involving the N-finger suggest higher maintenance of this activity at the dimer. Docking analyses suggest that the ability to vary the active site width can be important to improve the access of the ligand to the active site in different ways. So, we carry out a multiconformational virtual screening with different ligand bases. The results point to the importance of taking into account the protein conformational multiplicity for new promissors anti MCoV2pro ligands. We hope these results will be useful in prospecting, repurposing and/or designing new anti SARS-CoV-2 drugs.Communicated by Ramaswamy H. Sarma.

Nucleotide-induced folding of cell division protein FtsZ from Staphylococcus aureus

The essential bacterial division protein FtsZ uses GTP binding and hydrolysis to assemble into dynamic filaments that treadmill around the Z-ring, guiding septal wall synthesis and cell division. FtsZ is a structural homolog of tubulin and a target for discovering new antibiotics. Here, using FtsZ from the pathogen S. aureus (SaFtsZ), we reveal that, prior to assembly, FtsZ monomers require nucleotide binding for folding; this is possibly relevant to other mesophilic FtsZs. Apo-SaFtsZ is essentially unfolded, as assessed by nuclear magnetic resonance and circular dichroism. Binding of GTP (≥ 1 mm) dramatically shifts the equilibrium toward the active folded protein. Supportingly, SaFtsZ refolded with GDP crystallizes in a native structure. Apo-SaFtsZ also folds with 3.4 m glycerol, enabling high-affinity GTP binding (K_D 20 nm determined by isothermal titration calorimetry) similar to thermophilic stable FtsZ. Other stabilizing agents that enhance nucleotide binding include ethylene glycol, trimethylamine N-oxide, and several bacterial osmolytes. High salt stabilizes SaFtsZ without bound nucleotide in an inactive twisted conformation. We identified a cavity behind the SaFtsZ-GDP nucleotide-binding pocket that harbors different small compounds, which is available for extended nucleotide-replacing inhibitors. Furthermore, we devised a competition assay to detect any inhibitors that overlap the nucleotide site of SaFtsZ, or Escherichia coli FtsZ, employing osmolyte-stabilized apo-FtsZs and the specific fluorescence anisotropy change in mant-GTP upon dissociation from the protein. This robust assay provides a basis to screening for high-affinity GTP-replacing ligands, which combined with structural studies and phenotypic profiling should facilitate development of a next generation of FtsZ-targeting antibacterial inhibitors.

Thermal stability modulation of the native and chemically-unfolded state of bovine serum albumin by amino acids

Cells are crowded with various cosolutes including salts, osmolytes, nucleic acids, peptides and proteins.

Factors Stabilizing β-Sheets in Protein Structures from a Quantum-Chemical Perspective

Protein folds are determined by the interplay between various (de)stabilizing forces, which can be broadly divided into a local strain of the protein chain and intramolecular interactions. In contrast to the α-helix, the β-sheet secondary protein structure is significantly stabilized by long-range interactions between the individual β-strands. It has been observed that quite diverse amino acid sequences can form a very similar small β-sheet fold, such as in the three-β-strand WW domain. Employing "calibrated" quantum-chemical methods, we show herein on two sequentially diverse examples of the WW domain that the internal strain energy is higher in the β-strands and lower in the loops, while the interaction energy has an opposite trend. Low strain energy computed for peptide sequences in the loop 1 correlates with its postulated early formation in the folding process. The relatively high strain energy within the β-strands (up to 8 kcal mol^-1 per amino acid residue) is compensated by even higher intramolecular interaction energy (up to 15 kcal mol^-1 per residue). It is shown in a quantitative way that the most conserved residues across the structural family of WW domains have the highest contributions to the intramolecular interaction energy. On the other hand, the residues in the regions with the lowest strain are not conserved. We conclude that the internal interaction energy is the physical quantity tuned by evolution to define the β-sheet protein fold.

Dynamics of Dystrophin's Actin-Binding Domain

We have used pulsed electron paramagnetic resonance, calorimetry, and molecular dynamics simulations to examine the structural mechanism of binding for dystrophin's N-terminal actin-binding domain (ABD1) and compare it to utrophin's ABD1. Like other members of the spectrin superfamily, dystrophin's ABD1 consists of two calponin-homology (CH) domains, CH1 and CH2. Several mutations within dystrophin's ABD1 are associated with the development of severe degenerative muscle disorders Duchenne and Becker muscular dystrophies, highlighting the importance of understanding its structural biology. To investigate structural changes within dystrophin ABD1 upon binding to actin, we labeled the protein with spin probes and measured changes in inter-CH domain distance using double-electron electron resonance. Previous studies on the homologous protein utrophin showed that actin binding induces a complete structural opening of the CH domains, resulting in a highly ordered ABD1-actin complex. In this study, double-electron electron resonance shows that dystrophin ABD1 also undergoes a conformational opening upon binding F-actin, but this change is less complete and significantly more structurally disordered than observed for utrophin. Using molecular dynamics simulations, we identified a hinge in the linker region between the two CH domains that grants conformational flexibility to ABD1. The conformational dynamics of both dystrophin's and utrophin's ABD1 showed that compact conformations driven by hydrophobic interactions are preferred and that extended conformations are energetically accessible through a flat free-energy surface. Considering that the binding free energy of ABD1 to actin is on the order of 6-7 kcal/mole, our data are compatible with a mechanism in which binding to actin is largely dictated by specific interactions with CH1, but fine tuning of the binding affinity is achieved by the overlap between conformational ensembles of ABD1 free and bound to actin.

Probabilistic analysis for identifying the driving force of protein folding

Toward identifying the driving force of protein folding, energetics was analyzed in water for Trp-cage (20 residues), protein G (56 residues), and ubiquitin (76 residues) at their native (folded) and heat-denatured (unfolded) states. All-atom molecular dynamics simulation was conducted, and the hydration effect was quantified by the solvation free energy. The free-energy calculation was done by employing the solution theory in the energy representation, and it was seen that the sum of the protein intramolecular (structural) energy and the solvation free energy is more favorable for a folded structure than for an unfolded one generated by heat. Probabilistic arguments were then developed to determine which of the electrostatic, van der Waals, and excluded-volume components of the interactions in the protein-water system governs the relative stabilities between the folded and unfolded structures. It was found that the electrostatic interaction does not correspond to the preference order of the two structures. The van der Waals and excluded-volume components were shown, on the other hand, to provide the right order of preference at probabilities of almost unity, and it is argued that a useful modeling of protein folding is possible on the basis of the excluded-volume effect.

A component analysis of the free energies of folding of 35 proteins: A consensus view on the thermodynamics of folding at the molecular level

What factors favor protein folding? This is a textbook question. Parsing the experimental free energies of folding/unfolding into diverse enthalpic and entropic components of solute and solvent favoring or disfavoring folding is not an easy task. In this study, we present a computational protocol for estimating the free energy contributors to protein folding semi-quantitatively using ensembles of unfolded and native states generated via molecular dynamics simulations. We tested the methodology on 35 proteins with diverse structural motifs and sizes and found that the calculated free energies correlate well with experiment (correlation coefficient ∼ 0.85), enabling us to develop a consensus view of the energetics of folding. As a more sensitive test of the methodology, we also investigated the free energies of folding of an additional 33 single point mutants and obtained a correlation coefficient of 0.8. A notable observation is that the folding free energy components appear to carry signatures of the fold (SCOP classification) of the protein. © 2017 Wiley Periodicals, Inc.

The Dynameomics Entropy Dictionary: A Large-Scale Assessment of Conformational Entropy across Protein Fold Space

Molecular dynamics (MD) simulations contain considerable information with regard to the motions and fluctuations of a protein, the magnitude of which can be used to estimate conformational entropy. Here we survey conformational entropy across protein fold space using the Dynameomics database, which represents the largest existing data set of protein MD simulations for representatives of essentially all known protein folds. We provide an overview of MD-derived entropies accounting for all possible degrees of dihedral freedom on an unprecedented scale. Although different side chains might be expected to impose varying restrictions on the conformational space that the backbone can sample, we found that the backbone entropy and side chain size are not strictly coupled. An outcome of these analyses is the Dynameomics Entropy Dictionary, the contents of which have been compared with entropies derived by other theoretical approaches and experiment. As might be expected, the conformational entropies scale linearly with the number of residues, demonstrating that conformational entropy is an extensive property of proteins. The calculated conformational entropies of folding agree well with previous estimates. Detailed analysis of specific cases identifies deviations in conformational entropy from the average values that highlight how conformational entropy varies with sequence, secondary structure, and tertiary fold. Notably, α-helices have lower entropy on average than do β-sheets, and both are lower than coil regions.

Knowledge-based entropies improve the identification of native protein structures

Evaluating protein structures requires reliable free energies with good estimates of both potential energies and entropies. Although there are many demonstrated successes from using knowledge-based potential energies, computing entropies of proteins has lagged far behind. Here we take an entirely different approach and evaluate knowledge-based conformational entropies of proteins based on the observed frequencies of contact changes between amino acids in a set of 167 diverse proteins, each of which has two alternative structures. The results show that charged and polar interactions break more often than hydrophobic pairs. This pattern correlates strongly with the average solvent exposure of amino acids in globular proteins, as well as with polarity indices and the sizes of the amino acids. Knowledge-based entropies are derived by using the inverse Boltzmann relationship, in a manner analogous to the way that knowledge-based potentials have been extracted. Including these new knowledge-based entropies almost doubles the performance of knowledge-based potentials in selecting the native protein structures from decoy sets. Beyond the overall energy-entropy compensation, a similar compensation is seen for individual pairs of interacting amino acids. The entropies in this report have immediate applications for 3D structure prediction, protein model assessment, and protein engineering and design.

Kinetic study on bonding reaction of gelatin with CdS nanopaticles by UV-visible spectroscopy

The chemical kinetics on gelatin-CdS direct conjugates has been systematically investigated as a function of different temperature and reactant concentration (i.e. Cd(2+), S(2-) and gelatin) by UV-visible spectroscopy, for the first time. The nonlinear fitting and the differential method were used to calculate the initial rate based on the absorbance-time data. A double logarithmic linear equation for calculating the rate constant (k) and the reaction order (n) was introduced. The reaction kinetic parameters (n, k, Ea, and Z) and activation thermodynamic parameters (ΔG(≠), ΔH(≠), and ΔS(≠)) were obtained from variable temperature kinetic studies. The overall rate equation allowing evaluation of conditions that provide required reaction rate could be expressed as: r = 1.11 × 10(8) exp(-4971/T)[Cd(2+)][gelatin](0.6)[S(2-)](0.6) (M/S) The calculated values of the reaction rate are well coincide with the experimental results. A suitable kinetic model is also proposed. This work will provide guidance for the rational design of gelatin-directed syntheses of metal sulfide materials, and help to understand the biological effects of nanoparticles at the molecular level.

Loss of conformational entropy in protein folding calculated using realistic ensembles and its implications for NMR-based calculations

The loss of conformational entropy is a major contribution in the thermodynamics of protein folding. However, accurate determination of the quantity has proven challenging. We calculate this loss using molecular dynamic simulations of both the native protein and a realistic denatured state ensemble. For ubiquitin, the total change in entropy is TΔSTotal = 1.4 kcal⋅mol(-1) per residue at 300 K with only 20% from the loss of side-chain entropy. Our analysis exhibits mixed agreement with prior studies because of the use of more accurate ensembles and contributions from correlated motions. Buried side chains lose only a factor of 1.4 in the number of conformations available per rotamer upon folding (ΩU/ΩN). The entropy loss for helical and sheet residues differs due to the smaller motions of helical residues (TΔShelix-sheet = 0.5 kcal⋅mol(-1)), a property not fully reflected in the amide N-H and carbonyl C=O bond NMR order parameters. The results have implications for the thermodynamics of folding and binding, including estimates of solvent ordering and microscopic entropies obtained from NMR.

Notable Stabilization of α-Chymotrypsin by the Protic Ionic Additive, [ch][dhp]: Calorimetric Evidence for a Fine Enthalpy/Entropy Balance

An impact of 0.5 to 3 M choline dihydrogen phosphate, [ch][dhp], the biotechnologically relevant ionic substance, on the thermal stability of a model globular protein, α-chymotrypsin (α-CT), has been studied exploiting the highly sensitive differential scanning calorimetry (DSC) technique. The notable overall stabilizing effect of 11 ± 2 K regarding the thermal transition (melting) temperature, T m , has been detected. For this kind of series, for the first time, the calorimetric melting enthalpy (ΔH cal) and transition entropy (ΔS m ) parameters have been determined simultaneously throughout. The first analysis indicated a two-phase impact implying (a) the initial, dramatic drop in both ΔH cal and ΔS m , obviously connected to specific, direct interaction between the [ch][dhp] components and α-CT's charged groups (within 0 to 1 mol/L [ch][dhp]), leading to the essential rearrangement of the interfacial hydrogen-bonded (HB) network; and (b) the follow-up (within 1 to 3.0 mol/L [ch][dhp]), modest changes in ΔH cal and lack of changes in ΔS m , seemingly connected with a subsequent steady strengthening of already reformed HB network, respectively. These changes, presumably, are primarily facilitated by Coulombic interactions between the [dhp] anions and solvent-exposed positively charged amino groups of α-CT.

Context and force field dependence of the loss of protein backbone entropy upon folding using realistic denatured and native state ensembles

The loss of conformational entropy is the largest unfavorable quantity affecting a protein's stability. We calculate the reduction in the number of backbone conformations upon folding using the distribution of backbone dihedral angles (ϕ,ψ) obtained from an experimentally validated denatured state model, along with all-atom simulations for both the denatured and native states. The average loss of entropy per residue is TΔS(BB)(U-N) = 0.7, 0.9, or 1.1 kcal·mol(-1) at T = 298 K, depending on the force field used, with a 0.6 kcal·mol(-1) dispersion across the sequence. The average equates to a decrease of a factor of 3-7 in the number of conformations available per residue (f = Ω(Denatured)/Ω(Native)) or to a total of f(tot) = 3(n)-7(n) for an n residue protein. Our value is smaller than most previous estimates where f = 7-20, that is, our computed TΔS(BB)(U-N) is smaller by 10-100 kcal mol(-1) for n = 100. The differences emerge from our use of realistic native and denatured state ensembles as well as from the inclusion of accurate local sequence preferences, neighbor effects, and correlated motions (vibrations), in contrast to some previous studies that invoke gross assumptions about the entropy in either or both states. We find that the loss of entropy primarily depends on the local environment and less on properties of the native state, with the exception of α-helical residues in some force fields.

Contribution of hydrophobic interactions to protein stability

Our goal was to gain a better understanding of the contribution of hydrophobic interactions to protein stability. We measured the change in conformational stability, Δ(ΔG), for hydrophobic mutants of four proteins: villin headpiece subdomain (VHP) with 36 residues, a surface protein from Borrelia burgdorferi (VlsE) with 341 residues, and two proteins previously studied in our laboratory, ribonucleases Sa and T1. We compared our results with those of previous studies and reached the following conclusions: (1) Hydrophobic interactions contribute less to the stability of a small protein, VHP (0.6±0.3 kcal/mol per -CH(2)- group), than to the stability of a large protein, VlsE (1.6±0.3 kcal/mol per -CH(2)- group). (2) Hydrophobic interactions make the major contribution to the stability of VHP (40 kcal/mol) and the major contributors are (in kilocalories per mole) Phe18 (3.9), Met13 (3.1), Phe7 (2.9), Phe11 (2.7), and Leu21 (2.7). (3) Based on the Δ(ΔG) values for 148 hydrophobic mutants in 13 proteins, burying a -CH(2)- group on folding contributes, on average, 1.1±0.5 kcal/mol to protein stability. (4) The experimental Δ(ΔG) values for aliphatic side chains (Ala, Val, Ile, and Leu) are in good agreement with their ΔG(tr) values from water to cyclohexane. (5) For 22 proteins with 36 to 534 residues, hydrophobic interactions contribute 60±4% and hydrogen bonds contribute 40±4% to protein stability. (6) Conformational entropy contributes about 2.4 kcal/mol per residue to protein instability. The globular conformation of proteins is stabilized predominantly by hydrophobic interactions.

Biochemical comparisons of osteoarthritic human synovial fluid with calf sera used in knee simulator wear testing

Osteoarthritic human synovial fluid was obtained from the knees of 20 patients and was compared with four different calf sera solutions frequently used as lubricants in knee simulator wear testing. Assuming that the fluid after arthroplasty was the same as the fluid in patients with osteoarthritis, the total protein concentration, protein constituent fractions, osmolality, trace element concentrations, and the thermal stability obtained via differential scanning calorimetry were determined. Human synovial fluid, with an average total protein concentration of 34 g/L, was significantly different from all undiluted calf sera. However, alpha-calf serum and iron-supplemented alpha-calf serum were closest in protein constituent fractions (albumin, alpha-1-globulin, alpha-2-globulin, ss-globulin, and gamma-globulin) to human synovial fluid. Diluting calf sera with low-ion distilled water to a total protein concentration of 17 g/L (as recommended by ISO 14243) produced non-clinically relevant total protein concentration and osmolality levels. Performing the same dilution of iron-supplemented alpha-calf serum with phosphate-buffered saline solution and 1.5 g/L hyaluronic acid produced an artificial lubricant with both a clinically relevant level of osmolality and clinically relevant thermal stability as seen in human synovial fluid from patients with osteoarthritis. The present study suggested that alpha-calf serum, phosphate-buffered saline solution and hyaluronic acid were essential constituents of an artificial lubricant to mimic the major biochemical properties of human synovial fluid for simulator wear testing of total knee replacements.

Computing protein stabilities from their chain lengths

New amino acid sequences of proteins are being learned at a rapid rate, thanks to modern genomics. The native structures and functions of those proteins can often be inferred using bioinformatics methods. We show here that it is also possible to infer the stabilities and thermal folding properties of proteins, given only simple genomics information: the chain length and the numbers of charged side chains. In particular, our model predicts DeltaH(T), DeltaS(T), DeltaC(p), and DeltaF(T)--the folding enthalpy, entropy, heat capacity, and free energy--as functions of temperature T; the denaturant m values in guanidine and urea; the pH-temperature-salt phase diagrams, and the energy of confinement F(s) of the protein inside a cavity of radius s. All combinations of these phase equilibria can also then be computed from that information. As one illustration, we compute the pH and salt conditions that would denature a protein inside a small confined cavity. Because the model is analytical, it is computationally efficient enough that it could be used to automatically annotate whole proteomes with protein stability information.

Modeling of folding and unfolding mechanisms in alanine-based alpha-helical polypeptides

alpha-Helix formation is known to be opposed by the entropy loss due to the folding and favored by the energy of molecular interactions. However, the underlying mechanism of these factors is still being discussed. Here we have used the experimental and calculation data for short alanine-based peptides embedded in water to model the mechanism of helix folding and unfolding and to calculate microscopically the free energy factors of alanine in the frame of helix coil conformational integrals. Classical helix-coil transition theories take into account the interactions in a peptide chain only if the i, i + 3 peptide bond participates in hydrogen bonding. But quantum mechanical calculations showed that interactions of the i, i + 2 peptide bond play an important role in helix folding too. We also included the short-range repulsive interactions due to molecular steric clashes and the end effects due to polar/hydrogen-bonding interactions at the N and C termini. The helix and coil regions of peptide conformational space were defined using an experimental steric criterion for hydrogen bonding. Arginine helix propensity was discussed and estimated. Monte Carlo numerical simulations of thermodynamics and kinetics for the 21 amino acid alpha-helical polypeptide Ac-A5(AAARA)3A-NMe were carried out and found to be in an agreement with the experimental results.

Changes in thermodynamic quantities upon contact of two solutes in solvent under isochoric and isobaric conditions

The changes in excess thermodynamic quantities upon the contact of two solutes immersed in a solvent are analyzed using the radial-symmetric and three-dimensional versions of the integral equation theory. A simple model mimicking a solute in water is employed. The solute-solute interaction energy is not included in the calculations. Under the isochoric condition, the solute contact always leads to a positive entropy change irrespective of the solute solvophobicity or solvophilicity. The energy change is negative for solvophobic solutes while it is positive for solvophilic ones. Under the isobaric condition, the contact of solvophobic solutes results in system-volume compression but that of solvophilic ones gives rise to expansion. Effects of the compression and expansion on the changes in enthalpy and entropy are enlarged with rising temperature. When the solute solvophobicity is sufficiently high, the entropy change (multiplied by the absolute temperature) can become negative due to the compression, except at low temperatures with the result of an even larger, negative enthalpy change. The expansion in the case of solvophilic solutes leads to a large, positive entropy change accompanied by an even larger, positive enthalpy change. The changes in enthalpy and entropy are strongly dependent on the temperature. However, the changes in enthalpy and entropy are largely cancelled out and the temperature dependency of the free-energy change is much weaker. The authors also discuss possible relevance to the enthalpy-entropy compensation experimentally known for a variety of physicochemical processes in aqueous solution such as protein folding.

Cofactor effects on the protein folding reaction: acceleration of alpha-lactalbumin refolding by metal ions

About 30% of proteins require cofactors for their proper folding. The effects of cofactors on the folding reaction have been investigated with alpha-lactalbumin as a model protein and metal ions as cofactors. Metal ions accelerate the refolding of alpha-lactalbumin by lessening the energy barrier between the molten globule state and the transition state, mainly by decreasing the difference of entropy between the two states. These effects are linked to metal ion binding to the protein in the native state. Hence, relationships between the metal affinities for the intermediate states and those for the native state are observed. Some residual specificity for the calcium ion is still observed in the molten globule state, this specificity getting closer in the transition state to that of the native state. The comparison between kinetic and steady-state data in association with the Phi value method indicates the binding of the metal ions on the unfolded state of alpha-lactalbumin. Altogether, these results provide insight into cofactor effects on protein folding. They also suggest new possibilities to investigate the presence of residual native structures in the unfolded state of protein and the effects of such structures on the protein folding reaction and on protein stability.

Effects of co-operative ligand binding on protein amide NH hydrogen exchange

Amide protection factors have been determined from NMR measurements of hydrogen/deuterium amide NH exchange rates measured on assigned signals from Lactobacillus casei apo-DHFR and its binary and ternary complexes with trimethoprim (TMP), folinic acid and coenzymes (NADPH/NADP(+)). The substantial sizes of the residue-specific DeltaH and TDeltaS values for the opening/closing events in NH exchange for most of the measurable residues in apo-DHFR indicate that sub-global or global rather than local exchange mechanisms are usually involved. The amide groups of residues in helices and sheets are those most protected in apo-DHFR and its complexes, and the protection factors are generally related to the tightness of ligand binding. The effects of ligand binding that lead to changes in amide protection are not localised to specific binding sites but are spread throughout the structure via a network of intramolecular interactions. Although the increase in protein stability in the DHFR.TMP.NADPH complex involves increased ordering in the protein structure (requiring TDeltaS energy) this is recovered, to a large extent, by the stronger binding (enthalpic DeltaH) interactions made possible by the reduced motion in the protein. The ligand-induced protection effects in the ternary complexes DHFR.TMP.NADPH (large positive binding co-operativity) and DHFR.folinic acid.NADPH (large negative binding co-operativity) mirror the co-operative effects seen in the ligand binding. For the DHFR.TMP.NADPH complex, the ligand-induced protection factors result in DeltaDeltaG(o) values for many residues being larger than the DeltaDeltaG(o) values in the corresponding binary complexes. In contrast, for DHFR.folinic acid.NADPH, the DeltaDeltaG(o) values are generally smaller than many of those in the corresponding binary complexes. The results indicate that changes in protein conformational flexibility on formation of the ligand complex play an important role in determining the co-operativity in the ligand binding.

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

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

The Study of Protein Folding and Dynamics by Determination of Intramolecular Distance Distributions and Their Fluctuations Using Ensemble and Single-Molecule FRET Measurements

The folding and dynamics of globular proteins is a multidimensional problem. The structures of the heterogeneous population of refolding protein molecules are characterized by multiple distances and time constants. Deciphering the mechanism of folding depends on studies of the processes rather than the folded structures alone. Spectroscopy is indispensable for these sorts of studies. Herein, it is shown that the determination of intramolecular distance distributions by ensemble and single-molecule FRET experiments enable the exploration of partially folded states of refolding protein molecules.

Stabilizing roles of residual structure in the empty heme binding pockets and unfolded states of microsomal and mitochondrial apocytochrome b5

The microsomal (Mc) and mitochondrial (OM) isoforms of mammalian cytochrome b5 are the products of different genes, which likely arose via duplication of a primordial gene and subsequent functional divergence. Despite sharing essentially identical folds, heme-polypeptide interactions are stronger in OM b5s than in Mc b5s due to the presence of two conserved patches of hydrophobic amino acid side chains in the OM heme binding pockets. This is of fundamental interest in terms of understanding heme protein structure-function relationships, because stronger heme-polypeptide interactions in OM b5s in comparison to Mc b5s may represent a key source of their more negative reduction potentials. Herein we provide evidence that interactions amongst the amino acid side chains contributing to the hydrophobic patches in rat OM (rOM) b5 persist when heme is removed, rendering the empty heme binding pocket of rOM apo-b5 more compact and less conformationally dynamic than that in bovine Mc (bMc) apo-b5. This may contribute to the stronger heme binding by OM apo-b5 by reducing the entropic penalty associated with polypeptide folding. We also show that when bMc apo-b5 unfolds it adopts a structure that is more compact and contains greater nonrandom secondary structure content than unfolded rOM apo-b5. We propose that a more robust beta-sheet in Mc apo-b5s compensates for the absence of the hydrophobic packing interactions that stabilize the heme binding pocket in OM apo-b5s.

Helical Shifts Generate Two Distinct Conformers in the Atomic Resolution Structure of the CheA Phosphotransferase Domain from Thermotoga maritima

Helical histidine phosphotransferase (HPt) domains play a central role in many aspects of bacterial signal transduction. The 0.98 A resolution crystallographic structure of the amino-terminal HPt domain (P1) from the chemotaxis kinase CheA of Thermotoga maritima reveals a remarkable degree of structural heterogeneity within a four-helix bundle. Two of the four helices have alternate main-chain conformations that differ by a 1.3-1.7A shift along the bundle axis. These dual conformers were only resolved with atomic resolution diffraction data and their inclusion significantly improved refinement statistics. Neither conformer optimizes packing within the helical core, consistent with their nearly equal refined occupancies. Altered hydrogen bonding within an inter-helical loop may facilitate transition between conformers. Two discrete structural states rather than a continuum of closely related conformations indicates an energetic barrier to conversion between conformers in the crystal at 100K, although many more states are expected in solution at physiological temperatures. Anisotropic atomic thermal B factors within the two conformers indicate modest overall atomic displacement that is largest perpendicular to the helical bundle and not along the direction of apparent motion. Despite the conformational heterogeneity of P1 in the crystal at low temperature, the protein displays high thermal stability in solution (T(m)=100 degrees C). Addition of a variable C-terminal region that corresponds to a mobile helix in other CheA structures significantly narrows the temperature width of the unfolding transition and may affect domain dynamics. Helices that compose the kinase recognition site and contain the phospho-accepting His45 do not have alternate conformations. In this region, atomic resolution provides detailed structural parameters for a conserved hydrogen-bonding network that tunes the reactivity of His45. A neighboring glutamate (E67), essential for phosphotransferase activity hydrogen bonds directly to His45 N(delta1). E67 generates a negative electrostatic surface surrounding the reactive His that is conserved by most CheA kinases, but absent in related phosphotransferase proteins. The P1 conformations that we observe are likely relevant to other helical or coiled-coil proteins and may be important for generating switches in signaling processes.

The temperature dependence of the hydrogen exchange in the SH3 domain of alpha-spectrin

The amide hydrogen-deuterium exchange (HX) in the Src homology region 3 (SH3) domain of alpha-spectrin has been measured by nuclear magnetic resonance as a function of temperature between 8 and 46 degrees C. The analysis of the temperature dependence of HX from a statistical thermodynamic point of view has allowed us to estimate the enthalpies and entropies of the conformational processes leading to HX. The results indicate that under native conditions the domain undergoes a wide variety of conformational fluctuations, ranging from local motions, mainly located in loops, turns and chain ends and involving only low enthalpy and entropy, to extensive structural disruptions affecting its core and involving enthalpies and entropies that come fairly close to those observed during global unfolding.

Thermodynamics of a diffusional protein folding reaction

The folding reactions of several proteins are well described as diffusional barrier crossing processes, which suggests that they should be analyzed by Kramers' rate theory rather than by transition state theory. For the cold shock protein Bc-Csp from Bacillus caldolyticus, we measured stability and folding kinetics, as well as solvent viscosity as a function of temperature and denaturant concentration. Our analysis indicates that diffusional folding reactions can be treated by transition state theory, provided that the temperature and denaturant dependence of the solvent viscosity is properly accounted for, either at the level of the measured rate constants or of the calculated activation parameters. After viscosity correction the activation barriers for folding become less enthalpic and more entropic. The transition from an enthalpic to an entropic folding barrier with increasing temperature is, however, apparent in the data before and after this correction. It is a consequence of the negative activation heat capacity of refolding, which is independent of solvent viscosity. Bc-Csp and its mesophilic homolog Bs-CspB from Bacillus subtilis differ strongly in stability but show identical enthalpic and entropic barriers to refolding. The increased stability of Bc-Csp originates from additional enthalpic interactions that are established after passage through the activated state. As a consequence, the activation enthalpy of unfolding is increased relative to Bs-CspB.

Speeding protein folding beyond the G(o) model: how a little frustration sometimes helps

By perturbing a G(o) model toward a realistic protein Hamiltonian by adding non-native interactions, we find that the folding rate is in general enhanced as ruggedness is initially increased, as long as the protein is sufficiently large and flexible. Eventually, the rate drops rapidly toward zero when ruggedness significantly slows conformational transitions. Energy landscape arguments for thermodynamics and kinetics are coupled with a treatment of non-native collapse to elucidate this effect.

Dramatic structural and thermodynamic consequences of repacking a protein's hydrophobic core

BACKGROUND

Rop is an RNA binding, dimeric, four-helix bundle protein with a well-defined, regular hydrophobic core ideally suited for redesign studies. A family of Rop variants in which the hydrophobic core was systematically redesigned has previously been created and characterized.

RESULTS

We present a structural and thermodynamic analysis of Ala2Ile2-6, a variant of Rop with an extensively redesigned hydrophobic core. The structure of Ala2Ile2-6 reveals a completely new fold formed by a conformational "flip" of the two protomers around the dimeric interface. The free-energy profile of Ala2Ile2-6 is also very different from that of wild-type Rop. Ala2Ile2-6 has a higher melting temperature than Rop, but undergoes a slightly smaller free-energy change on unfolding.

CONCLUSIONS

The structure of Ala2Ile2-6, along with molecular modeling results, demonstrate the importance of tight packing of core residues and the adoption of favorable core side chain rotamer values in determining helix-helix interactions in the four-helix bundle fold. Structural disorder at the N and C termini of Ala2Ile2-6 provides a basis for the large differences in the enthalpy and entropy of Ala2Ile2-6 folding compared with wildtype Rop.

A systematic study of the vibrational free energies of polypeptides in folded and random states

Molecular vibrations, especially low frequency motions, may be used as an indication of the rigidity or the flatness of the protein folding energy landscape. We have studied the vibrational properties of native folded as well as random coil structures of more than 60 polypeptides. The picture we obtain allows us to perceive how and why the energy landscape progressively rigidifies while still allowing potential flexibility. Compared with random coil structures, both alpha-helices and beta-hairpins are vibrationally more flexible. The vibrational properties of loop structures are similar to those of the corresponding random coil structures. Inclusion of an alpha-helix tends to rigidify peptides and so-called building blocks of the structure, whereas the addition of a beta-structure has less effect. When small building blocks coalesce to form larger domains, the protein rigidifies. However, some folded native conformations are still found to be vibrationally more flexible than random coil structures, for example, beta(2)-microglobulin and the SH3 domain. Vibrational free energy contributes significantly to the thermodynamics of protein folding and affects the distribution of the conformational substates. We found a weak correlation between the vibrational folding energy and the protein size, consistent with both previous experimental estimates and theoretical partition of the heat capacity change in protein folding.

A study on the enthalpy-entropy compensation in protein unfolding

A large number of thermodynamic data including the free energy, enthalpy, entropy, and heat capacity changes were collected for the denaturation of various proteins. Regression indicated that remarkable enthalpy-entropy compensation occurred in protein unfolding, which meant that the change in enthalpy was almost compensated by a corresponding change in entropy resulting in a smaller net free energy change. This behavior was proposed to result from the water molecule reorganization, which contributed significantly to the enthalpy and entropy changes but little to the free energy change in protein unfolding. It turned out that the enthalpy-entropy compensation could provide novel insights into the problem of enthalpy and entropy convergence in protein unfolding.

Conformational analysis of a farnesyltransferase peptide inhibitor, CVIM

The conformational states of the peptide Cys-Val-Ile-Met (or CVIM) were computed and characterized. CVIM inhibits farnesylation of the Ras oncogene product, p21ras, at the cysteine residue of the C-terminal segment. CVIM is active in an extended conformation. A similar peptide (KTKCVFM) appears to bind the enzyme in the Type I bend conformation. In the present study, the conformations of CVIM were computed in an aqueous environment with the peptide in the zwitterionic state. Solvation free energy based on solvent accessible surface area and a distance dependent dielectric were used in the calculations. Final conformations of multiple independent Monte Carlo simulated annealing (MCSA) conformational searches were used as starting points for Metropolis Monte Carlo (MMC) runs. Conformations saved at intervals during MMC runs were analyzed. Conformers were separated by interactive clustering in dihedral angle coordinates. The four lowest energy conformers corresponding to a Type I bend, extended, AB-bend, and BA-bend were within 0.3 kcal/mol of each other, and dominant in terms of population. The Type I bend and extended conformers were supported by the binding studies. The extended conformer was the most populated. In the AB-bend conformer, 'A' indicates the alpha-helix conformation of Val, and 'B' indicates the beta-strand conformation of Ile. The AB- and BA-bend conformations differed from the extended conformation in the value of Val psi and Ile psi, respectively, and from the Type I bend conformation in the value of Ile psi and Val psi, respectively. The four lowest energy conformers were characterized in terms of energy, density of low energy conformations (or entropy), structure, side chain rotamer fraction population, and interatomic distances.