Structure based prediction of protein folding intermediates

Structural and Energetic Characterization of the Denatured State from the Perspectives of Peptides, the Coil Library, and Intrinsically Disordered Proteins

The α and polyproline II (PPII) basins are the two most populated regions of the Ramachandran map when constructed from the protein coil library, a widely used denatured state model built from the segments of irregular structure found in the Protein Data Bank. This indicates the α and PPII conformations are dominant components of the ensembles of denatured structures that exist in solution for biological proteins, an observation supported in part by structural studies of short, and thus unfolded, peptides. Although intrinsic conformational propensities have been determined experimentally for the common amino acids in short peptides, and estimated from surveys of the protein coil library, the ability of these intrinsic conformational propensities to quantitatively reproduce structural behavior in intrinsically disordered proteins (IDPs), an increasingly important class of proteins in cell function, has thus far proven elusive to establish. Recently, we demonstrated that the sequence dependence of the mean hydrodynamic size of IDPs in water and the impact of heat on the coil dimensions, provide access to both the sequence dependence and thermodynamic energies that are associated with biases for the α and PPII backbone conformations. Here, we compare results from peptide-based studies of intrinsic conformational propensities and surveys of the protein coil library to those of the sequence-based analysis of heat effects on IDP hydrodynamic size, showing that a common structural and thermodynamic description of the protein denatured state is obtained.

Impact of Heat on Coil Hydrodynamic Size Yields the Energetics of Denatured State Conformational Bias

Conformational equilibria in the protein denatured state have key roles regulating folding, stability, and function. The extent of conformational bias in the protein denatured state under folding conditions, however, has thus far proven elusive to quantify, particularly with regard to its sequence dependence and energetic character. To better understand the structural preferences of the denatured state, we analyzed both the sequence dependence to the mean hydrodynamic size of disordered proteins in water and the impact of heat on the coil dimensions, showing that the sequence dependence and thermodynamic energies associated with intrinsic biases for the α and polyproline II (PPII) backbone conformations can be obtained. Experiments that evaluate how the hydrodynamic size changes with compositional changes in the protein reveal amino acid specific preferences for PPII that are in good quantitative agreement with calorimetry-measured values from unfolded peptides and those inferred by survey of the protein coil library. At temperatures above 25 °C, the denatured state follows the predictions of a PPII-dominant ensemble. Heat effects on coil hydrodynamic size indicate the α bias is comparable to the PPII bias at cold temperatures. Though historically thought to give poor resolution to structural details, the hydrodynamic size of the unfolded state is found to be an effective reporter on the extent of the biases for the α and PPII backbone conformations.

Sequence Reversal Prevents Chain Collapse and Yields Heat-Sensitive Intrinsic Disorder

Sequence patterns of charge, hydrophobicity, hydrogen bonding, and other amino acid physicochemical properties contribute to mechanisms of protein folding, but how sequence composition and patterns influence the conformational dynamics of the denatured state ensemble is not fully understood. To investigate structure-sequence relationships in the denatured state, we reversed the sequence of staphylococcal nuclease and characterized its structure, thermodynamic character, and hydrodynamic radius using circular dichroism spectroscopy, dynamic light scattering, analytical ultracentrifugation, and size-exclusion chromatography as a function of temperature. The macromolecular size of "Retro-nuclease" is highly expanded in solution with characteristics similar to biological intrinsically disordered proteins. In contradistinction to a disordered state, Retro-nuclease exhibits a broad sigmoid transition of its hydrodynamic dimensions as temperature is increased, indicating a thermodynamically controlled compaction. Counterintuitively, the magnitude of these temperature-induced hydrodynamic changes exceed that observed from thermal denaturation of folded unaltered staphylococcal nuclease. Undetectable by calorimetry and intrinsic tryptophan fluorescence, the lack of heat capacity or fluorescence changes throughout the thermal transition indicate canonical hydrophobic collapse did not drive the Retro-nuclease structural transitions. Temperature-dependent circular dichroism spectroscopy performed on Retro-nuclease and computer simulations correlate to temperature sensitivity in the intrinsic sampling of backbone conformations for polyproline II and α-helix. The experimental results indicate a role for sequence direction in mediating the collapse of the polypeptide chain, whereas the simulation trends illustrate the generality of the observed heat effects on disordered protein structure.

Prp40 Homolog A Is a Novel Centrin Target

Pre-mRNA processing protein 40 (Prp40) is a nuclear protein that has a role in pre-mRNA splicing. Prp40 possesses two leucine-rich nuclear export signals, but little is known about the function of Prp40 in the export process. Another protein that has a role in protein export is centrin, a member of the EF-hand superfamily of Ca²⁺-binding proteins. Prp40 was found to be a centrin target by yeast-two-hybrid screening using both Homo sapiens centrin 2 (Hscen2) and Chlamydomonas reinhardtii centrin (Crcen). We identified a centrin-binding site within H. sapiens Prp40 homolog A (HsPrp40A), which contains a hydrophobic triad W₁L₄L₈ that is known to be important in the interaction with centrin. This centrin-binding site is highly conserved within the first nuclear export signal consensus sequence identified in Saccharomyces cerevisiae Prp40. Here, we examine the interaction of HsPrp40A peptide (HsPrp40Ap) with both Hscen2 and Crcen by isothermal titration calorimetry. We employed the thermodynamic parameterization to estimate the polar and apolar surface area of the interface. In addition, we have defined the molecular mechanism of thermally induced unfolding and dissociation of the Crcen-HsPrp40Ap complex using two-dimensional infrared correlation spectroscopy. These complementary techniques showed for the first time, to our knowledge, that HsPrp40Ap interacts with centrin in vitro, supporting a coupled functional role for these proteins in pre-mRNA splicing.

Structural Stability of the Coiled-Coil Domain of Tumor Susceptibility Gene (TSG)-101

The tumor susceptibility gene-101 coiled coil domain (TSG101cc) is an integral component of the endosomal maturation machinery and cytokinesis, and also interacts with several transcription factors. The TSG101cc has been crystallized as a homotetramer but is known to interact with two of its binding partners as a heterotrimer. To investigate this apparent discrepancy, we examined the solution thermodynamics of the TSG101cc. Here, we use circular dichroism, differential scanning calorimetry, analytical ultracentrifugation, fluorescence, and structural thermodynamic analysis to investigate the structural stability and the unfolding of the TSG101cc. We demonstrate that TSG101cc exists in solution primarily as a tetramer, which unfolds in a two-state manner. Surprisingly, no homodimeric or homotrimeric species were detected. Structural thermodynamic analysis of the homotetrameric structure and comparison with known oligomeric coiled-coils suggests that the TSG101cc homotetramer is comparatively unstable on a per residue basis. Furthermore, the homotrimeric coiled-coil is predicted to be much less stable than the functional heterotrimeric coiled-coil in the endosomal sorting complex required for transport 1 (ESCRT1). These results support a model whereby the tetramer–monomer equilibrium of TSG101 serves as the cellular reservoir of TSG101, which is effectively outcompeted when its binding partners are present and the heteroternary complex can form.

Entropic stabilization of a deubiquitinase provides conformational plasticity and slow unfolding kinetics beneficial for functioning on the proteasome

Human ubiquitin C-terminal hydrolyase UCH-L5 is a topologically knotted deubiquitinase that is activated upon binding to the proteasome subunit Rpn13. The length of its intrinsically disordered cross-over loop is essential for substrate recognition. Here, we showed that the catalytic domain of UCH-L5 exhibits higher equilibrium folding stability with an unfolding rate on the scale of 10⁻⁸ s⁻¹, over four orders of magnitudes slower than its paralogs, namely UCH-L1 and -L3, which have shorter cross-over loops. NMR relaxation dynamics analysis confirmed the intrinsic disorder of the cross-over loop. Hydrogen deuterium exchange analysis further revealed a positive correlation between the length of the cross-over loop and the degree of local fluctuations, despite UCH-L5 being thermodynamically and kinetically more stable than the shorter UCHs. Considering the role of UCH-L5 in removing K48-linked ubiquitin to prevent proteasomal degradation of ubiquitinated substrates, our findings offered mechanistic insights into the evolution of UCH-L5. Compared to its paralogs, it is entropically stabilized to withstand mechanical unfolding by the proteasome while maintaining structural plasticity. It can therefore accommodate a broad range of substrate geometries at the cost of unfavourable entropic loss.

Intrinsic α helix propensities compact hydrodynamic radii in intrinsically disordered proteins

Proteins that lack tertiary stability under normal conditions, known as intrinsically disordered, exhibit a wide range of biological activities. Molecular descriptions for the biology of intrinsically disordered proteins (IDPs) consequently rely on disordered structural models, which in turn require experiments that assess the origins to structural features observed. For example, while hydrodynamic size is mostly insensitive to sequence composition in chemically denatured proteins, IDPs show strong sequence-specific effects in the hydrodynamic radius (R_h ) when measured under normal conditions. To investigate sequence-modulation of IDP R_h , disordered ensembles generated by a hard sphere collision model modified with a structure-based parameterization of the solution energetics were used to parse the contributions of net charge, main chain dihedral angle bias, and excluded volume on hydrodynamic size. Ensembles for polypeptides 10-35 residues in length were then used to establish power-law scaling relationships for comparison to experimental R_h from 26 IDPs. Results showed the expected outcomes of increased hydrodynamic size from increases in excluded volume and net charge, and compaction from chain-solvent interactions. Chain bias representing intrinsic preferences for α helix and polyproline II (PP_II ), however, modulated R_h with intricate dependence on the simulated propensities. PP_II propensities at levels expected in IDPs correlated with heightened R_h sensitivity to even weak α helix propensities, indicating bias for common (φ, ψ) are important determinants of hydrodynamic size. Moreover, data show that IDP R_h can be predicted from sequence with good accuracy from a small set of physicochemical properties, namely intrinsic conformational propensities and net charge. Proteins 2017; 85:296-311. © 2016 Wiley Periodicals, Inc.

Hydrodynamic Radii of Intrinsically Disordered Proteins Determined from Experimental Polyproline II Propensities

The properties of disordered proteins are thought to depend on intrinsic conformational propensities for polyproline II (PP_II) structure. While intrinsic PP_II propensities have been measured for the common biological amino acids in short peptides, the ability of these experimentally determined propensities to quantitatively reproduce structural behavior in intrinsically disordered proteins (IDPs) has not been established. Presented here are results from molecular simulations of disordered proteins showing that the hydrodynamic radius (R_h) can be predicted from experimental PP_II propensities with good agreement, even when charge-based considerations are omitted. The simulations demonstrate that R_h and chain propensity for PP_II structure are linked via a simple power-law scaling relationship, which was tested using the experimental R_h of 22 IDPs covering a wide range of peptide lengths, net charge, and sequence composition. Charge effects on R_h were found to be generally weak when compared to PP_II effects on R_h. Results from this study indicate that the hydrodynamic dimensions of IDPs are evidence of considerable sequence-dependent backbone propensities for PP_II structure that qualitatively, if not quantitatively, match conformational propensities measured in peptides.

Molecular models of disordered protein structures are needed to elucidate the functional mechanisms of intrinsically disordered proteins, a class of proteins implicated in many disease pathologies and human health issues. Several studies have measured intrinsic conformational propensities for polyproline II helix, a key structural motif of disordered proteins, in short peptides. Whether or not these experimental polyproline II propensities, which vary by amino acid type, reproduce structural behavior in intrinsically disordered proteins has yet to be demonstrated. Presented here are simulation results showing that polyproline II propensities from short peptides accurately describe sequence-dependent variability in the hydrodynamic dimensions of intrinsically disordered proteins. Good agreement was observed from a simple molecular model even when charge-based considerations were ignored, predicting that global organization of disordered protein structure is strongly dependent on intrinsic conformational propensities and, for many intrinsically disordered proteins, modulated only weakly by coulombic effects.

Using the COREX/BEST server to model the native-state ensemble

Protein structures under normal conditions exist as ensembles of interconverting, transient microstates. A computer algorithm known as COREX/BEST (Biology using Ensemble-based Structural Thermodynamics) was developed to model microstate structures and describe the native ensembles of proteins in statistical thermodynamic terms. This algorithm has been tested extensively and validated through experimental comparisons examining a range of biophysical and functional phenomena, such as structural cooperativity, pH-dependent stability, and cold denaturation. Here, we describe a Web-based implementation of the COREX/BEST algorithm, called the COREX/BEST Server, and demonstrate how to use this online resource to characterize the structural and thermodynamic properties of the native protein ensemble.

Temperature effects on the hydrodynamic radius of the intrinsically disordered N-terminal region of the p53 protein

Intrinsically disordered proteins (IDPs) are often characterized in terms of the hydrodynamic radius, Rh . The Rh of IDPs are known to depend on fractional proline content and net charge, where increased numbers of proline residues and increased net charge cause larger Rh . Though sequence and charge effects on the Rh of IDPs have been studied, the temperature sensitivity has been noted only briefly. Reported here are Rh measurements in the temperature range of 5-75°C for the intrinsically disordered N-terminal region of the p53 protein, p53(1-93). Of note, the Rh of this protein fragment was highly sensitive to temperature, decreasing from 35 Å at 5°C to 26 Å at 75°C. Computer generated simulations of conformationally dynamic and disordered polypeptide chains were performed to provide a hypothesis for the heat-induced compaction of p53(1-93) structure, which was opposite to the heat-induced increase in Rh observed for a model folded protein. The simulations demonstrated that heat caused Rh to trend toward statistical coil values for both proteins, indicating that the effects of heat on p53(1-93) structure could be interpreted as thermal denaturation. The simulation data also predicted that proline content contributed minimally to the native Rh of p53(1-93), which was confirmed by measuring Rh for a substitution variant that had all 22 proline residues changed for glycine.

Solution structures of polcalcin Phl p 7 in three ligation states: Apo-, hemi-Mg2+-bound, and fully Ca2+-bound

Polcalcins are small EF-hand proteins believed to assist in regulating pollen-tube growth. Phl p 7, from timothy grass (Phleum pratense), crystallizes as a domain-swapped dimer at low pH. This study describes the solution structures of the recombinant protein in buffered saline at pH 6.0, containing either 5.0 mM EDTA, 5.0 mM Mg(2+), or 100 μM Ca(2+). Phl p 7 is monomeric in all three ligation states. In the apo-form, both EF-hand motifs reside in the closed conformation, with roughly antiparallel N- and C-terminal helical segments. In 5.0 mM Mg(2+), the divalent ion is bound by EF-hand 2, perturbing interhelical angles and imposing more regular helical structure. The structure of Ca(2+)-bound Phl p 7 resembles that previously reported for Bet v 4-likewise exposing apolar surface to the solvent. Occluded in the apo- and Mg(2+)-bound forms, this surface presumably provides the docking site for Phl p 7 targets. Unlike Bet v 4, EF-hand 2 in Phl p 7 includes five potential anionic ligands, due to replacement of the consensus serine residue at -x (residue 55 in Phl p 7) with aspartate. In the Phl p 7 crystal structure, D55 functions as a helix cap for helix D. In solution, however, D55 apparently serves as a ligand to the bound Ca(2+). When Mg(2+) resides in site 2, the D55 carboxylate withdraws to a distance consistent with a role as an outer-sphere ligand. (15)N relaxation data, collected at 600 MHz, indicate that backbone mobility is limited in all three ligation states.

Mutational analysis of m-values as a strategy to identify cold-resistant substructures of the protein ensemble

Characterizing the native ensemble of protein is an important yet difficult objective of structural biology. The structural dynamics of protein macromolecules play key roles in biological function, but the short lifetimes and low population of near-native states of the protein ensemble limit their ability to be studied directly. In part to address such issues, it was shown recently that the cooperative substructures that populate a protein ensemble could be ascertained by NMR methods performed at very cold temperatures. What is presented here is an argument that these same substructures can also be determined by denaturant-induced unfolding studies performed on protein at room temperature. Data supporting this argument are given for Staphylococcal nuclease, chymotrypsin inhibitor 2, and ubiquitin. The observation of an agreement between the thermodynamics of the protein ensemble simulated under very cold temperatures to the apparent sensitivity of the ensemble to chemical denaturants at room temperature also suggests that the overall structural-thermodynamic character of an ensemble is surprisingly robust and preserved even in the presence of strong denaturing conditions.

Polcalcin divalent ion-binding behavior and thermal stability: comparison of Bet v 4, Bra n 1, and Bra n 2 to Phl p 7

Polcalcins are pollen-specific proteins containing two EF-hands. Atypically, the C-terminal EF-hand binding loop in Phl p 7 (from timothy grass) harbors five, rather than four, anionic side chains, due to replacement of the consensus serine at -x by aspartate. This arrangement has been shown to heighten parvalbumin Ca(2+) affinity. To determine whether Phl p 7 likewise exhibits anomalous divalent ion affinity, we have also characterized Bra n 1 and Bra n 2 (both from rapeseed) and Bet v 4 (from birch tree). Relative to Phl p 7, they exhibit N-terminal extensions of one, five, and seven residues, respectively. Interestingly, the divalent ion affinity of Phl p 7 is unexceptional. For example, at -17.84 +/- 0.13 kcal mol(-1), the overall standard free energy for Ca(2+) binding falls within the range observed for the other three proteins (-17.30 +/- 0.10 to -18.15 +/- 0.10 kcal mol(-1)). In further contrast to parvalbumin, replacement of the -x aspartate, via the D55S mutation, actually increases the overall Ca(2+) affinity of Phl p 7, to -18.17 +/- 0.13 kcal mol(-1). Ca(2+)-free Phl p 7 exhibits uncharacteristic thermal stability. Whereas wild-type Phl p 7 and the D55S variant denature at 77.3 and 78.0 degrees C, respectively, the other three polcalcins unfold between 56.1 and 57.9 degrees C. This stability reflects a low denaturational heat capacity increment. Phl p 7 and Phl p 7 D55S exhibit DeltaC(p) values of 0.34 and 0.32 kcal mol(-1) K(-1), respectively. The corresponding values for the other three polcalcins range from 0.66 to 0.95 kcal mol(-1) K(-1).

Heterodimerization of the human RNase P/MRP subunits Rpp20 and Rpp25 is a prerequisite for interaction with the P3 arm of RNase MRP RNA

Rpp20 and Rpp25 are two key subunits of the human endoribonucleases RNase P and MRP. Formation of an Rpp20–Rpp25 complex is critical for enzyme function and sub-cellular localization. We present the first detailed in vitro analysis of their conformational properties, and a biochemical and biophysical characterization of their mutual interaction and RNA recognition. This study specifically examines the role of the Rpp20/Rpp25 association in the formation of the ribonucleoprotein complex. The interaction of the individual subunits with the P3 arm of the RNase MRP RNA is revealed to be negligible whereas the 1:1 Rpp20:Rpp25 complex binds to the same target with an affinity of the order of nM. These results unambiguously demonstrate that Rpp20 and Rpp25 interact with the P3 RNA as a heterodimer, which is formed prior to RNA binding. This creates a platform for the design of future experiments aimed at a better understanding of the function and organization of RNase P and MRP. Finally, analyses of interactions with deletion mutant proteins constructed with successively shorter N- and C-terminal sequences indicate that the Alba-type core domain of both Rpp20 and Rpp25 contains most of the determinants for mutual association and P3 RNA recognition.

An energetic representation of protein architecture that is independent of primary and secondary structure

Protein fold classification often assumes that similarity in primary, secondary, or tertiary structure signifies a common evolutionary origin. However, when similarity is not obvious, it is sometimes difficult to conclude that particular proteins are completely unrelated. Clearly, a set of organizing principles that is independent of traditional classification could be valuable in linking different structural motifs and identifying common ancestry from seemingly disparate folds. Here, a four-dimensional ensemble-based energetic space spanned by a diverse set of proteins was defined and its characteristics were contrasted with those of Cartesian coordinate space. Eigenvector decomposition of this energetic space revealed the dominant physical processes contributing to the more or less stable regions of a protein. Unexpectedly, those processes were identical for proteins with different secondary structure content and were also identical among different amino-acid types. The implications of these results are twofold. First, it indicates that excited conformational states comprising the protein native state ensemble, largely invisible upon inspection of the high-resolution structure, are the major determinant of the energetic space. Second, it suggests that folds dissimilar in sequence or structure could nonetheless be energetically similar if their respective excited conformational states are considered, one example of which was observed in the N-terminal region of the Arc repressor switch mutant. Taken together, these results provide a surface area-based framework for understanding folds in energetic terms, a framework that may eventually yield a means of identifying common ancestry among structurally dissimilar proteins.

Characterizing the role of ensemble modulation in mutation-induced changes in binding affinity

Protein conformational fluctuations are key contributors to biological function, mediating important processes such as enzyme catalysis, molecular recognition, and allosteric signaling. To better understand the role of conformational fluctuations in substrate/ligand recognition, we analyzed, experimentally and computationally, the binding reaction between an SH3 domain and the recognition peptide of its partner protein. The fluctuations in this SH3 domain were enumerated by using an algorithm based on the hard sphere collision model, and the binding energetics resulting from these fluctuations were calculated using a structure-based energy function parametrized to solvent accessible surface areas. Surprisingly, this simple model reproduced the effects of mutations on the experimentally determined SH3 binding energetics, within the uncertainties of the measurements, indicating that conformational fluctuations in SH3, and in particular the RT loop region, are structurally diverse and are well-approximated by the randomly configured states. The mutated positions in SH3 were distant to the binding site and involved Ala and Gly substitutions of solvent exposed positions in the RT loop. To characterize these fluctuations, we applied principal coordinate analysis to the computed ensembles, uncovering the principal modes of conformational variation. It is shown that the observed differences in binding affinity between each mutant, and thus the apparent coupling between the mutated sites, can be described in terms of the changes in these principal modes. These results indicate that dynamic loops in proteins can populate a broad conformational ensemble and that a quantitative understanding of molecular recognition requires consideration of the entire distribution of states.

Exploring the impact of polyproline II (PII) conformational bias on the binding of peptides to the SEM-5 SH3 domain

The left-handed polyproline II helical structure (P(II)) is observed to be a dominant conformation in the disordered states of protein and small polypeptide chains, even when no prolines are present in the sequence. Recently, in work by Ferreon and Hilser, the energetics associated with Ala and Gly substitutions at a surface exposed proline site were determined calorimetrically by measuring the binding energetics of Sos peptide variants to the C-terminal Src Homology 3 domain of SEM-5. The results were interpreted as a significant conformational bias toward the bound conformation (i.e., P(II)), even when the ligand is unbound. That study was not able to determine, however, whether the conformational bias of the peptides could be explained in terms other than that of a P(II) preference. Here, we test, using a computer algorithm based on the hard sphere collision (HSC) model, the notion of whether a bias in the unbound states of the peptide ligands is specific for the P(II) conformation, or if a bias to any other region of (phi, psi) space can also result in the same observed binding energetics. The results of these computer simulations indicate that, of the regions of (phi, psi) modeled for bias in the small peptides, only the bias to the P(II) conformation, and at rates of bias similar to the experimentally observed rates, quantitatively reproduced the experimental binding energetics.

Energetics of OCP1-OCP2 complex formation

OCP1 and OCP2, the most abundant proteins in the cochlea, are putative subunits of an SCF E3 ubiquitin ligase. Previous work has demonstrated that they form a heterodimeric complex. The thermodynamic details of that interaction are herein examined by isothermal titration calorimetry. At 25 degrees C, addition of OCP1 to OCP2 yields an apparent association constant of 4.0 x 10(7) M(-1). Enthalpically-driven (DeltaH=-35.9 kcal/mol) and entropically unfavorable (-TDeltaS=25.5 kcal/mol), the reaction is evidently unaccompanied by protonation/deprotonation events. DeltaH is strongly dependent on temperature, with DeltaC(p)=-1.31 kcal mol(-1) K(-1). Addition of OCP2 to OCP1 produces a slightly less favorable DeltaH, presumably due to the requirement for dissociation of the OCP2 homodimer prior to OCP1 binding. The thermodynamic signature for OCP1/OCP2 complex formation is inconsistent with a rigid-body association and suggests that the reaction is accompanied by a substantial degree of folding.

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

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

The flavodoxin from Helicobacter pylori: structural determinants of thermostability and FMN cofactor binding

Flavodoxin has been recently recognized as an essential protein for a number of pathogenic bacteria including Helicobacter pylori, where it has been proposed to constitute a target for antibacterial drug development. One way we are exploring to screen for novel inhibitory compounds is to perform thermal upshift assays, for which a detailed knowledge of protein thermostability and cofactor binding properties is of great help. However, very little is known on the stability and ligand binding properties of H. pylori flavodoxin, and its peculiar FMN binding site together with the variety of behaviors observed within the flavodoxin family preclude extrapolations. We have thus performed a detailed experimental and computational analysis of the thermostability and cofactor binding energetics of H. pylori flavodoxin, and we have found that the thermal unfolding equilibrium is more complex that any other previously described for flavodoxins as it involves the accumulation of two distinct equilibrium intermediates. Fortunately the entire stability and binding data can be satisfactorily fitted to a model, summarized in a simple phase diagram, where the cofactor only binds to the native state. On the other hand, we show how variability of thermal unfolding behavior within the flavodoxin family can be predicted using structure-energetics relationships implemented in the COREX algorithm. The different distribution and ranges of local stabilities of the Anabaena and H. pylori apoflavodoxins explain the essential experimental differences observed: much lower Tm1, greater resistance to global unfolding, and more pronounced cold denaturation in H. pylori. Finally, a new strategy is proposed to identify using COREX structural characteristics of equilibrium intermediate states populated during protein unfolding.

Functional residues serve a dominant role in mediating the cooperativity of the protein ensemble

Conformational fluctuations in proteins have emerged as a potentially important aspect of biological function, although the precise relationship and the implications have yet to be fully explored. Numerous studies have reported that the binding of ligand can influence fluctuations. However, the role of the binding site in mediating these fluctuations is not known. Of particular interest is whether in addition to serving as structural scaffolds for recognition and catalysis, active-site residues may also play a role in modulating the cooperative network. To address this question, we employ an experimentally validated ensemble-based description of proteins to elucidate the extent to which perturbations at different sites can influence the cooperative network in the protein. Applying this method to a database of test proteins, it is found statistically that binding sites are located in regions most able to affect the cooperative network, even for cooperative interactions between residues distant to the binding sites. This indicates that the conformational manifold under native conditions is determined by the network of cooperative interactions within the protein and suggests that proteins have evolved to use these conformational fluctuations in carrying out their functions. Furthermore, because the energetic coupling pattern calculated for each protein is robust and relatively insensitive to sequence, these studies further suggest that binding sites evolved in regions of the protein that are inherently poised to take advantage of the fluctuations in the native structure.

Temperature-dependent variations of ligand-receptor contact points in hAT1

Photoaffinity labelling is regularly used to investigate proteins, including peptidergic G protein-coupled receptors (GPCR). To this purpose benzophenone photolabels have been widely used to identify many contact residues in ligand-binding pockets. The three-dimensional binding environment of the human angiotensin II type 1 receptor hAT(1) has been determined using an iterative methionine mutagenesis strategy based on the photochemical properties and preferential incorporation of benzophenone onto methionine. This has led to the construction of a ligand-bound receptor structure. The present study investigated the effect of temperature on the accessibility of some of these contact points. The hAT(1) receptor and two representative Met mutants (H256M-hAT(1) and F293M-hAT(1)) from the iterative mutagenesis study were photolabelled with the benzophenone-ligand (125)I-[Sar(1), Bpa(8)]AngII at temperatures ranging from - 15 degrees C to 37 degrees C. Labelled receptors were partially purified and digested with cyanogen bromide to identify the contact points or segments. There were no changes in receptor contacts or labelling in the 7th transmembrane domains (TMD) of hAT(1) and F293M-hAT(1) across the temperature range. However, a temperature-dependent change in the ligand-receptor contact of H256M-hAT(1) was observed. At - 15 degrees C, H256M labelling was identical to that of hAT(1), indicating that the interaction was specific to the 7th TMD. Significant labelling changes were observed at higher temperatures and at 37 degrees C labelling occurred almost exclusively at mutated residue H256M-hAT(1) in the 6th TMD. Simultaneous competitive labelling of different areas of this target protein indicated that the ligand-receptor structure became increasingly fluctual at physiological temperatures, while a more compact, low mobility, and low energy conformation prevailed at low temperatures.

Ensemble-based signatures of energy propagation in proteins: a new view of an old phenomenon

The ability of a protein to transmit the energetic effects of binding from one site to another constitutes the underlying basis for allosterism and signal transduction. Despite clear experimental evidence indicating the ability of proteins to transmit the effects of binding, the means by which this propagation is facilitated is not well understood. Using our previously developed ensemble-based description of the equilibrium, we investigated the physical basis of energy propagation and identified several fundamental and general aspects of energetic coupling between residues in a protein. First, partitioning of a conformational ensemble into four distinct sub-ensembles allows for explanation of the range of experimentally observed coupling behaviors (i.e., positive, neutral, and negative coupling between various regions of the protein structure). Second, the relative thermodynamic properties of these four sub-ensembles define the energetic coupling between residues as either positive, neutral, or negative. Third, analysis of the structural and thermodynamic features of the states within each sub-ensemble reveals significant variability. This third result suggests that a quantitative description of energy propagation in proteins requires an understanding of the structural and energetic features of more than just one or a few low-energy states, but also of many high-energy states. Such findings illuminate the difficulty in interpreting energy propagation in proteins in terms of a structural pathway that physically links coupled sites.

Local conformational fluctuations can modulate the coupling between proton binding and global structural transitions in proteins

Local conformational fluctuations in proteins can affect the coupling between ligand binding and global structural transitions. This finding was established by monitoring quantitatively how the population distribution in the ensemble of microstates of staphylococcal nuclease was affected by proton binding. Analysis of acid unfolding and proton-binding data with an ensemble-based model suggests that local fluctuations: (i) can be effective modulators of ligand-binding affinities, (ii) are important determinants of the cooperativity of ligand-driven global structural transitions, and (iii) are well represented thermodynamically as local unfolding processes. These studies illustrate how an ensemble-based description of proteins can be used to describe quantitatively the interdependence of local conformational fluctuations, ligand-binding processes, and global structural transitions. This level of understanding of the relationship between conformation, energy, and dynamics is required for a detailed mechanistic understanding of allostery, cooperativity, and other complex functional and regulatory properties of macromolecules.

Analysis of the "thermodynamic information content" of a Homo sapiens structural database reveals hierarchical thermodynamic organization

Classification of the amounts and types of lower order structural elements in proteins is a prerequisite to effective comparisons between protein folds. In an effort to provide an additional vehicle for fold comparison, we present an alternative classification scheme whereby protein folds are represented in statistical thermodynamic terms in such a way as to illuminate the energetic building blocks within protein structures. The thermodynamic relationship is examined between amino acid sequences and the conformational ensembles for a database of 159 Homo sapiens protein structures ranging from 50 to 250 amino acids. Using hierarchical clustering, it is shown through fold-recognition experiments that (1) eight thermodynamic environmental descriptors sufficiently accounts for the energetic variation within the native state ensembles of the H. sapiens structural database, (2) an amino acid library of only six residue types is sufficient to encode >90% of the thermodynamic information required for fold specificity in the entire database, and (3) structural resolution of the statistically derived environments reveals sequential cooperative segments throughout the protein, which are independent of secondary structure. As the first level of thermodynamic organization in proteins, these segments represent the thermodynamic counterpart to secondary structure.

Thermodynamic characterization of the interaction of human cyclophilin 18 with cyclosporin A

Isothermal titration calorimetry (ITC) was used to investigate thermodynamic parameters of the cyclosporin A (CsA)-cyclophilin 18 (hCyp18) association reaction. We have calculated the thermodynamic parameters (enthalpy, entropy, heat capacity, and free energy of binding) of the CsA/hCyp18 complexation. All but two methods described in the literature underestimate the affinity to hCyp18 of CsA. We found that the association constant (1.1.10(8) M(-1) at 10 degrees C) of CsA to hCyp18 is in close agreement with the reciprocal of the reported inhibitory constant of the peptidylprolyl cis/trans isomerase activity of hCyp18. Interpretation of the thermodynamic parameters in buffered solution of water, 30% glycerol and D(2)O leads to the conclusion that the highly specific binding of CsA to hCyp18 is mainly mediated through hydrogen bonding and to a lesser degree through hydrophobic interaction. Furthermore, the pH dependence of the association constant was determined and analyzed according to a single proton linkage model, resulting in a pK(a) value of 5.7 in free hCyp18 and below 4.5 in the CsA complexed form. Titration experiments using different single component buffers possessing different heats of ionization allowed us to estimate that statistically half a proton is transferred upon CsA binding from the binding interface of hCyp18 to the buffer at pH 5.5. No proton transfer was detected at pH 7.5. The thermodynamic results are discussed in relation to the published X-ray and NMR structure of the free and CsA complexed hCyp18.

Clustering of large hydrophobes in the hydrophobic core of two-stranded alpha-helical coiled-coils controls protein folding and stability

The de novo design and biophysical characterization of two 60-residue peptides that dimerize to fold as parallel coiled-coils with different hydrophobic core clustering is described. Our goal was to investigate whether designing coiled-coils with identical hydrophobicity but with different hydrophobic clustering of non-polar core residues (each contained 6 Leu, 3 Ile, and 7 Ala residues in the hydrophobic core) would affect helical content and protein stability. The disulfide-bridged P3 and P2 differed dramatically in alpha-helical structure in benign conditions. P3 with three hydrophobic clusters was 98% alpha-helical, whereas P2 was only 65% alpha-helical. The stability profiles of these two analogs were compared, and the enthalpy and heat capacity changes upon denaturation were determined by measuring the temperature dependence by circular dichroism spectroscopy and confirmed by differential scanning calorimetry. The results showed that P3 assembled into a stable alpha-helical two-stranded coiled-coil and exhibited a native protein-like cooperative two-state transition in thermal melting, chemical denaturation, and calorimetry experiments. Although both peptides have identical inherent hydrophobicity (the hydrophobic burial of identical non-polar residues in equivalent heptad coiled-coil positions), we found that the context dependence of an additional hydrophobic cluster dramatically increased stability of P3 (Delta Tm approximately equal to 18 degrees C and Delta[urea](1/2) approximately equal to 1.5 M) as compared with P2. These results suggested that hydrophobic clustering significantly stabilized the coiled-coil structure and may explain how long fibrous proteins like tropomyosin maintain chain integrity while accommodating polar or charged residues in regions of the protein hydrophobic core.

Structurally homologous all beta-barrel proteins adopt different mechanisms of folding

Acidic fibroblast growth factors from human (hFGF-1) and newt (nFGF-1) (Notopthalamus viridescens) are 16-kDa, all beta-sheet proteins with nearly identical three-dimensional structures. Guanidine hydrochloride (GdnHCl)-induced unfolding of hFGF-1 and nFGF-1 monitored by fluorescence and far-UV circular dichroism (CD) shows that the FGF-1 isoforms differ significantly in their thermodynamic stabilities. GdnHCl-induced unfolding of nFGF-1 follows a two-state (Native state to Denatured state(s)) mechanism without detectable intermediate(s). By contrast, unfolding of hFGF-1 monitored by fluorescence, far-UV circular dichroism, size-exclusion chromatography, and NMR spectroscopy shows that the unfolding process is noncooperative and proceeds with the accumulation of stable intermediate(s) at 0.96 M GdnHCl. The intermediate (in hFGF-1) populated maximally at 0.96 M GdnHCl has molten globule-like properties and shows strong binding affinity to the hydrophobic dye, 1-Anilino-8-naphthalene sulfonate (ANS). Refolding kinetics of hFGF-1 and nFGF-1 monitored by stopped-flow fluorescence reveal that hFGF-1 and nFGF-1 adopts different folding mechanisms. The observed differences in the folding/unfolding mechanisms of nFGF-1 and hFGF-1 are proposed to be either due to differential stabilizing effects of the charged denaturant (Gdn(+) Cl(-)) on the intermediate state(s) and/or due to differences in the structural interactions stabilizing the native conformation(s) of the FGF-1 isoforms.

Thermodynamic environments in proteins: fundamental determinants of fold specificity

To investigate the relationship between an amino acid sequence and its corresponding protein fold, a database of thermodynamic stability information was assembled as a function of residue type from 81 nonhomologous proteins. This information was obtained using the COREX algorithm, which computes an ensemble-based description of the native state of proteins. Dissection of the COREX stability constant into its fundamental energetic components resulted in 12 thermodynamic environments describing the tertiary architecture of protein folds. Because of the observation that residue types partitioned unequally between these environments, it was hypothesized that thermodynamic environments contained energetic information that connected sequence to fold. To test the significance of this hypothesis, the thermodynamic stability information was incorporated into a three-dimensional-to-one-dimensional scoring matrix, and simple fold recognition experiments were performed in a manner such that information about the fold target was never included in the scoring. For 60 out of 81 fold targets, the correct sequence for the target scored in the top 5% of 3858 decoy sequences, with Z-scores ranging from 1.76 to 12.23. Furthermore, a scoring matrix assembled from the residues of 40 nonhomologous all-alpha proteins was used to thread sequences against 12 nonhomologous all-beta protein targets. In 10 of 12 cases, sequences known to adopt the native all-beta structure scored in the top 5% of 3858 decoy sequences, with Z-scores ranging from 1.99 to 7.94. These results indicate that energetic information encoded by thermodynamic environments represents a fundamental property of proteins that underlies classifications based on secondary structure.

Thermodynamic propensities of amino acids in the native state ensemble: implications for fold recognition

An amino acid sequence, in the context of the solvent environment, contains all of the thermodynamic information necessary to encode a three-dimensional protein structure. To investigate the relationship between an amino acid sequence and its corresponding protein fold, a database of thermodynamic stability information was assembled that spanned 2951 residues from 44 nonhomologous proteins. This information was obtained using the COREX algorithm, which computes an ensemble-based description of the native state of a protein. It was observed that amino acid types partitioned unequally into high, medium, and low thermodynamic stability environments. Furthermore, these distributions were reproducible and were significantly different than those expected from random partitioning. To assess the structural importance of the distributions, simple fold-recognition experiments were performed based on a 3D-1D scoring matrix containing only COREX residue stability information. This procedure was able to recover amino acid sequences corresponding to correct target structures more effectively than scoring matrices derived from randomized data. High-scoring sequences were often aligned correctly with their corresponding target profiles, suggesting that calculated thermodynamic stability profiles have the potential to encode sequence information. As a control, identical fold-recognition experiments were performed on the same database of proteins using DSSP secondary structure information in the scoring matrix, instead of COREX residue stability information. The comparable performance of both approaches suggested that COREX residue stability information and secondary structure information could be of equivalent utility in more sophisticated fold-recognition techniques. The results of this work are a consequence of the idea that amino acid sequences fold not into single, rigidly stable structures but rather into thermodynamic ensembles best represented by a time-averaged structure.

Binding sites in Escherichia coli dihydrofolate reductase communicate by modulating the conformational ensemble

To explore how distal mutations affect binding sites and how binding sites in proteins communicate, an ensemble-based model of the native state was used to define the energetic connectivities between the different structural elements of Escherichia coli dihydrofolate reductase. Analysis of this model protein has allowed us to identify two important aspects of intramolecular communication. First, within a protein, pair-wise couplings exist that define the magnitude and extent to which mutational effects propagate from the point of origin. These pair-wise couplings can be identified from a quantity we define as the residue-specific connectivity. Second, in addition to the pair-wise energetic coupling between residues, there exists functional connectivity, which identifies energetic coupling between entire functional elements (i.e., binding sites) and the rest of the protein. Analysis of the energetic couplings provides access to the thermodynamic domain structure in dihydrofolate reductase as well as the susceptibility of the different regions of the protein to both small-scale (e.g., point mutations) and large-scale perturbations (e. g., binding ligand). The results point toward a view of allosterism and signal transduction wherein perturbations do not necessarily propagate through structure via a series of conformational distortions that extend from one active site to another. Instead, the observed behavior is a manifestation of the distribution of states in the ensemble and how the distribution is affected by the perturbation.

Correlated motions in native proteins from MS analysis of NH exchange: evidence for a manifold of unfolding reactions in ovomucoid third domain

Native-state amide hydrogen exchange monitored by NMR spectroscopy and mass spectrometry (MS) has the potential to provide detailed residue-level information regarding correlated motions occurring on the microseconds to seconds timescale. To expand the applicability of MS to these studies, a new algorithm has been developed to interpret MS data for exchange occurring between the EX2 and EX1 kinetic limits. Re-interpretation of MS data for ovomucoid third domain reveals multiple unfolding or partial unfolding reactions.

The sarcosine effect on protein stability: a case of nonadditivity?

We have used differential scanning calorimetry to determine the effect of low concentrations (C = 0-2 M) of the osmolyte sarcosine on the Gibbs energy changes (deltaG) for the unfolding of hen-egg-white lysozyme, ribonuclease A, and ubiquitin, under the same buffer and pH conditions. We have also computed this effect on the basis of the additivity assumption and using published values of the transfer Gibbs energies for the amino acid side chains and the peptide backbone unit. The values thus predicted for the slope delta deltaG/deltaC agree with the experimental ones, but only if the unfolded state is assumed to be compact (that is, if the accessibility to solvent of the unfolded state is modeled using segments excised from native structures). The additivity-based calculations predict similar delta deltaG/deltaC values for the three proteins studied. We point out that, to the extent that this approximate constancy of delta deltaG/deltaC holds, osmolyte-induced increases in denaturation temperature will be larger for proteins with low unfolding enthalpy (small proteins that bury a large proportion of apolar surface). The experimental results reported here are consistent with this hypothesis.

A mechanistic analysis of carrier-mediated oral delivery of protein therapeutics

This article summarizes the results of a theoretical analysis of protein absorption into the systemic circulation from the small intestine, with and without molecular 'carriers' designed to enhance absorption. The predictions are compared with experimental systemic protein concentrations following intraduodenal delivery of insulin, interferon alpha-2b, and human growth hormone. The results show that, from the standpoint of improving oral absorption, the primary consequence of carrier molecules is to increase epithelial membrane permeability, thereby leading to higher bioavailability. Several possible mechanisms of this permeability enhancement are discussed.

Fourier-transform infrared spectroscopy study of the pressure-induced changes in the structure of the bovine alpha-lactalbumin: the stabilizing role of the calcium ion

The Fourier-transform infrared spectroscopy (FTIR) technique with a diamond anvil cell has been applied for examination of the pressure-induced changes occurring in the secondary structure of the alpha-lactalbumin. This is the first high-pressure FTIR study of a calcium-binding protein which simultaneously takes into account spectral changes in both the calcium-ion-binding carboxyl groups' band and the amide I/I' vibrational band. Spectral behavior of three kinds of the protein: the undeuterated holoform, the fully deuterated holoform, and the undeuterated apoform was compared in the pressure range from 0.1 MPa up to 740 MPa. We found that the binding of calcium remarkably stabilizes the alpha-lactalbumin against pressure as it is followed approximately by a 200-MPa increase of the value of pressure at which denaturation occurs. A quantitative analysis of the band of antisymmetrical stretching vibrations of the calcium-binding carboxyl groups revealed that the pressure-induced changes in the calcium-binding loop occur in two stages. Binding of the calcium ion seemingly increases the pressure-stability of the calcium-binding loop to a higher degree than the pressure-stability of the secondary structure of the alpha-lactalbumin. We have also discussed in detail the complex pressure-enhanced H/D exchange in the alpha-lactalbumin. Finally, we have proposed a new assignment of major peaks in the helical region of the amide I/I' spectral band of the partially deuterated alpha-lactalbumin.

Protein folding via binding and vice versa

The terms intermolecular and intramolecular recognition are often used when referring to binding and folding, highlighting the common ground between the two processes. Most studies, however, are aimed at either one process or the other. Here, we show how knowledge from binding can aid in understanding folding and vice versa.

A descriptive analysis of populations of three-dimensional structures calculated from primary sequences of proteins by OSIRIS

Among different ab initio approaches to calculate 3D-structures of proteins out of primary sequences, a few are using restricted dihedral spaces and empirical equations of energy as is OSIRIS. All those approaches were calibrated on a few proteins or fragments of proteins. To optimize the calculation over a larger diversity of structures, we need first to define for each sequence what are good conditions of calculations in order to choose a consensus procedure fitting most 3D-structures best. This requires objective classification of calculated 3D-structures. In this work, populations of avian and bovine pancreatic polypeptides (APP, BPP) and of calcium-binding protein (CaBP) are obtained by varying the rate of the angular dynamics of the second step of OSIRIS. Then, 3D-structures are clustered using a nonhierarchical method, SICLA, using rmsd as a distance parameter. A good clustering was obtained for four subpopulations of APP, BPP and CaBP. Each subpopulation was characterized by its barycenter, relative frequency and dispersion. For the three alpha-helix proteins, after the step 1 of OSIRIS, most secondary structures were correct but molecules have a few atomic contacts. Step 2, i.e., the angular dynamics, resolves those atomic contacts and clustering demonstrates that it generates subpopulations of topological conformers as the barycenter topologies show.

Isothermal titration calorimetric studies on the associations of putidaredoxin to NADH-putidaredoxin reductase and P450cam

Putidaredoxin (Pdx), an iron-sulfur protein containing a 2Fe-2S cluster, serves as a physiological electron mediator from NADH-putidaredoxin reductase (PdR) to P450cam in the P450cam monooxygenation reaction cycle. Previous studies have revealed that the associations of Pdx with P450cam and PdR are not strongly dominated by electrostatic interactions, although such interactions stabilize most electron-transfer complexes [A.R. De Pascalis, I. Jelesarov, F. Ackermann, W.H. Koppenol, M. Hiroasawa, D.B. Knaff, H.R. Bosshard, Protein Sci. 2 (1993) 1126-1135]. In the present study, to elucidate the interactions dominating the specific associations in the electron-transfer reaction mediated by Pdx, the thermodynamic properties--entropy (delta S), enthalpy (delta H), and heat capacity changes (delta Cp)--for PdR/Pdx and P450cam/Pdx association reactions have been examined by isothermal titration calorimetry (ITC). Although the binding enthalpy change, delta Hbind, for the PdR/Pdx association is positive at 10 degrees C, it declines linearly with temperature in the range 10-22 degrees C and becomes negative above 11 degrees C. On the other hand, the binding entropy change, delta Sbind, is positive at all temperatures examined in this study, indicating that the association of Pdx to PdR is entropically driven. On the basis of the temperature dependence of delta Hbind, delta Cpbind for the association of Pdx to PdR was estimated as -1.24 kJ mol-1 K-1. This value is larger than those reported for other electron-transfer protein systems (e.g., -0.68 kJ mol-1 K-1 for ferredoxin/ferredoxin: NADP+ reductase), suggesting that the PdR/Pdx association may be dominated by hydrophobic rather than electrostatic components. For the P450cam/Pdx association, the negative delta Sbind and highly favorable delta Hbind were observed, behavior that stands in sharp contrast to the association reactions in other electron-transfer proteins. The energetics of the P450cam/Pdx association are similar to those of binding reaction of antibody to antigen in which van der Waals and hydrogen bonding interactions are dominant, resulting in high specificity in the association of Pdx with P450cam.

Favorable domain size in proteins

BACKGROUND

It has been observed that single-domain proteins and domains in multidomain proteins favor a chain length in the range 100-150 amino acids. To understand the origin of the favored size, we construct an empirical function for the free energy of unfolding versus the chain length. The parameters in the function are derived by fitting to the energy of hydration, entropy and enthalpy of unfolding of nine proteins. Our energy function cannot be used to calculate the energetics accurately for individual proteins because the energetics also depend on other factors, such as the composition and the conformation of the protein. Nevertheless, the energy function statistically characterizes the general relationship between the free energy of unfolding and the size of the protein.

RESULTS

The predicted optimal number of residues, which corresponds to the maximum free energy of unfolding, is 100. This is in agreement with a statistical analysis of protein domains derived from their experimental structures. When a chain is too short, our energy function indicates that the change in enthalpy of internal interactions is not favorable enough for folding because of the limited number of inter-residue contacts. A long chain is also unfavorable for a single domain because the cost of configurational entropy increases quadratically as a function of the chain length, whereas the favorable change in enthalpy of internal interactions increases linearly.

CONCLUSIONS

Our study shows that the energetic balance is the dominant factor governing protein sizes and it forces a large protein to break into several domains during folding.

Empirical free energy calculation: comparison to calorimetric data

An effective free energy potential, developed originally for binding free energy calculation, is compared to calorimetric data on protein unfolding, described by a linear combination of changes in polar and nonpolar surface areas. The potential consists of a molecular mechanics energy term calculated for a reference medium (vapor or nonpolar liquid), and empirical terms representing solvation and entropic effects. It is shown that, under suitable conditions, the free energy function agrees well with the calorimetric expression. An additional result of the comparison is an independent estimate of the side-chain entropy loss, which is shown to agree with a structure-based entropy scale. These findings confirm that simple functions can be used to estimate the free energy change in complex systems, and that a binding free energy evaluation model can describe the thermodynamics of protein unfolding correctly. Furthermore, it is shown that folding and binding leave the sum of solute-solute and solute-solvent van der Waals interactions nearly invariant and, due to this invariance, it may be advantageous to use a nonpolar liquid rather than vacuum as the reference medium.

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

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

Predicting the equilibrium protein folding pathway: structure-based analysis of staphylococcal nuclease

The equilibrium folding pathway of staphylococcal nuclease (SNase) has been approximated using a statistical thermodynamic formalism that utilizes the high-resolution structure of the native state as a template to generate a large ensemble of partially folded states. Close to 400,000 different states ranging from the native to the completely unfolded states were included in the analysis. The probability of each state was estimated using an empirical structural parametrization of the folding energetics. It is shown that this formalism predicts accurately the stability of the protein, the cooperativity of the folding/unfolding transition observed by differential scanning calorimetry (DSC) or urea denaturation and the thermodynamic parameters for unfolding. More importantly, this formalism provides a quantitative account of the experimental hydrogen exchange protection factors measured under native conditions for SNase. These results suggest that the computer-generated distribution of states approximates well the ensemble of conformations existing in solution. Furthermore, this formalism represents the first model capable of quantitatively predicting within a unified framework the probability distribution of states seen under native conditions and its change upon unfolding.

Energetics of cyclic dipeptide crystal packing and solvation

Calculations of the thermodynamics of transfer of the cyclic alanine-alanine (cAA) and glycine-glycine (cGG) dipeptides between the gas, water, and crystal phases were carried out using a combination of molecular mechanics, normal mode analysis, and continuum electrostatics. The experimental gas-to-water solvation free energy and the enthalpy of gas-to-crystal transfer of cGG are accurately reproduced by the calculations. The enthalpies of cGG and cAA crystal-to-water transfer are close to the experimental values. A combination of experimental data and normal mode analysis of cGG provides an accurate estimate of the association entropy penalty (loss of rational and translational entropy and gain in vibrational entropy) for "binding" in the crystalline phase of -14.1 cal/mol/k. This is a smaller number than most previous theoretical estimates, but it is similar to previous experimental estimates. Calculated entropies of the crystal phase underestimate the experimental entropy by about 15 cal/mol/k because of neglect of long-range lattice motions. Comparison of the intermolecular interactions in the crystals of cGG and cAA provides a possible explanation of the puzzling decrease in enthalpy, with increasing hydrophobicity seen previously for both cyclic dipeptide dissolution and protein unfolding. This decrease arises from a favorable long-range electrostatic interaction between dipeptide molecules in the crystals, which is attenuated by the more hydrophobic side chains.

Solvation: how to obtain microscopic energies from partitioning and solvation experiments

Oil-water partitioning, solubilities, and vapor pressure experiments on small-molecule compounds are often used as models to obtain energies for biomolecular modeling. For example, measured partition coefficients, K, are often inserted into the formula -RT in K to obtain quantities thought to represent microscopic contact interaction free energies. We review evidence here that this procedure does not always give microscopically meaningful free energies. Some partitioning processes, particularly involving polymeric solvents such as octanol or hexadecane, are governed not only by translational entropies and contact interactions, but also by free energies resulting from changes in the conformations of the polymer chains upon solute insertion. The Flory-Huggins theory is more suitable for these situations than is the classical approach. We discuss the physical bases for both approaches.