Backbone Conformational Entropy Research Articles

Effects of Conformational Constraint on Peptide Solubility Limits.

Liquid-liquid phase separation of proteins preferentially involves intrinsically disordered proteins or disordered regions. Understanding the solution chemistry of these phase separations is key to learning how to quantify and manipulate systems that involve such processes. Here, we investigate the effect of cyclization on the liquid-liquid phase separation of short polyglycine peptides. We simulated separate aqueous systems of supersaturated cyclic and linear GGGGG and observed spontaneous liquid-liquid phase separation in each of the solutions. The cyclic GGGGG phase separates less robustly than linear GGGGG and has a higher aqueous solubility, even though linear GGGGG has a more favorable single molecule solvation free energy. The versatile and abundant interpeptide contacts formed by the linear GGGGG stabilize the condensed droplet phase, driving the phase separation in this system. In particular, we find that van der Waals close contact interactions are enriched in the droplet phase as opposed to electrostatic interactions. An analysis of the change in backbone conformational entropy that accompanies the phase transition revealed that cyclic peptides lose significantly less entropy in this process as expected. However, we find that the enhanced interaction enthalpy of linear GGGGG in the droplet phase is enough to compensate for a larger decrease in conformational entropy.

Thermodynamic Compensation in Peptides Following Liquid-Liquid Phase Separation.

Liquid-liquid phase separation of proteins often incorporates intrinsically disordered proteins or those with disordered regions. Examining these processes via the entropy change is desirable for establishing a quantitative foundation with which to probe and understand these phase transitions. Of interest is the effect of residue sequence on the entropy of the peptide backbone. In this work we model these systems via all atom simulations of liquid-liquid phase separation of peptides. Systems of supersaturated pentapeptides separate into a peptide-dense liquid droplet phase as well as a dilute (saturated) aqueous phase. An analysis of the change in backbone conformational entropy associated with the phase transition was performed. We examined systems of four different pentapeptides (GGGGG, GGQGG, GGNGG, and GGVGG) in order to explore the effect of sequence variation on the conformational entropy, as well as the effect of side chain variation on the physical characteristics of the droplet phases. We find that the loss of conformational entropy that accompanies aqueous → droplet transitions is more than compensated by a decrease in interaction enthalpy as contributions to the free energy change for the process.

Tuning Free Energy by Backbone Conformational Entropy: A Strategy from Disordered Proteins

Tuning Free Energy by Backbone Conformational Entropy: A Strategy from Disordered Proteins

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Conformational entropy is expected to contribute significantly to the thermodynamics of structural transitions in intrinsically disordered proteins or regions in response to protein/ligand binding, posttranslational modifications, and environmental changes. We calculated the backbone (dihedral) conformational entropy of oligoglycine (GlyN), a protein backbone mimic and model intrinsically disordered region, as a function of chain length (N=3, 4, 5, 10, and 15) from simulations using three different approaches. The backbone conformational entropy scales linearly with chain length with a slope consistent with the entropy of folding of well-structured proteins. The entropic contributions of second-order dihedral correlations are predominantly through intraresidue ϕ-ψ pairs, suggesting that oligoglycine may be thermodynamically modeled as a system of independent glycine residues. We find the backbone conformational entropy to be largely independent of global structural parameters, like the end-to-end distance and radius of gyration. We introduce a framework referred to herein as “ensemble confinement” to estimate the loss (gain) of conformational free energy and its entropic component when individual residues are constrained to (released from) particular regions of the ϕ-ψ map. Quantitatively, we show that our protein backbone model resists ordering/folding with a significant, unfavorable ensemble confinement free energy because of the loss of a substantial portion of the absolute backbone entropy. Proteins can couple this free-energy reservoir to distal binding events as a regulatory mechanism to promote or suppress binding.

Thermodynamic contribution of backbone conformational entropy in the binding between SH3 domain and proline-rich motif

Biological functions of intrinsically disordered proteins (IDPs), and proteins containing intrinsically disordered regions (IDRs) are often mediated by short linear motifs, like proline-rich motifs (PRMs). Upon binding to their target proteins, IDPs undergo a disorder-to-order transition which is accompanied by a large conformational entropy penalty. Hence, the molecular mechanisms underlying control of conformational entropy are critical for understanding the binding affinity and selectivity of IDPs-mediated protein-protein interactions (PPIs). Here, we investigated the backbone conformational entropy change accompanied by binding of the N-terminal SH3 domain (nSH3) of CrkII and PRM derived from guanine nucleotide exchange factor 1 (C3G). In particular, we focused on the estimation of conformational entropy change of disordered PRM upon binding to the nSH3 domain. Quantitative characterization of conformational dynamics of disordered peptides like PRMs is limited. Hence, we combined various methods, including NMR model-free analysis, δ2D, DynaMine, and structure-based calculation of entropy loss. This study demonstrates that the contribution of backbone conformational entropy change is significant in the PPIs mediated by IDPs/IDRs.

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations.

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes.In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.

Conformational Entropy of Intrinsically Disordered Proteins from Amino Acid Triads.

This work quantitatively characterizes intrinsic disorder in proteins in terms of sequence composition and backbone conformational entropy. Analysis of the normalized relative composition of the amino acid triads highlights a distinct boundary between globular and disordered proteins. The conformational entropy is calculated from the dihedral angles of the middle amino acid in the amino acid triad for the conformational ensemble of the globular, partially and completely disordered proteins relative to the non-redundant database. Both Monte Carlo (MC) and Molecular Dynamics (MD) simulations are used to characterize the conformational ensemble of the representative proteins of each group. The results show that the globular proteins span approximately half of the allowed conformational states in the Ramachandran space, while the amino acid triads in disordered proteins sample the entire range of the allowed dihedral angle space following Flory’s isolated-pair hypothesis. Therefore, only the sequence information in terms of the relative amino acid triad composition may be sufficient to predict protein disorder and the backbone conformational entropy, even in the absence of well-defined structure. The predicted entropies are found to agree with those calculated using mutual information expansion and the histogram method.

Insight into the allosteric mechanism of Scapharca dimeric hemoglobin.

Allosteric regulation is an essential function of many proteins that control a variety of different processes such as catalysis, signal transduction, and gene regulation. Structural rearrangements have historically been considered the main means of communication between different parts of a protein. Recent studies have highlighted the importance, however, of changes in protein flexibility as an effective way to mediate allosteric communication across a protein. Scapharca dimeric hemoglobin (HbI) is the simplest possible allosteric system, with cooperative ligand binding between two identical subunits. Thermodynamic equilibrium studies of the binding of oxygen to HbI have shown that cooperativity is an entropically driven effect. The change in entropy of the system observed upon ligand binding may arise from changes in the protein, the ligand, or the water of the system. The goal of this study is to determine the contribution of the change in entropy of the protein backbone to HbI cooperative binding. Molecular dynamics simulations and nuclear magnetic resonance relaxation techniques have revealed that the fast internal motions of HbI contribute to the cooperative binding to carbon monoxide in two ways: (1) by contributing favorably to the free energy of the system and (2) by participating in the cooperative mechanism at the HbI subunit interface. The internal dynamics of the weakly cooperative HbI mutant, F97Y, were also investigated with the same methods. The changes in backbone NH dynamics observed for F97Y HbI upon ligand binding are not as large as for the wild type, in agreement with the reduced cooperativity observed for this mutant. The results of this study indicate that interface flexibility and backbone conformational entropy of HbI participate in and are important for the cooperative mechanism of carbon monoxide binding.

Solution structure, dynamics and binding studies of a family 11 carbohydrate-binding module from Clostridium thermocellum (CtCBM11)

Non-catalytic cellulosomal CBMs (carbohydrate-binding modules) are responsible for increasing the catalytic efficiency of cellulosic enzymes by selectively putting the substrate (a wide range of poly- and oligo-saccharides) and enzyme into close contact. In the present study we carried out an atomistic rationalization of the molecular determinants of ligand specificity for a family 11 CBM from thermophilic Clostridium thermocellum [CtCBM11 (C. thermocellum CBM11)], based on a NMR and molecular modelling approach. We have determined the NMR solution structure of CtCBM11 at 25°C and 50°C and derived information on the residues of the protein that are involved in ligand recognition and on the influence of the length of the saccharide chain on binding. We obtained models of the CtCBM11-cellohexaose and CtCBM11-cellotetraose complexes by docking in accordance with the NMR experimental data. Specific ligand-protein CH-π and Van der Waals interactions were found to be determinant for the stability of the complexes and for defining specificity. Using the order parameters derived from backbone dynamics analysis in the presence and absence of ligand and at 25°C and 50°C, we determined that the protein's backbone conformational entropy is slightly positive. This data in combination with the negative binding entropy calculated from ITC (isothermal titration calorimetry) studies supports a selection mechanism where a rigid protein selects a defined oligosaccharide conformation.

Are ambivalent α-helices entropically driven?

This work is a first attempt to characterise the conformational preference of structurally ambivalent helices in terms of their backbone conformational entropy. Ambivalent sequences conform to two different secondary structures (helix-sheet or helix-random coil or sheet-random coil, etc.) in two different proteins. For variable ambivalent helices, the helical conformations are found to possess less conformational entropy as compared with their non-helical counterparts when the ϕ-ψ dihedral angle range of the entire peptide segment is used to calculate the backbone conformational entropy. The favourable number of native contacts is a primary stabilising factor for these helical conformations. However, an opposite trend is observed when the ϕ-ψ angles of the individual amino acids are used to calculate the backbone conformational entropy. The results show that these peptide segments are rather reluctant to form helices, but are driven to form helices due to the favourable number of native contacts and optimum range of ϕ-ψ angle of the segments. Both procedures are validated by applying on conserved helices in the non-redundant database and their corresponding counterparts in the Structural Classification of Proteins database. Although context is a major determinant in deciding conformations of ambivalent sequences, no significant difference in the conformational entropy of sequences flanking ambivalent helical sequences in helical and non-helical forms is observed in this study. The results may be useful in understanding the structural context and environmental factors which leads to the formation of ambivalent helices and designing de novo proteins.

Intra- and Interdomain Effects Due to Mutation of Calcium-binding Sites in Calmodulin

The IQ-motif protein PEP-19, binds to the C-domain of calmodulin (CaM) with significantly different k(on) and k(off) rates in the presence and absence of Ca(2+), which could play a role in defining the levels of free CaM during Ca(2+) transients. The initial goal of the current study was to determine whether Ca(2+) binding to sites III or IV in the C-domain of CaM was responsible for affecting the kinetics of binding PEP-19. EF-hand Ca(2+)-binding sites were selectively inactivated by the common strategy of changing Asp to Ala at the X-coordination position. Although Ca(2+) binding to both sites III and IV appeared necessary for native-like interactions with PEP-19, the data also indicated that the mutations caused undesirable structural alterations as evidenced by significant changes in amide chemical shifts for apoCaM. Mutations in the C-domain also affected chemical shifts in the unmodified N-domain, and altered the Ca(2+) binding properties of the N-domain. Conversion of Asp(93) to Ala caused the greatest structural perturbations, possibly due to the loss of stabilizing hydrogen bonds between the side chain of Asp(93) and backbone amides in apo loop III. Thus, although these mutations inhibit binding of Ca(2+), the mutated CaM may not be able to support potentially important native-like activity of the apoprotein. This should be taken into account when designing CaM mutants for expression in cell culture.

Conformational entropy of alanine versus glycine in protein denatured states.

The presence of a solvent-exposed alanine residue stabilizes a helix by 0.4-2 kcal.mol(-1) relative to glycine. Various factors have been suggested to account for the differences in helical propensity, from the higher conformational freedom of glycine sequences in the unfolded state to hydrophobic and van der Waals' stabilization of the alanine side chain in the helical state. We have performed all-atom molecular dynamics simulations with explicit solvent and exhaustive sampling of model peptides to address the backbone conformational entropy difference between Ala and Gly in the denatured state. The mutation of Ala to Gly leads to an increase in conformational entropy equivalent to approximately 0.4 kcal.mol(-1) in a fully flexible denatured, that is, unfolded, state. But, this energy is closely counterbalanced by the (measured) difference in free energy of transfer of the glycine and alanine side chains from the vapor phase to water so that the unfolded alanine- and glycine-containing peptides are approximately isoenergetic. The helix-stabilizing propensity of Ala relative to Gly thus mainly results from more favorable interactions of Ala in the folded helical structure. The small difference in energetics in the denatured states means that the Phi-values derived from Ala --> Gly scanning of helices are a very good measure of the extent of formation of structure in proteins with little residual structure in the denatured state.

Generation and analysis of proline mutants in protein G

The pyrrolidine ring of the amino acid proline reduces the conformational freedom of the protein backbone in its unfolded form and thus enhances protein stability. The strategy of inserting proline into regions of the protein where it does not perturb the structure has been utilized to stabilize many different proteins including enzymes. However, most of these efforts have been based on trial and error, rather than rational design. Here, we try to understand proline's effect on protein stability by introducing proline mutations into various regions of the B1 domain of Streptococcal protein G. We also applied the Optimization of Rotamers By Iterative Techniques computational protein design program, using two different solvation models, to determine the extent to which it could predict the stabilizing and destabilizing effects of prolines. Use of a surface area dependent solvation model resulted in a modest correlation between the experimental free energy of folding and computed energies; on the other hand, use of a Gaussian solvent exclusion model led to significant positive correlation. Including a backbone conformational entropy term to the computational energies increases the statistical significance of the correlation between the experimental stabilities and both solvation models.

Interaction of a peptide from the receptor-binding domain of Pseudomonas aeruginosa pili strain PAK with a cross-reactive antibody: changes in backbone dynamics induced by binding.

The C-terminal receptor-binding region of Pseudomonas aeruginosa pilin protein strain PAK (residues 128-144) has been the target for the design of a vaccine effective against P. aeruginosa infections. We have recently cloned and expressed a (15)N-labeled PAK pilin peptide spanning residues 128-144 of the PAK pilin protein. The peptide exists as a major (trans) and minor (cis) species in solution, arising from isomerization around a central Ile(138)-Pro(139) peptide bond. The trans isomer adopts two well-defined turns in solution, a type I beta-turn spanning Asp(134)-Glu-Gln-Phe(137) and a type II beta-turn spanning Pro(139)-Lys-Gly-Cys(142). The cis isomer adopts only one well-defined type II beta-turn spanning Pro(139)-Lys-Gly-Cys(142) but displays evidence of a less ordered turn spanning Asp(132)-Gln-Asp-Glu(135). These turns have been implicated in cross-reactive antibody recognition. (15)N NMR relaxation experiments of the (15)N-labeled recombinant PAK pilin peptide in complex with an Fab fragment of a cross-reactive monoclonal antibody, PAK-13, raised against the intact PAK pilus, were performed in order to probe for changes in the mobilities and dynamics of the peptide backbone as a result of antibody binding. The major results of these studies are as follows: binding of Fab leads to the preferential ordering of the first turn over the second turn in each isomer, binding of Fab partially stabilizes peptide backbone regions undergoing slow (microsecond to millisecond) exchange-related motions, and binding of Fab leads to a greater loss in backbone conformational entropy at pH 7.2 versus pH 4.5. The biological implications of these results will be discussed in relation to the role that fast and slow backbone motions play in PAK pilin peptide immunogenicity and within the framework of developing a pilin peptide vaccine capable of conferring broad immunity across P. aeruginosa strains.

The Backbone Conformational Entropy of Protein Folding: Experimental Measures from Atomic Force Microscopy

The energy dissipated during the atomic force microscopy-based mechanical unfolding and extension of proteins is typically an order of magnitude greater than their folding free energy. The vast majority of the “excess” energy dissipated is thought to arise due to backbone conformational entropy losses as the solvated, random-coil unfolded state is stretched into an extended, low-entropy conformation. We have investigated this hypothesis in light of recent measurements of the energy dissipated during the mechanical unfolding of “polyproteins” comprised of multiple, homogeneous domains. Given the assumption that backbone conformational entropy losses account for the vast majority of the energy dissipated (an assumption supported by numerous lines of experimental evidence), we estimate that ∼19(±2) J/(mol K residue) of entropy is lost during the extension of three mechanically stable β-sheet polyproteins. If, as suggested by measured peak-to-peak extension distances, pulling proceeds to near completion, this estimate corresponds to the absolute backbone conformational entropy of the unfolded state. As such, it is exceedingly close to previous theoretical and semi-empirical estimates that place this value at ∼20 J/(mol K residue). The estimated backbone conformational entropy lost during the extension of two helical polyproteins, which, in contrast to the mechanically stable β-sheet polyproteins, rupture at very low applied forces, is three- to sixfold less. Either previous estimates of the backbone conformational entropy are significantly in error, or the reduced mechanical strength of the helical proteins leads to the rupture of a subsequent domain before full extension (and thus complete entropy loss) is achieved.

Polyproline II structure in a sequence of seven alanine residues.

A sequence of seven alanine residues-too short to form an alpha-helix and whose side chains do not interact with each other-is a particularly simple model for testing the common description of denatured proteins as structureless random coils. The (3)J(HN alpha) coupling constants of individual alanine residues have been measured from 2 to 56 degrees C by using isotopically labeled samples. The results display a thermal transition between different backbone conformations, which is confirmed by CD spectra. The NMR results suggest that polyproline II is the dominant conformation at 2 degrees C and the content of beta strand is increased by approximately 10% at 55 degrees C relative to that at 2 degrees C. The polyproline II conformation is consistent with recent studies of short alanine peptides, including structure prediction by ab initio quantum mechanics and solution structures for both a blocked alanine dipeptide and an alanine tripeptide. CD and other optical spectroscopies have found structure in longer "random coil" peptides and have implicated polyproline II, which is a major backbone conformation in residues within loop regions of protein structures. Our result suggests that the backbone conformational entropy in alanine peptides is considerably smaller than estimated by the random coil model. New thermodynamic data confirm this suggestion: the entropy loss on alanine helix formation is only 2.2 entropy units per residue.

Computational stabilization of human growth hormone

Recombinant human growth hormone (hGH) is used worldwide for the treatment of pediatric hypopituitary dwarfism and in children suffering from low levels of hGH. It has limited stability in solution, and because of poor oral absorption, is administered by injection, typically several times a week. Development has therefore focused on more stable or sustained-release formulations and alternatives to injectable delivery that would increase bioavailability and make it easier for patients to use. We redesigned hGH computationally to improve its thermostability. A more stable variant of hGH could have improved pharmacokinetics or enhanced shelf-life, or be more amenable to use in alternate delivery systems and formulations. The computational design was performed using a previously developed combinatorial optimization algorithm based on the dead-end elimination theorem. The algorithm uses an empirical free energy function for scoring designed sequences. This function was augmented with a term that accounts for the loss of backbone and side-chain conformational entropy. The weighting factors for this term, the electrostatic interaction term, and the polar hydrogen burial term were optimized by minimizing the number of mutations designed by the algorithm relative to wild-type. Forty-five residues in the core of the protein were selected for optimization with the modified potential function. The proteins designed using the developed scoring function contained six to 10 mutations, showed enhancement in the melting temperature of up to 16 degrees C, and were biologically active in cell proliferation studies. These results show the utility of our free energy function in automated protein design.

Structure, dynamics, and thermodynamics of the structural domain of troponin C in complex with the regulatory peptide 1-40 of troponin I.

The structure of the calcium-saturated C-domain of skeletal troponin C (CTnC) in complex with a regulatory peptide comprising residues 1-40 (Rp40) of troponin I (TnI) was determined using nuclear magnetic resonance (NMR) spectroscopy. The solution structure determined by NMR is similar to the structure of the C-domain from intact TnC in complex with TnI(1)(-)(47) determined by X-ray crystallography [Vassylyev, D. G., Takeda, S., Wakatsuki, S., Maeda, K., and Maeda, Y. (1998) Proc. Natl. Acad. Sci. U.S.A. 95, 4847-4852]. Changes in the dynamic properties of CTnC.2Ca2+ induced by Rp40 binding were investigated using backbone amide (15)N NMR relaxation measurements. Analysis of NMR relaxation data allows for extraction of motional order parameters on a per residue basis, from which the contribution of changes in picosecond to nanosecond time scale motions to the conformational entropy associated with complex formation can be estimated. The results indicate that binding of Rp40 decreases backbone flexibility in CTnC, particularly at the end of the C-terminal helix. The backbone conformational entropy change (-TDeltaS) associated with binding of Rp40 to CTnC.2Ca2+ determined from (15)N relaxation data is 9.6 +/- 0.7 kcal mol(-1) at 30 degrees C. However, estimation of thermodynamic quantities using a structural approach [Lavigne, P., Bagu, J. R., Boyko, R., Willard, L., Holmes, C. F., and Sykes, B. D. (2000) Protein Sci. 9, 252-264] reveals that the change in solvation entropy upon complex formation is dominant and overcomes the thermodynamic "cost" associated with "stiffening" of the protein backbone upon Rp40 binding. Additionally, backbone amide (15)N relaxation data measured at different concentrations of CTnC.2Ca2+.Rp40 reveal that the complex dimerizes in solution. Fitting of the apparent global rotational correlation time as a function of concentration to a monomer-dimer equilibrium yields a dimerization constant of approximately 8.3 mM.

Long-range order in the src SH3 folding transition state.

One of the outstanding questions in protein folding concerns the degree of heterogeneity in the folding transition state ensemble: does a protein fold via a large multitude of diverse "pathways," or are the elements of native structure assembled in a well defined order? Herein, we build on previous point mutagenesis studies of the src SH3 by directly investigating the association of structural elements and the loss of backbone conformational entropy during folding. Double-mutant analysis of polar residues in the distal beta-hairpin and the diverging turn indicates that the hydrogen bond network between these elements is largely formed in the folding transition state. A 10-glycine insertion in the n-src loop (which connects the distal hairpin and the diverging turn) and a disulfide crosslink at the base of the distal beta-hairpin exclusively affect the folding rate, showing that these structural elements are nearly as ordered in the folding transition state as in the native state. In contrast, crosslinking the base of the RT loop or the N and C termini dramatically slows down the unfolding rate, suggesting that dissociation of the termini and opening of the RT loop precede the rate-limiting step in unfolding. Taken together, these results suggest that essentially all conformations in the folding transition state ensemble have the central three-stranded beta-sheet formed, indicating that, for the src homology 3 domain, there is a discrete order to structure assembly during folding.

Increased protein backbone conformational entropy upon hydrophobic ligand binding.

For complexes between proteins and very small hydrophobic ligands, hydrophobic effects alone may be insufficient to outweigh the unfavorable entropic terms resulting from bimolecular association. NMR relaxation experiments indicate that the backbone flexibility of mouse major urinary protein increases upon binding the hydrophobic mouse pheromone 2-sec-butyl-4,5-dihydrothiazole. The associated increase in backbone conformational entropy of the protein appears to make a substantial contribution toward stabilization of the protein-pheromone complex. This term is likely comparable in magnitude to other important free energy contributions to binding and may represent a general mechanism to promote binding of very small ligands to macromolecules.