Elucidating quantitative stability/flexibility relationships within thioredoxin and its fragments using a distance constraint model

Protein Function Analysis through Machine Learning

Machine learning (ML) has been an important arsenal in computational biology used to elucidate protein function for decades. With the recent burgeoning of novel ML methods and applications, new ML approaches have been incorporated into many areas of computational biology dealing with protein function. We examine how ML has been integrated into a wide range of computational models to improve prediction accuracy and gain a better understanding of protein function. The applications discussed are protein structure prediction, protein engineering using sequence modifications to achieve stability and druggability characteristics, molecular docking in terms of protein–ligand binding, including allosteric effects, protein–protein interactions and protein-centric drug discovery. To quantify the mechanisms underlying protein function, a holistic approach that takes structure, flexibility, stability, and dynamics into account is required, as these aspects become inseparable through their interdependence. Another key component of protein function is conformational dynamics, which often manifest as protein kinetics. Computational methods that use ML to generate representative conformational ensembles and quantify differences in conformational ensembles important for function are included in this review. Future opportunities are highlighted for each of these topics.

Rational Design of Disulfide Bonds for Enhancing the Thermostability of the 1,4-α-Glucan Branching Enzyme from Geobacillus thermoglucosidans STB02

Disulfide bonds play crucial roles in thermostabilization, recognition, or activation of proteins. They are vital in maintaining the respective conformations of globular structures, thereby enhancing thermostability. Bioinformatic approaches provide practical strategies to build disulfide bonds based on structural information. We constructed nine mutants by rational analysis of the 1,4-α-glucan branching enzyme (EC 2.4.1.18) from Geobacillus thermoglucosidans STB02, which catalyzes the synthesis of α-1,6-glucosidic bonds by acting on α-(1,4) and/or α-(1,6) glucosidic linkages. Four of the mutations enhanced thermostability, and five of them had adverse or negligible effects on stability. Circular dichroism spectra and intrinsic fluorescence analysis showed that introducing disulfide bonds might only affect secondary structures. The results also demonstrated that the distances of Cα carbons and thiol groups, as well as the sequence between the two cysteines, need to be considered when designing disulfide bonds.

Novel Ricin Subunit Antigens With Enhanced Capacity to Elicit Toxin-Neutralizing Antibody Responses in Mice

RiVax is a candidate ricin toxin subunit vaccine antigen that has proven to be safe in human phase I clinical trials. In this study, we introduced double and triple cavity-filling point mutations into the RiVax antigen with the expectation that stability-enhancing modifications would have a beneficial effect on overall immunogenicity of the recombinant proteins. We demonstrate that 2 RiVax triple mutant derivatives, RB (V81L/C171L/V204I) and RC (V81I/C171L/V204I), when adsorbed to aluminum salts adjuvant and tested in a mouse prime-boost-boost regimen were 5- to 10-fold more effective than RiVax at eliciting toxin-neutralizing serum IgG antibody titers. Increased toxin neutralizing antibody values and seroconversion rates were evident at different antigen dosages and within 7 days after the first booster. Quantitative stability/flexibility relationships analysis revealed that the RB and RC mutations affect rigidification of regions spanning residues 98-103, which constitutes a known immunodominant neutralizing B-cell epitope. A more detailed understanding of the immunogenic nature of RB and RC may provide insight into the fundamental relationship between local protein stability and antibody reactivity.

Dynamics and thermodynamic properties of CXCL7 chemokine

Chemokines form a family of signaling proteins mainly responsible for directing the traffic of leukocytes, where their biological activity can be modulated by their oligomerization state. We characterize the dynamics and thermodynamic stability of monomer and homodimer structures of CXCL7, one of the most abundant platelet chemokines, using experimental methods that include circular dichroism (CD) and nuclear magnetic resonance (NMR) spectroscopy, and computational methods that include the anisotropic network model (ANM), molecular dynamics (MD) simulations and the distance constraint model (DCM). A consistent picture emerges for the effects of dimerization and Cys5-Cys31 and Cys7-Cys47 disulfide bonds formation. The presence of disulfide bonds is not critical for maintaining structural stability in the monomer or dimer, but the monomer is destabilized more than the dimer upon removal of disulfide bonds. Disulfide bonds play a key role in shaping the characteristics of native state dynamics. The combined analysis shows that upon dimerization flexibly correlated motions are induced between the 30s and 50s loop within each monomer and across the dimer interface. Interestingly, the greatest gain in flexibility upon dimerization occurs when both disulfide bonds are present, and the homodimer is least stable relative to its two monomers. These results suggest that the highly conserved disulfide bonds in chemokines facilitate a structural mechanism that is tuned to optimally distinguish functional characteristics between monomer and dimer.

Rigidity Emerges during Antibody Evolution in Three Distinct Antibody Systems: Evidence from QSFR Analysis of Fab Fragments

The effects of somatic mutations that transform polyspecific germline (GL) antibodies to affinity mature (AM) antibodies with monospecificity are compared among three GL-AM Fab pairs. In particular, changes in conformational flexibility are assessed using a Distance Constraint Model (DCM). We have previously established that the DCM can be robustly applied across a series of antibody fragments (VL to Fab), and subsequently, the DCM was combined with molecular dynamics (MD) simulations to similarly characterize five thermostabilizing scFv mutants. The DCM is an ensemble based statistical mechanical approach that accounts for enthalpy/entropy compensation due to network rigidity, which has been quite successful in elucidating conformational flexibility and Quantitative Stability/Flexibility Relationships (QSFR) in proteins. Applied to three disparate antibody systems changes in QSFR quantities indicate that the VH domain is typically rigidified, whereas the VL domain and CDR L2 loop become more flexible during affinity maturation. The increase in CDR H3 loop rigidity is consistent with other studies in the literature. The redistribution of conformational flexibility is largely controlled by nonspecific changes in the H-bond network, although certain Arg to Asp salt bridges create highly localized rigidity increases. Taken together, these results reveal an intricate flexibility/rigidity response that accompanies affinity maturation.

Antibodies are protective proteins used by the immune system to recognize and neutralize foreign objects through interactions with a specific part of the target, called an antigen. Antibody structures are Y-shaped, contain multiple protein chains, and include two antigen-binding sites. The binding sites are located at the end of the Fab fragments, which are the upward facing arms of the Y-structure. The Fab fragments maintain binding affinity by themselves, and are thus often used as surrogates to student antibody-antigen interactions. High affinity antibodies are produced during the course of an immune response by successive mutations to germline gene-encoded antibodies. Germline antibodies are more likely to be polyspecific, whereas the affinity maturation process yields monoclonal antibodies that bind specifically to the target antigen. In this work, we use a computational Distance Constraint Model to characterize how mechanical properties change as three disparate germline antibodies are converted to affinity mature. Our results reveal a rich set of mechanical responses throughout the Fab structure. Nevertheless, increased rigidity in the VH domain is consistently observed, which is consistent with the transition from polyspecificity to monospecificity. That is, flexible antibody structures are able to recognize multiple antigens, while increased affinity and specificity is achieved—in part—by structural rigidification.

Redistribution of flexibility in stabilizing antibody fragment mutants follows Le Châtelier's principle

Le Châtelier's principle is the cornerstone of our understanding of chemical equilibria. When a system at equilibrium undergoes a change in concentration or thermodynamic state (i.e., temperature, pressure, etc.), La Châtelier's principle states that an equilibrium shift will occur to offset the perturbation and a new equilibrium is established. We demonstrate that the effects of stabilizing mutations on the rigidity ⇔ flexibility equilibrium within the native state ensemble manifest themselves through enthalpy-entropy compensation as the protein structure adjusts to restore the global balance between the two. Specifically, we characterize the effects of mutation to single chain fragments of the anti-lymphotoxin-β receptor antibody using a computational Distance Constraint Model. Statistically significant changes in the distribution of both rigidity and flexibility within the molecular structure is typically observed, where the local perturbations often lead to distal shifts in flexibility and rigidity profiles. Nevertheless, the net gain or loss in flexibility of individual mutants can be skewed. Despite all mutants being exclusively stabilizing in this dataset, increased flexibility is slightly more common than increased rigidity. Mechanistically the redistribution of flexibility is largely controlled by changes in the H-bond network. For example, a stabilizing mutation can induce an increase in rigidity locally due to the formation of new H-bonds, and simultaneously break H-bonds elsewhere leading to increased flexibility distant from the mutation site via Le Châtelier. Increased flexibility within the VH β4/β5 loop is a noteworthy illustration of this long-range effect.

A case study comparing quantitative stability-flexibility relationships across five metallo-β-lactamases highlighting differences within NDM-1

The Distance Constraint Model (DCM) is an ensemble-based biophysical model that integrates thermodynamic and mechanical viewpoints of protein structure. The DCM outputs a large number of structural characterizations that collectively allow for Quantified Stability-Flexibility Relationships (QSFR) to be identified and compared across protein families. Using five metallo-β-lactamases (MBLs) as a representative set, we demonstrate how QSFR properties are both conserved and varied across protein families. Similar to our characterizations on other protein families, the backbone flexibility of the five MBLs are overall visually conserved, yet there are interesting specific quantitative differences. For example, the plasmid-encoded NDM-1 enzyme, which leads to a fast spreading drug-resistant version of Klebsiella pneumoniae, has several regions of significantly increased rigidity relative to the other four. In addition, the set of intramolecular couplings within NDM-1 are also atypical. While long-range couplings frequently vary significantly across protein families, NDM-1 is distinct because it has limited correlated flexibility, which is isolated within the active site S3/S4 and S11/H6 loops. These loops are flexibly correlated in the other members, suggesting it is important to function, but the others also have significant amounts of correlated flexibility throughout the rest of their structures.

Variations within class-A β-lactamase physiochemical properties reflect evolutionary and environmental patterns, but not antibiotic specificity

The bacterial enzyme β-lactamase hydrolyzes the β-lactam ring of penicillin and chemically related antibiotics, rendering them ineffective. Due to rampant antibiotic overuse, the enzyme is evolving new resistance activities at an alarming rate. Related, the enzyme's global physiochemical properties exhibit various amounts of conservation and variability across the family. To that end, we characterize the extent of property conservation within twelve different class-A β-lactamases, and conclusively establish that the systematic variations therein parallel their evolutionary history. Large and systematic differences within electrostatic potential maps and pairwise residue-to-residue couplings are observed across the protein, which robustly reflect phylogenetic outgroups. Other properties are more conserved (such as residue pKa values, electrostatic networks, and backbone flexibility), yet they also have systematic variations that parallel the phylogeny in a statistically significant way. Similarly, the above properties also parallel the environmental condition of the bacteria they are from in a statistically significant way. However, it is interesting and surprising that the only one of the global properties (protein charge) parallels the functional specificity patterns; meaning antibiotic resistance activities are not significantly constraining the global physiochemical properties. Rather, extended spectrum activities can emerge from the background of nearly any set of electrostatic and dynamic properties.

Protein mechanics: how force regulates molecular function

BACKGROUND

Regulation of proteins is ubiquitous and vital for any organism. Protein activity can be altered chemically, by covalent modifications or non-covalent binding of co-factors. Mechanical forces are emerging as an additional way of regulating proteins, by inducing a conformational change or by partial unfolding.

SCOPE

We review some advances in experimental and theoretical techniques to study protein allostery driven by mechanical forces, as opposed to the more conventional ligand driven allostery. In this respect, we discuss recent single molecule pulling experiments as they have substantially augmented our view on the protein allostery by mechanical signals in recent years. Finally, we present a computational analysis technique, Force Distribution Analysis, that we developed to reveal allosteric pathways in proteins.

MAJOR CONCLUSIONS

Any kind of external perturbation, being it ligand binding or mechanical stretching, can be viewed as an external force acting on the macromolecule, rendering force-based experimental or computational techniques, a very general approach to the mechanics involved in protein allostery.

GENERAL SIGNIFICANCE

This unifying view might aid to decipher how complex allosteric protein machineries are regulated on the single molecular level.

Changes in Lysozyme Flexibility upon Mutation Are Frequent, Large and Long-Ranged

We investigate changes in human c-type lysozyme flexibility upon mutation via a Distance Constraint Model, which gives a statistical mechanical treatment of network rigidity. Specifically, two dynamical metrics are tracked. Changes in flexibility index quantify differences within backbone flexibility, whereas changes in the cooperativity correlation quantify differences within pairwise mechanical couplings. Regardless of metric, the same general conclusions are drawn. That is, small structural perturbations introduced by single point mutations have a frequent and pronounced affect on lysozyme flexibility that can extend over long distances. Specifically, an appreciable change occurs in backbone flexibility for 48% of the residues, and a change in cooperativity occurs in 42% of residue pairs. The average distance from mutation to a site with a change in flexibility is 17–20 Å. Interestingly, the frequency and scale of the changes within single point mutant structures are generally larger than those observed in the hen egg white lysozyme (HEWL) ortholog, which shares 61% sequence identity with human lysozyme. For example, point mutations often lead to substantial flexibility increases within the β-subdomain, which is consistent with experimental results indicating that it is the nucleation site for amyloid formation. However, β-subdomain flexibility within the human and HEWL orthologs is more similar despite the lowered sequence identity. These results suggest compensating mutations in HEWL reestablish desired properties.

The functional importance of protein dynamics is universally accepted, making the study of dynamical similarities and differences among proteins of the same function an intriguing problem. While some metrics are likely to be conserved across family, differences are also very common. In previous works we have used a Distance Constraint Model to quantify flexibility differences across sets of orthologous proteins, which reproduce this diversity. In the same manner, this work investigates changes occurring upon individual point mutations. Somewhat surprisingly, the small structural perturbations caused by mutation lead to changes throughout the protein. These changes can be quite large, actually surpassing the scale for differences between ortholog pairs. Moreover, changes in flexibility frequently occur at sites far from the mutation site. These results underscore the sensitivity of protein dynamics in connection with allostery, and help explain why differences across protein families are so common.

Calculating ensemble averaged descriptions of protein rigidity without sampling

Previous works have demonstrated that protein rigidity is related to thermodynamic stability, especially under conditions that favor formation of native structure. Mechanical network rigidity properties of a single conformation are efficiently calculated using the integer body-bar Pebble Game (PG) algorithm. However, thermodynamic properties require averaging over many samples from the ensemble of accessible conformations to accurately account for fluctuations in network topology. We have developed a mean field Virtual Pebble Game (VPG) that represents the ensemble of networks by a single effective network. That is, all possible number of distance constraints (or bars) that can form between a pair of rigid bodies is replaced by the average number. The resulting effective network is viewed as having weighted edges, where the weight of an edge quantifies its capacity to absorb degrees of freedom. The VPG is interpreted as a flow problem on this effective network, which eliminates the need to sample. Across a nonredundant dataset of 272 protein structures, we apply the VPG to proteins for the first time. Our results show numerically and visually that the rigidity characterizations of the VPG accurately reflect the ensemble averaged properties. This result positions the VPG as an efficient alternative to understand the mechanical role that chemical interactions play in maintaining protein stability.

Ensemble properties of network rigidity reveal allosteric mechanisms

The distance constraint model (DCM) is a unique computational modeling paradigm that integrates mechanical and thermodynamic descriptions of macromolecular structure. That is, network rigidity calculations are used to account for nonadditivity within entropy components, thus restoring the utility of free-energy decomposition. The DCM outputs a large number of structural characterizations that collectively allow for quantified stability-flexibility relationships (QSFR) to be identified. In this review, we describe the theoretical underpinnings of the DCM and introduce several common QSFR metrics. Application of the DCM across protein families highlights the sensitivity within the set of protein structure residue-to-residue couplings. Further, we have developed a perturbation method to identify putative allosteric sites, where large changes in QSFR upon rigidification (mimicking ligand-binding) detect sites likely to invoke allosteric changes.

Characterizing protein motions from structure

To clarify the extent structure plays in determining protein dynamics, a comparative study is made using three models that characterize native state dynamics of single domain proteins starting from known structures taken from four distinct SCOP classifications. A geometrical simulation using the framework rigidity optimized dynamics algorithm (FRODA) based on rigid cluster decomposition is compared to the commonly employed elastic network model (specifically the Anisotropic Network Model ANM) and molecular dynamics (MD) simulation. The essential dynamics are quantified by a mode subspace constructed from ANM and a principal component analysis (PCA) on FRODA and MD trajectories. Aggregate conformational ensembles are constructed to provide a basis for quantitative comparisons between FRODA runs using different parameter settings to critically assess how the predictions of essential dynamics depend on a priori arbitrary user-defined distance constraint rules. We established a range of physicality for these parameters. Surprisingly, FRODA maintains greater intra-consistent results than obtained from MD trajectories, comparable to ANM. Additionally, a mode subspace is constructed from PCA on an exemplar set of myoglobin structures from the Protein Data Bank. Significant overlap across the three model subspaces and the experimentally derived subspace is found. While FRODA provides the most robust sampling and characterization of the native basin, all three models give similar dynamical information of a native state, further demonstrating that structure is the key determinant of dynamics.

Nonadditivity in conformational entropy upon molecular rigidification reveals a universal mechanism affecting folding cooperativity

Previously, we employed a Maxwell counting distance constraint model (McDCM) to describe α-helix formation in polypeptides. Unlike classical helix-coil transition theories, the folding mechanism derives from nonadditivity in conformational entropy caused by rigidification of molecular structure as intramolecular cross-linking interactions form along the backbone. For example, when a hydrogen bond forms within a flexible region, both energy and conformational entropy decrease. However, no conformational entropy is lost when the region is already rigid because atomic motions are not constrained further. Unlike classical zipper models, the same mechanism also describes a coil-to-β-hairpin transition. Special topological features of the helix and hairpin structures allow the McDCM to be solved exactly. Taking full advantage of the fact that Maxwell constraint counting is a mean field approximation applied to the distribution of cross-linking interactions, we present an exact transfer matrix method that does not require any special topological feature. Upon application of the model to proteins, cooperativity within the folding transition is yet again appropriately described. Notwithstanding other contributing factors such as the hydrophobic effect, this simple model identifies a universal mechanism for cooperativity within polypeptide and protein-folding transitions, and it elucidates scaling laws describing hydrogen-bond patterns observed in secondary structure. In particular, the native state should have roughly twice as many constraints as there are degrees of freedom in the coil state to ensure high fidelity in two-state folding cooperativity, which is empirically observed.

Nonadditivity in the alpha-helix to coil transition

The Lifson-Roig Model (LRM) and all its variants describe the α-helix to coil transition in terms of additive component-free energies within a free energy decomposition scheme, and these contributions are interpreted through sequence-context dependent nucleation and propagation parameters. Although this phenomenological approach is able to adequately fit experimental data on helix content and heat capacity, the number of required parameters increases dramatically with additional sequence variation. Moreover, due to nonadditive competing microscopic effects that are difficult to disentangle within a LRM, large uncertainties within the parameters emerge. We offer an alternative view that removes the need for sequence-context parameterization by focusing on individual microsopic interactions within a free energy decomposition and explicitly account for nonadditivity in conformational entropy through network rigidity using a Distance Constraint Model (DCM). We apply a LRM and a DCM to previously published experimental heat capacity and helix content data for a series of heterogeneous polypeptides. Both models describe the experimental data well, and the parameters from both models are consistent with prior work. However, the number of DCM parameters is independent of sequence-variability, the parameter values exhibit better transferability, and the helix nucleation is predicted by the DCM explicitly through the nonadditive nature of conformational entropy. The importance of these results is that the DCM offers a system-independent approach for modeling stability within polypeptides and proteins, where the demonstrated accuracy for the α-helix to coil transition over a series of heterogeneous polypeptides described here is one case in point.

Allosteric response is both conserved and variable across three CheY orthologs

A computational method to identify residues likely to initiate allosteric signals has been developed. The method is based on differences within stability and flexibility profiles between wild-type and perturbed structures as computed by a distance constraint model. Application of the approach to three bacterial chemotaxis protein Y (CheY) orthologs provides a comparison of allosteric response across protein family divergence. Interestingly, we observe a rich mixture of both conservation and variability within the identified allosteric sites. While similarity within the overall response parallels the evolutionary relationships, >50% of the best scoring putative sites are only identified in a single ortholog. These results suggest that detailed descriptions of intraprotein communication are substantially more variable than structure and function, yet do maintain some evolutionary relationships. Finally, structural clusters of large response identify four allosteric hotspots, including the β4/α4 loop known to be critical to relaying the CheY phosphorylation signal.

A signal processing method to explore similarity in protein flexibility

Understanding mechanisms of protein flexibility is of great importance to structural biology. The ability to detect similarities between proteins and their patterns is vital in discovering new information about unknown protein functions. A Distance Constraint Model (DCM) provides a means to generate a variety of flexibility measures based on a given protein structure. Although information about mechanical properties of flexibility is critical for understanding protein function for a given protein, the question of whether certain characteristics are shared across homologous proteins is difficult to assess. For a proper assessment, a quantified measure of similarity is necessary. This paper begins to explore image processing techniques to quantify similarities in signals and images that characterize protein flexibility. The dataset considered here consists of three different families of proteins, with three proteins in each family. The similarities and differences found within flexibility measures across homologous proteins do not align with sequence-based evolutionary methods.

Ensemble-based methods for describing protein dynamics

Molecular dynamics (MD) simulation is a natural approach for studying protein dynamics, and coupled with the ideas of multiscale modeling, MD proves to be the gold standard in computational biology to investigate mechanistic details related to protein function. In principle, if MD trajectories are long enough, the ensemble of protein conformations generated allows thermodynamic and kinetic properties to be predicted. We know from experiments that proteins exhibit a high degree of fidelity in function, and that empirical kinetic models are successful in describing kinetics, suggesting that the ensemble of conformations cluster into well-defined thermodynamic states, which are frequently metastable. The experimental evidence suggest that more efficient computational models that retain only essential properties of the protein can be constructed to faithfully reproduce the relatively few observed thermodynamic states, and perhaps describe transition states if the model is sufficiently detailed. Indeed, there are many so-called ensemble-based methods that attempt to generate more complete ensembles than MD can provide by focusing on the most important driving forces through simplified representations of how elements within the protein interact. Although coarse-graining is employed in MD and other approaches, such as in elastic network models, the key distinguishing factor of ensemble-based methods is that they are meant to efficiently generate a large ensemble of conformations without solving explicit equations of motion. This review highlights three types of ensemble-based methods, illustrated by 'COREX' and the Wako-Saito-Munoz-Eaton (WSME) model, the Framework Rigidity Optimized Dynamic Algorithm (FRODA) and the distance constraint model (DCM).

Helix/coil nucleation: a local response to global demands

A complete description of protein structure and function must include a proper treatment of mechanisms that lead to cooperativity. The helix/coil transition serves as a simple example of a cooperative folding process, commonly described by a nucleation-propagation mechanism. The prevalent view is that coil structure must first form a short segment of helix in a localized region despite paying a free energy cost (nucleation). Afterward, helical structure propagates outward from the nucleation site. Both processes entail enthalpy-entropy compensation that derives from the loss in conformational entropy on helix formation with concomitant gain in favorable interactions. Nucleation-propagation models inherently assume that cooperativity arises from a sequential series of local events. An alternative distance constraint model asserts there is a direct link between available degrees of freedom and cooperativity through the nonadditivity in conformational entropy. That is, helix nucleation is a concerted manifestation of rigidity propagating through atomic structure. The link between network rigidity and nonadditivity of conformational entropy is shown in this study by solving the distance constraint model using a simple global constraint counting approximation. Cooperativity arises from competition between excess and deficiency in available degrees of freedom in the coil and helix states respectively.

Unifying mechanical and thermodynamic descriptions across the thioredoxin protein family

We compare various predicted mechanical and thermodynamic properties of nine oxidized thioredoxins (TRX) using a Distance Constraint Model (DCM). The DCM is based on a nonadditive free energy decomposition scheme, where entropic contributions are determined from rigidity and flexibility of structure based on distance constraints. We perform averages over an ensemble of constraint topologies to calculate several thermodynamic and mechanical response functions that together yield quantitative stability/flexibility relationships (QSFR). Applied to the TRX protein family, QSFR metrics display a rich variety of similarities and differences. In particular, backbone flexibility is well conserved across the family, whereas cooperativity correlation describing mechanical and thermodynamic couplings between the residue pairs exhibit distinctive features that readily standout. The diversity in predicted QSFR metrics that describe cooperativity correlation between pairs of residues is largely explained by a global flexibility order parameter describing the amount of intrinsic flexibility within the protein. A free energy landscape is calculated as a function of the flexibility order parameter, and key values are determined where the native-state, transition-state, and unfolded-state are located. Another key value identifies a mechanical transition where the global nature of the protein changes from flexible to rigid. The key values of the flexibility order parameter help characterize how mechanical and thermodynamic response is linked. Variation in QSFR metrics and key characteristics of global flexibility are related to the native state X-ray crystal structure primarily through the hydrogen bond network. Furthermore, comparison of three TRX redox pairs reveals differences in thermodynamic response (i.e., relative melting point) and mechanical properties (i.e., backbone flexibility and cooperativity correlation) that are consistent with experimental data on thermal stabilities and NMR dynamical profiles. The results taken together demonstrate that small-scale structural variations are amplified into discernible global differences by propagating mechanical couplings through the H-bond network.

Identification of putative, stable binding regions through flexibility analysis of HIV-1 gp120

The acquired-immunodeficiency syndrome has evolved into a major worldwide epidemic. Significant effort has been made in the development of antiviral therapies. A new strategy for vaccine and drug design that complements the existing cocktail therapy is to target entry of the human immunodeficiency virus (HIV). Such an approach provides the advantage of interfering with multiple intermediates in this multi-step process. The extraordinary conformational flexibility, glycosylation, and strain variations of viral glycoprotein gp120 cause general viral evasion of humoral immune response and thus complicate the development of an effective vaccine. Especially difficult to define are the conformation of gp120 before CD4 engagement as well as the relative orientations of the V1/V2 and V3 loops with respect to the inner and outer domains. In this study, we used Floppy Inclusion and Rigid Substructure Topography (FIRST), a program based on graph theory, to analyze the flexibility and rigidity of all known HIV-1 gp120 structures. A flexibility index is used to describe and compare the spatial distribution of protein flexibility and rigidity of these structures in isolation and in complex with CD4, CD4-mimics, and neutralizing antibodies. Using this flexibility analysis, we identified a universal rigid region (the alpha2 helix) as well as the consensus largest rigid cluster involving a beta-sheet located on the coreceptor binding face. Both of these regions may serve as stable targets for vaccine design and drug discovery. Detailed comparisons of the changes in flexibility based on strain variations, stabilizing mutations, binding features of CD4 mimics, and impact of b12 binding are reported.

Conformational Entropy of an Ideal Cross-Linking Polymer Chain

We present a novel analytical method to calculate conformational entropy of ideal cross-linking polymers from the configuration integral by employing a Mayer series expansion. Mayer-functions describing chemical bonds within the chain and for cross-links are sharply peaked over the temperature range of interest, and, are well approximated as statistically weighted Dirac delta-functions that enforce distance constraints. All geometrical deformations consistent with a set of distance constraints are integrated over. Exact results for a contiguous series of connected loops are employed to substantiate the validity of a previous phenomenological distance constraint model that describes protein thermodynamics successfully based on network rigidity.

Three dimensional structure directs T-cell epitope dominance associated with allergy

BACKGROUND

CD4+ T-cell epitope immunodominance is not adequately explained by peptide selectivity in class II major histocompatibility proteins, but it has been correlated with adjacent segments of conformational flexibility in several antigens.

METHODS

The published T-cell responses to two venom allergens and two aeroallergens were used to construct profiles of epitope dominance, which were correlated with the distribution of conformational flexibility, as measured by crystallographic B factors, solvent-accessible surface, COREX residue stability, and sequence entropy.

RESULTS

Epitopes associated with allergy tended to be excluded from and lie adjacent to flexible segments of the allergen.

CONCLUSION

During the initiation of allergy, the N- and/or C-terminal ends of proteolytic processing intermediates were preferentially loaded into antigen presenting proteins for the priming of CD4+ T cells.

Hydrogen bond networks determine emergent mechanical and thermodynamic properties across a protein family

Background

Gram-negative bacteria use periplasmic-binding proteins (bPBP) to transport nutrients through the periplasm. Despite immense diversity within the recognized substrates, all members of the family share a common fold that includes two domains that are separated by a conserved hinge. The hinge allows the protein to cycle between open (apo) and closed (ligated) conformations. Conformational changes within the proteins depend on a complex interplay of mechanical and thermodynamic response, which is manifested as an increase in thermal stability and decrease of flexibility upon ligand binding.

Results

We use a distance constraint model (DCM) to quantify the give and take between thermodynamic stability and mechanical flexibility across the bPBP family. Quantitative stability/flexibility relationships (QSFR) are readily evaluated because the DCM links mechanical and thermodynamic properties. We have previously demonstrated that QSFR is moderately conserved across a mesophilic/thermophilic RNase H pair, whereas the observed variance indicated that different enthalpy-entropy mechanisms allow similar mechanical response at their respective melting temperatures. Our predictions of heat capacity and free energy show marked diversity across the bPBP family. While backbone flexibility metrics are mostly conserved, cooperativity correlation (long-range couplings) also demonstrate considerable amount of variation. Upon ligand removal, heat capacity, melting point, and mechanical rigidity are, as expected, lowered. Nevertheless, significant differences are found in molecular cooperativity correlations that can be explained by the detailed nature of the hydrogen bond network.

Conclusion

Non-trivial mechanical and thermodynamic variation across the family is explained by differences within the underlying H-bond networks. The mechanism is simple; variation within the H-bond networks result in altered mechanical linkage properties that directly affect intrinsic flexibility. Moreover, varying numbers of H-bonds and their strengths control the likelihood for energetic fluctuations as H-bonds break and reform, thus directly affecting thermodynamic properties. Consequently, these results demonstrate how unexpected large differences, especially within cooperativity correlation, emerge from subtle differences within the underlying H-bond network. This inference is consistent with well-known results that show allosteric response within a family generally varies significantly. Identifying the hydrogen bond network as a critical determining factor for these large variances may lead to new methods that can predict such effects.

New insight into long-range nonadditivity within protein double-mutant cycles

Additivity principles in chemistry, biochemistry, and biophysics have been used extensively for decades. Nevertheless, it is well known that additivity frequently breaks down in complex biomacromolecules. Nonadditivity within protein double mutant free energy cycles of spatially close residue pairs is a generally well-understood phenomenon, whereas a robust description of nonadditivity extending over large distances remains to be developed. Here, we test the hypothesis that the mutational effects tend to be nonadditive if two structurally well-separated mutated residues belong to the same rigid cluster within the wild type protein, and additive if they are located within different clusters. We find the hypothesis to be statistically significant with P-values that range from 10(-5) to 10(-6). To the best of our knowledge, this result represents the first demonstration of a statistically significant preponderance for nonadditivity over long distances. These findings provide new insight into the origins of long-range nonadditivity in double mutant cycles, which complements the conventional wisdom that nonadditivity arises in double mutations involving contacting residues. Consequently, these results should have far-reaching implications for a proper understanding of protein stability, structure/function analyses, and protein design.

Consolidation of the Thioredoxin Fold by Peptide Recognition: Interaction between E. coli Thioredoxin Fragments 1−93 and 94−108

Escherichia coli thioredoxin (TRX) catalyzes redox reactions via the reversible oxidation of the conserved active center WCGPC. TRX is a monomeric alpha/beta protein with a fold characterized by a central beta-sheet surrounded by alpha-helical elements. The interaction of the C-terminal alpha-helix (helix 5) of TRX against the remainder of the protein involves the close packing of hydrophobic surfaces, opening the possibility of studying a fine-tuned molecular recognition phenomenon. To evaluate the relevance of this interaction on the folding mechanism of TRX, we characterize TRX1-93, a truncated variant of TRX devoid of the last stretch of 15 amino acid residues that includes helix 5. TRX1-93 may possibly represent a molecular form where the folding process becomes interrupted, giving rise to a structure exhibiting the features of a molten globule state. This was assessed by circular dichroism, intrinsic fluorescence, binding of the probe ANS, size-exclusion chromatography, limited proteolysis, and calorimetry. Remarkably, fragment TRX1-93 interacts with peptide TRX94-108 (KD approximately 2-12 microM), bringing forth the restoration of native-like signatures and enzymic function. This represents a molecular event of reciprocal structure selection where both partners gain order, thus leading to long-range consequences on conformation. In this context, the binding of the C-terminal helix could signify a late event in the consolidation of the overall TRX fold.