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. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Flexibility Correlation between Active Site Regions Is Conserved across Four AmpC β-Lactamase Enzymes

β-lactamases are bacterial enzymes that confer resistance to β-lactam antibiotics, such as penicillins and cephalosporins. There are four classes of β-lactamase enzymes, each with characteristic sequence and structure properties. Enzymes from class A are the most common and have been well characterized across the family; however, less is known about how physicochemical properties vary across the C and D families. In this report, we compare the dynamical properties of four AmpC (class C) β-lactamases using our distance constraint model (DCM). The DCM reliably predicts thermodynamic and mechanical properties in an integrated way. As a consequence, quantitative stability/flexibility relationships (QSFR) can be determined and compared across the whole family. The DCM calculates a large number of QSFR metrics. Perhaps the most useful is the flexibility index (FI), which quantifies flexibility along the enzyme backbone. As typically observed in other systems, FI is well conserved across the four AmpC enzymes. Cooperativity correlation (CC), which quantifies intramolecular couplings within structure, is rarely conserved across protein families; however, it is in AmpC. In particular, the bulk of each structure is composed of a large rigid cluster, punctuated by three flexibly correlated regions located at the active site. These regions include several catalytic residues and the Ω-loop. This evolutionary conservation combined with active their site location strongly suggests that these coupled dynamical modes are important for proper functioning of the enzyme.     

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.     

A flexible approach for understanding protein stability

A distance constraint model (DCM) is presented that identifies flexible regions within protein structure consistent with specified thermodynamic condition. The DCM is based on a rigorous free energy decomposition scheme representing structure as fluctuating constraint topologies. Entropy non-additivity is problematic for naive decompositions, limiting the success of heat capacity predictions. The DCM resolves non-additivity by summing over independent entropic components determined by an efficient network-rigidity algorithm. A minimal 3-parameter DCM is demonstrated to accurately reproduce experimental heat capacity curves. Free energy landscapes and quantitative stability-flexibility relationships are obtained in terms of global flexibility. Several connections to experiment are made.     

Local fluctuations vs. global unfolding of proteins investigated by limited proteolysis

The structure of a protein molecule consists of both rigid and flexible sections to satisfy the demands for stability and catalysis. Because the flexibility of a protein segment is indispensable for a proteolytic attack, limited proteolysis is a superb tool to analyse both confined local fluctuations and global unfolding events in proteins. While the identification of the primary cleavage products allows the assignment of the flexible regions to the primary structure, the kinetics of proteolytic degradation enables differentiation between local fluctuations in the native protein molecule and the global unfolding process during denaturation. Modifications of the amino acid sequence in the concerned regions can tune proteolytic susceptibility and alter protein stability. In the present paper, we summarise our results on native-state and unfolded-state proteolysis of ribonuclease A (RNase A) and the effect of mutations in the detected flexible regions on the stability and unfolding of the RNase A molecule.     

Local fluctuations vs. global unfolding of proteins investigated by limited proteolysis

The structure of a protein molecule consists of both rigid and flexible sections to satisfy the demands for stability and catalysis. Because the flexibility of a protein segment is indispensable for a proteolytic attack, limited proteolysis is a superb tool to analyse both confined local fluctuations and global unfolding events in proteins. While the identification of the primary cleavage products allows the assignment of the flexible regions to the primary structure, the kinetics of proteolytic degradation enables differentiation between local fluctuations in the native protein molecule and the global unfolding process during denaturation. Modifications of the amino acid sequence in the concerned regions can tune proteolytic susceptibility and alter protein stability. In the present paper, we summarise our results on native-state and unfolded-state proteolysis of ribonuclease A (RNase A) and the effect of mutations in the detected flexible regions on the stability and unfolding of the RNase A molecule.     

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

Numerous quantitative stability/flexibility relationships, within Escherichia coli thioredoxin (Trx) and its fragments are determined using a minimal distance constraint model (DCM). A one-dimensional free energy landscape as a function of global flexibility reveals Trx to fold in a low-barrier two-state process, with a voluminous transition state. Near the folding transition temperature, the native free energy basin is markedly skewed to allow partial unfolded forms. Under native conditions the skewed shape is lost, and the protein forms a compact structure with some flexibility. Predictions on ten Trx fragments are generally consistent with experimental observations that they are disordered, and that complementary fragments reconstitute. A hierarchical unfolding pathway is uncovered using an exhaustive computational procedure of breaking interfacial cross-linking hydrogen bonds that span over a series of fragment dissociations. The unfolding pathway leads to a stable core structure (residues 22-90), predicted to act as a kinetic trap. Direct connection between degree of rigidity within molecular structure and non-additivity of free energy is demonstrated using a thermodynamic cycle involving fragments and their hierarchical unfolding pathway. Additionally, the model provides insight about molecular cooperativity within Trx in its native state, and about intermediate states populating the folding/unfolding pathways. Native state cooperativity correlation plots highlight several flexibly correlated regions, giving insight into the catalytic mechanism that facilitates access to the active site disulfide bond. Residual native cooperativity correlations are present in the core substructure, suggesting that Trx can function when it is partly unfolded. This natively disordered kinetic trap, interpreted as a molten globule, has a wide temperature range of metastability, and it is identified as the "slow intermediate state" observed in kinetic experiments. These computational results are found to be in overall agreement with a large array of experimental data.     

Combining phylogenetic data with co-regulated genes to identify regulatory motifs

MOTIVATION: Discovery of regulatory motifs in unaligned DNA sequences remains a fundamental problem in computational biology. Two categories of algorithms have been developed to identify common motifs from a set of DNA sequences. The first can be called a 'multiple genes, single species' approach. It proposes that a degenerate motif is embedded in some or all of the otherwise unrelated input sequences and tries to describe a consensus motif and identify its occurrences. It is often used for co-regulated genes identified through experimental approaches. The second approach can be called 'single gene, multiple species'. It requires orthologous input sequences and tries to identify unusually well conserved regions by phylogenetic footprinting. Both approaches perform well, but each has some limitations. It is tempting to combine the knowledge of co-regulation among different genes and conservation among orthologous genes to improve our ability to identify motifs. RESULTS: Based on the Consensus algorithm previously established by our group, we introduce a new algorithm called PhyloCon (Phylogenetic Consensus) that takes into account both conservation among orthologous genes and co-regulation of genes within a species. This algorithm first aligns conserved regions of orthologous sequences into multiple sequence alignments, or profiles, then compares profiles representing non-orthologous sequences. Motifs emerge as common regions in these profiles. Here we present a novel statistic to compare profiles of DNA sequences and a greedy approach to search for common subprofiles. We demonstrate that PhyloCon performs well on both synthetic and biological data. AVAILABILITY: Software available upon request from the authors. http://ural.wustl.edu/softwares.html     

RNase YI* and RNA structure studies.

The enzymology of RNase YI*, a recently discovered endoribonuclease from yeast, was studied and compared to other endonucleases for detection of single-strand regions and base pair mismatches in RNA. Its value for RNA structure analyses was assessed with Escherichia coli 5S rRNA as a model substrate. The generally accepted structure of the 5S rRNA is based on thermodynamic energy considerations as well as structures conserved in regions of the molecule during evolution. S1 and mung bean nucleases gave similar results with very marked preference only for the longest single-stranded region in the model. RNase YI* was much more discriminating for detecting unpaired nucleotides as well as short single-strand regions and predicted the generally accepted 5S rRNA structure. Preliminary experiments also indicated that RNase YI* was more sensitive than RNase I for detecting single or multiple base pair mismatches in an RNA-DNA hybrid.     

An inserted Gly residue fine tunes dynamics between mesophilic and thermophilic ribonucleases H

Dynamic processes are inherent properties of proteins and are crucial for a wide range of biological functions. To address how changes in protein sequence and structure affect dynamic processes, a quantitative comparison of microsecond-to-microsecond time scale conformational changes, measured by solution NMR spectroscopy, within homologous mesophilic and thermophilic ribonuclease H (RNase H) enzymes is presented. Kinetic transitions between the observed major state (high population) and alternate (low population) conformational state(s) of the substrate-binding handle region in RNase H from the mesophile Escherichia coli (ecRNH) and thermophile Thermus thermophilus (ttRNH) occur with similar kinetic exchange rate constants, but the difference in stability between exchanging conformers is smaller in ttRNH compared to ecRNH. The altered thermodynamic equilibrium between kinetically exchanging conformers in the thermophile is recapitulated in ecRNH by the insertion of a Gly residue within a putative hinge between alpha-helices B and C. This Gly insertion is conserved among thermophilic RNases H, and allows the formation of additional intrahelical hydrogen bonds. A Gly residue inserted between alpha-helices B and C appears to relieve unfavorable interactions in the transition state and alternate conformer(s) and represents an important adaptation to adjust conformational changes within RNase H for activity at high temperatures.     

Vibrations-determined properties of green fluorescent protein

The physicochemical characteristics of the green fluorescent protein (GFP), including the thermodynamic properties (entropy, enthalpy, Gibbs' free energy, heat capacity), normal mode vibrations, and atomic fluctuations, were investigated. The Gaussian 03 computational chemistry program was employed for normal mode analysis using the AMBER force field. The thermodynamic parameters and atomic fluctuations were then calculated from the vibrational eigenvalues (frequencies) and eigenvectors. The regions of highest rigidity were shown to be the beta-sheet barrel with the central alpha-helix, which bears the chromophore. The most flexible parts of the GFP molecule were the outlying loops that cover the top and bottom of the beta-barrel. This way, the balance between rigidity and flexibility is maintained, which is the optimal relationship for protein stability in terms of Gibbs' free energy. This dual-schemed structure satisfies the requirements for GFP function. In this sense, the structure of GFP resembles a nanoscale drum: a stiff cylinder with flexible vibrating end(s).     

Functional flexibility of human cyclin-dependent kinase-2 and its evolutionary conservation

Cyclin-dependent kinase 2 (CDK2) is the most thoroughly studied of the cyclin-dependent kinases that regulate essential cellular processes, including the cell cycle, and it has become a model for studies of regulatory mechanisms at the molecular level. This contribution identifies flexible and rigid regions of CDK2 based on temperature B-factors acquired from both X-ray data and molecular dynamics simulations. In addition, the biological relevance of the identified flexible regions and their motions is explored using information from the essential dynamics analysis related to conformational changes of CDK2 and knowledge of its biological function(s). The conserved regions of CMGC protein kinases' primary sequences are located in the most rigid regions identified in our analyses, with the sole exception of the absolutely conserved G13 in the tip of the glycine-rich loop. The conserved rigid regions are important for nucleotide binding, catalysis, and substrate recognition. In contrast, the most flexible regions correlate with those where large conformational changes occur during CDK2 regulation processes. The rigid regions flank and form a rigid skeleton for the flexible regions, which appear to provide the plasticity required for CDK2 regulation. Unlike the rigid regions (which as mentioned are highly conserved) no evidence of evolutionary conservation was found for the flexible regions.     

Structural,energetic, and dynamic responses of the native state ensemble of staphylococcal nuclease to cavity‐creating mutations

The effects of cavity‐creating mutations on the structural flexibility, local and global stability, and dynamics of the folded state of staphylococcal nuclease (SNase) were examined with NMR spectroscopy, MD simulations, H/D exchange, and pressure perturbation. Effects on global thermodynamic stability correlated well with the number of heavy atoms in the vicinity of the mutated residue. Variants with substitutions in the C‐terminal domain and the interface between α and β subdomains showed large amide chemical shift variations relative to the parent protein, moderate, widespread, and compensatory perturbations of the H/D protection factors and increased local dynamics on a nanosecond time scale. The pressure sensitivity of the folded states of these variants was similar to that of the parent protein. Such observations point to the capacity of the folded proteins to adjust to packing defects in these regions. In contrast, cavity creation in the β‐barrel subdomain led to minimal perturbation of the structure of the folded state, However, significant pressure dependence of the native state amide resonances, along with strong effects on native state H/D exchange are consistent with increased probability of population of excited state(s) for these variants. Such contrasted responses to the creation of cavities could not be anticipated from global thermodynamic stability or crystal structures; they depend on the local structural and energetic context of the substitutions. © 2012 Wiley Periodicals, Inc.     

Thermodynamic stability of histone H3 is a necessary but not sufficient driving force for its evolutionary conservation

Determining the forces that conserve amino acid positions in proteins across species is a fundamental pursuit of molecular evolution. Evolutionary conservation is driven by either a protein's function or its thermodynamic stability. Highly conserved histone proteins offer a platform to evaluate these driving forces. While the conservation of histone H3 and H4 "tail" domains and surface residues are driven by functional importance, the driving force behind the conservation of buried histone residues has not been examined. Using a computational approach, we determined the thermodynamically preferred amino acids at each buried position in H3 and H4. In agreement with what is normally observed in proteins, we find a significant correlation between thermodynamic stability and evolutionary conservation in the buried residues in H4. In striking contrast, we find that thermodynamic stability of buried H3 residues does not correlate with evolutionary conservation. Given that these H3 residues are not post-translationally modified and only regulate H3-H3 and H3-H4 stabilizing interactions, our data imply an unknown function responsible for driving conservation of these buried H3 residues.     

Salt bridge as a gatekeeper against partial unfolding

Salt bridges are frequently observed in protein structures. Because the energetic contribution of salt bridges is strongly dependent on the environmental context, salt bridges are believed to contribute to the structural specificity rather than the stability. To test the role of salt bridges in enhancing structural specificity, we investigated the contribution of a salt bridge to the energetics of native‐state partial unfolding in a cysteine‐free version of Escherichia coli ribonuclease H (RNase H*). Thermolysin cleaves a protruding loop of RNase H^* through transient partial unfolding under native conditions. Lys86 and Asp108 in RNase H^* form a partially buried salt bridge that tethers the protruding loop. Investigation of the global stability of K86Q/D108N RNase H^* showed that the salt bridge does not significantly contribute to the global stability. However, K86Q/D108N RNase H^* is greatly more susceptible to proteolysis by thermolysin than wild‐type RNase H^* is. The free energy for partial unfolding determined by native‐state proteolysis indicates that the salt bridge significantly increases the energy for partial unfolding by destabilizing the partially unfolded form. Double mutant cycles with single and double mutations of the salt bridge suggest that the partially unfolded form is destabilized due to a significant decrease in the interaction energy between Lys86 and Asp108 upon partial unfolding. This study demonstrates that, even in the case that a salt bridge does not contribute to the global stability, the salt bridge may function as a gatekeeper against partial unfolding that disturbs the optimal geometry of the salt bridge.     

Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity

Given the three-dimensional structure of a protein, its thermodynamic properties are calculated using a recently introduced distance constraint model (DCM) within a mean-field treatment. The DCM is constructed from a free energy decomposition that partitions microscopic interactions into a variety of constraint types, i.e., covalent bonds, salt-bridges, hydrogen-bonds, and torsional-forces, each associated with an enthalpy and entropy contribution. A Gibbs ensemble of accessible microstates is defined by a set of topologically distinct mechanical frameworks generated by perturbing away from the native constraint topology. The total enthalpy of a given framework is calculated as a linear sum of enthalpy components over all constraints present. Total entropy is generally a nonadditive property of free energy decompositions. Here, we calculate total entropy as a linear sum of entropy components over a set of independent constraints determined by a graph algorithm that builds up a mechanical framework one constraint at a time, placing constraints with lower entropy before those with greater entropy. This procedure provides a natural mechanism for enthalpy-entropy compensation. A minimal DCM with five phenomenological parameters is found to capture the essential physics relating thermodynamic response to network rigidity. Moreover, two parameters are fixed by simultaneously fitting to heat capacity curves for histidine binding protein and ubiquitin at five different pH conditions. The three free parameter DCM provides a quantitative characterization of conformational flexibility consistent with thermodynamic stability. It is found that native hydrogen bond topology provides a key signature in governing molecular cooperativity and the folding-unfolding transition.     

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. Proteins 2015; 83:1987–2007. © 2015 Wiley Periodicals, Inc.