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.

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 ß4/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.

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.