Unifying mechanical and thermodynamic descriptions across the thioredoxin protein family

Abstract

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 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.

Calculating Ensemble Averaged Descriptions of Protein Rigidity without Sampling

“…Unlike the binary RCMs, MCMs are based on a continuous scale that identifies the fractional number of pebbles shared between each carbon pair. In this sense, the MCMs are similar to the cooperativity correlation plots calculated by our statistical mechanical DCM [18], [19], [22]–[25]. Fig.…”

Ensemble Properties of Network Rigidity Reveal Allosteric Mechanisms

“…Specifically, our results identify drastic CC differences across datasets of the RNase H pair (8), four bacterial periplasmic binding proteins (10) and nine oxidized thioredoxin mutants (11). In addition, even greater CC changes are observed across pairs of holo/apo binding proteins (10) and oxidized/reduced thioredoxins (11). Taken together, these results highlight the sensitivity within the set of pairwise allosteric couplings present in protein structures.…”

“…As a consequence, quantified stability/flexibility relationships (QSFR) can be predicted (8-11), which provides a high dimensional characterization of protein stability, flexibility and their interrelationships. Each QSFR metric integrates mechanical and thermodynamic descriptions of structure.…”

“…With the theoretical framework laid out, the DCM is solved using an efficient graph-rigidity algorithm in conjunction with a hybrid Monte Carlo and mean field approximation (6). The consequence of this approach is the ability to calculate a large number mechanical network properties in a thermodynamically meaningful way, including pairwise residue-to-residue couplings intrinsic to the native structure ensemble (7-11) and putative allosteric sites via a perturbation method (12). …”

An Interfacial Thermodynamics Model for Protein Stability

“…Moreover, the DCM predicts substructures within a protein that are rigid or flexible, and identifies sets of atoms that are co-rigid or co-flexible within a correlated motion. Many studies on proteins using a minimal DCM (mDCM) have elucidated stability/flexibility relationships important to function [Livesay & Jacobs, 2006;Livesay, et al 2008;Mottonen, et al 2009;Verma, et al 2010] including the study of allostery [Mottonen, et al 2010]. The DCM provides a good estimate for conformational entropy in simple loop systems compared to exact calculations .…”