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 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.

Figure 1

Oxidized thioredoxin heat capacity, C_p, curves. (a) C_p curves of the E. coli and S. aureus homologs are shown. Open circles are experimental data [26, 27], whereas lines are predicted best-fit C_p curves obtained from simulated annealing. In addition, the predicted C_p curves after crossing the “crossing” the best-fit parameters are also shown. (b) C_p curves, shifted to a relative melting point, of all nine thioredoxins using the E. coli best-fit parameters.

Figure 2

An exemplar (a) free energy and (b) rigid cluster susceptibility landscape. The native state, unfolded state, and crossover point are labeled in each panel.

Figure 3

Rigid cluster susceptibility curves for all nine thioredoxins. The peak marks the mechanical transition of the protein from being predominantly composed of a small number of larger rigid clusters to it being composed of a large number of small clusters.

Figure 4

(a) Relative locations of key points along the free energy landscape and mechanical response functions are indicated. The grey and white squares indicate θ_nat and θ_TS, respectively, whereas the black squares indicate θ_RP (the solid line is provided to guide the eye). (b) Across the TRX family, most of the differences within QSFR can be explained by the relative locations of the native state and mechanical transition, θ_RP − θ_nat. Specifically, TRX homologs in which the native state basin significantly precedes the mechanical transition (i.e., Anabaena sp. and E. coli) are predicted to be more compact, whereas TRX-f from spinach chloroplast is expected to be voluminous since θ_RP < θ_nat.

Figure 5

Multiple sequence alignment of the nine oxidized thioredoxins color-coded by F_index values. Isostatic residues, F_index = 0, are colored white, flexible residues are colored red, and rigid residues are colored blue. While local variations are present, a global conservation of backbone flexibility that is consistent with secondary structure is observed.

Figure 6

Ribbon diagrams of the nine oxidized thioredoxins color-coded by F_index. Obvious differences within the active site are present; nevertheless, an overall conservation of flexibility/rigidity is observed. Each structure is oriented in the same way and centered on the active site region. Ordering is based on the relative values of θ_RP and θ_nat.

Figure 7

Cooperativity correlation plots describing intramolecular couplings for the nine oxidized thioredoxins. Blue regions indicate the extent that two residues are simultaneously within the same rigid cluster. Red regions indicate the extent that two residues exist within the same flexible region where the flexibility contiguously propagates. White indicates no correlation between two residues in regards to their rigidity and flexibility. While some similarity in patterns can be seen, the details of each protein are quite distinct. The presented dendrogram describes the hierarchical clustering of a correlation matrix constructed from all 36 pairwise comparisons using the Pearson correlation coefficient. In all cases but one, clustering preserves the relative values of θ_RP and θ_nat.

Figure 8

Pairwise H-bond comparisons across the dataset. (a) Pairwise H-bond conservation vs. pairwise RMSD. Closed circles represent the 36 pairwise comparison of the nine oxidized thioredoxins. Grey indicates the two pairs described in (c) and (d), whereas open circles identify the three redox pairs. (b) Pairwise H-bond conservation vs. pairwise sequence identity (%). Color-coding is the same as in (a). (c) Pairwise H-bond conservation vs. H-bond cut-off energy for the Anabaena sp. TRX-2 to E. coli TRX pair (grey) and the Anabaena sp. TRX-2 to spinach chloroplast TRX-f pair (black). As can be clearly seen, the extent of H-bond conservation diminishes at more stringent cut-offs. (d) The rank ordering (1=most conserved; 36=least conserved) of the H-bond conservation over each of cut-off energy.

Figure 9

Pairwise comparisons of QSFR descriptions. The TRX-2 from Anabaena sp. and TRX from E. coli pair are shown on top, whereas the TRX-2 from Anabaena sp. and TRX-f from spinach chloroplast pair on shown on bottom. The thermodynamic (G(T=T_m,θ)) and mechanical (RCS) landscapes are shown in (a) and (d). G(T=T_m,θ) is shown in solid line, whereas RCS is shown in dashed line. Backbone flexibility, F_index, is shown in (b) and (e). In panels (a), (b), (d), and (e), TRX-2 from Anabaena sp. is colored black, TRX from E. coli is colored red, and TRX-f from spinach chloroplast is colored blue. In panels (c) and (f), cooperativity correlation is compared for each TRX pair (TRX-2 is always in the top-left). Color-coding in the cooperativity correlation plots is the same as in Figure 7.

Figure 10

(a) Heat capacity curves for oxidized (solid lines) and reduced (dashed lines) TRX pairs. In each case the reduced form curve shifts to a lower T_m. (b) Change in backbone flexibility, $F_{\mathit{index}}^{\mathit{red}}-F_{\mathit{index}}^{ox}$, upon variation within redox state. (c) Cooperativity correlation plots comparing each reduced (top triangle) and oxidized (bottom triangle) TRX pairs. Color-coding is the same as in Figure 7.