Approximation to the Pareto set of optimum primary/promiscuous activities.

<p>(A) Values of the primary and promiscuous activities for 29 variants randomly selected from a combinatorial library based on the 10 mutations derived from SCA analysis (see text and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g004" target="_blank">Figure 4</a>). Values for the wild-type thioredoxin from <i>E. coli</i> and the background P34H variant are also included. Note that logarithms of activities are used here in and also in all the other panels of this figure. (B) Partial-least-squares (PLS) reconstruction of the data for the whole combinatorial library (small red data points). The experimental data of panel A (used as a basis for the reconstruction) are also shown, although, for the sake clarity we have omitted the errors bars here (as well as in panels C and D). The reconstructed data (red points) are actually derived from 20 bootstrapping replicas (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#s3" target="_blank">Methods</a> for details). (C) Prediction of the Pareto set from the PLS-reconstructed data. The 11 variants belonging to this predicted Pareto set are shown with blue circles. (D) The actual experimental activity values for the 11 variants are shown (open green squares). (E) Expanded experimental variant set including the original 29 variants (panel A), the wild-type thioredoxin from <i>E. coli</i>, the P34H background variant and the 11 variants added as a result of PLS-reconstruction/Pareto-set-prediction (panels C and D). (F) The actual Pareto set of the expanded variant set is shown (green data points).</p

Basic mechanism for disulfide oxidation catalyzed by a thioredoxin-fold domain.

<p>(Thioredoxin domain shown in blue). The mixed disulfide intermediate has been highlighted in grey. Note that, unlike the mechanism of disulfide reduction shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g002" target="_blank">Figure 2</a>, resolution of the intermediate occurs through attack of a thiolate group of the substrate. Actually, attack of the thiolate from the catalyst (as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g002" target="_blank">Figure 2</a>) must be prevented since it would revert the substrate to the initial reduced state.</p

The shape of the primary/promiscuous Pareto set is consistent with the conformational diversity hypothesis.

<p>(A) Values of the reductase and catalysis of oxidative folding activities for the 40-variant experimental set. The Pareto set is shown with green data points. This plot is analogous to that in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g005" target="_blank">Figure 5F</a> but linear activity scales (instead of logarithms) are used here and error bars have been omitted for the sake of clarity. The line represents the least-squares fit to the Pareto set data. (B) A partial least squares reconstruction of the data for the whole combinatorial library based on the experimental data of panel A. The data shown correspond to a single bootstrapping replica; however, other replicas show the same general pattern The Pareto set (green points) and the corresponding linear fit are shown. (C) Simple conformational diversity model used in the simulation summarized in panels D and E. Conformation a₀ is not active, while conformations a₁ and a₂ are responsible for the promiscuous and primary activities, respectively. (D) Relevant regions in the primary/promiscuous activity diagram according to the model shown in panel C. Optimal situations correspond to a zero mol fraction of the inactive conformation and define a <i>trade-off line</i> in the plot. Sub-optimal situations correspond to a mol fraction of a₀ higher than zero and are located in a triangular-shaped region below the trade-off line. (E) Stochastic simulation of 40-variant set based on the model shown in panel C. The Pareto set (green data points) approaches the trade-off line.</p

Assessment of the modulation ranges achieved for the primary and promiscuous activities.

<p>(A) Experimental reductase and catalysis of oxidative folding data for the expanded 40-variant set, the wild-type thioredoxin from <i>E. coli</i> and the background P34H variant. The meaning of symbols is as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g005" target="_blank">Figure 5A</a>. The approximate modulation ranges achieved are indicated with arrowed red lines. Data of bovine protein disulfide isomerase (blue data point labeled PDI) are also included to provide an evolutionary relevant scale for comparison. Note that specific activity data for PDI are given per molar concentration of active thioredoxin domain. (B) Comparison of the PDI experimental data with the partial least squares reconstruction of the reductase/catalysis-of-oxidative-folding data for the whole combinatorial library. The reconstructed data (grey squares) are actually derived from 20 bootstrapping replicas. (C) Experimental disulfide-reshuffling activity and catalysis of oxidative folding data for the expanded variant set, the wild-type thioredoxin from <i>E. coli</i> and the background P34H variant. Data of bovine PDI are also included to provide an evolutionary relevant scale for comparison. (D) Comparison of the PDI experimental data with the partial least squares reconstruction of the reshuffling/catalysis-of-oxidative-folding data for the whole combinatorial library. The reconstructed data (grey squares) are actually derived from 20 bootstrapping replicas.</p

Use of the Pareto set to define the patterns of primary/promiscuous activity modulation.

<p>In all plots, each data point represents the primary and promiscuous activity data for a given protein variant. Different variants may be thought as corresponding to different combinations of mutations from a given set. (A) Illustration of Pareto set construction. Variant “b” is dominated by variant “a”, since the latter shows higher values of <i>both</i> activities. Variant “a” is not dominated by variant “c”, since promiscuous-activity(a)>promiscuous-activity(c). Variant “c” has the highest value for the primary activity and is not dominated neither by “a” nor “b”. The non-dominated variants “a” and “c” form the Pareto set (green data points) for this three-variant example. (B), (C) and (D) are illustrative examples of the relation between the Pareto set (green data points) and the primary/promiscuous trade-offs. In (B) and (C) the starting variant (marked with a red circle) belongs to the Pareto set and, therefore, increasing the promiscuous activity necessarily implies a decrease of the primary activity. The plot in (B) is meant to illustrate a weak trade-off along the Pareto set (a significant increase in promiscuous activity can be achieved with only a small decrease in primary activity) while (C) is meant to illustrate a strong trade-off. In (D) the starting variant does <i>not</i> belong to the Pareto set and, hence, the simultaneous enhancement of both activities is possible.</p

Diversity of mutational paths in the primary/promiscuous activity space.

<p>Grey data points represent the results of a PLS reconstruction based on the 40-variant experimental set. Mutational paths (red lines) connecting a starting variant (red data point) and a final variant (blue data point) are shown. (A) The starting variant shows a low level of the promiscuous activity and a comparatively high level of the primary activity. Mutational steps are allowed if promiscuous activity is increased and the primary activity is maintained above a given threshold (shown as a vertical black line). (B) The starting variant shows high level of both, the primary and promiscuous activities. Mutational steps are allowed if the primary activity is decreased and the promiscuous activity is maintained above a given threshold (shown as a horizontal black line).</p

Stochastic simulations of primary/promiscuous activities based on different conformational diversity models.

<p>(A) Simulation based on a 3-conformation model identical to that used in the simulation of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g008" target="_blank">Figure 8E</a>, except that a low (but different from zero) level of primary and promiscuous activities for the suboptimal conformation (<b>a₀</b>) is assumed. Here, as well as in the other panels, the Pareto set is shown with green circles. (B) Simulation based on a 4-conformation model with two suboptimal conformations. (C) Same as in (B), except that each one of the optimal conformations (<b>a₂</b> and <b>a₃</b>) has a low level of the alternative activity. (D) Same as in (C), but assuming that the optimal conformations show high level of both activities. The models used in (A), (B) and (C) include the existence of trade-offs between the optimal conformations and yield roughly linear Pareto sets with a significant number of data points below the Pareto set due to the presence of suboptimal conformations. This is actually the experimental pattern we have found for the catalysis-of-oxidative-folding/reductase activities (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g008" target="_blank">Figure 8A</a>). The model used in (D) does <i>not</i> include trade-offs between the optimal conformations (i.e., <b>a₂</b> and <b>a₃</b> efficiently catalyze both, the primary and the promiscuous processes) and the pattern is completely different: a significant correlation between the two activities and a very small Pareto set are observed.</p

Full-library partial-least-squares reconstructions of the reductase/catalyis-of-oxidative-folding data based upon the expanded 40-variant set.

<p>The black squares represent the first-round 29-variant set and the circles represent the 11 variants added as a result of the experimental validation of the Pareto prediction shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g005" target="_blank">Figure 5C</a> (green data points are used here for the Pareto set). Error bars have been omitted for clarity, but they are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g005" target="_blank">Figures 5E and 5F</a>. The reconstructed data (grey squares) are derived from 20 bootstrapping replicas of the 40-variant data. Note that the PLS reconstructions shown here are based on the expanded 40-variant set, while those of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002558#pcbi-1002558-g005" target="_blank">Figure 5B</a> were based on the first-round 29-variant set. The full-library reconstructions shown here suggest only small enhancements over the 40-variant Pareto set would be obtained in additional screening rounds and, further, they support that the 40-variant Pareto set is already close to the full-library Pareto set.</p

Statistical coupling analysis of the emergence of folding catalysis activities in thioredoxin domains.

<p>(A) Statistical free energies for the coupling of position 34 with all the other positions (<i>E. coli</i> thioredoxin numbering is used). These values have been calculated using as perturbation the signature P34H mutation. The 13 positions with the highest values for the coupling energies are labeled. (B) Determination of ten favored mutations at the positions selected in step 1 (see text for details and for the definition of the Γ_Ec→X function. (C) Mapping of the 10 positions selected for mutation (panel B) on the <i>E. coli</i> thioredoxin 3D structure (blue). The active site disulfide bridge is shown in yellow and the proline at position 34 is shown in red. (D) Occurrence of the 10 mutations selected (panel B) in the MSA sequences that include a histidine at position 34. Most of these sequences belong to eukaryotic protein disulfide isomerases. Note that many different combinations of these mutations are actually found in extant PDIs.</p

Basic mechanism of disulfide reduction catalyzed by a thioredoxin-fold domain.

<p>(Thioredoxin domain shown in blue). The mixed disulfide intermediate has been highlighted in gray. Note the resolution of this intermediate through attack of the thiolate form of the C-terminal cysteine group of the catalyst.</p