Effect of a rudimentary π-π potential for Phe (F) and Tyr (Y) residues on the G_A/G_B switch.

<p>(a) Three geometric variables are used to characterize the relative position and orientation of a pair of aromatic rings in F or Y: center-to-center distance <i>r</i> (spatial separation between the centers of the two rings), planar tilt angle <i>θ</i>, and center dislocation angle <i>φ</i>. (b) PDB statistics for F-F, Y-Y, and F-Y contacts were used to derive an interaction strength of the π-π potential as a function of <i>r</i>, <i>θ</i>, and <i>φ</i>. The vertical variable here corresponds to |<i>E</i>_ππ(<i>r</i>, <i>θ</i>, <i>φ</i>)/<i>ε</i>_ππ| defined in <i>Methods</i>. (c) Difference landscape for the L45Y mutation. Free energy of GB98 minus free energy of GA98 as a function of Q_A and Q_B computed in our hybrid model with two different transferrable components: the original Lund potential (left), and the modified potential (right) that incorporates the F,Y potential with interaction strengths given in (b) and <i>ε</i>_ππ = 1.5.</p

Rationalization of the G_A/G_B switch and model prediction of incremental stabilization of the alternate fold.

<p>(a) Free energy landscapes as a function of the progress variables Q_A and Q_B are simulated in our hybrid model (ε_B = −0.37). The Q_A/Q_B scale (bottom-left axes for GBwt) is identical for all GA/GB variants. Free energy, in units of <i>k</i>_B<i>T</i>, is the negative natural logarithm of the sampled population (<i>Methods</i>). For each sequence, this quantity is computed for points on a ~100×100 grid at the sequence’s melting temperature <i>T</i>_m. The free energies for the grid points are plotted according to the color code on the right, with the lowest free energy on the grid normalized to zero for each sequence. Note that all resulting free energy values ≥ 6 are shown in the same color. (b) Free energy differences ΔF(G_A-G_B). (c) Comparing sequence-dependent <i>T</i>_ms from experiment and simulation, each normalized to the range defined by GA77 (set to 1) and GB98 (set to 0). The <i>T</i>_m values in (c) are in an arbitrary unit for a non-absolute temperature scale. (d) Scatter plot between absolute melting temperatures in simulation (model unit) and in experiment (in K). The experimental <i>T</i>_ms used in the comparison in (c) and (d) are from refs. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004960#pcbi.1004960.ref019" target="_blank">19</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004960#pcbi.1004960.ref020" target="_blank">20</a>].</p

Theoretical Insights into the Biophysics of Protein Bi-stability and Evolutionary Switches

<div><p>Deciphering the effects of nonsynonymous mutations on protein structure is central to many areas of biomedical research and is of fundamental importance to the study of molecular evolution. Much of the investigation of protein evolution has focused on mutations that leave a protein’s folded structure essentially unchanged. However, to evolve novel folds of proteins, mutations that lead to large conformational modifications have to be involved. Unraveling the basic biophysics of such mutations is a challenge to theory, especially when only one or two amino acid substitutions cause a large-scale conformational switch. Among the few such mutational switches identified experimentally, the one between the G_A all-α and G_B α+β folds is extensively characterized; but all-atom simulations using fully transferrable potentials have not been able to account for this striking switching behavior. Here we introduce an explicit-chain model that combines structure-based native biases for multiple alternative structures with a general physical atomic force field, and apply this construct to twelve mutants spanning the sequence variation between G_A and G_B. In agreement with experiment, we observe conformational switching from G_A to G_B upon a single L45Y substitution in the GA98 mutant. In line with the latent evolutionary potential concept, our model shows a gradual sequence-dependent change in fold preference in the mutants before this switch. Our analysis also indicates that a sharp G_A/G_B switch may arise from the orientation dependence of aromatic π-interactions. These findings provide physical insights toward rationalizing, predicting and designing evolutionary conformational switches.</p></div

The twelve GA/GB sequence variants used in our computational investigation.

<p>Sequences range from wildtype GAwt to GBwt. Intermediate sequences are labeled by their pairwise sequence similarity, e.g. GA88 and GB88 are 88% identical [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004960#pcbi.1004960.ref019" target="_blank">19</a>]. From top to bottom, new amino acid substitutions are marked in red. The L45Y mutation is highlighted with yellow shading. The blue (G_A) and red (G_B) backgrounds indicate the experimentally observed native fold of the sequences. As an example, the ribbon diagrams show the experimental folded structures of GA98 and GB98 with residue 45 in yellow and aromatic residues depicted as sticks.</p

Clustering analysis of GA98 and GB98 suggests putative folding trajectories.

<p>50<i>k</i>-means clusters were obtained from a combined pool of 40,000 randomly sampled GA98 and GB98 conformations (<i>Methods</i>). The positions of their centroids are indicated on the Q_A/Q_B plane. Each centroid is represented by a grey filled circle of size commensurate with the number of conformations in the given cluster. Included in the background, as a positional reference, is the GA98 free energy landscape (<b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004960#pcbi.1004960.g003" target="_blank">Fig 3a</a></b>). The clusters are numbered arbitrarily from 0 to 49. In the interest of readability, only number labels for selected clusters deemed to be important for the sequences’ folding pathways are shown. The centroid conformation is depicted for some clusters. A pair of centroid positions is connected by a line if their distance measure RMSD_sm ≤ 5.75 Å (<i>Methods</i>). Increased thickness/darkness of the connecting lines indicates that the connected centroid conformations are structurally more similar with smaller RMSD_sm. Conformations in the yellow boxes are taken to constitute a single putative transition state TS-G_A for G_A folding and two putative transition states TS1-G_B and TS2-G_B for G_B folding. The TS-G_A, TS1-G_B, and TS2-G_B regions encompass, respectively, 452, 834, and 805 of the 40,000 sampled conformations. The centroid structure of each putative transition state (TS) is exhibited to illustrate the structural characteristics of the TSs; but it is important to note that the putative TS ensembles are structurally diverse (<b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004960#pcbi.1004960.s014" target="_blank">S14 Fig</a></b>). This property is reflected by the fact that the conformations in each TS ensemble belong to multiple clusters. The three clusters (nos. 43, 46, 23) that contribute most conformations to TS-G_A account for only 38% of the TS-G_A ensemble. The three clusters that contribute most to TS1-G_B and TS2-G_B (nos. 0, 25, 12 and nos. 22, 29, 13) account for 36% and 64% of their respective ensembles. We mark each of these most TS-related clusters by a yellow ring around the grey circle representing the cluster’s centroid position. In the conformational drawings, parts of the chain corresponding to β-hairpin 1 (residues 1–20) and β-hairpin 2 (residues 42–56) in the native G_B fold are highlighted, respectively, in purple and orange. Shown as sticks are aromatic residues to be considered further below for possible participation in π-interactions. The positions of these aromatics also serve to highlight the locations of the main hydrophobic regions in the folded and partially folded conformations shown.</p

Evolutionary Dynamics on Protein Bi-stability Landscapes can Potentially Resolve Adaptive Conflicts

<div><p>Experimental studies have shown that some proteins exist in two alternative native-state conformations. It has been proposed that such bi-stable proteins can potentially function as evolutionary bridges at the interface between two neutral networks of protein sequences that fold uniquely into the two different native conformations. Under adaptive conflict scenarios, bi-stable proteins may be of particular advantage if they simultaneously provide two beneficial biological functions. However, computational models that simulate protein structure evolution do not yet recognize the importance of bi-stability. Here we use a biophysical model to analyze sequence space to identify bi-stable or multi-stable proteins with two or more equally stable native-state structures. The inclusion of such proteins enhances phenotype connectivity between neutral networks in sequence space. Consideration of the sequence space neighborhood of bridge proteins revealed that bi-stability decreases gradually with each mutation that takes the sequence further away from an exactly bi-stable protein. With relaxed selection pressures, we found that bi-stable proteins in our model are highly successful under simulated adaptive conflict. Inspired by these model predictions, we developed a method to identify real proteins in the PDB with bridge-like properties, and have verified a clear bi-stability gradient for a series of mutants studied by Alexander et al. (Proc Nat Acad Sci USA 2009, 106:21149–21154) that connect two sequences that fold uniquely into two different native structures via a bridge-like intermediate mutant sequence. Based on these findings, new testable predictions for future studies on protein bi-stability and evolution are discussed.</p> </div

Bridge proteins persist under unequal selection pressures for two native-state structures.

<p>In our biophysical protein chain model, and serve as the selection pressures on and , respectively, by setting the minimum required stability for optimal fitness. Here and values are plotted in units of , where is the stability of the (equally stable) native-state structures ( and ) of the most stable bridge protein . The magenta area is the range of and values within which bridge proteins have higher fitness than the specialized prototypes of neutral networks A and B.</p

Free energy landscapes of additional switch sequences in the G_A/G_B system.

<p>Plotted in the same style as that in <b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004960#pcbi.1004960.g005" target="_blank">Fig 5</a></b>. (a) GB98-T25I (PDB:2LHG). (b) GB98-T25I,L20A (PDB:2LHE). PDB structures in (a) and (b) are depicted by the ribbon diagrams. (c) Predicted switch sequence “S1” prefers G_B whereas (d) sequence “S2” prefers G_A [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004960#pcbi.1004960.ref066" target="_blank">66</a>]. The arrows mark the global minimum in each of the energy landscapes.</p

Bridge proteins as connectors in sequence space.

<p>A bi- or multi-stable protein (with a degenerate native state) is a bridge sequence if it has at least two 1-error mutants that fold non-degenerately into at least two different structures among the sequence's multiple native-state structures, i.e., each mutant folds uniquely to a different structure. In other words, there is at least one connection to the core of each of the two or more neutral networks. In total, for sequences with chain length studied here (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#s4" target="_blank">Methods</a>), there are sequences in the model sequence space, 6349 of which have non-degenerate () native states.</p

Bi-stability decreases with increasing sequence distance from bridge proteins.

<p>(<b>a</b>) An example of the distribution of bi-stability in a small section of a model sequence space. The difference in the number of hydrophobic contacts, , (stability difference) for the native-state structures and of two adjacent neutral networks and (blue and red, respectively) are depicted by a two-dimensional representation of sequence space (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#s4" target="_blank">Methods</a>). Nodes represent sequence variants. Node sizes are scaled according to native-state stability (, a larger node size corresponds to a large value). Edges connect sequences that differ by one mutation. The arrow indicates a mutation from a sequence with a stability difference of to a sequence with a stability difference of . In other words, this mutation increases stability for while conserving as the native state. Bridge proteins (magenta squares) are equally stable for both native states and thus have a stability difference of zero. (<b>b</b>) Generalization of smooth bi-stability gradients around bridge proteins. Each box plot gives the distribution (i.e. the entire data range with vertical lines delimiting quartile boundaries as specified in the caption for <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002659#pcbi-1002659-g001" target="_blank">Figure 1b</a> above) of 623 average stability differences computed for individual sequences that belong to the same neutral network and can be mutated into a bridge protein with the same given number of mutations (i.e. have the same Hamming distance from a bridge). The stability difference was calculated between the native structures of all 623 pairs of extended neutral networks (that have at least 5 core nodes, and at least one bridge). Data for each pair was counted only once, and the color blue is used in this plot for the larger network of each pair. The further away a sequence is located from a bridge in sequence space, the higher its stability difference towards one of the two structures, and the lower its bi-stability. All differences between box plots were significant (Wilcoxon Rank Sum Test, ).</p