Evolutionary Dynamics on Protein Bi-stability Landscapes can Potentially Resolve Adaptive Conflicts
(a) Proteins with degenerate native states (two or more structures with maximum stability) can function as connectors between neutral networks. Bi-stability is indicated for a bi-stable protein by a schematic folding funnel with two free energy minima. In an ideal case, the neutral network of sequences for each native-state structure can be reached by a single mutation from a centrally located sequence. This would enable efficient evolutionary transitions between those neutral networks. The frequency of such a bridge protein sequence may be maintained at an appreciable level in populations evolving under adaptive conflicts. Bridge proteins with up to six-fold native-state degeneracy () are illustrated. (b) Box plots of native-state stability (i.e., fractional population ) versus native state degeneracy () of all model sequences with (grey), and the subset of all bridge sequences (magenta). Here we follow the standard convention for box plots in descriptive statistics: For each sample defined by a given value of the variable plotted along the horizontal axis ( for bridge or non-bridge sequences in this case), the lowest and highest bars are, respectively, the lowest and highest values of the property of interest ( in this case) observed for the given sample. The top and bottom of the box are, respectively, the corresponding lower and upper quartiles of the sample, whereas the median of the sample is shown by the line within the box. The box plots here indicate that bridge sequences are significantly more stable than non-bridge sequences (Wilcoxon Rank Sum Test; in all cases, except , where ). In the biophysical protein chain model used here (see Methods), the upper bound of , given , is (black dashed line).