Evolutionary Dynamics on Protein Bi-stability Landscapes can Potentially Resolve Adaptive Conflicts
(a) 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 Methods). 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) 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 Figure 1b 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, ).