Fig. 1.

(a) Evolution of energy of the native conformations of proteins. Each data point represents average over 75 consecutive evolved structures. Squares correspond to the first run of evolutionary selection where stability condition is applied (see Methods); circles correspond to the second evolution run that starts from the same seed structure but where sequences are required to fold but not necessarily be stable in their native conformations. (b) Evolution of compactness of evolved structures as measured by TrC². Thirty-six, the total number of monomers of the chain, normalize this quantity. TrC² is double the total number of contacts. The data averaging and the meaning of symbols is as in a.(c) Evolution of TrC⁸ normalized by total number of monomers. This quantity reflects topological properties of a structure related to the number of uninterrupted closed long loops of length 8 that can be drawn on the system of contacts. It was calculated as trace of 8th power of contact matrix from which reduced elements, such as TrC⁴TrC⁴, etc., were subtracted (see Methods). The data averaging and the meaning of symbols are as in a.