Amino acid coevolution induces an evolutionary Stokes shift

Abstract

The process of amino acid replacement in proteins is context-dependent, with substitution rates influenced by local structure, functional role, and amino acids at other locations. Predicting how these differences affect replacement processes is difficult. To make such inference easier, it is often assumed that the acceptabilities of different amino acids at a position are constant. However, evolutionary interactions among residue positions will tend to invalidate this assumption. Here, we use simulations of purple acid phosphatase evolution to show that amino acid propensities at a position undergo predictable change after an amino acid replacement at that position. After a replacement, the new amino acid and similar amino acids tend to become gradually more acceptable over time at that position. In other words, proteins tend to equilibrate to the presence of an amino acid at a position through replacements at other positions. Such a shift is reminiscent of the spectroscopy effect known as the Stokes shift, where molecules receiving a quantum of energy and moving to a higher electronic state will adjust to the new state and emit a smaller quantum of energy whenever they shift back down to the original ground state. Predictions of changes in stability in real proteins show that mutation reversals become less favorable over time, and thus, broadly support our results. The observation of an evolutionary Stokes shift has profound implications for the study of protein evolution and the modeling of evolutionary processes.

Fig. 1.

Propensities shift caused by coevolution. Results are shown for propensities of various amino acids at site 168 during an evolutionary period encompassing 500 substitutions. Black lines represent changes in the amino acid resident at this location, with the current occupant during each time period noted. During this time, site 168 underwent substitutions from aspartic acid (D) to glycine (G) to alanine (A) and then, to threonine (T). The propensities of the 20 amino acids are indicated by different colored lines, which are indicated by the single-letter International Union of Pure and Applied Chemistry (IUPAC) amino acid codes in the legend. For clarity, amino acids with low propensities during this time period were omitted.

Fig. 2.

Long-term distribution of propensities. Distributions of marginal propensities for all 20 amino acids across 18 simulations totaling over 2.4 million substitutions are shown for partially buried site 168. Line colors are as in Fig. 1. Similar plots for all six focal locations are shown in Fig. S1.

Fig. 3.

Decay of the autocorrelation function of amino acid propensities. The dynamics of the decay of the autocorrelation function are shown for exposed locations (blue, site 111; cyan, site 147), partially exposed locations (red, site 168; orange, site 273, and buried location (green, site 135; lime, site 7). Dashed lines fit to a stretched exponential plus baseline as described in the text. Value of the fit at infinity represents the baseline value. Note the modified logarithmic scale on the abscissa.

Fig. 4.

Increase in propensity for current amino acid caused by coevolution. For each location, the average propensity of all amino acids during free simulations (red) was compared with the average propensity of new amino acids after a substitution (green), the average propensity of resident amino acids during their residency (blue), and the average propensity of fixed amino acids (magenta). The six locations examined were exposed locations 111 and 147, partially exposed locations 168 and 273, and buried locations 7 and 135.

Fig. 5.

Effect of current amino acid on amino acid propensities. Average propensity of selected amino acids at location 168 () depending on the amino acid fixed at that location. Results are shown for X equal to lysine (L; red), threonine (T; orange), serine (S; yellow), aspartic acid (D; green), and arginine (R; blue).

Fig. 6.

Evolution of the change in stability for the back mutation () after an R110D mutation. Three sequences were chosen for which an R111D mutation was slightly deleterious (). This mutation was made, and the D was fixed at this location. Red, blue, and green traces represent individual simulations. Black curve represents the average of 1,000 simulations for each of the three initial sequences.

Fig. 7.

Evolution of changes in propensities after mutation. Evolution of amino acid propensities at site 110 over 1,000 substitutions. As in Fig. 5, three sequences were chosen for which an R110D mutation was slightly deleterious (). This mutation was made, and the D was fixed at this location. Curves represent the average of 1,000 simulations for each of the three initial sequences. Amino acid color codes are as in Figs. 1 and 2.

Fig. 8.

Correlation between energetics of forward and backward mutations. (A, C, and E) Values of compared with for mutations where one sequence is changed to match the amino acid in the other sequence at that location as a function of the pairwise identity at other locations: (A) 100%, (C) 75%, and (E) 20%. If all locations are independent, , which is the case for A. (B, D, and F) Similar calculations for different homologs of ferrodoxin, where the values of and are computed using Rosetta (31). Calculations were based on the crystal structures of the two proteins for sets of proteins where the pairwise identity at other locations was (B) 100%, (D) 70–80%, or (E) <25%. Correlation coefficients (cc), calculated after excluding outliers (), are included in the plots.

Fig. P1.

Trajectories of amino acid propensity. Average propensity of the resident amino acid at location 168 before (red line), during (blue line), and after (red line) its residency. Before residency, amino acids have a lower average propensity (red dashed line) than they did at the time of a substitution (green circle), indicating that substitutions in the rest of the protein randomly preadapt the position to make the new amino acid relatively acceptable before substitution. Subsequently, the average propensity of the resident amino acid (blue dashed line) rises. After substitution away from the resident amino acid (cyan circle), the propensity falls again to a postresidency average (red dashed line) similar to the preresidency average. Amino acids that establish long-term residency will, however, tend to greater resident amino acid propensities over time, slowly approaching the equilibrium propensity of fixed resident amino acids (magenta line). Averages are over 26 residencies, each of length 100 substitutions.