Widespread compensatory substitutions in a deep mutational scanning library.

(A) Schematic demonstrating modes of rescue of loss-of-function genotypes via compensatory substitutions. (B) An example of compensatory substitutions in which a genotype with the fitness of zero (blue) is four substitutions away from WT and for which we measured the fitness of 23 genotypes with additional substitutions. The green edges connect to rescuing genotypes, and the red edges connect to non-rescuing genotypes. (C) Fitness data from panel (B) illustrating computations for rescuability. The dark blue dot represents a rescuable unfit genotype, whereas the black dots represent genotypes that cannot be rescued. Error bars denote the standard deviation in the estimation of fitness. (D) The distribution of rescuability of all unfit genotypes. (E) Comparison of rescuability distributions among different genotype classes, N denotes the number of synonymous variants used in fitness estimation for the same amino acid genotype. Purple, all missense genotypes; blue, missense genotypes carrying ≥ 10 synonymous variants; green, nonsense genotypes (premature stop codons) serving as a low-rescuability control.

Rescuability correlates with protein structural features.

(A) The rescuability of each position in the His3p monomer was calculated as the average rescuability of all genotypes with that position substituted. Error bars represent the standard deviation. (B) Position-wise rescuability correlates with protein structural features and evolutionary conservation. (C) Rescuable genotypes exhibit lower predicted ΔΔG_fold values than non-rescuable ones (one-tailed Wilcoxon rank-sum test). (D) Most rescuing genotypes show lower ΔΔG_fold values than the corresponding rescuable genotypes. (E) Among genotypes with more than 50% of substitutions located in subunit-interface regions, rescuable genotypes display lower ΔΔG_bind values than non-rescuable genotypes (one-tailed Wilcoxon rank-sum test). (F) For genotypes with more than 50% substitutions in subunit interface regions, most rescuing genotypes have smaller ΔΔG_bind than rescuable genotypes.

Super compensatory substitutions increase fitness across diverse genetic backgrounds.

(A) A schematic figure quantifies the compensatory ability of A110D in the 115E background. For substitution A110D in non-WT state 115E, paired genotypes differing only at position 110 are compared. Fitness differences (Δf) are computed and genotype pairs with Δf ≥ 0.5 are considered compensatory. The resulting compensatory ratio is represented as a directed edge from 115E to 110D. (B) Directed network of compensatory interactions. Nodes represent non-WT amino acid states and directed edges compensatory effects of substitutions. Edge shading indicates fraction of substituted genotypes considered compensatory. (C) Compensatory ability of individual substitutions, defined as the sum of incoming edge weights in (B). Only substitutions from Segment 1 are shown. (D) Distribution of compensatory ability across all substitutions, showing that only a small subset of substitutions exhibits high compensatory capacity. (E) Neural-network model predicting fitness via a latent variable (fitness potential), computed as the sum of amino acid specific fitness impact scores mapped to fitness by a non-linear transformation. (F) An example illustrating modulation of fitness and fitness potential by substitutions: A110D (red) increases fitness potential and fitness, whereas K115E (blue) decreases both. (G) Substitutions with higher compensatory ability tend to exhibit higher fitness impact scores relative to WT.

Super compensators buffer the fitness effects of both deleterious and beneficial substitutions.

(A) Representative examples showing that super compensator 110D attenuates the fitness effects of both a deleterious (K115T) and beneficial (V114I) substitution. (B-D) A non-super compensator (110Q, x-axis) shows no systemic effect on substitution fitness compared with the WT amino acid state (110A, y-axis). Paired fitness effects were evaluated using relative (B) and absolute (c) fitness difference and skewness of the absolute differences (D). (E-G) A super compensator (110D, x-axis) reduces the fitness effects of substitutions relative to the WT state (110A, y-axis). Comparisons using relative (E) and absolute (F) fitness difference reveal buffering through collapse toward the vertical and produce a positively skewed distribution of fitness effect differences (G). (H) Conceptual model linking buffering to the sigmoidal relationship between fitness potential and predicted fitness. Non-WT amino acid states with positive fitness impact scores (eg., 110D) can shift genotypes towards a high-fitness plateau where fitness is insensitive to additional substitutions. States with negative impact scores (eg., 115E) can shift genotypes off the plateau, increasing sensitivity. (I) Amino acid states with higher fitness impact scores relative to WT exhibit greater buffering capacity, quantified as increased positive skewness of fitness effect differences (Spearman R= 0.78, p-value = 0). (J) Non-WT amino acid states with higher compensatory capacity similarly exhibit stronger buffering, as indicated by increased positive skewness (Spearman R= 0.67, p-value = 0). (K) Example of local landscape smoothing by a super compensator. 93V reduces fitness variability among neighboring variants, effectively flattening the local fitness landscape. (L) Non-WT amino acid states with higher fitness impact scores relative to WT are associated with more stable protein structures, reflected by lower ΔΔG_bind values.

The Super compensator 189A buffers the fitness effects of deleterious substitutions.

(A) Amino-acid composition of the constructed DMS library. (B) Genotypes with premature stop codons exhibit similar fitness as those without in the presence of histidine and show reduced fitness in its absence. (C) Super compensators increase the fitness of most genotypes carrying random mutations. (D) The average fitness difference between genotypes with 189A and with 189S is higher than zero (blue), and the fitness difference is more pronounced among deleterious genotypes (orange).

The DMS library is derived from extant yeast sequences and spans nearly the full length of His3p.

(A) Position wise conservation and amino acid conservation across His3p. The red track shows conservation score across 21 extant yeast species at each position of the His3p monomer. The blue track shows the conservation score in the DMS library with the heatmap below showing the frequency of each amino acid in each position in the library. (B) Most genotypes in the library are composed of extant amino acids. (C) Fitness distribution of all genotypes in the library, the blue bar indicates percentage of unfit genotypes. (D) We defined “rescue” as a fitness increase from 0 to a value significantly above 0, and calculated rescuability accordingly. The correlation between rescuability values was then examined across a range of fitness thresholds used to define unfit and fit genotypes. (E) Different rescuability calculation methods produce strong agreement of rescuability estimates for unfit genotypes (R2 = 0.84). (F) Unfit genotypes span nearly the entire length of His3p.

Rescuable genotypes are more structurally stable than non-rescuable genotypes.

(A) Across varying numbers of substitutions, rescuable genotypes display higher predicted structural stability than non-rescuable genotypes. (B) Among genotypes with more than 50% substitutions in subunit interface regions, rescuable genotypes remain more structurally stable than non-rescuable genotypes across varying numbers of substitutions.

There exist several substitutions that increase fitness of diverse genotypes.

Compensatory relationships of all pairs of substitutions and non-WT amino acid states at distinct positions for all segments, excluding segment 9.

Several substitutions can increase fitness across diverse genetic backgrounds.

Compensatory capacity of each substitution across all segments, excluding segment 9.

Fitness potential is a latent variable that can predict fitness.

Each panel illustrates the non-linear mapping learned by a neural network model for each of the 12 His3p segments analyzed, excluding segment 9.

Distance from substituted position of each non-WT amino acid state to the substrate.

Distance from each non-WT amino acid state to the substrate (Å, y-axis) was plotted against compensatory ability (x-axis) for all segments except segment 9. There is no significant correlation between the distance from each non-WT amino acid state to the substrate and its compensatory ability.

Super compensators identified across diverse proteins.

(A) Distribution of compensatory ability for individual substitution across different proteins. Substitutions with prominent compensatory ability ( ≥ 0.6) are labeled. The fitness metric used in each dataset (stability or fluorescence intensity) is indicated in the title of each panel. (B) Super compensators buffer the fitness effects of other substitutions. Each panel corresponds to the super compensator highlighted in panel A (which showed the highest compensatory ability for that protein). The percentage of substitutions exhibiting reduced fitness effects in the super compensator background is labeled.

Amino acid physicochemical properties can predict fitness.

The heatmap shows Spearman correlations between fitness and physicochemical properties (AAindex values) distance from WT. Columns correspond to AAindex descriptors and rows to distinct mutation sets. High negative spearman correlations indicate that moving the AAindex values of variants closer to those of the WT increases fitness.

Co-occurring amino-acid state pairs in extant His3p orthologs, across all segments excluding segments 9 and 10.

(A) Co-occurrence network of amino acid state pairs across 355 extant yeast species. Nodes represent amino acid states and edges the co-occurrence of a pair. Edge shading reflects the fraction of species in which a given pair co-occurs. Non-extant amino acid states are denoted by lighter node shading. Pairs that co-occur in at least 10 species are labeled with white text. (B) Among pairs of non-WT amino-acid states observed in extant species, amino-acids states with lower fitness impact scores relative to WT (x-axis, binned) tend to co-occur with states exhibiting higher fitness-impact scores (y-axis).

Structural effects of super compensatory and non-compensatory substitutions.

Predicted structural effects of 7 super compensators (highest fitness impact score relative to WT) and five non compensatory substitutions (lowest fitness impact score relative to WT).