Co-evolution of interacting proteins through non-contacting and non-specific mutations

Abstract

Proteins often accumulate neutral mutations that do not affect current functions but can profoundly influence future mutational possibilities and functions. Understanding such hidden potential has major implications for protein design and evolutionary forecasting but has been limited by a lack of systematic efforts to identify potentiating mutations. Here, through the comprehensive analysis of a bacterial toxin-antitoxin system, we identified all possible single substitutions in the toxin that enable it to tolerate otherwise interface-disrupting mutations in its antitoxin. Strikingly, the majority of enabling mutations in the toxin do not contact and promote tolerance non-specifically to many different antitoxin mutations, despite covariation in homologues occurring primarily between specific pairs of contacting residues across the interface. In addition, the enabling mutations we identified expand future mutational paths that both maintain old toxin-antitoxin interactions and form new ones. These non-specific mutations are missed by widely used covariation and machine learning methods. Identifying such enabling mutations will be critical for ensuring continued binding of therapeutically relevant proteins, such as antibodies, aimed at evolving targets.

Extended Data Fig. 1. Orthogonal validation of growth rate inference, structural explanation for antitoxin mutation effects, and covariational signal between toxin-antitoxin ParE3/ParD3.

a, Comparison of growth rates inferred by high-throughput vs. individual growth measurement. X-axis error bars indicate +/− 2x standard deviation derived from n=10 or n=11 technical plate reader replicates (see Methods). Y-axis error bars indicate 95% posterior highest density interval. The Pearson correlation coefficient (r) is indicated. b, Raw log read ratio reproducibility between replicates (+1 pseudocount) for all single and double mutants. The Pearson correlation coefficient (r) is indicated. c, Mean mutation effect of residues in the C-terminal α-helix 3 of the ParD3 antitoxin indicates that residues facing the toxin are more susceptible to mutations that disrupt the ParD3-ParE3 interaction, producing negative ∆growth rate values. d, Mean mutation effect in the N-terminal oligomerization region of the antitoxin highlights residues susceptible to disrupting the ParD3-ParE3 interaction when mutated. Cartoon illustrates arrangement of ParE3-ParD3 octamer observed in the co-crystal structure (PDB: 5CEG). One of the 4 antitoxin monomers is colored by the mean mutation effect. e, Top 10 toxin-antitoxin covarying residue pairs indicated for reference. f, The 90% precision cutoff yields 29 toxin-antitoxin covarying residue pairs (black in upper, right quadrant) of which 28 pairs fall within toxin-antitoxin interface residues that are < 6Å minimum atom distance (ochre dots) in the ParE3-D3 crystal structure (PDB ID: 5CEG).

Extended Data Fig. 2. Titration of toxin and antitoxin expression levels, and sensitive identification of toxin substitutions which do not disrupt toxicity.

a, Cartoon illustration of the expression system. IPTG induces antitoxin, arabinose induces toxin. b, Growth rate of cells harboring wild-type toxin ParE3 without antitoxin at different arabinose induction levels in arabinose titratable E. coli strain BW27783. c, d, Growth rate of cells harboring wild-type toxin-antitoxin ParE3/ParD3 under different antitoxin induction levels modulated with IPTG and 0.00012% arabinose induction (c) or 0.0008% arabinose induction (d). e, Distribution of ∆growth rates(T*-T) for all toxin single substitutions under different arabinose inducer concentrations, with positive ∆growth rate(T*-T) values indicating loss of toxin function. The set of ‘most toxic’ toxin substitutions (n=310) is colored in light blue, the set of ‘toxic’ substitutions (n=781) is colored in green (see Methods). Other classes of substitutions are indicated. The dynamic range (difference between 0 and the truncated toxin mutants) shrinks, as expected, for lower expression levels that do not fully inhibit growth with the wild-type toxin, and a higher fraction of mutants show loss of toxicity (higher ∆growth rates) under lower expression conditions. The toxin substitution A28Q is highlighted (dark blue) as an example that shows no growth rate difference relative to wild-type toxin at high expression conditions, but is not as toxic as wild-type toxin at lower expression conditions. f, Schematic illustrating loss of toxicity detection using growth rate measurements in different expression regimes. g, Mean ∆growth rates(T*-T) of residue positions mapped onto the ParE3 toxin structure. Values shown for 0.00012% [arabinose] inducer. h, The mean ∆growth rates(T*-T) of a residue are correlated with the relative solvent accessibility of the residue (Pearson r = −0.66). Values shown for 0.00012% [arabinose] inducer. i,j, Distribution of ∆growth rate(T*-T) for all toxin substitutions (black) or top 10 coevolving residue substitutions (purple) in the toxin in absence of antitoxin (g) or presence of antitoxin (h). Values shown for 0.00012% [arabinose] inducer, and antitoxin is induced with 10 µM IPTG. k, The ∆growth rate(T*-T) values of each substitution at any position along the toxin ParE3. Green highlights the top 10 covarying positions between toxin and antitoxin in natural homologs. Values shown for 0.00012% [arabinose] inducer.

Extended Data Fig. 3. Volcano plot visualizing significant and substantial beneficial toxin variants in different antitoxin backgrounds, and beneficial toxin variants in various antitoxin backgrounds under ‘high’ and ‘low’ antitoxin expression conditions.

a, For each deleterious antitoxin variant background, the mean posterior change in the number of doublings, ∆growth rate(T*/AT* - T/AT*), of the most toxic toxin mutants are plotted vs. their significance (-log10(p(∆growth rate<0))) of deviation from the AT* single mutation. This is based on 10,000 discrete samples of the posterior ∆growth rate(T*/AT* - T/AT*) values inferred from the hierarchical Bayesian inference model (see Methods). Vertical line: +0.5 ∆growth rate, horizontal line: p(∆growth rate>0) = 0.0001. Red indicates significant and substantial beneficial toxin substitution using this cutoff. Experiments performed under ‘high antitoxin’ expression conditions. b, The minimum atom distance from a given deleterious antitoxin residue to each beneficial toxin is plotted vs. ∆growth rate(T*/AT* - T/AT*). Experiments performed under ‘high antitoxin’ expression conditions. c, The minimum atom distance from a given deleterious antitoxin residue to each beneficial toxin is plotted vs. ∆growth rate(T*/AT* - T/AT*). Experiments performed under ‘low antitoxin’ expression conditions. d, Distance vs. ∆growth rate(T*/AT* - T/AT*) of beneficial toxin variants for all deleterious antitoxin variant backgrounds. Experiments performed under ‘low antitoxin’ expression conditions. Values for (b-d) shown for double mutants with ∆growth rate effect size >+0.5 and p(∆growth rate>0) < 0.0001.

Extended Data Fig. 4. A non-specific, non-linear model can explain most of the observed single and double mutant growth rates.

a, Schematic of nonlinear, non-specific model: double mutant expected growth rates (brown) are based on the independent (non-specific) sum of underlying toxin and antitoxin mutant effects, passed through a sigmoid function (yellow). b,c, Residuals for non-linear, non-specific model (b) or linear non-specific model of the same structure without a non-linearity (c) showing unbiased residuals for the nonlinear model, but a complete misfit of the linear model. Model built using ‘high antitoxin’ expression levels. Explained variance (R2) is indicated. Significant and substantially positively (dark green) or negatively (green) deviating mutations are shown in (b) (see Methods). d, Inferred independent toxin single substitution effects among the set of most toxic toxin mutants demonstrating a tail of independently beneficial toxin variants. Experiment performed under ‘high antitoxin’ expression levels. e,f, Nonlinear independent model fit to growth rates measured under ‘high antitoxin’ (e) or ‘low antitoxin’ (f) expression conditions. The wild-type toxin -antitoxin pair is inferred to be differently close to the sigmoid ‘cliff’ between expression conditions. g, Cartoon illustrating different detection of single mutant effects depending on expression conditions. h-j, Correlation of inferred single mutant effects (h), observed single mutant ∆growth rate(T*/AT* - T/AT) effects (i), and double mutant deviations of observed from expected growth rates (j) from separate inference under ‘high antitoxin’ (x-axis) or ‘low antitoxin’ (y-axis) expression conditions.

Extended Data Fig. 5. Deviation of observed from expected double mutant growth rates reveals toxin variants with specific or with only non-specific beneficial effects, and fraction of specific vs. non-specific toxin variants.

a, For each beneficial toxin mutation (indicated above each plot) combined with each antitoxin variant indicated on the x-axis, the plot shows the growth-rate relative to the wild-type toxin-antitoxin pair (mean posterior ∆growth rate(T*/AT* - T/AT)). Grey dots represent T*/AT*, error bars indicate 95% posterior highest density interval. The ∆growth rate for each antitoxin mutant combined with wild-type toxin (T/AT*) is shown (black dots) along with the ∆growth rate for T*/AT* expected under the non-specific, nonlinear model (green dots). b, Deviation of the observed (dots) from the expected double mutant growth rates (orange line) highlights classification of specific and non-specific toxin variants. Beneficial toxin substitutions (rows, n=32) ordered by their range of growth rate deviations across deleterious antitoxin variants as in panel b. c-g, Specific vs. non-specific enabling toxin variants under ‘high’ antitoxin expression for all enabling toxin variants grouped by deleterious antitoxin for the more stringent set of 310 ‘most toxic’ toxins (c) and less stringent set of 781 ‘toxic’ toxins (d). Orange and purple indicate mutant pairs involving non-specific and specific, respectively, rescuing mutations in the toxin. Enabling toxin variants under ‘low’ antitoxin expression at different absolute growth rate cutoffs relative to the wild-type toxin/antitoxin growth rate (e), or grouped by ‘most toxic’ (f) or ‘toxic’ (g) toxin variants. h, Inferred non-specific toxin variant effect vs. minimum atom distance to any antitoxin atom for 21 non-specifically rescuing toxin variants (orange). i, j, For specific and non-specific beneficial toxin mutants, the change in growth rate in a deleterious antitoxin mutant background, ∆growth rate (T*/AT* - T/AT*), is plotted vs. minimum atom distance to the deleterious antitoxin mutation it rescues (i) or any antitoxin atom (j) in the ‘low antitoxin’ expression condition.

Extended Data Fig. 6. Natural sequence statistics, EVcouplings or DeepSequence models are not predictive of beneficial toxin substitution effects.

a, Distribution of number of specific and non-specific beneficial toxin substitutions (purple) vs. all possible toxin variants (grey) observed in natural sequences. b, Frequency distribution of beneficial toxin and deleterious antitoxin mutant pairs in natural sequences, with 29/51 pairs never observed. c-e, Effect size of toxin variant rescue vs. frequency of variant pair in natural sequences (c), conditional frequency of toxin variant given natural sequences containing the particular deleterious antitoxin substitution (d), or enrichment of beneficial toxin variant in natural sequences containing the deleterious antitoxin substitution (e). f-g, EVcouplings model inferred site-wise toxin mutant preferences (h_i) vs. toxin mutant effect inferred in suppressor scan with the Pearson correlation coefficient indicated (f), or EVcouplings pairwise T*/AT* variant preference (J_ij) vs. effect size of beneficial toxin mutation effect in a deleterious antitoxin variant background (g). h, Scatterplot of observed beneficial toxin effect in deleterious antitoxin mutant backgrounds (AT*), vs EVmutation (top row) or DeepSequence (variational autoencoder) mutation effect predictions (bottom row). Pearson correlation (r) is indicated. i, Distribution of natural sequence identity fractions across the alignment. Different histograms illustrate fraction mutated for homologs containing the full concatenated toxin and antitoxin (grey), the toxin homologs only (blue), or the antitoxin homologs only (turqouise).

Extended Data Fig. 7. Non-specific suppressor toxin ParE3 variants are as or almost as toxic as wild-type ParE3, and reproducibility of antitoxin combinatorial variant log read ratios.

a, Growth rates of ParE3 non-specific suppressor toxin variants (blue) compared to wild-type toxin ParE3 without antitoxin (black) and wild type toxin and antitoxin (grey) under fully inhibitory toxin expression conditions (0.00012% [arabinose]) or half-maximal inhibitory expression conditions (0.00006% [arabinose]). Dark lines represent the mean OD600, shaded regions show standard deviation of the replicates (n=10 or n=11). b, Raw log read ratio reproducibility between biological replicates (+1 pseudocount) for the combinatorial antitoxin library (8000 amino acid variants) in different toxin mutant backgrounds. Specific classes of antitoxin mutants, and Pearson correlation coefficients (r) are indicated.

Extended Data Fig. 8. Bayesian hierarchical model.

a, Simplified description of the Bayesian hierarchical model. Pre- and post-selection reads for each codon are drawn from a Poisson distribution. The log-ratios of these Poisson parameters are not fixed between synonymous codons but are instead drawn from a normal distribution, whose mean forms the amino acid mutant growth rate of interest. This model allows for different synonymous codons to inform each other as well as the amino acid mutant growth rate without being completely fixed. b, Full plate diagram description of the hierarchical Bayesian model capturing both replicates. Replicate index i takes values 1 or 2, amino acid index m takes on values ranging from 1–2040 (20*102) for the toxin or 1–1840 (92 * 20) for the antitoxin, codon index n takes on values ranging from 1–6426 (63*102) for the toxin or 1–5796 (63*92) for the antitoxin. Circles indicate random variables, grey circles represent observed random variables. c, Description of variables, likelihood function and priors used. The likelihood function incorporates maximum entropy distributions for the observed variables, and the priors incorporate computationally tractable, vague priors for the amino acid substitution growth rates. The relative priors on the standard deviation of replicate σ_rep_n vs. synonymous variant σ_syn_m reflect our prior belief that replicate experiment noise is larger than synonymous mutant noise. σ_b_i and r_scale have improper priors.

Extended Data Fig. 9. Validation of Bayesian growth rate inference on synthetic datasets.

a, Three different true synthetic growth rate distributions used for simulating pre- and post-selection codon variant read count data. Synthetic growth rate distributions were chosen from observed toxin single mutant growth rate distributions in 3 different antitoxin backgrounds, spanning the range of distributions observed. b,c, Inferred growth rates using the Bayesian hierarchical model (b) show less bias and incorporate uncertainty estimates compared to mean log read ratio summary of pre-and post-selection read counts (+1 pseudocount) (c). Error bars in panel b reflect the 95% highest density posterior intervals, with the measure of centre being the mean posterior growth rate. d, Model uncertainties accurately reflect deviations of inferred true growth rates. Percentage of true synthetic amino acid growth rates falling into a certain highest density interval among all 2040 simulated toxin amino acid variants.

Extended Data Fig. 10. Posterior predictive checks show that the Bayesian hierarchical model can capture observed data statistics for both replicate experiments, whereas a non-hierarchical model cannot.

a,b, A non-hierarchical model, in which all synonymous codon variants have the same growth rate (a), cannot explain the observed data. (b) The observed standard deviation of log read ratios for synonymous wild-type toxin codon variants (red) (n=278) fall outside of the non-hierarchical model’s expectations (grey). c, The synonymous amino acid mutant standard deviations within a replicate (y-axis) are higher than codon mutant standard deviations between replicates (x-axis). Light green indicates binned average. d, Bayesian hierarchical model allows for growth rate variation between synonymous codon mutants by drawing these from a Gaussian distribution. e-g, Observed data statistics fall within the hierarchical Bayesian model’s expected values. (e) The observed standard deviation of synonymous wild-type toxin codon mutant log read ratios (red) fall within the model simulated values (stdev(log(c_post1_k/c_pre1_k) or stdev(log(c_post2_k/c_pre2_k) for biological replicate 1 or 2 respectively), see model code). Compare to panel (b) for the non-hierarchical model. (f) For each codon mutant, the hierarchical Bayesian model allows for simulating pre- and post-selection read counts (log(c_post_i,n/c_pre_i,n), see ED Fig. 9), including log read ratios, using the posterior parameter distribution. For each codon mutant, we calculate the p-value statistic (ie. the fraction of simulated samples falling below the observed log read ratio). (g) Distribution of posterior simulated p-values for various statistics, demonstrating that no observed data statistic is biased to fall outside of the posterior simulated statistics.

Figure 1:. Comprehensive identification of neutral and enabling mutations for the toxin-antitoxin system ParE3-ParD3.

a, Schematic of possible future mutational trajectories enabled by specific or non-specific neutral mutations. Yellow and green circles represent interacting proteins, shaded circles indicate mutated proteins, and arrows represent single mutations to sequences that retain binding. Specific mutations allow only particular subsequent mutations (left), whereas non-specific mutations enable tolerating many different subsequent mutations in the partner protein (right). b-c, Schematic examples of local vs. non-local (b) and specific vs. non-specific (c) compensatory mutations that rescue interface-disrupting mutations. Dots represent mutations. d, Schematic summary of experimental pipeline for identifying enabling mutations across the antitoxin-toxin interface. A library of all possible toxin single mutants is transformed into cells with a given, interface-disrupting mutation in the antitoxin (top). Cells are then grown in bulk and the abundance of each toxin variant over time is measured by sequencing. These changes are used to infer growth rates. Dots represent mutations. e, A single chain of the ParD3 antitoxin (yellow) in complex with the ParE3 toxin (green), from PDB:5CEG (right), with isolated antitoxin (left) and toxin (middle). The top 10 covarying positions are spacefilled.

Figure 2:. Deep mutational scanning reveals mutational tolerance and interface-disrupting substitutions in ParE3-ParD3.

a, Comprehensive single mutant scan of all possible antitoxin variants. The histograms indicate the change in growth rate for each mutant (with a blow-up histogram inset), relative to the wild-type antitoxin or toxin, with the greyscale-coded categories indicated. b, Heatmap of ∆growth-rate values for each possible antitoxin single mutant showing mutations that disrupt toxin neutralization (blue). The antitoxin-antitoxin oligomerization and antitoxin-toxin binding regions are indicated above. Top 8 positions that covary with positions in the toxin are shaded in yellow on the primary sequence. The substituted residue (or stop codon indicated with *) is listed on the far left and far right. Mean effects for each row and column are shown below and to the right. c, Structure of ParD3-ParE3 (PDB ID: 5CEG) highlighting antitoxin residue W59 with its pocket in the toxin and antitoxin residue G62 where single substitutions disrupt the interaction most. The mean effect at each position (see panel b) in ParD3 is color-coded, as indicated, on the structure. d,e, Same as (a) but for all toxin variants in presence of wild-type antitoxin (d) or absence of antitoxin (e). Experiments performed using 1.2 × 10⁻⁴ % w/v [arabinose], and 10 mM [IPTG] in the arabinose-titratable strain BW27783.

Figure 3.. Beneficial, interaction-restoring mutations can be far from the deleterious mutation they rescue.

a, Schematic overview of ‘suppressor scanning’. Cells expressing antitoxin ParD3(W59T) and a library of all possible toxin single substitutions were grown and analyzed as in Fig. 2c to identify toxin variants (T*) that can rescue the growth defect of ParD3(W59T). b, Distribution of growth rates for each toxin variant (T*) relative to the wild-type toxin (T) when co-expressed with antitoxin ParD3(W59T) reveals toxin variants alleviating the growth defect of the antitoxin W59T mutation (with a blow-up inset). Various categories of toxin variants are color-coded as indicated (right), including toxin variants that maintain toxicity at different thresholds (blue: 310 most toxic toxin variants, green: 781 toxic toxin variants). c, The significantly beneficial toxin variants for the deleterious antitoxin W59T (blue spacefilled, from set of most toxic toxin variants) are distributed across the toxin in the ParD3-ParE3 structure (PDB ID: 5CEG). Red indicates the deleterious antitoxin residue W59. d, Plot of distance between W59 in ParD3 and each significantly beneficial toxin mutant from the set of toxic (green) or most toxic (blue) toxin variants vs. effect size of rescue. e, Schematic indicating that all toxin single mutants were screened against 9 deleterious antitoxin mutants (G62L/D/Y, W59A/L/T/V, K63D,F73K). f, Same as (d) but for significantly beneficial toxins from all 9 suppressor scans. Experiments performed using 1.2 × 10⁻⁴ % w/v [arabinose], and 10mM [IPTG] in the arabinose-titratable strain BW27783.

Figure 4.. Non-specific enabling mutations outnumber specific mutations, and can be far from the deleterious mutation as well as the interface.

a-b, For a specifically enabling toxin mutation E73K (a) or non-specifically enabling toxin mutation V5L (b), the growth-rate relative to the wild-type pair T/AT (∆growth rate) is shown when combined with each antitoxin variant indicated on the x-axis (large dots represent mean posterior T*/AT* ∆growth rate; error bars indicate 95% posterior highest density interval). The mean posterioir ∆growth rate for each AT* combined with wild-type T is shown (small black dots) along with the ∆growth rate for T*/AT* expected under the independent, nonlinear model (green lines). Purple and orange indicate T*/AT* pairs (T*/AT*) where the toxin substitution is specific or non-specific, respectively. c, For each toxin variant (n=32) beneficial to at least one deleterious antitoxin mutant (51 pairs), the plot shows their effect size of rescue (∆growth rate) combined with each of the 9 deleterious AT*. The effect of each T* inferred by the nonlinear model is indicated on the heatmap. d, The number of non-specific and specific pairs of rescue at different ∆growth rate thresholds relative to the wild-type T/AT. e, Minimum atom distance of rescuing toxin mutation to deleterious antitoxin mutation (left) or to any antitoxin residue (right) vs. effect size of rescue (∆growth rate). For color codes of toxin-antitoxin double mutant pairs, see panels (a)-(b). f, Specific (purple) and non-specific (orange) enabling toxin mutations in each antitoxin mutation background they rescue are shown (spacefilling) on the ParD3-ParE3 structure (PDB ID: 5CEG). Antitoxin is yellow; toxin is green. Experiments performed using 1.2 × 10⁻⁴ % w/v [arabinose], and 10 mM [IPTG] in the arabinose-titratable strain BW27783.

Figure 5.. Natural sequences and models trained on these provide insufficient information to predict enabling mutations.

a, Schematic of identifying covarying pairs of residues in natural sequences. b, Mean covariation score of top 10 pairs of residues in ParD/ParE homologs (grey) compared to ~350 complexes with covariation signal (black). c, Distribution of covariation scores for beneficial pairs of residues (blue, see Fig. 2e) is similar to the null distribution for all possible pairs of positions (black). d, Amino-acid mutant frequency in toxin homologs at a particular site is not correlated with the non-specific enabling effect of that amino acid variant, as inferred from suppressor scanning. e, Predicted vs. observed rescue (∆growth rate of each double mutant (T*/AT*) relative to the antitoxin single mutant effect (T/AT*)). Predictions are made using EVmutation. Blue indicates observed significant rescue.

Figure 6.. Non-specifically enabling mutations expand mutational paths to maintain old and evolve new interactions.

a-c, For the antitoxin ParD3, a library of all 8,000 possible variant combinations at three key specificity-determining residues (shown on the structure of ParD3-ParE3 (PDB ID: 5CEG) in (a)) was screened for binding to wild-type toxin ParE3 or ParE3 harboring non-specifically enabling variants (purple) shown in (b). Schematic of the experiment is shown in (c). d, The fitness distribution of 8,000 antitoxin variants screened against the wild-type toxin ParE3 (left) or 10 different variants of ParE3 (right) reveals that non-specifically enabling mutations in the toxin allow binding to more combinatorial antitoxin variants than the wild-type toxin. e, Correlation of inferred independent effect from suppressor scan (see Fig. 4c) with the number of combinatorial antitoxin variants neutralized above half-maximal for each toxin single variant. f,g, Scatterplots showing fitness values for 8,000 antitoxin variants (dots) screened against the wild-type toxin ParE3 (y-axis) and the non-cognate toxin ParE2 (x-axis) (f), or against toxin ParE3 with a non-specifically enabling mutation (ParE3(V5L)) (y-axis) and ParE2 (x-axis) (g). Various classes of AT* are color-coded as shown on the right, including the AT* variants that have gained the ability to bind the non-cognate ParE2 (red), as well as the rewired antitoxin (green) that binds the non-cognate toxin ParE2 but not the cognate ParE3. h, Differences in the number of promiscuous antitoxin variants that neutralize both the non-cognate toxin ParE2 as well as the wild-type type toxin ParE3 (left) or a toxin variant harboring a non-specific suppressor indicated on the x-axis (fitness > 0.9). i, Force-directed graph of antitoxin variants that bind toxin ParE3 with (left) or without (right) the non-specifically enabling mutation V5L. Nodes represent individual antitoxin sequences (fitness >0.9), edges correspond to single mutational steps. Color codes as in panels f-g.