Epistatic hotspots organize antibody fitness landscape and boost evolvability

Abstract

The course of evolution is strongly shaped by interaction between mutations. Such epistasis can yield rugged sequence-function maps and constrain the availability of adaptive paths. While theoretical intuition is often built on global statistics of large, homogeneous model landscapes, mutagenesis measurements necessarily probe a limited neighborhood of a reference genotype. It is unclear to what extent local topography of a real epistatic landscape represents its global shape. Here, we demonstrate that epistatic landscapes can be heterogeneously rugged and this heterogeneity may render biomolecules more evolvable. By characterizing a multipeaked fitness landscape of a SARS-CoV-2 antibody mutant library, we show that heterogeneous ruggedness arises from sparse epistatic hotspots, whose mutation impacts the fitness effect of numerous sequence sites. Surprisingly, mutating an epistatic hotspot may enhance, rather than reduce, the accessibility of the fittest genotype, while increasing the overall ruggedness. Further, migratory constraints in real space alleviate mutational constraints in sequence space, which not only diversify direct paths taken but may also turn a road-blocking fitness peak into a stepping stone leading toward the global optimum. Our results suggest that a hierarchy of epistatic hotspots may organize the fitness landscape in such a way that path-orienting ruggedness confers global smoothness.

Keywords: combinatorial mutagenesis; epistasis; evolvability; heterogeneity; sequence–function map.

Fig. 1.

Inferring local and global epistasis in an antibody fitness landscape: topographical impact of an epistatic hotspot. (A) Sequence space is defined by $L=10$ frequently mutated residues across HCDR1 and HCDR2 ($5$ sites each) of SARS-CoV-2-specific antibody COV107-23. Each residue $i$ is endowed with a spin variable $s_i$ that denotes the wild-type ($s_i=0$) or mutated ($s_i=1$) state. Orange sites are mutated in the global fitness maximum of the specific epistasis model (C). (B and C) Fitness landscape models $F(\mathbf{s})$ fitted to the enrichment data of all $2^L$ possible sequences, namely a global epistasis model (B) and an Ising-type specific epistasis model (C). For global epistasis, the latent phenotype $\varphi =\sum _i{h}_i{s}_i$ (colored strip of $h_i$) and the global nonlinearity $g(\varphi )$ (black curve) are inferred simultaneously. Sequences (points) are colored according to the state of site $i=53$. For specific epistasis, inferred additive and epistatic coefficients, $h_i$, $J_{\mathit{ij}}$, and $K_{ij·}=\frac{1}{L-2}\sum _{k\ne i,j}|K_{\mathit{ijk}}|$, are shown. Matrices of directed epistatic effects ${\gamma }_{i\to j}$ indicate how strongly mutation $i$ alters the fitness effect of mutation $j$. (D) 2D force-directed network layout of the landscape. Each point represents one of $2^L$ sequences, colored according to its fitness $F(\mathbf{s})$. Intracluster sequences have similar fitness, while intercluster gaps indicate fitness jumps. Pairs of mutational neighbors are connected by gray lines. Black dots mark local fitness optima in the specific epistasis model (C). Arrows point to the germline genotype and the global fitness maximum ($F_{\max }$). (E) Superposition of $9$-site sublandscapes defined by holding the indicated site in its wild-type (blue) or mutated (orange) state. Shown are sublandscapes in the force-directed embedding with the epistatic hotspot ($i=53$) and a weakly epistatic site ($i=35$) being respectively held constant in the genetic background. Crosses mark fitness optima in either sublandscape.

Fig. 2.

Structural interpretation of the epistatic hotspot. (A) Left: 3D distances (in Å) between pairs of $C_{\alpha }$ positions in the antibody fold. Right: Apo crystal structure of COV107-23 (PDB: 7LKA). Residue S53 in the variable region of the heavy chain is colored in red. Pink: heavy chain, light blue: light chain, orange: HCDR1, gray: HCDR2, teal: HCDR3. (B) Predicted $\mathrm{\Delta }\mathrm{\Delta }G$ for each mutation from simulations in Rosetta. Data points from independent replicates (orange dots) are shown, together with the mean (gray bars) $\pm$ SD (black lines). Site 27 has three biochemically similar mutations. (C) Replicate-averaged $\mathrm{\Delta }\mathrm{\Delta }G$ versus inferred fitness effect $\mathrm{\Delta }F$ for each mutation in the F58 background (blue dots). A linear fit to all data points excluding site 27 crosses the origin (dashed line).

Fig. 3.

Hotspot mutation increases ruggedness of antibody landscape yet enhances $F_{\max }$ accessibility. (A) Ruggedness of $9$-site sublandscapes with the remaining site being pinned (i.e., held constant), measured by the correlation of fitness effects of mutations $\gamma (n,d)$ between genotypes $d$ mutations apart with $n$ pinned sites (Left) and the number of local fitness optima (Right). For each choice of the pinned site $i$, a comparison is made between the wild-type state ($s_i=0$, blue) and the mutated state ($s_i=1$, orange). Also see SI Appendix, Fig. S5 A and B. (B) Accessibility of the global fitness optimum $F_{\max }$ in $9$-site sublandscapes when site $50$ or site $53$ is pinned, measured by the distribution of absorbing probabilities under Monte-Carlo evolutionary dynamics. The histograms show the fraction of starting genotypes that lead to a certain absorbing probability at the global optimum; the vertical lines indicate starting from the germline genotype. Results for other choices of the pinned site are shown in SI Appendix, Fig. S5C.

Fig. 4.

Epistatic hotspot induces heterogeneous ruggedness and restricts path diversity. (A) Strong variation of ruggedness with respect to the size and location of the antibody sublandscape. To quantify heterogeneity, we vary the number ($n$) and identity (in total $\left(\genfrac{}{}{0pt}{}{L}{n}\right)$ choices) of the pinned sites and compute the ruggedness of the resulting $(L-n)$-dimensional sublandscapes. Colored violins at each choice of $n$ represents the range of ruggedness values due to varying locations, when the hotspot (site 53) is included in the pinned background (orange) or excluded from it (blue). The antibody landscape appears more rugged (low-lying $\gamma$ values) when the hotspot is held in its mutated state. The corresponding distributions in the NK landscape are shown for comparison (gray violins). Note that the range of $\gamma$ values is independent of the degree of ruggedness controlled by $K$, indicating statistical homogeneity. (B) Scaled path entropy $S_{\pi }$ measures the diversity of adaptive paths from the germline to the global optimum under Markov-chain Monte-Carlo evolutionary dynamics. Results are shown for the full antibody landscape (blue horizontal line) and $9$-site sublandscapes (symbols). Hotspot mutation is strongly path-constraining. Gray lines show the expectations from NK landscapes with moderate ruggedness.

Fig. 5.

Spatial structure relaxes mutational constraints and diversifies direct paths taken. (A) Representative paths taken by an adapting population in the antibody landscape, evolving from the germline to the global fitness maximum $F_{\max }$ under Wright–Fisher dynamics. Consecutive arrows indicate mutational steps in the t-SNE layout of sequence space (with darker shade reflecting path overlap). In the well-mixed condition (black), mutation S53P (purple arrow) occurs ahead of any other mutation, while S56T (green arrow) occurs toward the end. In spatially structured populations (red), S53P may occur at later steps (lower path) and occasionally, S53P and S56T swap their order (upper path as an example). (B) Order constraints between pairs of mutations required to reach $F_{\max }$, shown by the matrix of probabilities $P[t(i)<t(j)]$ that mutation $i$ precedes mutation $j$ (upper row) and the corresponding histogram of matrix entries (lower row), under well-mixed (Left) and structured (Right) conditions. Purple (green) bars highlight the entries corresponding to mutation at site $i=53$ ($i=56$). (C) Diversity and abundances of successful paths (reaching $F_{\max }$) depend on the path step at which hotspot mutation occurs. Successful paths are sorted by the path step of mutation 53. In each category, a realized path weight $w_{\pi }$ (dot) is colored by the number of unique paths taken by a fraction of $w_{\pi }$ evolving populations; the solid lines trace the cumulative path weight across the categories. In comparison with the well-mixed condition (Left), spatial structure diversifies viable paths (Right), yielding a larger overall path entropy (Lower panels).

Fig. 6.

Heterogeneously rugged antibody landscape supports smooth adaptive paths and efficient navigation. (A) Success rate at which replicate populations evolving in the antibody landscape under Wright–Fisher dynamics first enrich the global optimum, as opposed to any local optimum, to a certain occupancy threshold (criterion of success). Spatial structure (red) enhances success at intermediate values of the occupancy threshold over the well-mixed condition (black). (B) Success rate as a function of occupancy threshold in smooth ($K=0$) and rugged ($K=2$) NK landscapes, without (black) and with (red) spatial structure. The curves for $K=2$ are an ensemble average over 50 independent realizations of the landscape, constrained to have the same number of fitness optima and the same mutational distance from the germline to $F_{\max }$ as the antibody landscape. (C) Distribution of fitness effects of mutations, $\mathrm{\Delta }F$, along successful paths collected from replicate populations evolving in the antibody (Left) and constrained NK (Right) landscapes, without (black) and with (red) spatial structure. (D–F) Characteristics of top-$3$ successful paths at occupancy threshold 0.5, without (upper row) and with (lower row) spatial structure. (D) Mutational paths in t-SNE representation. Line width is proportional to the path weight. Dots indicate 7 fitness optima. The orange dot represents the local optimum that is a road block bypassed by successful well-mixed populations but may serve as a stepping stone to structured populations taking a direct path. (E) Temporal occupancy of the fitness optima along the paths shown in (D). Each curve is an average over successful populations taking that path, with the same color codes as the fitness optima in (D). (F) Fitness effect of mutations out of each genotype along the paths shown in (D). The stepping-stone genotype is marked with an orange dot. Line width is proportional to the path weight.

Fig. 7.

Summary sketch: Epistatic hotspot induces heterogeneous ruggedness that confers a funnel-like shape to fitness landscape. Left: An early mutation of the hotspot grants a large fitness gain and turns on path-orienting heterogeneous ruggedness. The dominant adaptive paths to the global optimum $F_{\max }$ are effectively smooth and characterized by diminishing return in fitness gain. Right: Homogeneous ruggedness, in contrast, would cause repeated trapping at local optima, hindering navigation toward $F_{\max }$. Fitness increases top–down.