Fitness landscapes1,2 depict how genotypes manifest at the phenotypic level and form the basis of our understanding of many areas of biology2,3,4,5,6,7, yet their properties remain elusive. Previous studies have analysed specific genes, often using their function as a proxy for fitness2,4, experimentally assessing the effect on function of single mutations and their combinations in a specific sequence2,5,8,9,10,11,12,13,14,15 or in different sequences2,3,5,16,17,18. However, systematic high-throughput studies of the local fitness landscape of an entire protein have not yet been reported. Here we visualize an extensive region of the local fitness landscape of the green fluorescent protein from Aequorea victoria (avGFP) by measuring the native function (fluorescence) of tens of thousands of derivative genotypes of avGFP. We show that the fitness landscape of avGFP is narrow, with 3/4 of the derivatives with a single mutation showing reduced fluorescence and half of the derivatives with four mutations being completely non-fluorescent. The narrowness is enhanced by epistasis, which was detected in up to 30% of genotypes with multiple mutations and mostly occurred through the cumulative effect of slightly deleterious mutations causing a threshold-like decrease in protein stability and a concomitant loss of fluorescence. A model of orthologous sequence divergence spanning hundreds of millions of years predicted the extent of epistasis in our data, indicating congruence between the fitness landscape properties at the local and global scales. The characterization of the local fitness landscape of avGFP has important implications for several fields including molecular evolution, population genetics and protein design.
We assayed the local fitness landscape of avGFP by estimating the fluorescence levels of genotypes obtained by random mutagenesis of the avGFP sequence (Fig. 1). We used fluorescence-activated cell sorting (Supplementary Fig. 1) and sequenced the entire GFP coding region to assay the fluorescence of many thousands of genotypes created by random mutagenesis of the wild-type sequence (Supplementary Information 2 and Extended Data Fig. 1). We applied several strategies to minimize the error of our estimate of fluorescence (Supplementary Information 3.4 and 4.4), which was estimated from thousands of independent measurements of the wild-type sequence (false negative error rate = 0.08%) and genotypes incorporating mutations known to eliminate fluorescence (false positive error rate = 0.24%). Our final data set included 56,086 unique nucleotide sequences coding for 51,715 different protein sequences. Our procedure introduced an average of 3.7 mutations per gene sequence, and most assayed genotypes contained several, up to 15, missense mutations. Still, since the total number of possible sequences grows exponentially with the number of mutations, the fraction of sampled sequences was tiny for sequences containing more than two mutations (Extended Data Table 1). We used these data to survey the local fitness landscape of GFP, analysing the effect of single, double and multiple mutations.
The distribution of fitness effects of individual missense mutations was assayed by comparing the distribution of fluorescence of wild-type avGFP amino acid sequences, tagged by different molecular barcodes, and the distribution of fluorescence of sequences carrying a single mutation (Supplementary Information 4.1). We found that at least 75% of mutations had a deleterious effect on fluorescence, including 9.4% of single mutations conferring a more than fivefold decrease in fluorescence, but for many mutations the effect was small (Fig. 2a). Accordingly, genotypes with multiple missense mutations were more likely to have low fluorescence, and most genotypes carrying five or more missense mutations were non-fluorescent (Extended Data Fig. 2). Mutations with a strong effect on fluorescence preferably resided at sites that coded for amino acid residues oriented internally towards the chromophore (Fig. 2b, c), which is consistent with data on other proteins on the preference of deleterious mutations to target buried residues9,11,12,13. The effect of mutations on fluorescence was positively correlated with site conservation (Extended Data Fig. 3a, Spearman’s rank correlation coefficient = 0.40, P = 1.44 × 10−10), and mutations with a deleterious impact were less likely to be found in orthologous sequences (Extended Data Fig. 3b) and more likely to be found in sites with a deleterious deletion (Supplementary Fig. 2). Still, ~10% of mutant states conferring a non-fluorescent phenotype were nevertheless fixed in long-term evolution (Extended Data Fig. 3b), and a substantial fraction of genotypes containing only mutations leading to amino acid states from GFP orthologues was non-fluorescent (Supplementary Fig. 3), indicating that epistasis affects the avGFP fitness landscape16.
Interaction of deleterious mutations can manifest in positive epistasis, when the joint effect of mutations is weaker than their independent contribution, or negative epistasis when the joint effect is stronger (Fig. 3a). Light intensity is perceived in the logarithmic scale by living beings, including jellyfish19. Thus, we defined epistasis e as the deviation from additivity of effects of single mutations on the logarithmic scale. We compared the decrement of the log-fluorescence of a multiple mutant Fmult to the sum of decrements of individual mutants, such that where FWT and Fi are the log-fluorescence values conferred by wild-type avGFP and avGFP with the i-th single missense mutation, respectively. We restricted the expected fluorescence of the multiple mutant to the observed maximum or minimum levels (Supplementary Information 4.2). This eliminated spurious detection of epistasis, which could otherwise occur, for example, when a non-fluorescent double mutant consists of two mutations, both of which individually confer a non-fluorescent genotype. We defined strong epistasis as |e| > 0.7, or as cases in which the observed fluorescence differed from the expected by at least fivefold, with a false discovery rate of <1% (Supplementary Fig. 4).
Negative epistasis affected up to 30% of all genotypes, depending on the number of mutations (Fig. 3b, c), which resulted in a larger than expected fraction of non-fluorescent genotypes (Fig. 3c). Genotypes carrying more than seven mutations showed a decrease in the prevalence of negative epistasis because many genotypes carrying multiple mutations were expected to lose fluorescence even without epistasis (Fig. 3b). Positive epistasis was rare in avGFP, on the order of accuracy of our method. We sampled ~2% of all possible pairs of mutations (Extended Data Table 1), assaying 30% of pairs of amino acid sites (16,898 out of 55,696, Extended Data Fig. 4a). Epistatic pairs of sites were located across the avGFP sequence (Extended Data Fig. 4a), mostly beyond the range of direct physical interaction of amino acid residues (Extended Data Fig. 4b) but marginally closer together than random (Extended Data Fig. 4c, P < 0.0004, Mann–Whitney U-test). Epistasis was found among 96% of mutations with weak effect (Extended Data Fig. 4d), suggesting that their joint effect brings the protein over some stability margin8,20. Finally, epistasis was more common between pairs of sites in which both residues are internally oriented (Extended Data Fig. 4e). Taken together, these data indicate that epistasis was more common at functionally important sites.
In a unidimensional landscape, fitness is a monotonic function of an intermediate variable known as fitness potential21,22, which is the sum of effects of individual mutations. We used multiple regression considering a non-epistatic fitness function in which log-fluorescence, F, is equal to the linear predictor, the fitness potential, p, such that F = f(p) = p. This simplest, non-epistatic model explained only 70% of the initial sample variance (σ2 = 1.12 and σ2 = 0.34 before and after the application of the model, respectively). Using the variance of the 2,442 wild-type fluorescence measurements, we estimated that ~1% of the initial sample variance can be attributed to noise (σ2 = 0.0097), indicating that the remaining 29% of sample variance cannot be explained without epistasis.
The simplest form of an epistatic fitness function is when fitness is a monotonic nonlinear function of p21,22. The lack of genotypes with intermediate fluorescence (Extended Data Fig. 5a) suggests that the avGFP fitneses landscape can be described by a truncation-like fitness function23. We therefore modelled F as a sigmoid function of p, which explained 85% of the initial sample variance (σ2 = 0.17). A more complex sigmoid-shaped fitness function refined with a neural network approach (Supplementary Information 4.6) explained 93.5% of the initial sample variance (σ2 = 0.065, Extended Data Fig. 5), confirming that the fitness landscape can mostly be represented by a unidimensional threshold function (Fig. 4), which can arise from the joint contribution of mutations to protein stability8,13,14,20,24. The average fluorescence of single mutants of avGFP as a function of the predicted protein destabilization, ΔΔG, reveals a threshold around 7–9 kcal mol−1 (Fig. 4). Notably, the hidden value found by the artificial neural network for single mutants correlated to the predicted ΔΔG (Fig. 4 and Extended Data Fig. 5f), confirming a probable influence of protein stability on the nature of epistasis in avGFP. The threshold fitness function does a remarkably good job in approximating the entire fitness landscape, explaining ~95% of all variance. However, when taking into account the error rate of our data set, we estimate that at least 0.3% of genotypes cannot be explained by the threshold fitness function (Supplementary Information 4.5 and Extended Data Fig. 5d), representing instances of multidimensional epistasis2,5,7.
We compared the local avGFP fitness peak to the global GFP fitness landscape using sequences of GFP orthologues. Negative, threshold-like epistasis, leading to truncation selection23 against slightly deleterious mutations may prevent their accumulation in evolution25,26. Thus, we compared the fraction of neutral single mutations to the rate of nonsynonymous and synonymous evolution (dN/dS), a proxy for the average strength of selection. The average dN/dS across a broad phylogenetic range was 0.35 ± 0.1 (mean ± s.d.), and 0.17 when avGFP was compared to the orthologue from the closest fluorescent relative Aequorea macrodactyla. These measurements are similar to the estimated proportion of neutral mutations in avGFP (0.23), suggesting that the proportion of neutral mutations is similar across distant fitness peaks. The rate at which the phenotypic effect of amino acid substitutions changes across evolution, which is reflected in the changing rate of convergent evolution across the phylogenetic tree27,28, can be used to model the prevalence of epistasis with the fitness matrix model28. This model approximates the prevalence of epistasis as the proportion of amino acid mutations that markedly change their effect on fitness after the occurrence of substitutions at other sites (Supplementary Information 5). Applying the fitness matrix model to the GFP multiple alignment, we predicted the proportion of mutations that change their effects on fluorescence when found in a different genetic background, revealing prevalence of positive and negative epistasis, which concur with our experimental observations (Fig. 5 and Supplementary Fig. 5). The congruence of the data from an evolutionary trajectory spanning hundreds of millions of years with experimental data are remarkable, suggesting similarity in the local and global structures of the fitness landscape shaped by strong epistatic interactions.
Our study provides complementary results of the analysis of single and double mutations to several previous studies9,11,12,13,14, and a novel depiction of a large segment of the fitness landscape of a single protein. The proportion of neutral single mutations in our data was similar to that observed when fitness was assayed directly or through competition experiments10,24,29 but substantially lower than that observed in functional studies4,10,11,13,17. Furthermore, the propensity of multiple mutations to have a stronger negative effect on fitness than the sum of individual mutation effects has been observed9,10,12,14. However, because our analysis considered genotypes carrying multiple mutations, we infer a wider picture of the local fitness landscape (Supplementary Video 1). The avGFP fitness peak is narrow and defined by negative epistasis, best described by truncation selection in which fluorescence is eliminated if the joint effect of mutations exceeds a threshold of an intermediate property, possibly protein stability8,20. Such a landscape increases the efficacy of selection against slightly deleterious mutations23, preventing their accumulation in evolution25,26. Simultaneously, the fitness landscape is approximately non-epistatic near the fitness peak. If other proteins have a similar fitness landscape it would support the nearly neutral theory of evolution30, explaining the selective forces and evolutionary dynamics of mutations with negligible individual effects on fitness.
The broad congruence of our data with the prevalence of epistasis from long-term evolution suggests that the shape of the local fitness landscape can be extrapolated to a larger scale. Yet, epistasis between sites coding for residues with a direct interaction in protein structure was rare, contrasting with observation of such instances in long-term evolution16 and a mutation assay of the RNA recognition motif (RRM) domain12. Thus, the local fitness landscape spanning a few mutations from a single fitness peak may be approximated by a unidimensional threshold fitness potential function; however, this simple fitness function may not be appropriate to describe fitness landscapes that incorporate fitness ridges connecting sequences of more divergent orthologues27. The nature of global fitness landscapes, especially the interaction between local and global scales, remains to be explored.
Sequence Read Archive
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We thank Y. Kulikova and G. Filion for discussion on statistical analysis and I. Osterman, R. Moretti and J. Meiler for technical assistance and M. Friesen for a critical reading of the manuscript. We thank H. Himmelbauer, CRG Genomic Unit and the Russian Science Foundation project (14-50-00150) for sequencing. Experiments were partially carried out using the equipment provided by the IBCH core facility (CKP IBCH). The work was supported by HHMI International Early Career Scientist Program (55007424), the EMBO Young Investigator Programme, MINECO (BFU2012-31329), Spanish Ministry of Economy and Competitiveness Centro de Excelencia Severo Ochoa 2013-2017 grant (SEV-2012-0208), Secretaria d’Universitats i Recerca del Departament d’Economia i Coneixement de la Generalitat’s AGAUR program (2014 SGR 0974), Russian Science Foundation (14-25-00129) and the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013, ERC grant agreement, 335980_EinME).
The authors declare no competing financial interests.
Extended data figures and tables
The depiction of the construct design, expression and cell sorting.
A violin plot of the measured levels of fluorescence for genotypes carrying different numbers of missense mutations.
a, b, The log-fluorescence and evolutionary conservation expressed as Shannon entropy (a), and fraction of mutant amino acid states found in avGFP orthologues (b). The y-axis error bars in b show the binomial proportion confidence interval level (68%), and other error bars denote s.e.m.
a, Pairs of amino acid sites for which we assayed at least one combination of mutations (in blue, top left). The distribution of the maximum level of epistasis observed between sites (blue scale, bottom right) and unknown values (white). b, Pairs of sites under exceptionally strong epistatic interaction (e < −2) connected by a blue line on the GFP structure. c, The distribution of distances in the GFP structure between sites with at least one pair of epistatically interacting mutations (red) and all pairs of sites in the structure (grey). d, Epistasis between pairs of mutations as a function of their individual fluorescence. e, The contribution of internally and externally oriented amino acid residues in the avGFP structure relative to pairs of missense mutations showing no epistasis (|e| < 0.3), weak (0.3 < |e| < 0.7) and strong (|e| > 0.7) epistasis.
a, A multiple linear regression in which fluorescence is linear combination of effects of individual single mutations. b, A multiple regression in which mutations contribute linearly to a fitness potential and fluorescence is a sigmoidal function of p where F ≈ e−p/(1 + e−p). c, d, The predicted fluorescence by a neural network approach. Predicted fitness function by a neural network with one hidden neuron and two neurons in the outer layer. e, The scheme of our neural network approach. The genotype data was passed to the input layer of the neural network as an array of 0s or 1s corresponding to the absence or presence of amino acid mutations in the genotype, respectively. The first hidden layer consisted of a single neuron that calculated the weighted sum of inputs using weights obtained during training. The output of the first hidden layer was passed through an output subnetwork that transformed this value with a nonlinear function to make the final prediction of fluorescence. The output subnetwork consisted of several neurons with a sigmoidal transfer function, allowing the subnetwork to approximate a broad range of nonlinear functions. The final mapping of the hidden value to fluorescence was determined by the weights of connections between neurons inside the output subnetwork. During training all weights were optimized to find the best prediction of fluorescence from the hidden value. The resulting function that was defined during training is shown in Fig. 4. f, Correlation between the hidden value of the neural network and Rosetta-predicted ΔΔG for single mutants.
This file contains Supplementary Text and Data, Supplementary Figures 1-5, Supplementary Table 1 and Supplementary references –see contents page for details. (PDF 2608 kb)
A 3D rendering of our dataset that is also depicted in Figure 1b. The protein sequence is arranged in a circle, with the N terminal and the chromophore labelled on the outer circle. Black line markers outside the fitness landscape representation are positioned every 10 sites of avGFP. The Z-axis, height, represents the level of fluorescence, which is colour-coded from green to black. The surface is shown as the median fluorescence brightness levels of all mutations at a given site with fluorescence levels conferred by individual mutations shown by dots. The centre represents the fluorescence of avGFP with distance away from it corresponding to the number of mutations in the genotype. The median surface extends up to genotypes with 10 mutations. (MP4 26274 kb)
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Sarkisyan, K., Bolotin, D., Meer, M. et al. Local fitness landscape of the green fluorescent protein. Nature 533, 397–401 (2016). https://doi.org/10.1038/nature17995
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