A genome-wide analysis of nine pairs of closely related species established that codon substitution rates under prevailing negative selection follow a nearly universal rule: the rate decreases strongly with the composite physicochemical distance ΔU between the amino acids exchanged, but the rule is tight (R2>0.8R^2 > 0.8) only where negative selection dominates. Four issues were left open: whether positive selection follows the same small-step rule (resolved by the companion study — it does not), why the human–chimpanzee comparison is anomalous (R2=0.627R^2 = 0.627), whether the rule survives strong positive selection such as domestication or extreme environments, and — the central remaining question — the precise quantitative mapping from combinations of physicochemical property differences to fitness effects and hence substitution rates, given that no small subset of properties explains the pattern. The problem is to determine this mapping and its domain of validity across selection regimes and taxa, and to account for documented departures such as the weakly constrained hominoid genomes.

Background

When a DNA point mutation alters a codon, it is either synonymous (no amino-acid change) or nonsynonymous (amino-acid change). The ratio of nonsynonymous to synonymous substitution rates, Ka/KsK_a/K_s, is a standard index of selection: values well below 1 indicate purifying (negative) selection removing deleterious protein changes, while values near or above 1 suggest relaxed constraint or adaptive (positive) selection.

Since the 1970s, evolutionary geneticists have tried to express the deleteriousness of an amino-acid replacement through physicochemical distances between the two amino acids, such as Grantham's distance combining composition, polarity, and volume. Tang, Wyckoff, Lu, and Wu (2004) refined this into a universal evolutionary index UiU_i for each of the 75 amino-acid pairs reachable by a single nucleotide substitution, computed from empirical substitution likelihoods relative to synonymous changes; the index generalizes across taxa from primates to yeast.

The idea that 'evolution proceeds in small steps' rests on two logically independent premises: that negative selection acts most strongly against mutations producing large differences, and that positive selection favors small-step changes, an argument from Fisher's geometric model (the picture of adaptation as approaching an optimum in a high-dimensional trait space, where a random large step is likelier to overshoot the optimum than a small one). Chen, Lan, Shen, and Wu (2019) tested the first premise genome-wide. They measured substitution rates between coding sequences of nine closely related species pairs spanning plants, invertebrates, and vertebrates, and regressed them against a composite amino-acid distance ΔU\Delta U (scaled to [0, 1]) built from 48 physicochemical properties of amino acids, analyzed by principal component analysis (PCA), a standard technique that decomposes correlated property measures into orthogonal components ordered by variance explained. Strikingly, 47 of the 48 properties contribute to the rate, no single property dominates (the largest contributor to the first principal component accounts for about 4%), and the first principal component explains only about 61% of the variation in UiU_i — so the distance is genuinely high-dimensional, and the previous hope that a few properties (e.g., volume and polarity) would suffice appears untenable.

Two qualifications emerged. First, the negative correlation between rate and ΔU\Delta U is strong (R2>0.8R^2 > 0.8) only when the genes are predominantly under negative selection; within species pairs, R2R^2 is generally above 0.6 for gene groups with Ka/Ks<0.4K_a/K_s < 0.4, and its drop becomes steeper once Ka/KsK_a/K_s exceeds 0.4. Since most genes in most taxa are so constrained, ΔU\Delta U behaves as a nearly universal measure, but its predictive power collapses as constraint weakens. Second, the human–chimpanzee comparison is an outlier with R2=0.627R^2 = 0.627. Because substitutions at CpG dinucleotide sites (hypermutable CG motifs whose elevated mutation rate can mimic selection patterns) were masked, this obvious explanation was ruled out; the anomaly is shared across the human, chimpanzee, and gorilla lineages and reflects hominoid genomes as a group having many genes with Ka/Ks>0.6K_a/K_s > 0.6 — but why hominoids are so weakly constrained, selectively or demographically, was not resolved.

A companion study by Chen, He, Lan, Shen, Wen, and Wu (2019), using the McDonald–Kreitman test (a comparison of within-species polymorphism and between-species divergence at synonymous versus nonsynonymous sites that separates the contributions of positive and negative selection) and an analytical model, answered the complementary question: positive selection does not follow the small-step rule. For 65 of the 75 amino-acid pairs, positive selection is comparable in strength regardless of amino-acid distance, and the ten pairs under the strongest positive selection all involve large leaps in chemical properties — adaptive evolution proceeds in large steps.

What remains open is the quantitative core of the original finding: the precise mapping from specific combinations of physicochemical property differences to fitness differences and thence to substitution rates, the rule's behavior under regimes of strong positive selection (domestication, extreme environments) where unusual substitution patterns have been reported, and the explanation of departures such as the hominoid anomaly. Recent work has advanced pieces of this: amino-acid exchangeabilities (relative substitution propensities between amino-acid pairs, as tabulated in empirical substitution matrices) are known to vary across the tree of life; distributions of fitness effects (DFEs) for each amino-acid replacement type, measured over hundreds of thousands of experimental replacements by deep mutational scanning (a technique measuring the fitness of nearly all single mutants of a protein in a pooled selection), appear to follow truncated-exponential maximum-entropy distributions; and analyses of charge and size differences confirm that these properties constrain substitution rates across taxa. But no accepted functional mapping from property combinations to fitness effects — or a regime-aware account of when the small-step rule of negative selection and the large-step tendency of positive selection apply — exists.

Problem Statement

Determine the quantitative relationship between amino-acid physicochemical property combinations and fitness effects — and hence codon substitution rates — together with the domain of validity of the resulting rules across selection regimes. Concretely: (i) given that the composite distance ΔU\Delta U predicts genome-wide substitution rates under prevailing negative selection (R2>0.8R^2 > 0.8) while its first principal component explains only about 61% of the variation in the evolutionary index UiU_i and no single property dominates, establish a predictive mapping from combinations of physicochemical property differences between amino acids to fitness differences and substitution rates, together with a quantitative account of the residual high-dimensional variation it leaves unexplained; (ii) quantify how this mapping, the small-step rule of negative selection, and the large-step tendency of positive selection change across regimes of strong positive selection — such as domestication and extreme environments — where unusual substitution patterns have been reported; and (iii) identify the selective or demographic factors that make weakly constrained genomes, notably hominoids (human–chimpanzee R2=0.627R^2 = 0.627 with CpG substitutions masked), depart from the rule. Each of the three questions is independently open, and the unifying objective is a single regime-aware, quantitative law of amino-acid replacement that answers all three.

References

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