Optimality of the genetic code with respect to protein stability and amino-acid frequencies

Table 4 Fraction f for different sets of allowed amino-acid interchanges in the alternative codes

f	Φ^FH	Φ^equif	Φ^faa
Unrestricted set	2.3 × 10^-6	6.0 × 10^-7	2.0 × 10^-9 (97%)
Biosynthesis-restricted set	6.1 × 10^-6	1.9 × 10^-6	2.9 × 10^-8 (98%)
Degeneracy-restricted set	2.3 × 10^-6	2.1 × 10^-6	1.3 × 10^-6 (97%)

Fraction f of random codes that have a lower value of the fitness function (Φ^FH, Φ^equif or Φ^faa) than the natural code, using the cost function g^mutate. For the unrestricted set, the f values were estimated from 10⁹ randomly generated codes, where the only constraint is the preservation of the code's block structure (as in Table 2). For the biosynthesis-restricted set, only permutations of amino acids sharing the same metabolic pathway were considered, that is, interchanges of amino acids contained in one of the four sets {F, S, Y, C, W}, {L, P, H, Q, R}, {I, M, T, N, K}, {V, A, D, E, G} (single-letter amino-acid notation) [34]. As the number of alternative codes is reasonable (207,360,000), they have not been randomly chosen, but all have been tested. The degeneracy-restricted set contains results obtained by shuffling only amino acids with the same degeneracy in the natural code, corresponding to the sets {M, W}, {C, D, E, F, H, K, N, Q, Y}, {I}, {A, G, P, T, V}, {L, R, S}. Here also, all 522,547,200 possible codes have been systematically tested. The percentage of optimization of the natural code compared to the optimal alternative ones, as defined in the text, is given in parentheses for Φ^faa. For the two restricted sets, for which all alternative codes were exhaustively generated, the Φ^faa value of the optimal code was computed exactly. For the unrestricted set, the optimal Φ^faa value was taken as the best of the unrestricted and two restricted sets.

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