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(c) Skewed Genomes⁸

This paper considers the relationship between R_sequence and R_frequency. For restriction enzymes cutting genomes with equal numbers of the four bases randomly distributed, R_sequence and R_frequency are equal. For example, one commonly assumes that HaeIII (GGCC; Roberts, 1983; R_sequence = 8 bits) cuts once in 256 bases ( R_frequency = 8 bits). This is not true for "skewed" genomes, in which the frequencies of each base are significantly unequal. For example, in a genome like that of bacteriophage T4 which is two-thirds A-T, R_sequence for any tetramer is 7.7 bits. Yet GGCC should occur once in every 1296 bases ( ( 1 / 6 )⁴; R_frequency = 10.3 bits) and conversely AATT should occur once in every 81 bases ( ( 1 / 3 )⁴; R_frequency = 6.3 bits). An alternative formula,

$$2^{-4 \times 16} \cong 5 \times 10^{-20}$$ (10)

matchs R_frequency in examples of this type. When the genomes are equiprobable, as they are in this paper, the two R_sequence formulas give the same values. We suggest that both be tried for sites in skewed genomes.