  We introduce a model of DNA sequence evolution which can account for biases
in mutation rates that depend on the identity of the neighboring bases. An
analytic solution for this class of non-equilibrium models is developed by
adopting well-known methods of nonlinear dynamics. Results are presented for
the CpG-methylation-deamination process which dominates point substitutions in
vertebrates. The dinucleotide frequencies generated by the model (using
empirically obtained mutation rates) match the overall pattern observed in
non-coding DNA. A web-based tool has been constructed to compute single- and
dinucleotide frequencies for arbitrary neighbor-dependent mutation rates.
Alsoprovided is the backward procedure to infer the mutation rates using
maximum likelihood analysis given the observed single- and dinucleotide
frequencies. Reasonable estimates of the mutation rates can be obtained very
efficiently, using generic non-coding DNA sequences as input, after masking
outlong homonucleotide subsequences. Our method is much more convenient and
versatile to use than the traditional method of deducing mutation rates by
counting mutation events in carefully chosen sequences. More generally, our
approach provides a more realistic but still tractable description of
non-coding genomic DNA, and may be used as a null model for various sequence
analysis applications.
