Genomic heterogeneity of background substitutional patterns in Drosophila melanogaster

Mutation is the underlying force that provides the variation upon which evolutionary forces can act. It is important to understand how mutation rates vary within genomes and how the probabilities of fixation of new mutations vary as well. If substitutional processes across the genome are heterogeneous, then examining patterns of coding sequence evolution without taking these underlying variations into account may be misleading. Here we present the first rigorous test of substitution rate heterogeneity in the Drosophila melanogaster genome using almost 1500 nonfunctional fragments of the transposable element DNAREP1_DM. Not only do our analyses suggest that substitutional patterns in heterochromatic and euchromatic sequences are different, but also they provide support in favor of a recombination-associated substitutional bias toward G and C in this species. The magnitude of this bias is entirely sufficient to explain recombination-associated patterns of codon usage on the autosomes of the D. melanogaster genome. We also document a bias toward lower GC content in the pattern of small insertions and deletions (indels). In addition, the GC content of noncoding DNA in Drosophila is higher than would be predicted on the basis of the pattern of nucleotide substitutions and small indels. However, we argue that the fast turnover of noncoding sequences in Drosophila makes it difficult to assess the importance of the GC biases in nucleotide substitutions and small indels in shaping the base composition of noncoding sequences.

DNA sequence evolution with neighbor-dependent mutation

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 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 noncoding DNA. A web-based tool has been constructed to compute single- and dinucleotide frequencies for arbitrary neighbor-dependent mutation rates. Also provided 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 noncoding DNA sequences as input, after masking out long 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 noncoding genomic DNA and may be used as a null model for various sequence analysis applications.

Distinct changes of genomic biases in nucleotide substitution at the time of Mammalian radiation

Differences in the regional substitution patterns in the human genome created patterns of large-scale variation of base composition known as genomic isochores. To gain insight into the origin of the genomic isochores, we develop a maximum-likelihood approach to determine the history of substitution patterns in the human genome. This approach utilizes the vast amount of repetitive sequence deposited in the human genome over the past approximately 250 Myr. Using this approach, we estimate the frequencies of seven types of substitutions: the four transversions, two transitions, and the methyl-assisted transition of cytosine in CpG. Comparing substitutional patterns in repetitive elements of various ages, we reconstruct the history of the base-substitutional process in the different isochores for the past 250 Myr. At around 90 MYA (around the time of the mammalian radiation), we find an abrupt fourfold to eightfold increase of the cytosine transition rate in CpG pairs compared with that of the reptilian ancestor. Further analysis of nucleotide substitutions in regions with different GC content reveals concurrent changes in the substitutional patterns. Although the substitutional pattern was dependent on the regional GC content in such ways that it preserved the regional GC content before the mammalian radiation, it lost this dependence afterward. The substitutional pattern changed from an isochore-preserving to an isochore-degrading one. We conclude that isochores have been established before the radiation of the eutherian mammals and have been subject to the process of homogenization since then.

Yang-Lee theory for a nonequilibrium phase transition

To analyze phase transitions in a nonequilibrium system, we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found by Yang and Lee under general conditions for equilibrium systems, can also be applied to nonequilibrium phase transitions. We consider a one-dimensional diffusion model with periodic boundary conditions. Depending on the diffusion rates, we find real and positive roots and can distinguish two regions of analyticity, which can be identified with two different phases. In a region of the parameter space, both of these phases coexist. The condensation point can be computed with high accuracy.