Estimation of evolutionary distances under stationary and nonstationary models of nucleotide substitution

Estimation of evolutionary distances has always been a major issue in the study of molecular evolution because evolutionary distances are required for estimating the rate of evolution in a gene, the divergence dates between genes or organisms, and the relationships among genes or organisms. Other closely related issues are the estimation of the pattern of nucleotide substitution, the estimation of the degree of rate variation among sites in a DNA sequence, and statistical testing of the molecular clock hypothesis. Mathematical treatments of these problems are considerably simplified by the assumption of a stationary process in which the nucleotide compositions of the sequences under study have remained approximately constant over time, and there now exist fairly extensive studies of stationary models of nucleotide substitution, although some problems remain to be solved. Nonstationary models are much more complex, but significant progress has been recently made by the development of the paralinear and LogDet distances. This paper reviews recent studies on the above issues and reports results on correcting the estimation bias of evolutionary distances, the estimation of the pattern of nucleotide substitution, and the estimation of rate variation among the sites in a sequence.

The Boron Requirement and Cell Wall Properties of Growing and Stationary Suspension-Cultured Chenopodium album L. Cells1

Suspension-cultured Chenopodium album L. cells are capable of continuous, long-term growth on a boron-deficient medium. Compared with cultures grown with boron, these cultures contained more enlarged and detached cells, had increased turbidity due to the rupture of a small number of cells, and contained cells with an increased cell wall pore size. These characteristics were reversed by the addition of boric acid (≥7 μm) to the boron-deficient cells. C. album cells grown in the presence of 100 μm boric acid entered the stationary phase when they were not subcultured, and remained viable for at least 3 weeks. The transition from the growth phase to the stationary phase was accompanied by a decrease in the wall pore size. Cells grown without boric acid or with 7 μm boric acid were not able to reduce their wall pore size at the transition to the stationary phase. These cells could not be kept viable in the stationary phase, because they continued to expand and died as a result of wall rupture. The addition of 100 μm boric acid prevented wall rupture and the wall pore size was reduced to normal values. We conclude that boron is required to maintain the normal pore structure of the wall matrix and to mechanically stabilize the wall at growth termination.

Stationary-phase mutation in the bacterial chromosome: Recombination protein and DNA polymerase IV dependence

Several microbial systems have been shown to yield advantageous mutations in slowly growing or nongrowing cultures. In one assay system, the stationary-phase mutation mechanism differs from growth-dependent mutation, demonstrating that the two are different processes. This system assays reversion of a lac frameshift allele on an F′ plasmid in Escherichia coli. The stationary-phase mutation mechanism at lac requires recombination proteins of the RecBCD double-strand-break repair system and the inducible error-prone DNA polymerase IV, and the mutations are mostly −1 deletions in small mononucleotide repeats. This mutation mechanism is proposed to occur by DNA polymerase errors made during replication primed by recombinational double-strand-break repair. It has been suggested that this mechanism is confined to the F plasmid. However, the cells that acquire the adaptive mutations show hypermutation of unrelated chromosomal genes, suggesting that chromosomal sites also might experience recombination protein-dependent stationary-phase mutation. Here we test directly whether the stationary-phase mutations in the bacterial chromosome also occur via a recombination protein- and pol IV-dependent mechanism. We describe an assay for chromosomal mutation in cells carrying the F′ lac. We show that the chromosomal mutation is recombination protein- and pol IV-dependent and also is associated with general hypermutation. The data indicate that, at least in these male cells, recombination protein-dependent stationary-phase mutation is a mechanism of general inducible genetic change capable of affecting genes in the bacterial chromosome.

A stationary-phase stress-response sigma factor from Mycobacterium tuberculosis.

Alternative RNA polymerase sigma factors are a common means of coordinating gene regulation in bacteria. Using PCR amplification with degenerate primers, we identified and cloned a sigma factor gene, sigF, from Mycobacterium tuberculosis. The deduced protein encoded by sigF shows significant similarity to SigF sporulation sigma factors from Streptomyces coelicolor and Bacillus subtilis and to SigB, a stress-response sigma factor, from B. subtilis. Southern blot surveys with a sigF-specific probe identified cross-hybridizing bands in other slow-growing mycobacteria, Mycobacterium bovis bacille Calmette-Guérin (BCG) and Mycobacterium avium, but not in the rapid-growers Mycobacterium smegmatis or Mycobacterium abscessus. RNase protection assays revealed that M. tuberculosis sigF mRNA is not present during exponential-phase growth in M. bovis BCG cultures but is strongly induced during stationary phase, nitrogen depletion, and cold shock. Weak expression of M. tuberculosis sigF was also detected during late-exponential phase, oxidative stress, anaerobiasis, and alcohol shock. The specific expression of M. tuberculosis sigF during stress or stationary phase suggests that it may play a role in the ability of tubercle bacilli to adapt to host defenses and persist during human infection.

Cortical activity flips among quasi-stationary states.

Parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden Markov process. The parallel spike trains were considered as a multivariate Poisson process whose vector firing rates change with time. As a consequence of this approach, the complete recording can be segmented into a sequence of a few statistically discriminated hidden states, whose dynamics are modeled as a first-order Markov chain. The biological validity and benefits of this approach were examined in several independent ways: (i) the statistical consistency of the segmentation and its correspondence to the behavior of the animals; (ii) direct measurement of the collective flips of activity, obtained by the model; and (iii) the relation between the segmentation and the pair-wise short-term cross-correlations between the recorded spike trains. Comparison with surrogate data was also carried out for each of the above examinations to assure their significance. Our results indicated the existence of well-separated states of activity, within which the firing rates were approximately stationary. With our present data we could reliably discriminate six to eight such states. The transitions between states were fast and were associated with concomitant changes of firing rates of several neurons. Different behavioral modes and stimuli were consistently reflected by different states of neural activity. Moreover, the pair-wise correlations between neurons varied considerably between the different states, supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons.