Restriction-modification systems and bacteriophage invasion: who wins?

The success of a phage that infects a bacterial cell possessing a restriction-modification (R-M) system depends on the activities of the host methyltransferase and restriction endonuclease, and the number of susceptible sites in the phage genome. However, there is no model describing this dependency and linking it to observable parameters such as the fraction of surviving cells under excess phage, or probability of plating at low amount of phages. We model the phage infection of a cell with a R-M system as a pure birth process with a killing state. We calculate the transitional probabilities and the stationary distribution for this process. We generalize the model developed for a single cell to the case of multiple identical cells invaded by a Poisson-distributed number of phages. The R-M enzyme activities are assumed to be constant, time-dependent, or random. The obtained results are used to estimate the ratio of the methyltransferase and endonuclease activities from the observed fraction of surviving cells.

A model of evolution with constant selective pressure for regulatory DNA sites.

BACKGROUND: Molecular evolution is usually described assuming a neutral or weakly non-neutral substitution model. Recently, new data have become available on evolution of sequence regions under a selective pressure, e.g. transcription factor binding sites. To reconstruct the evolutionary history of such sequences, one needs evolutionary models that take into account a substantial constant selective pressure. RESULTS: We present a simple evolutionary model with a single preferred (consensus) nucleotide and the neutral substitution model adopted for all other nucleotides. This evolutionary model has a rate matrix in which all substitutions that do not involve the consensus nucleotide occur with the same rate. The model has two time scales for achieving a stationary distribution; in the general case only one of the two rate parameters can be evaluated from the stationary distribution. In the middle-time zone, a counterintuitive behavior was observed for some parameter values, with a probability of conservation for a non-consensus nucleotide greater than that for the consensus nucleotide. Such an effect can be observed only in the case of weak preference for the consensus nucleotide, when the probability to observe the consensus nucleotide in the stationary distribution is less than 1/2. If the substitution rate is represented as a product of mutation and fixation, only the fixation can be calculated from the stationary distribution. The exhibited conservation of non-consensus nucleotides does not take place if the elements of mutation matrix are identical, and can be related to the reduced mutation rate between the non-consensus nucleotides. This bias can have no effect on the stationary distribution of nucleotide frequencies calculated over the ensemble of multiple alignments, e.g. transcription factor binding sites upstream of different sets of co-regulated orthologous genes. CONCLUSION: The derived model can be used as a null model when analyzing the evolution of orthologous transcription factor binding sites. In particular, our findings show that a nucleotide preferred at some position of a multiple alignment of binding sites for some transcription factor in the same genome is not necessarily the most conserved nucleotide in an alignment of orthologous sites from different species. However, this effect can take place only in the case of a mutation matrix whose elements are not identical.