The physical map of {\it Escherichia coli\/} K-12 strain MG1655: Construction, comparison with other strains and implications for mechanisms controlling oligonucleotide frequency

Complete NotI, SfiI, XbaI and BlnI cleavage maps of Escherichia coli K-12 strain MG1655 were constructed. Techniques used included: CHEF pulsed field gel electrophoresis; transposon mutagenesis; fragment hybridization to the ordered $\lambda$ library of Kohara et al.; fragment and cosmid hybridization to Southern blots; correlation of fragments and cleavage sites with EcoMap, a sequence-modified version of the genomic restriction map of Kohara et al.; and correlation of cleavage sites with DNA sequence databases. In all, 105 restriction sites were mapped and correlated with the EcoMap coordinate system.^ NotI, SfiI, XbaI and BlnI restriction patterns of five commonly used E. coli K-12 strains were compared to those of MG1655. The variability between strains, some of which are separated by numerous steps of mutagenic treatment, is readily detectable by pulsed-field gel electrophoresis. A model is presented to account for the difference between the strains on the basis of simple insertions, deletions, and in one case an inversion. Insertions and deletions ranged in size from 1 kb to 86 kb. Several of the larger features have previously been characterized and some of the smaller rearrangements can potentially account for previously reported genetic features of these strains.^ Some aspects of the frequency and distribution of NotI, SfiI, XbaI and BlnI cleavage sites were analyzed using a method based on Markov chain theory. Overlaps of Dam and Dcm methylase sites with XbaI and SfiI cleavage sites were examined. The one XbaI-Dam overlap in the database is in accord with the expected frequency of this overlap. The occurrence of certain types of SfiI-Dcm overlaps are overrepresented. Of the four subtypes of SfiI-Dcm overlap, only one has a partial inhibitory effect on the activity of SfiI. Recognition sites for all four enzymes are rarer than expected based on oligonucleotide frequency data, with this effect being much stronger for XbaI and BlnI than for NotI and SfiI. The latter two enzyme sites are rare mainly due to apparent negative selection against GGCC (both) and CGGCCG (NotI). The former two enzyme sites are rare mainly due to effects of the VSP repair system on certain di-tri- and tetranucleotides, most notably CTAG. Models are proposed to explain several of the anomalies of oligonucleotide distribution in E. coli, and the biological significance of the systems that produce these anomalies is discussed. ^

The theory of runs with application to drought predictions

The primary interest was in predicting the distribution runs in a sequence of Bernoulli trials. Difference equation techniques were used to express the number of runs of a given length k in n trials under three assumptions (1) no runs of length greater than k, (2) no runs of length less than k, (3) no other assumptions about the length of runs. Generating functions were utilized to obtain the distributions of the future number of runs, future number of minimum run lengths and future number of the maximum run lengths unconditional on the number of successes and failures in the Bernoulli sequence. When applying the model to Texas hydrology data, the model provided an adequate fit for the data in eight of the ten regions. Suggested health applications of this approach to run theory are provided. ^