String Matching and 1d Lattice Gases

We calculate the probability distributions for the number of occurrences $n$ of a given $l$ letter word in a random string of $k$ letters. Analytical expressions for the distribution are known for the asymptotic regimes (i) $k \gg r^l \gg 1$ (Gaussian) and $k,l \to \infty$ such that $k/r^l$ is finite (Compound Poisson). However, it is known that these distributions do now work well in the intermediate regime $k \gtrsim r^l \gtrsim 1$. We show that the problem of calculating the string matching probability can be cast into a determining the configurational partition function of a 1d lattice gas with interacting particles so that the matching probability becomes the grand-partition sum of the lattice gas, with the number of particles corresponding to the number of matches. We perform a virial expansion of the effective equation of state and obtain the probability distribution. Our result reproduces the behavior of the distribution in all regimes. We are also able to show analytically how the limiting distributions arise. Our analysis builds on the fact that the effective interactions between the particles consist of a relatively strong core of size $l$, the word length, followed by a weak, exponentially decaying tail. We find that the asymptotic regimes correspond to the case where the tail of the interactions can be neglected, while in the intermediate regime they need to be kept in the analysis. Our results are readily generalized to the case where the random strings are generated by more complicated stochastic processes such as a non-uniform letter probability distribution or Markov chains. We show that in these cases the tails of the effective interactions can be made even more dominant rendering thus the asymptotic approximations less accurate in such a regime.Comment: 44 pages and 8 figures. Major revision of previous version. The lattice gas analogy has been worked out in full, including virial expansion and equation of state. This constitutes the main part of the paper now. Connections with existing work is made and references should be up to date now. To be submitted for publicatio

Prognostic role of p27Kip1 and apoptosis in human breast cancer

Human breast carcinoma is biologically heterogeneous, and its clinical course may vary from an indolent slowly progressive one to a course associated with rapid progression and metastatic spread. It is important to establish prognostic factors which will define subgroups of patients with low vs high risk of recurrence so as to better define the need for additional therapy. Additional characterization of the molecular make-up of breast cancer phenotypes should provide important insights into the biology of breast cancer. In the present study, we investigated apoptosis, expression of p27Kip1 and p53 retrospectively in 181 human breast cancer specimens. In addition, their relevance to the biological behaviour of breast cancer was examined. Our studies found a significant association among high histological grade, high p53, low apoptosis and low p27. Our results also demonstrated that, in human breast cancer, low levels of p27 and apoptotic index (AI) strongly correlated with the presence of lymph node metastasis and decreased patient survival. In node-negative patients, however, p27 also had prognostic value for relapse-free and overall survival in multivariate analysis. Furthermore p27 and AI had predictive value for the benefits of chemotherapy. These latter observations should prompt prospective randomized studies designed to investigate the predictive role of p27 and AI in determining who should receive chemotherapy in node-negative patients. © 1999 Cancer Research Campaig

Broad Spectrum Pro-Quorum-Sensing Molecules as Inhibitors of Virulence in Vibrios

Quorum sensing (QS) is a bacterial cell-cell communication process that relies on the production and detection of extracellular signal molecules called autoinducers. QS allows bacteria to perform collective activities. Vibrio cholerae, a pathogen that causes an acute disease, uses QS to repress virulence factor production and biofilm formation. Thus, molecules that activate QS in V. cholerae have the potential to control pathogenicity in this globally important bacterium. Using a whole-cell high-throughput screen, we identified eleven molecules that activate V. cholerae QS: eight molecules are receptor agonists and three molecules are antagonists of LuxO, the central NtrC-type response regulator that controls the global V. cholerae QS cascade. The LuxO inhibitors act by an uncompetitive mechanism by binding to the pre-formed LuxO-ATP complex to inhibit ATP hydrolysis. Genetic analyses suggest that the inhibitors bind in close proximity to the Walker B motif. The inhibitors display broad-spectrum capability in activation of QS in Vibrio species that employ LuxO. To the best of our knowledge, these are the first molecules identified that inhibit the ATPase activity of a NtrC-type response regulator. Our discovery supports the idea that exploiting pro-QS molecules is a promising strategy for the development of novel anti-infectives