Scaling Laws and Similarity Detection in Sequence Alignment with Gaps

We study the problem of similarity detection by sequence alignment with gaps, using a recently established theoretical framework based on the morphology of alignment paths. Alignments of sequences without mutual correlations are found to have scale-invariant statistics. This is the basis for a scaling theory of alignments of correlated sequences. Using a simple Markov model of evolution, we generate sequences with well-defined mutual correlations and quantify the fidelity of an alignment in an unambiguous way. The scaling theory predicts the dependence of the fidelity on the alignment parameters and on the statistical evolution parameters characterizing the sequence correlations. Specific criteria for the optimal choice of alignment parameters emerge from this theory. The results are verified by extensive numerical simulations.Comment: 25 pages, 11 figure

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 ~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 Myr ago (around the time of the mammalian radiation), we find an abrupt 4- to 8-fold increase of the cytosine transition rate in CpG pairs compared to that of the reptilian ancestor. Further analysis of nucleotide substitutions in regions with different GC-content reveals concurrent changes in the substitutional patterns. While 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 afterwards. 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

Substantial regional variation in substitution rates in the human genome: importance of GC content, gene density and telomere-specific effects

This study presents the first global, 1 Mbp level analysis of patterns of nucleotide substitutions along the human lineage. The study is based on the analysis of a large amount of repetitive elements deposited into the human genome since the mammalian radiation, yielding a number of results that would have been difficult to obtain using the more conventional comparative method of analysis. This analysis revealed substantial and consistent variability of rates of substitution, with the variability ranging up to 2-fold among different regions. The rates of substitutions of C or G nucleotides with A or T nucleotides vary much more sharply than the reverse rates suggesting that much of that variation is due to differences in mutation rates rather than in the probabilities of fixation of C/G vs. A/T nucleotides across the genome. For all types of substitution we observe substantially more hotspots than coldspots, with hotspots showing substantial clustering over tens of Mbp's. Our analysis revealed that GC-content of surrounding sequences is the best predictor of the rates of substitution. The pattern of substitution appears very different near telomeres compared to the rest of the genome and cannot be explained by the genome-wide correlations of the substitution rates with GC content or exon density. The telomere pattern of substitution is consistent with natural selection or biased gene conversion acting to increase the GC-content of the sequences that are within 10-15 Mbp away from the telomere.Comment: 35 pages, 6 figure

Deterministic characterization of stochastic genetic circuits

For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of deterministic rate equation models. Unfortunately, there are few analytic methods for examining the qualitative behavior of stochastic systems. Here we describe such a method that extends deterministic analysis to include leading-order corrections due to the molecular noise. The method allows the steady-state behavior of the stochastic model to be easily computed, facilitates the mapping of stability phase diagrams that include stochastic effects and reveals how model parameters affect noise susceptibility, in a manner not accessible to numerical simulation. By way of illustration we consider two genetic circuits: a bistable positive-feedback loop and a negative-feedback oscillator. We find in the positive feedback circuit that translational activation leads to a far more stable system than transcriptional control. Conversely, in a negative-feedback loop triggered by a positive-feedback switch, the stochasticity of transcriptional control is harnessed to generate reproducible oscillations.Comment: 6 pages (Supplementary Information is appended

Polymer Adsorption on Disordered Substrate

We analyze the recently proposed "pattern-matching" phase of a Gaussian random heteropolymer adsorbed on a disordered substrate [S. Srebnik, A.K. Chakraborty and E.I. Shakhnovich, Phys. Rev. Lett. 77, 3157 (1996)]. By mapping the problem to that of a directed homopolymer in higher-dimensional random media, we show that the pattern-matching phase is asymptotically weakly unstable, and the large scale properties of the system are given by that of an adsorbed homopolymer.Comment: 5 pages, RevTeX, text also available at http://matisse.ucsd.edu/~hw