| Genome evolution. We view a genome as the list of protein structural domains with corresponding genes in the genome; we call this list the structural proteome. We construct a phenomenological model for the evolution of the network of kinship relationships amongst the domains in a structural proteome. New domains are added to the structural proteome by duplication-and-divergence. We use a probabilistic model for generating various outcomes for the extent of sequence-divergence of the duplicated gene. With this statistical ansatz, we simulate the growth of the kinship network of a structural proteome, comparing to genomic data.; Our dynamical model provides a good description of (a) the kinship network amongst domains within a single structural domain fold (b) the dynamics of the discovery of new folds. We thus present convincing evidence of the divergent scenario of protein evolution.; DNA unzipping phase diagram. We show how single-molecule forced unzipping experiments can provide strong evidence that the zero-force melting transition of long molecules of natural dsDNA should be classified as a phase transition of the higher-order type (continuous). We study a statistical mechanics model for the fluctuating structure of a long molecule of dsDNA, including both loops and sequence heterogeneity, at the level of random sequences. As a function of temperature, we calculate equilibrium properties via the replica method, e.g. we obtain the minimal force at which the molecule separates. This critical force curve is a line in the temperature-force phase diagram separating the regions where the molecule exists primarily as a helix, or as two separate strands. Our model is consistent with magnetic tweezer experiments performed on the 48502 bp genome of bacteriophage lambda, at temperatures between 24 and 50 degrees C. At higher temperatures, the shape of the critical force curve determines, via our theory, how the helix fraction falls to zero at melting. The helix fraction classifies the melting transition as a type of phase transition. The shape of the model's critical force curve suggests that the zero-force melting transition of long natural dsDNA should be classified as a higher-order (continuous) phase transition. Specifically, the order is 3rd or greater. |
