Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Frequency of migrants and migratory activity are genetically correlated in a bird population: Evolutionary implications

Most migratory bird populations are composed of individuals that migrate and individuals that remain resident. While the role of ecological factors in maintaining this behavioral dimorphism has received much attention, the importance of genetic constraints on the evolution of avian migration has not yet been considered. Drawing on the recorded migratory activities of 775 blackcaps (Sylvia atricapilla) from a partially migratory population in southern France, we tested two alternative genetic models about the relationship between incidence and amount of migratory activity. The amount of migratory activity could be the continuous variable “underlying” the phenotypic expression of migratory urge, or, alternatively, the expression of both traits could be controlled by two separate genetic systems. The distributions of migratory activities in five different cohorts and the inheritance pattern derived from selective breeding experiments both indicate that incidence and amount of migratory activity are two aspects of one trait. Thus, all birds without measurable activity have activity levels at the low end of a continuous distribution, below the limit of expression or detection. The phenotypic dichotomy “migrant–nonmigrant” is caused by a threshold which may not be fixed but influenced both genetically and environmentally. This finding has profound implications for the evolution of migration: the transition from migratoriness to residency should not only be driven by selection favoring resident birds but also by selection for lower migratory activity. This potential for selection on two aspects, residency and migration distance, of the same trait may enable extremely rapid evolutionary changes to occur in migratory behavior.