Motivated by experiments in which a polynucleotide is driven through a proteinaceous pore by an electric field, we study the diffusive motion of a polymer threaded through a narrow channel with which it may have strong interactions. We show that there is a range of polymer lengths in which the system is approximately translationally invariant, and we develop a coarse-grained description of this regime. From this description, general features of the distribution of times for the polymer to pass through the pore may be deduced. We also introduce a more microscopic model. This model provides a physically reasonable scenario in which, as in experiments, the polymer's speed depends sensitively on its chemical composition, and even on its orientation in the channel. Finally, we point out that the experimental distribution of times for the polymer to pass through the pore is much broader than expected from simple estimates, and speculate on why this might be.

We studied the unzipping of single molecules of double-stranded DNA by pulling one of their two strands through a narrow protein pore. Polymerase chain reaction analysis yielded the first direct proof of DNA unzipping in such a system. The time to unzip each molecule was inferred from the ionic current signature of DNA traversal. The distribution of times to unzip under various experimental conditions fit a simple kinetic model. Using this model, we estimated the enthalpy barriers to unzipping and the effective charge of a nucleotide in the pore, which was considerably smaller than previously assumed.

The orientation of cell division along the interphase cell long-axis, the century old Hertwig’s rule, has profound roles in tissue proliferation, morphogenesis, architecture and mechanics1,2. In epithelial tissues, the shape of the interphase cell is influenced by cell adhesion, mechanical stress, neighbour topology, and planar polarity pathways3–12. At mitosis, epithelial cells usually round up to ensure faithful chromosome segregation and to promote morphogenesis1. The mechanisms underlying interphase cell shape sensing in tissues are therefore unknown. We found that in Drosophila epithelia, tricellular junctions (TCJ) localize microtubule force generators, orienting cell division via the Dynein associated protein Mud independently of the classical Pins/Gαi pathway. Moreover, as cells round up during mitosis, TCJs serve as spatial landmarks, encoding information about interphase cell shape anisotropy to orient division in the rounded mitotic cell. Finally, experimental and simulation data show that shape and mechanical strain sensing by the TCJ emerge from a general geometric property of TCJ distributions in epithelial tissues. Thus, in addition to their function as epithelial barrier structures, TCJs serve as polarity cues promoting geometry and mechanical sensing in epithelial tissues.

We study a class of micromanipulation experiments, exemplified by the pulling apart of the two strands of double-stranded DNA. When the pulling force is increased to a critical value, an "unzipping" transition occurs. For random DNA sequences with short-ranged correlations, we obtain exact results for the number of monomers liberated and the specific heat, including the critical behavior at the transition. Related systems include a random heteropolymer pulled away from an adsorbing surface and a vortex line in a type II superconductor tilted away from a fragmented columnar defect.

In a recent series of ground-breaking experiments, Nakajima et al.[Nakajima M, Imai K, Ito H, Nishiwaki T, Murayama Y, Iwasaki H, Oyama T, Kondo T (2005) Science 308:414 -415] showed that the three cyanobacterial clock proteins KaiA, KaiB, and KaiC are sufficient in vitro to generate circadian phosphorylation of KaiC. Here, we present a mathematical model of the Kai system. At its heart is the assumption that KaiC can exist in two conformational states, one favoring phosphorylation and the other dephosphorylation. Each individual KaiC hexamer then has a propensity to be phosphorylated in a cyclic manner. To generate macroscopic oscillations, however, the phosphorylation cycles of the different hexamers must be synchronized. We propose a novel synchronization mechanism based on differential affinity: KaiA stimulates KaiC phosphorylation, but the limited supply of KaiA dimers binds preferentially to those KaiC hexamers that are falling behind in the oscillation. KaiB sequesters KaiA and stabilizes the dephosphorylating KaiC state. We show that our model can reproduce a wide range of published data, including the observed insensitivity of the oscillation period to variations in temperature, and that it makes nontrivial predictions about the effects of varying the concentrations of the Kai proteins.