Collapsing Bacterial Cylinders

Under special conditions bacteria excrete an attractant and aggregate. The high density regions initially collapse into cylindrical structures, which subsequently destabilize and break up into spherical aggregates. This paper presents a theoretical description of the process, from the structure of the collapsing cylinder to the spacing of the final aggregates. We show that cylindrical collapse involves a delicate balance in which bacterial attraction and diffusion nearly cancel, leading to corrections to the collapse laws expected from dimensional analysis. The instability of a collapsing cylinder is composed of two distinct stages: Initially, slow modulations to the cylinder develop, which correspond to a variation of the collapse time along the cylinder axis. Ultimately, one point on the cylinder pinches off. At this final stage of the instability, a front propagates from the pinch into the remainder of the cylinder. The spacing of the resulting spherical aggregates is determined by the front propagation.Comment: 33 pages, 15 figure

Helicase activity on DNA as a propagating front

We develop a propagating front analysis, in terms of a local probability of zipping, for the helicase activity of opening up a double stranded DNA (dsDNA). In a fixed-distance ensemble (conjugate to the fixed-force ensemble) the front separates the zipped and unzipped phases of a dsDNA and a drive acts locally around the front. Bounds from variational analysis and numerical estimates for the speed of a helicase are obtained. Different types of helicase behaviours can be distinguished by the nature of the drive.Comment: 5 pages, 5 eps figures; replaced by the published versio

A two-state model for helicase translocation and unwinding of nucleic acids

Helicases are molecular motors that unwind double-stranded nucleic acids (dsNA), such as DNA and RNA). Typically a helicase translocates along one of the NA single strands while unwinding and uses adenosine triphosphate (ATP) hydrolysis as an energy source. Here we model of a helicase motor that can switch between two states, which could represent two different points in the ATP hydrolysis cycle. Our model is an extension of the earlier Betterton-J\"ulicher model of helicases to incorporate switching between two states. The main predictions of the model are the speed of unwinding of the dsNA and fluctuations around the average unwinding velocity. Motivated by a recent claim that the NS3 helicase of Hepatitis C virus follows a flashing ratchet mechanism, we have compared the experimental results for the NS3 helicase with a special limit of our model which corresponds to the flashing ratchet scenario. Our model accounts for one key feature of the experimental data on NS3 helicase. However, contradictory observations in experiments carried out under different conditions limit the ability to compare the model to experiments.Comment: minor modification