Equilibrium Bundle Size of Rodlike Polyelectrolytes with Counterion-Induced Attractive Interactions

Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are point-like, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutralization of the bundle, thus forcing the equilibrium bundle size to be finite. We also consider the possibility that increasing the number of nearest neighbors for each rod in the bundle frustrates the attractive interaction between the rods. Such a frustration leads to the formation of finite size bundles as well, even when the counterions are small.Comment: 4 pages, 2 figures; v2: typos corrected, references added, minor changes made to conten

The effect of signal acquisition and processing choices on ApEn values: Towards a “gold standard” for distinguishing effort levels from isometric force records

Approximate Entropy (ApEn) is frequently used to identify changes in the complexity of isometric force records with ageing and disease. Different signal acquisition and processing parameters have been used, making comparison or confirmation of results difficult. This study determined the effect of sampling and parameter choices by examining changes in ApEn values across a range of submaximal isometric contractions of the First Dorsal Interosseus. Reducing the sample rate by decimation changed both the value and pattern of ApEn values dramatically. The pattern of ApEn values across the range of effort levels was not sensitive to the filter cut-off frequency, or the criterion used to extract the section of data for analysis. The complexity increased with increasing effort levels using a fixed ‘r’ value (which accounts for measurement noise) but decreased with increasing effort level when ‘r’ was set to 0.1 of the standard deviation of force. It is recommended isometric force records are sampled at frequencies >200 Hz, template length (‘m’) is set to 2, and 'r' set to measurement system noise or 0.1 SD depending on physiological process to be distinguished. It is demonstrated that changes in ApEn across effort levels are related to changes in force gradation strategy

Helicase processivity and not the unwinding velocity exhibits universal increase with force

Helicases, involved in a number of cellular functions, are motors that translocate along singlestranded nucleic acid and couple the motion to unwinding double-strands of a duplex nucleic acid. The junction between double and single strands creates a barrier to the movement of the helicase, which can be manipulated in vitro by applying mechanical forces directly on the nucleic acid strands. Single molecule experiments have demonstrated that the unwinding velocities of some helicases increase dramatically with increase in the external force, while others show little response. In contrast, the unwinding processivity always increases when the force increases. The differing responses of the unwinding velocity and processivity to force has lacked explanation. By generalizing a previous model of processive unwinding by helicases, we provide a unified framework for understanding the dependence of velocity and processivity on force and the nucleic acid sequence. We predict that the sensitivity of unwinding processivity to external force is a universal feature that should be observed in all helicases. Our prediction is illustrated using T7 and NS3 helicases as case studies. Interestingly, the increase in unwinding processivity with force depends on whether the helicase forces base pair opening by direct interaction or if such a disruption occurs spontaneously due to thermal uctuations. Based on the theoretical results, we propose that proteins like single-strand binding proteins associated with helicases in the replisome, may have co-evolved with helicases to increase the unwinding processivity even if the velocity remains unaffected

A Mediated Vision, a Measured Voice: Culture and Criticism in Whitman\u27s Prose

Examines a broad range of Whitman\u27s prose--from his early journalism through Democratic Vistas and Specimen Days--and stresses how Whitman\u27s "voices or visions alternate in his literary and cultural criticism"; concludes that in his prose Whitman "found a form to fit his microscopically attuned eye and his castigating voice--both of which had little, if any, place in his poetry.

A Mediated Vision, a Measured Voice: Culture and Criticism in Whitman\u27s Prose

Examines a broad range of Whitman\u27s prose--from his early journalism through Democratic Vistas and Specimen Days--and stresses how Whitman\u27s "voices or visions alternate in his literary and cultural criticism"; concludes that in his prose Whitman "found a form to fit his microscopically attuned eye and his castigating voice--both of which had little, if any, place in his poetry.

Singularity results for functional equations driven by linear fractional transformations

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.Comment: 14 pages, Title changed, to appear in Journal of Theoretical Probabilit