Analysis of a Length-Structured Density-Dependent Model for Fish.

We present a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We present mathematical results classifying the dynamics that this density-dependent model predicts. We illustrate these results with numerical simulations for an invasive white perch population and show how the mathematical results can be used to predict the persistence and/or boundedness of the population as well as an equilibrium structure that is dominated by small fish. We illustrate the results with management recommendations for an invasive white perch population.

Mixing and pumping by pairs of helices in a viscous fluid.

Here, we study the fluid dynamics of a pair of rigid helices rotating at a constant velocity, tethered at their bases, in a viscous fluid. Our computations use a regularized Stokeslet framework, both with and without a bounding plane, so we are able to discern precisely what flow features are unaccounted for in studies that ignore the surface from which the helices emanate. We examine how the spacing and phase difference between identical rotating helices affects their pumping ability, axial thrust, and power requirements. We also find that optimal mixing of the fluid around two helices is achieved when they rotate in opposite phase, and that the mixing is enhanced as the distance between the helices decreases.

Surface traction and the dynamics of elastic rods at low Reynolds number.

Molecular and cell biological processes often use proteins and structures that are significantly longer in one dimension than they are in the other two, for example, DNA, actin, and bacterial flagella. The dynamics of these structures are the consequence of the balance between the elastic forces from the structure itself and viscous forces from the surrounding fluid. Typically, the motion of these filamentary objects is described using variations of the Kirchhoff rod equations with resistive forces from the fluid treated as body forces acting on the centerline. In reality, though, these forces are applied to the surface of the filament; however, the standard derivation of the Kirchhoff equations ignores surface traction stresses. Here, we rederive the Kirchhoff rod equations in the presence of resistive traction stresses and determine the conditions under which treating the drag forces as body forces is reasonable. We show that in most biologically relevant cases the standard implementation of resistive forces into the Kirchhoff rod equations is applicable; however, we note one particular biological system where the Kirchhoff rod formalism may not apply.

The distribution of inverted repeat sequences in the Saccharomyces cerevisiae genome.

Although a variety of possible functions have been proposed for inverted repeat sequences (IRs), it is not known which of them might occur in vivo. We investigate this question by assessing the distributions and properties of IRs in the Saccharomyces cerevisiae (SC) genome. Using the IRFinder algorithm we detect 100,514 IRs having copy length greater than 6 bp and spacer length less than 77 bp. To assess statistical significance we also determine the IR distributions in two types of randomization of the S. cerevisiae genome. We find that the S. cerevisiae genome is significantly enriched in IRs relative to random. The S. cerevisiae IRs are significantly longer and contain fewer imperfections than those from the randomized genomes, suggesting that processes to lengthen and/or correct errors in IRs may be operative in vivo. The S. cerevisiae IRs are highly clustered in intergenic regions, while their occurrence in coding sequences is consistent with random. Clustering is stronger in the 3' flanks of genes than in their 5' flanks. However, the S. cerevisiae genome is not enriched in those IRs that would extrude cruciforms, suggesting that this is not a common event. Various explanations for these results are considered.