A Riemann hypothesis analogue for invariant rings

AbstractA Riemann hypothesis analogue for coding theory was introduced by I.M. Duursma [A Riemann hypothesis analogue for self-dual codes, in: A. Barg, S. Litsyn (Eds.), Codes and Association Schemes (Piscataway, NJ, 1999), American Mathematical Society, Providence, RI, 2001, pp. 115–124]. In this paper, we extend zeta polynomials for linear codes to ones for invariant rings, and we investigate whether a Riemann hypothesis analogue holds for some concrete invariant rings. Also we shall show that there is some subring of an invariant ring such that the subring is not an invariant ring but extremal polynomials all satisfy the Riemann hypothesis analogue

Cell morphology governs directional control in swimming bacteria

The ability to rapidly detect and track nutrient gradients is key to the ecological success of motile bacteria in aquatic systems. Consequently, bacteria have evolved a number of chemotactic strategies that consist of sequences of straight runs and reorientations. Theoretically, both phases are affected by fluid drag and Brownian motion, which are themselves governed by cell geometry. Here, we experimentally explore the effect of cell length on control of swimming direction. We subjected Escherichia coli to an antibiotic to obtain motile cells of different lengths, and characterized their swimming patterns in a homogeneous medium. As cells elongated, angles between runs became smaller, forcing a change from a run-and-tumble to a run-and-stop/reverse pattern. Our results show that changes in the motility pattern of microorganisms can be induced by simple morphological variation, and raise the possibility that changes in swimming pattern may be triggered by both morphological plasticity and selection on morphology

Eukaryotic catecholamine hormones influence the chemotactic control of Vibrio campbellii by binding to the coupling protein CheW

In addition to their well-known role as stress-associated catecholamine hormones in animals and humans, epinephrine (EPI) and norepinephrine (NE) act as interkingdom signals between eukaryotic hosts and bacteria. However, the molecular basis of their effects on bacteria is not well understood. In initial phenotypic studies utilizing Vibrio campbellii as a model organism, we characterized the bipartite mode of action of catecholamines, which consists of promotion of growth under iron limitation and enhanced colony expansion on soft agar. In order to identify the molecular targets of the hormones, we designed and synthesized tailored probes for chemical proteomic studies. As the catechol group in EPI and NE acts as an iron chelator and is prone to form a reactive quinone moiety, we devised a photoprobe based on the adrenergic agonist phenylephrine (PE), which solely influenced colony expansion. Using this probe, we identified CheW, located at the core of the chemotaxis signaling network, as a major target. In vitro studies confirmed that EPI, NE, PE, and labetalol, a clinically applied antagonist, bind to purified CheW with affinity constants in the submicromolar range. In line with these findings, exposure of V. campbellii to these adrenergic agonists affects the chemotactic control of the bacterium. This study highlights an effect of eukaryotic signaling molecules on bacterial motility.</p