Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility

We characterize the value function of maximizing the total discounted utility of dividend payments for a compound Poisson insurance risk model when strictly positive transaction costs are included, leading to an impulse control problem. We illustrate that well known simple strategies can be optimal in the case of exponential claim amounts. Finally we develop a numerical procedure to deal with general claim amount distributions.

Stochasticity and bistability in horizontal transfer control of a genomic island in Pseudomonas.

Genomic islands (GEI) comprise a recently recognized large family of potentially mobile DNA elements and play an important role in the rapid differentiation and adaptation of bacteria. Most importantly, GEIs have been implicated in the acquisition of virulence factors, antibiotic resistances or toxic compound metabolism. Despite detailed information on coding capacities of GEIs, little is known about the regulatory decisions in individual cells controlling GEI transfer. Here, we show how self-transfer of ICEclc, a GEI in Pseudomonas knackmussii B13 is controlled by a series of stochastic processes, the result of which is that only a few percent of cells in a population will excise ICEclc and launch transfer. Stochastic processes have been implicated before in producing bistable phenotypic transitions, such as sporulation and competence development, but never before in horizontal gene transfer (HGT). Bistability is instigated during stationary phase at the level of expression of an activator protein InrR that lays encoded on ICEclc, and then faithfully propagated to a bistable expression of the IntB13 integrase, the enzyme responsible for excision and integration of the ICEclc. Our results demonstrate how GEI of a very widespread family are likely to control their transfer rates. Furthermore, they help to explain why HGT is typically confined to few members within a population of cells. The finding that, despite apparent stochasticity, HGT rates can be modulated by external environmental conditions provides an explanation as to why selective conditions can promote DNA exchange.

Spontaneous cell polarization: Feedback control of Cdc42 GTPase breaks cellular symmetry.

Spontaneous polarization without spatial cues, or symmetry breaking, is a fundamental problem of spatial organization in biological systems. This question has been extensively studied using yeast models, which revealed the central role of the small GTPase switch Cdc42. Active Cdc42-GTP forms a coherent patch at the cell cortex, thought to result from amplification of a small initial stochastic inhomogeneity through positive feedback mechanisms, which induces cell polarization. Here, I review and discuss the mechanisms of Cdc42 activity self-amplification and dynamic turnover. A robust Cdc42 patch is formed through the combined effects of Cdc42 activity promoting its own activation and active Cdc42-GTP displaying reduced membrane detachment and lateral diffusion compared to inactive Cdc42-GDP. I argue the role of the actin cytoskeleton in symmetry breaking is not primarily to transport Cdc42 to the active site. Finally, negative feedback and competition mechanisms serve to control the number of polarization sites.