Network-level dynamics of diffusively coupled cells

We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular perturbation, which extend the classical asymptotic stability results for singularly perturbed systems. Based on these results, we show that with common models of intracellular dynamics, the cell population is coordinated in the sense that all cells converge close to a common equilibrium point. We then study a more specific example of coupled cells which behave as bistable switches, where the intracellular dynamics are such that cells may be in one of two equilibrium points. Here, we find that the whole population is bistable in the sense that it converges to a population state where either all cells are close to the one equilibrium point, or all cells are close to the other equilibrium point. Finally, we discuss applications of these results for the robustness of cellular decision making in coupled populations

On critical normal sections for two-dimensional immersions in R^n and a Riemann-Hilbert problem

For orthonormal normal sections of two-dimensional immersions in R^4 we define torsion coefficients and a functional for the total torsion. We discuss normal sections which are critical for this functional. In particular, a global estimate for the torsion coefficients of a critical normal section in terms of the curvature of the normal bundle is provided

CBBN in the CMSSM

Catalyzed big bang nucleosynthesis (CBBN) can lead to an overproduction of ^6Li in gravitino dark matter scenarios in which the lighter stau is the lightest Standard Model superpartner. Based on a treatment using the state-of-the-art result for the catalyzed ^6Li production cross section, we update the resulting constraint within the framework of the constrained minimal supersymmetric Standard Model (CMSSM). We confront our numerical findings with recently derived conservative limits on the gaugino mass parameter and the reheating temperature.Comment: 4 pages, 4 figures; Submitted for the SUSY07 proceeding