beta-Arrestin-mediated PDE4 cAMP phosphodiesterase recruitment regulates beta-adrenoceptor switching from Gs to Gi.

Phosphorylation of the beta(2) adrenoreceptor (beta(2)AR) by cAMP-activated protein kinase A (PKA) switches its predominant coupling from stimulatory guanine nucleotide regulatory protein (G(s)) to inhibitory guanine nucleotide regulatory protein (G(i)). beta-Arrestins recruit the cAMP-degrading PDE4 phosphodiesterases to the beta(2)AR, thus controlling PKA activity at the membrane. Here we investigate a role for PDE4 recruitment in regulating G protein switching by the beta(2)AR. In human embryonic kidney 293 cells overexpressing a recombinant beta(2)AR, stimulation with isoprenaline recruits beta-arrestins 1 and 2 as well as both PDE4D3 and PDE4D5 to the receptor and stimulates receptor phosphorylation by PKA. The PKA phosphorylation status of the beta(2)AR is enhanced markedly when cells are treated with the selective PDE4-inhibitor rolipram or when they are transfected with a catalytically inactive PDE4D mutant (PDE4D5-D556A) that competitively inhibits isoprenaline-stimulated recruitment of native PDE4 to the beta(2)AR. Rolipram and PDE4D5-D556A also enhance beta(2)AR-mediated activation of extracellular signal-regulated kinases ERK12. This is consistent with a switch in coupling of the receptor from G(s) to G(i), because the ERK12 activation is sensitive to both inhibitors of PKA (H89) and G(i) (pertussis toxin). In cardiac myocytes, the beta(2)AR also switches from G(s) to G(i) coupling. Treating primary cardiac myocytes with isoprenaline induces recruitment of PDE4D3 and PDE4D5 to membranes and activates ERK12. Rolipram robustly enhances this activation in a manner sensitive to both pertussis toxin and H89. Adenovirus-mediated expression of PDE4D5-D556A also potentiates ERK12 activation. Thus, receptor-stimulated beta-arrestin-mediated recruitment of PDE4 plays a central role in the regulation of G protein switching by the beta(2)AR in a physiological system, the cardiac myocyte.

Regularity of invariant densities for 1D systems with random switching

© 2015 IOP Publishing Ltd & London Mathematical Society.This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

Characterizing the Switching Thresholds of Magnetophoretic Transistors.

The switching thresholds of magnetophoretic transistors for sorting cells in microfluidic environments are characterized. The transistor operating conditions require short 20-30 mA pulses of electrical current. By demonstrating both attractive and repulsive transistor modes, a single transistor architecture is used to implement the full write cycle for importing and exporting single cells in specified array sites.