Christian Reinhardt

The prohibitin (PHB)-domain proteins are membrane proteins that regulate a variety of biological activities, including mechanosensation, osmotic homeostasis, and cell signaling, although the mechanism of this regulation is unknown. We have studied two members of this large protein family, MEC-2, which is needed for touch sensitivity in Caenorhabditis elegans, and Podocin, a protein involved in the function of the filtration barrier in the mammalian kidney, and find that both proteins bind cholesterol. This binding requires the PHB domain (including palmitoylation sites within it) and part of the N-terminally adjacent hydrophobic domain that attaches the proteins to the inner leaflet of the plasma membrane. By binding to MEC-2 and Podocin, cholesterol associates with ion-channel complexes to which these proteins bind: DEG/ENaC channels for MEC-2 and TRPC channels for Podocin. Both the MEC-2-dependent activation of mechanosensation and the Podocin-dependent activation of TRPC channels require cholesterol. Thus, MEC-2, Podocin, and probably many other PHB-domain proteins by binding to themselves, cholesterol, and target proteins regulate the formation and function of large protein-cholesterol supercomplexes in the plasma membrane.

A computational method based on Chebyshev series to rigorously compute solutions of initial and boundary value problems of analytic nonlinear vector fields is proposed. The idea is to recast solutions as fixed points of an operator defined on a Banach space of rapidly decaying Chebyshev coefficients and to use the so-called radii polynomials to show the existence of a unique fixed point near an approximate solution. As applications, solutions of initial value problems in the Lorenz equations and symmetric connecting orbits in the Gray--Scott equation are rigorously computed. The symmetric connecting orbits are obtained by solving a boundary value problem with one of the boundary values in the stable manifold.

ABSTRACT Despite many similarities, there are significant observed differences between Uranus and Neptune: While Uranus is tilted and has a regular set of satellites, suggesting their accretion from a disc, Neptune’s moons are irregular and are captured objects. In addition, Neptune seems to have an internal heat source, while Uranus is in equilibrium with solar insulation. Finally, structure models based on gravity data suggest that Uranus is more centrally condensed than Neptune. We perform a large suite of high-resolution SPH simulations to investigate whether these differences can be explained by giant impacts. For Uranus, we find that an oblique impact can tilt its spin axis and eject enough material to create a disc where the regular satellites are formed. Some of the discs are massive and extended enough, and consist of enough rocky material to explain the formation of Uranus’ regular satellites. For Neptune, we investigate whether a head-on collision could mix the interior, and lead to an adiabatic temperature profile, which may explain its larger flux and higher moment of inertia value. We find that massive and dense projectiles can penetrate towards the centre and deposit mass and energy in the deep interior, leading to a less centrally concentrated interior for Neptune. We conclude that the dichotomy between the ice giants can be explained by violent impacts after their formation.