Glucose dynamics in rat skeletal muscle : recovery from osmotic stress

The purpose of this study was to examine cell glucose kinetics in rat skeletal muscle during iso-osmotic recovery from hyper- and hypo-osmotic stress. Rat EDL muscles were incubated for sixty minutes in either HYPO (190 mmol/kg), ISO (290 mmol/kg), or HYPER (400 mmol/kg) media (Sigma medium-199, 8 mM glucose) according to an established in vitro whole muscle model. In addition to sixty minute baseline measures in aniso-osmotic conditions, (HYPO-0 n=8; ISO- 0, n=S; HYPER-0, n=8), muscles were subjected to either one minute (HYPO-1 n=8; ISO-1, n=8; HYPER-1, n=8) or five minutes (HYPO-5 n=8; ISO-5, n=8; HYPER-5, n=8) of iso-osmotic recovery media and analyzed for metabolite content and glycogen synthase percent activation. To determine glucose uptake during iso-osmotic recovery, muscles (n=6 per group) were incubated for sixty minutes in either hypo-, iso-, or hyper-osmotic media immediately followed by five minutes of iso-osmotic media containing 3H-glucose and 14 C-mannitol. Increased relative water content/decreased [glucose] (observed in HYPO-0) and decreased water content/increased [glucose] (observed in HYPER-0) returned to ISO levels within 5 minutes of recovery. Glycogen synthase percent activation increased significantly in HYPO-5 over iso-osmotic controls. Glucose uptake measurements revealed no significant differences between groups. It was determined that [glucose] and muscle water content rapidly recovered from osmotic stress demonstrating skeletal muscle's resilience to osmotic stress.

Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.