Agonist-induced calcium waves in oscillatory cells: a biological example of Burgers' equation

Oscillations in cytosolic Ca2+ concentrations in living cells are often a manifestation of propagating waves of Ca2+. Numerical simulations with a realistic model of inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ wave trains lead to wave speeds that increase linearly at long times when (a) IP3 levels are in the range for Ca2+ oscillations, (b) a gradient of phase is established by either an initial ramp or pulse of IP3, and (c) IP3 concentrations asymptotically become uniform. We explore this phenomenon with analytical and numerical methods using a simple two-variable reduction of the De Young-Keizer model of the IP3 receptor that includes the influence of Ca2+ buffers. For concentrations of IP3 in the oscillatory regime, numerical solution of the resulting reaction diffusion equations produces nonlinear wave trains that shows the same asymptotic growth of wave speed. Due to buffering, diffusion of Ca2+ is quite slow and, as previously noted, these waves occur without appreciable bulk movement of Ca2+. Thus, following Neu and Murray, we explore the behavior of these waves using an asymptotic expansion based on the small size of the buffered diffusion constant for Ca2+. We find that the gradient in phase of the wave obeys Burgers' equation asymptotically in time. This result is used to explain the linear increase of the wave speed observed in the simulations.     

Renal R2 chemoreceptor activity is attenuated after back heating in the rat

The aim of the present study was to determine the afferent connections of the nucleus accumbens in snakes, in particular its catecholaminergic input. For that purpose, in vitro and in vivo applications of retrograde tracers in the nucleus accumbens of Elaphe guttata were combined with tyrosine hydroxylase (TH) immunohistochemistry. Both techniques revealed telencephalic inputs to the nucleus accumbens originating from the diagonal band of Broca, ventral pallidum, amygdaloid complex, and dorsal cortex. Major diencephalic inputs arise from the dorsomedial thalamic nucleus and the hypothalamus. In the brainstem, a few retrogradely labeled cells were observed in the raphe nucleus and the locus coeruleus. Considerably more cells were found in the midbrain tegmentum. Within the confines of the locus coeruleus and, in particular, the midbrain tegmentum, retrogradely labeled cells stained also for TH suggesting that those areas constitute the major catecholaminergic input to the nucleus accumbens of snakes. The experimental approach used in the present study, in particular the in vitro technique, seems to be very suited for studying the development of basal ganglia organization of reptiles in the near future.