Crisis on skid row

We consider an idealized model of Ca2+ release from internal stores in living cells (the skid row relay) in order to explore the effect of the distribution of release sites. The skid row relay is an all or none release model in which a fixed amount of Ca2+ is released when the cytosolic Ca2+ density in the vicinity of the release site reaches a threshold. Depending on the time and space scales the skid row relay can support traveling waves with a velocity that scales as either D-1/2 Or D (where D is the diffusion coefficient for Ca2+). The former scaling holds when the continuum approximation for the distribution of release sites is valid. The latter holds when the release sites are sufficiently far apart. We determine an analytic expression for the velocity of propagating waves in the two regimes. In the discrete case it can be shown that traveling wave solutions do not exist if the release sites are too far apart or do not release enough Ca2+ or if the threshold for release is too high. Well before the traveling wave ceases to exist, the wave loses stability through period doubling and crisis. (C) 1998 Published by Elsevier Science B.V. All rights reserved.