A modified version of an allosteric model for adenylate cyclase [ATP pyrophosphate-lyase (cyclizing), EC 4.6.1.1] previously analyzed for sustained oscillations of adenosine 3':5'-cyclic monophosphate (cAMP) in Dictyostelium discoideum [Goldbeter, A. (1975) The cellular slime mold Dictyostelium discoideum is a major model for the study of development (1, 2). When deprived of nutrients, amoebae of this species aggregate around centers by a chemotactic response to adenosine 3':5'-cyclic monophosphate (cAMP), and further develop into multicellular fruiting bodies (3). The process of aggregation has a periodicity of several minutes. Successive "steps" of inward amoeboid movement appear to propagate outward from the center toward the periphery of the aggregation territory. It has long been suggested that aggregation centers autonomously release the attractant in periodic fashion. The other cells respond to attractant stimulation by moving towards its source and by relaying the signal (4-8). In addition to their role as chemotactic signals, periodic pulses of cAMP stimulate amoeboid differentiation (9, 10).Both the relay (11, 12) and the autonomous oscillation (13, 14) of cAMP have been demonstrated experimentally in suspensions of D. discoideum cells. We show here that oscillation and relay can be explained by a unified model based on regulatory mechanisms reported in the literature, the two different qualitative behaviors corresponding to two different parameter regimes. Our work can be regarded as extending Goldbeter's demonstration (15) that oscillation can be generated by the intracellular regulation (16) of adenylate cyclase [ATP pyrophosphate-lyase (cyclizing), EC 4.6.1.1]. Here, we consider a compartmental model in which control of intracellular cAMP synthesis by external cAMP is analyzed explicitly.The unified mechanism for relay and oscillation of cAMP suggests an explanation for the emergence of aggregation centers and for a temporal sequence of developmental events observed during interphase in D. discoideum.
RESULTSIn an attempt to capture the essential biochemical mechanisms responsible for oscillation and relay, let us consider the activating effect of extracellular cAMP on adenylate cyclase (17). This activation follows the binding of cAMP to a receptor that might be specific for relay (18). The simplest assumption one can make is that the cAMP receptor on the cell surface is a regulatory part of adenylate cyclase; such an assumption is consistent with the finding that the catalytic site of this membrane-bound enzyme faces the interior of the cell (19). We thus consider the following three concentration variables in a basic compartmental model (see Fig. 1):a, intracellular ATP; fB intracellular cAMP; -y, extracellular cAMP.[1] Here the actual concentrations are normalized by dividing them respectively by Ks, Kp, and Kp, where Ks and Kp are the Michaelis constant of adenylate cyclase for ATP and the dissociation constant of complexes formed by the enzyme with cAMP at the regulatory (receptor) ...