Waves Of Cyclic AMP Research Articles

Computational modelling suggests dynamic interactions between Ca2+, IP3 and G protein-coupled modules are key to robust Dictyostelium aggregation

Under conditions of starvation, Dictyostelium cells begin a programme of development during which they aggregate to form a multicellular structure by chemotaxis, guided by propagating waves of cyclic AMP that are relayed robustly from cell to cell. In this paper, we develop and analyse a new model for the intracellular and extracellular cAMP dependent processes that regulate Dictyostelium migration. The model allows, for the first time, a quantitative analysis of the dynamic interactions between calcium, IP(3) and G protein-dependent modules that are shown to be key to the generation of robust cAMP oscillations in Dictyostelium cells. The model provides a mechanistic explanation for the transient increase in cytosolic free Ca(2+) concentration seen in recent experiments with the application of the calmodulin inhibitor calmidazolium (R24571) to Dictyostelium cells, and also allows elucidation of the effects of varying both the conductivity of stretch-activated channels and the concentration of external phosphodiesterase on the oscillatory regime of an individual cell. A rigorous analysis of the robustness of the new model shows that interactions between the different modules significantly reduce the sensitivity of the resulting cAMP oscillations to variations in the kinetics of different Dictyostelium cells, an essential requirement for the generation of the spatially and temporally synchronised chemoattractant cAMP waves that guide Dictyostelium aggregation.

Oscillations and waves of cyclic AMP in Dictyostelium: A prototype for spatio-temporal organization and pulsatile intercellular communication

The amoebae Dictyostelium discoideum aggregate after starvation in a wavelike manner in response to periodic pulses of cyclic AMP (cAMP) secreted by cells which behave as aggregation centers. In addition to autonomous oscillations, the cAMP signaling system that controls aggregation is also capable of excitable behavior, which consists in the transient amplification of suprathreshold pulses of extracellular cAMP. Since the first theoretical model for slime mold aggregation proposed by Keller and Segel in 1970, many theoretical studies have addressed various aspects of the mechanism and function of cAMP signaling in Dictyostelium. This paper presents a brief overview of these developments as well as some reminiscences of the author's collaboration with Lee Segel in modeling the dynamics of cAMP relay and oscillations. Considered in turn are models for cAMP signaling in Dictyostelium, the developmental path followed by the cAMP signaling system after starvation, the frequency encoding of cAMP signals, and the origin of concentric or spiral waves of cAMP.

An autoregulatory circuit for long-range self-organization in Dictyostelium cell populations

Nutrient-deprived Dictyostelium amoebae aggregate to form a multicellular structure by chemotaxis, moving towards propagating waves of cyclic AMP that are relayed from cell to cell. Organizing centres are not formed by founder cells, but are dynamic entities consisting of cores of outwardly rotating spiral waves that self-organize in a homogeneous cell population. Spiral waves are ubiquitously observed in chemical reactions as well as in biological systems. Although feedback control of spiral waves in spatially extended chemical reactions has been demonstrated in recent years, the mechanism by which control is achieved in living systems is unknown. Here we show that mutants of the cyclic AMP/protein kinase A pathway show periodic signalling, but fail to organize coherent long-range wave territories, owing to the appearance of numerous spiral cores. A theoretical model suggests that autoregulation of cell excitability mediated by protein kinase A acts to optimize the number of signalling centres.

Migration and Thermotaxis of Dictyostelium discoideum Slugs, a Model Study

Dictyostelium discoideum slugs show a pronounced thermotaxis. We have modelled the motion of the D. discoideum slug in the absence and in the presence of a thermal gradient. Our model is an extension of the hybrid cellular automata/partial differential equation model, as formulated by Savill and Hogeweg [J. theor. Biol. , (1997) 184 , 229–235]. The modelled slugs maintain their shape and crawl, with a velocity depending on slug size, as found in experiments. Moreover, they show thermotactic behaviour: independent of the initial orientation, after some transient process, the slugs start moving along the temperature gradient. The slug behaviour in our model is due to the collective behaviour of the amoebae. Individual amoebae can neither respond to a shallow temperature gradient, nor show differentiation in motion velocity. The behaviour is achieved by a modification of the cyclic AMP waves: differences in temperature alter the excitability of the cell, and thereby the shape of the cyclic AMP wave. Chemotaxis towards cyclic AMP causes the slug to turn. We show that the mechanism still functions at very low signal-to-noise ratios.

Wave propagation in aggregation fields of the cellular slime mouldDictyostelium discoideum

A mathematical model developed earlier to describe adaptation, relay and oscillation in the cellular slime mouldDictyostelium discoideumis used here to study various aspects of wave propagation in aggregation fields. We first show that travelling waves of cyclic AMP do not result from Turing (diffusive) instabilities. We then display the numerically computed dispersion relation for travelling periodic waves in one space dimension, and compare the results with the experimentally measured relation. Numerical results on phase locking in axisymmetric fields are also presented and the failure of propagation at low cell densities is discussed. Finally, we demonstrate that this model supports spiral waves whose wavelength and speed agree well with the experimental observ­ations.

Cyclic AMP waves during aggregation of Dictyostelium amoebae

During the aggregation phase of their life cycle, Dictyostelium discoideum amoebae communicate with each other by traveling waves of cyclic AMP. These waves are generated by an interplay between random diffusion of cyclic AMP in the extracellular milieu and the signal-reception/signal/relaying capabilities of individual amoebae. Kinetic properties of the enzymes, transport proteins and cell-surface receptor proteins involved in the cyclic AMP signaling system have been painstakingly worked out over the past fifteen years in many laboratories. Recently Martiel & Goldbeter (1987) incorporated this biochemical information into a unified mathematical model of communication among Dictyostelium amoebae. Numerical simulations of the mathematical model, carried out by Tyson et al. (1989), agree in quantitative detail with experimental observations of cyclic AMP traveling waves in Dictyostelium cultures. Such mathematical modeling and numerical experimentation provide a necessary link between detailed studies of the molecular control mechanism and experimental observations of the intact developmental system.

Spiral waves of cyclic amp in a model of slime mold aggregation

During the aggregation phase of their life cycle, Dictyostelium discoideum amoebae communicate with each other by traveling waves of cyclic AMP (cAMP). These waves often have the geometry of rotating spirals. We calculate the properties of these spiral waves, their rotation period, wavespeed, and shape, from a model of the synthesis and degradation of cAMP by Dictyostelium cells. Our model is based on kinetic rate laws developed by Martiel and Goldbeter to account for oscillations and signal relaying by Dictyostelium amoebae in well-stirred cell suspensions. We show that the model also describes in quantitative detail experimental observations of rotating spiral waves of cAMP in fields of amoebae distributed over an agar surface. Furthermore, our numerically calculated spiral waves agree quantitatively with the singular perturbation theory of rotating spirals developed by Keener and Tyson.

Quantitative analysis of cyclic AMP waves mediating aggregation in Dictyostelium discoideum

We have previously reported the detection of cAMP waves within monolayers of aggregating Dictyostelium discoideum cells ( K. J. Tomchik and P. N. Devreotes, 1981, Science 212, 443–446). The computer-assisted analysis presented here of the fluorographic images of the cAMP waves reveals (1) all the waves have a consistent width and height; (2) cAMP concentrations within centers of concentric aggregation territories oscillate periodically while at spiral centers the concentration builds up to a plateau value within 2 mm; (3) cells within the region of intersection of two oppositely directed cAMP waves are stimulated to produce more cAMP than those responding to a single wave; (4) cells start to move when the cAMP level begins to increase and cease movement when the peak cAMP concentration reaches the cell.