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.     

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.     

A cell–cell repulsion model on a hyperbolic Keller–Segel equation

Journal of Mathematical Biology - In this work, we discuss a cell–cell repulsion model based on a hyperbolic Keller–Segel equation with two populations, which aims at describing the...     

Travelling Waves in Hyperbolic Chemotaxis Equations

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235–248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically.     

Aggregation during sexual development in Dictyostelium discoideum.

A microcinematographic analysis of the behaviour and movements of cells and cell masses in mated cultures (NC4 X VI2) of Dictyostelium discoideum indicates that a chemotactic process directs cell aggregation during macrocyst development. Zygote giant cells form before aggregation begins and act as the aggregation centres. Young multicellular macrocyst stages are sources of cyclic AMP, and amoebae from macrocyst cultures orient chemotactically to cyclic AMP. The data, coupled with other characteristics such as pulsatile streaming, suggest that the aggregation process leading to macrycyst development is the same as that occurring during fruit construction. Other aspects of sexual development are also discussed. Based upon these data, we propose a model for the sequence of events leading to macrocyst development in D. discoideum.     

Instability in a generalized Keller–Segel model

We present a generalized Keller–Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem. By matrix theoretic tools, we then provide easily verifiable sufficient conditions for destabilizing the homogeneous stationary states. In particular, one of the sufficient conditions is that the chemotactic feedback is sufficiently strong. Although this mechanism was already known to exist in the original Keller–Segel model, here we show that it is more generally applicable by significantly enlarging the class of models exhibiting this instability phenomenon which may lead to pattern formation.     

Extracellular cyclic AMP during development of the cellular slime mold Polysphondylium violaceum: comparison of accumulation in the wild type and an aggregation-defective mutant.

Cyclic AMP was synthesized by Polysphondylium violaceum after starvation and during the preaggregation stage of development. Most of the newly synthesized cyclic AMP accumulated in the extracellular medium, with very little change in the intracellular cyclic AMP concentration. The addition of 10(-3) to 10(-6) M exogenous cyclic AMP to starved amoebae caused a 20 to 50% decrease in the number of aggregation centers formed compared with untreated controls. An aggregation-defective mutant of P. violaceum (strain aggA586) excreted or accumulated very little cyclic AMP. Strain aggA586 aggregated normally in the presence of a dialyzable, excreted product (D factor) produced by wild-type amoebae. When the mutant was incubated with D factor, cyclic AMP accumulated in the medium, and the amount accumulated depended on the amount of D factor added to the mutant amoebae.     

Chemotaxis and binding of cyclic AMP in cellular slime molds.

To obtain more information about how cyclic AMP mediates cell aggregation as found in some species of the cellular slime molds, we determined the maximal binding activity of cyclic AMP in different species under various environmental conditions. The binding of cyclic AMP is limited to amoebae using this cyclic nucleotide as chemotactic agent. Maximal binding activity proved to coincide with a maximal chemotactic response and to be related to the length of the period between the vegetative and the aggregative phase. Of the species studied, Dictyostelium discoideum has the highest cellular density of cyclic AMP receptors and is the most sensitive to cyclic AMP as attractant. At 15 degrees C, aggregation begins later, chemotaxis takes effect over a greater distance, and the maximal binding activity is higher than 22 degrees C. The number of cyclic AMP receptors is independent of temperature. The delay in the onset of aggregation and the increased chemotactic response in darkness is not due to a change in the maximal binding activity. The binding of cyclic AMP and its inactivation is discussed in the light of cell aggregation.     

Inhibition of aggregation in Dictyostelium by EGTA-induced depletion of calcium

During aggregation of Dictyostelium discoideum, amoebae move towards collecting centres emitting cyclic AMP. Previous work has indicated that Ca(2+) can affect the operation of various parts of the chemotactic mechanism but there are contradictory reports about the role or requirement for Ca(2+) during aggregation of intact amoebae. In this study we show that there is a requirement for Ca(2+) during this aggregation process. Addition of EGTA (7 mM) and in some cases extensive washing with EGTA is needed to see inhibition of aggregation. Considerable stores of Ca(2+) present within cells may explain the failure of some previous attempts to see a Ca(2+) requirement during aggregation.     

Chemotaxis and binding of cyclic AMP in cellular slime molds

To obtain more information about how cyclic AMP mediates cell aggregation as found in some species of the cellular slime molds, we determined the maximal binding activity of cyclic AMP min different species under various environmental conditions. The binding of cyclic AMP is limited to amoebae using this cyclic nucleotide as chemotactic agent. Maximal binding activity proved to coincide with a maximal chemotactic response and to be related to the lenght of the period between the vegetative and the aggregative phase. Of the species studied, Dictyostelium discoideum has the highest cellular density of cyclic AMP receptors and is the most sensitive to cyclic AMP as attractant.At 15°C, aggregation begins later, chemotaxis takes effect over a greater distance, and the maximal binding activity is higher than at 22°C. The number of cyclic AMP receptors is independent of temperature. The delay in the onset of aggregation and the increased chemotactic response in darkness is not due to a change in the maximal binding activity. The binding of cyclic AMP and its inactivation is discussed in the light of cell aggregation.     

Evidence for a Second Chemotactic System in the Cellular Slime Mold, Dictyostelium discoideum

An unknown substance found in bacteria (Escherichia coli) is especially effective in attracting the vegetative amoebae of the cellular slime mold, Dictyostelium discoideum. However, the aggregating amoebae are not attracted to it at all. On the other hand, the vegetative amoebae show very little chemotactic response to cyclic adenosine monophosphate (cyclic AMP), whereas the aggregating amoebae are exceptionally responsive to it. It is suggested that the new factor may be used in food seeking, whereas cyclic AMP, the chemotactic substance responsible for aggregation, is the acrasin of this species. The important point is that the amoebae are differentially stage-specific in their responses to these two chemotactic agents.     

Cytokinin oxidase activity in the cellular slime mold, Dictyostelium discoideum

The cytokinin N6-(delta 2-isopentenyl)adenine (i6Ade) is produced during the development of the cellular slime mold, Dictyostelium discoideum, and functions in this organism as the immediate precursor of the spore germination inhibitor, discadenine. The metabolism of i6Ade in axenic cultures of D. discoideum Ax-3 amoebae has been investigated in the present study. An enzyme activity that specifically catalyzes the degradation of i6Ade has been detected in Ax-3 amoebae. This enzyme is similar to the cytokinin oxidases present in higher plant systems and cleaves the N6-side chain of i6Ade to form adenine. Discadenine synthase activity was also detected in axenically cultured Ax-3 amoebae. The cytokinin oxidase activity detected in Dictyostelium decreased during aggregation and development of Ax-3 amoebae and in starving Ax-3 amoebae maintained under either fast-shake (230 rpm) or slow-shake (70 rpm) conditions. In the latter case, the fall in enzyme activity was accelerated by treatment with cyclic AMP. In contrast to these results, discadenine synthase activity in Ax-3 amoebae rose sharply during the culmination phase of development, exhibited little change in starving Ax-3 amoebae maintained under fast-shake conditions, and fell under slow-shake conditions unless the amoebae were treated with cyclic AMP. Possible functions of the Dictyostelium cytokinin oxidase and the significance of the i6Ade metabolism observed in vegetative Dictyostelium amoebae are discussed.     

Calcium,cyclic GMP and the control of myosin II during chemotactic signal transduction ofDictyostelium

Evidence is presented for Ca²⁺ and cyclic GMP being involved in signal transduction between the cell surface cyclic AMP receptors and cytoskeletal myosin II involved in chemotactic cell movement. Ca²⁺ is shown to be required for chemotactic aggregation of amoebae. The evidence for uptake and/or eflux of this ion being regulated by the nucleotide cyclic GMP is discussed. The connection between Ca²⁺, cyclic GMP and chemotactic cell movement has been explored using “streamer F” mutants. The primary defect in these mutants is in the structural gene for the cyclic GMP-specific phosphodiesterase which results in the mutants producing an abnormally prolonged peak of accumulation of cyclic GMP in response to stimulation with the chernoattractant cyclic AMP. While events associated with production and relay of cyclic AMP signals are normal, certain events associated with movement are (like the cyclic GMP response) abnormally prolonged in the mutants. These events include Ca²⁺ uptake, myosin II association with the cytoskeleton and inhibition of myosin heavy and light chain phosphorylation. These changes can be correlated with the amoebae becoming elongated and transiently decreasing their locomotive speed after chemotactic stimulation. Other mutants studied in which the accumulation of cyclic GMP in response to cyclic AMP stimulation was absent produced no myosin II responses. Models are described in which cyclic GMP (directly or indirectly via Ca²⁺) regulates accumulation of myosin II on the cytoskeleton by inhibiting phosphorylation of the myosin heavy and light chain kinases.     

Effect of concanavalin A on cellular slime mold development: Premature appearance of membrane-bound cyclic AMP phosphodiesterase

Concanavalin A delays aggregation of slime mold amoebae, apparently by interfering with the cells' response to the chemotactic agent, cyclic AMP. Concanavalin A also induces the premature appearance in non-aggregating cells of a membrane-bound cyclic AMP phosphodiesterase normally found only at the time of aggregation. The appearance of this enzyme is not due to activation of an inactive form of the enzyme.     

Morphogenesis and differentiation of Dictyostelium cells interacting with immobilized glucosides: dependence on DIF production

Previous work has shown that multicellular morphogenesis of submerged Dictyostelium cells is inhibited when they bind to glucosides covalently linked to polyacrylamide gels. The amoebae aggregate normally, but then the aggregates repeatedly disperse and reaggregate, whereas control cells go on to form tight aggregates. We have investigated the role of the stalk cell differentiation inducing factors (DIFs) in this process. In the presence of cyclic AMP, amoebae submerged at high cell density accumulate DIF and differentiate into stalk cells. We find that stalk cell differentiation is inhibited by interaction of the cells with glucoside gels in these conditions, but can be restored by the addition of exogenous DIF-1. Since the responsiveness of cells to DIF-1 is not altered, it appears likely that the effect of the glucoside gel is to block DIF-1 production. Further, the addition of DIF-1 or DIF-2 stimulates the formation of tight aggregates by cells developing on glucoside gels in the absence of cyclic AMP, thus preventing the rounds of aggregation and disaggregation otherwise seen. This suggests a role for DIF in morphogenesis as well as in controlling cell differentiation. We propose a model in which immobilized glucosides activate a specific receptor ("food sensor") which drives the amoebae toward the vegetative state and inhibits DIF accumulation. DIF, on the other hand, induces tight aggregate formation and so locks the amoebae into the developmental program.     

Traveling waves in a chemotactic model

A model for chemotaxis in a bacteria-substrate mixture introduced by Keller and Segel, which is described by nonlinear partial differential equations, is studied analytically. The existence of traveling waves is shown for the system in which the substrate diffusion is taken into account and the chemotactic coefficient is greater than the motility one, and the instability of traveling waves is discussed.     

Streamers: chemotactic mutants of Dictyostelium discoideum with altered cyclic GMP metabolism

Mutants of Dictyostelium discoideum that developed huge aggregation streams in expanding clones were investigated using optical and biochemical techniques. Representatives of the six complementation groups previously identified (stmA-stmF) were found to be similar to the parental wild-type strain XP55 in both the extent and timing of their ability to initiate and relay chemotactic signals and in the formation of cyclic AMP receptors and phosphodiesterases. The mutants differed from the wild-type in producing an abnormal chemotactic (movement) response visible using both dark-field optics with synchronously aggregating amoebae on solid substrata and light scattering techniques with oxygenated cell suspensions. Mutants of complementation group stmF showed chemotactic movement responses lasting up to 520 s, rather than 100 s as seen in the parental and other strains. Measurements of cyclic GMP formed intracellularly in response to chemotactic pulses of cyclic AMP in stmF mutants showed that abnormally high concentrations of this nucleotide were formed within 10 s and were not rapidly degraded. A causal correlation between defective cyclic GMP metabolism and the altered chemotactic response is suggested, and a model is proposed that accounts for the formation of huge aggregation streams in clones of these mutants.U     

Cell Differentiation in Dictyostelium discoideum

We have shown previously that amoebae of D. discoideum strain V12 M2 starved at low density in the presence of cyclic AMP fail to form either stalk cells or prespore cells; a low molecular weight factor released by cells at high density promotes stalk formation under these conditions but formation of prespore cells requires 'cell contact'. Here we summarise evidence that:
1. Elevated intracellular cyclic AMP levels are required for all developmental gene expression beyond the preaggregative phase, and ammonia antagonises this expression in some way. However, the action of ammonia is not pathway specific.
2.'Cell contact' is a specific requirement for entry into the prespore pathway of gene expression since isolated cells provided with cyclic AMP synthesise much reduced amounts of the presporespecific enzyme uridine diphosphate (UDP) galactose polysaccharide transferase but normal amounts of the pathway-indifferent enzyme glycogen phosphorylase.
3. The 'cell contact' mechanism is uniquely sensitive to low concentrations of pronase. This protease selectively inhibits transferase synthesis and blocks in vitro spore differentiation (in a spore-forming mutant). It does not prevent chemotactic aggregation, stream formation, or stalk cell formation in the presence of cyclic AMP.     

Guanidine hydrochloride-induced shedding of a Dictyostelium discoideum plasma membrane fraction enriched in the cyclic adenosine 3',5'-monophosphate receptor

The cell surface cyclic AMP receptor of Dictyostelium discoideum is under study in a number of laboratories with respect to both its role in development of the organism and the physiology of excitation-response coupling. We report here that when starved amoebae are exposed to the chaotrope guanidine hydrochloride at 1.8 M, they shed a particulate cyclic AMP binding activity into the medium. This activity is due to membrane vesicles which originate from the cell surface. The vesicles are enriched up to 150-fold in cyclic AMP binding activity and up to 14-fold in phospholipid content when compared to the starting amoebae. The cyclic AMP binding activity of the membrane vesicles is identical to that of the cell surface receptor with respect to the following properties; (i) it is lacking in preparations from unstarved, vegetative amoebae; (ii) it is not inhibited by cyclic GMP and is stimulated by calcium ions; (iii) it has very rapid rates of association and dissociation of bound cyclic AMP; (iv) it has two classes of binding sites with dissociation constants similar to those of the surface receptors of whole amoebae. The binding activity of the isolated membranes is stable for several days at 4 degrees C and the lower affinity binding sites are stable up to several months when stored at -80 degrees C. Due to enrichment and stability of the receptor in this preparation, it should be highly suitable for many types of studies. The usefulness is enhanced by the fact that the preparation does not contain detectable cyclic AMP phosphodiesterase activity.