Cyclic AMP oscillations in suspensions of Dictyostelium discoideum

The role of acidocalcisomes in the stress response of Trypanosoma cruzi

Acidocalcisomes of Trypanosoma cruzi are acidic calcium-containing organelles rich in phosphorus in the form of pyrophosphate (PP(i)) and polyphosphate (poly P). Acidification of the organelles is driven by vacuolar proton pumps, one of which, the vacuolar-type proton pyrophosphatase, is absent in mammalian cells. A calcium ATPase is involved in calcium uptake, and an aquaporin is important for water transport. Enzymes involved in the synthesis and degradation of PPi and poly P are present within the organelle. Acidocalcisomes function as storage sites for cations and phosphorus, participate in PP(i) and poly P metabolism and volume regulation and are essential for virulence. A signalling pathway involving cyclic AMP generation is important for fusion of acidocalcisomes to the contractile vacuole complex, transference of aquaporin and volume regulation. This pathway is an excellent target for chemotherapy as shown by the effects of phosphodiesterase C inhibitors on parasite survival.

Receptor-Based Models with Diffusion-Driven Instability for Pattern Formation in Hydra

The aim of this paper is to show under which conditions a receptor-based model can produce and regulate patterns. Such model is applied to the pattern formation and regulation in a fresh water polyp, hydra. The model is based on the idea that both head and foot formation could be controlled by receptor-ligand binding. Positional value is determined by the density of bound receptors. The model is defined in the form of reaction-diffusion equations coupled with ordinary differential equations. The objective is to check what minimal processes are sufficient to produce patterns in the framework of a diffusion-driven (Turing-type) instability. Three-variable (describing the dynamics of ligands, free and bound receptors) and four-variable models (including also an enzyme cleaving the ligand) are analyzed and compared. The minimal three-variable model takes into consideration the density of free receptors, bound receptors and ligands. In such model patterns can evolve only if self-enhancement of free receptors, i.e., a positive feedback loop between the production of new free receptors and their present density, is assumed. The final pattern strongly depends on initial conditions. In the four-variable model a diffusion-driven instability occurs without the assumption that free receptors stimulate their own synthesis. It is shown that gradient in the density of bound receptors occurs if there is also a second diffusible substance, an enzyme, which degrades ligands. Numerical simulations are done to illustrate the analysis. The four-variable model is able to capture some results from cutting experiments and reflects de novo pattern formation from dissociated cells.

Acidocalcisomes

Acidocalcisomes are acidic organelles containing calcium and a high concentration of phosphorus in the form of pyrophosphate (PP(i)) and polyphosphate (poly P). Organelles with these characteristics have been found from bacteria to human cells implying an early appearance and persistence over evolutionary time or their appearance by convergent evolution. Acidification of the organelles is driven by the presence of vacuolar proton pumps, one of which, the vacuolar proton pyrophosphatase, is absent in animals, where it is substituted by a vacuolar proton ATPase. A number of other pumps, antiporters, and channels have been described in acidocalcisomes of different species and are responsible for their internal content. Enzymes involved in the synthesis and degradation of PP(i) and poly P are present within the organelle. Acidocalcisomes function as storage sites for cations and phosphorus, and participate in PP(i) and poly P metabolism, calcium homeostasis, maintenance of intracellular pH, and osmoregulation. Experiments in which the acidocalcisome Ca(2+)-ATPase of different parasites were downregulated or eliminated, or acidocalcisome Ca(2+) was depleted revealed the importance of this store in Ca(2+) signaling needed for host invasion and virulence. Acidocalcisomes interact with other organelles in a number of organisms suggesting their association with the endosomal/lysosomal pathway, and are considered part of the lysosome-related group of organelles.

Singular perturbation analysis of cAMP signalling in Dictyostelium discoideum aggregates

In this paper, we use singular perturbation methods to study the structure of travelling waves for some reaction-diffusion models obtained from the Martiel-Goldbeter and Goldbeter-Segel's models of cAMP signalling in Dictyostelium discoideum. As a consequence, we derive analytic formulae for quantities like wave speed, maximum concentration and other magnitudes in terms of the different biochemical constants that appear in the model.

Receptor-based models with hysteresis for pattern formation in hydra

In this paper, we propose a new receptor-based model for pattern formation and regulation in a fresh-water polyp, namely hydra. The model is defined in the form of a system of reaction-diffusion equations with zero-flux boundary conditions coupled with a system of ordinary differential equations. The production of diffusible biochemical molecules has a hysteretic dependence on the density of these molecules and is modeled by additional ordinary differential equations. We study the hysteresis-driven mechanism of pattern formation and we demonstrate the advantages and constraints of its ability to explain different aspects of pattern formation and regulation in hydra. The properties of the model demonstrate a range of stationary and oscillatory spatially heterogeneous patterns, arising from multiple spatially homogeneous steady states and switches in the production rates.

A Xestospongin C-sensitive Ca(2+) store is required for cAMP-induced Ca(2+) influx and cAMP oscillations in Dictyostelium

Xestospongin C (XeC) is known to bind to the inositol 1,4, 5-trisphosphate (IP(3))-sensitive store in mammalian cells and to inhibit IP(3)- and thapsigargin-induced Ca(2+) release. In this study we show that this is also true for Dictyostelium. In addition, XeC inhibited Ca(2+) uptake into purified vesicle fractions and induced Ca(2+) release. This suggests that, in the case of Dictyostelium, XeC opens rather than plugs the IP(3) receptor channel as was proposed for mammalian cells (Gafni, J., Munsch, J. A. , Lam, T. H., Catlin, M. C., Costa, L. G., Molinski, T. F., and Pessah, I. N. (1997) Neuron 19, 723-733). In order to elucidate the function of the XeC-sensitive Ca(2+) store in Dictyostelium during differentiation, we applied XeC to the cells and found that it caused a time-dependent increase of basal [Ca(2+)](i) and inhibited cAMP-induced Ca(2+) influx in single cells as well as in cell suspensions. Moreover, XeC blocked light scattering spikes and pulsatile cAMP signaling.

Cyclic AMP oscillations in Dictyostelium discoideum: models and observations

Oscillations in intra- and extracellular cyclic AMP are believed to underlie aggregation and morphogenesis in Dictyostelium discoideum. Upon comparing mathematical models with observations we find that the models are, qualitatively speaking, quite successful. At the same time many features remain unexplained. A strong case can be made for cyclic AMP-independent oscillations whose basis remains to be explored.

A discrete cell model with adaptive signalling for aggregation of Dictyostelium discoideum

Dictyostelium discoideum (Dd) is a widely studied model system from which fundamental insights into cell movement, chemotaxis, aggregation and pattern formation can be gained. In this system aggregation results from the chemotactic response by dispersed amoebae to a travelling wave of the chemoattractant cAMP. We have developed a model in which the cells are treated as discrete points in a continuum field of the chemoattractant, and transduction of the extracellular cAMP signal into the intracellular signal is based on the G protein model developed by Tang & Othmer. The model reproduces a number of experimental observations and gives further insight into the aggregation process. We investigate different rules for cell movement the factors that influence stream formation the effect on aggregation of noise in the choice of the direction of movement and when spiral waves of chemoattractant and cell density are likely to occur. Our results give new insight into the origin of spiral waves and suggest that streaming is due to a finite amplitude instability.

An increase in cytosolic Ca2+ delays cAMP oscillations in Dictyostelium cells

We have shown that calmidazolium (R24571) causes a transient increase in the cytosolic free Ca2+ concentration ([Ca2+]i) in Dictyostelium discoideum [Schlatterer and Schaloske (1996) Biochem. J. 313, 661-667]. Here we have used R24571 to artifically increase [Ca2+]i during light-scattering oscillations and have found that, depending on the time of addition during the oscillatory cycle, R24571 suppressed cAMP synthesis and delayed the next spike for several minutes. Addition of Ca2+ to the medium, which also elevates [Ca2+]i, induced phase delays and resulted in a similar phase response curve as R24571. The magnitude of the phase delay was correlated with the point during the oscillatory cycle at which Ca2+ was added, indicating that an artificial increase in [Ca2+]i also resets the phase of the intrinsic oscillator.

Excitation, oscillations and wave propagation in a G-protein-based model of signal transduction in Dictyostelium discoideum

In an earlier paper (Tang & Othmer 1994 Math. Biosci 120, 25-76), we developed a G-protein-based model for signal transduction in the cellular slime mould Dictyostelium discoideum and showed that it can account for the results from perfusion experiments done by Devreotes and coworkers (Devreotes et al. 1979 J. Cell. 80, 300-309; Devreotes & Steck 1979 J. Cell Biol. 80, 300-309; Dinauer et al. 1980 J. Cell Biol. 86, 537-561). The primary experimental observables are the amounts of cAMP secreted and the time scale of adaptation in response to various stimuli, and we showed that the predictions of the model agree well with the observations. Adaptation in the model arises from dual receptor-mediated pathways, one of which produces a stimulatory G protein Gs and the other of which produces an inhibitory G protein Gi. In this paper we use the model to simulate the suspension experiments of Gerisch & Wick (1975 Biochem. biophys. Res. Commun. 65, 364-370) and the experiments done in cell cultures on Petri dishes (Tomchik & Devreotes 1981 Science, Wash. 212, 443-446). The model predicts excitation to cAMP stimuli, sustained oscillations, or spiral waves and target patterns, depending on the developmental stage of the cells and experimental conditions. The interaction between different pacemakers is also studied.

A class of parametrically excited calcium oscillation detectors

Intracellular Ca2+ oscillations are often a response to external signals such as hormones. Changes in the external signal can alter the frequency, amplitude, or form of the oscillations suggesting that information is encoded in the pattern of Ca2+ oscillations. How might a cell decode this signal? We show that an excitable system whose kinetic parameters are modulated by the Ca2+ concentration can function as a Ca2+ oscillation detector. Such systems have the following properties: (1) They are more sensitive to an oscillatory than to a steady Ca2+ signal. (2) Their response is largely independent of the signal amplitude. (3) They can extract information from a noisy signal. (4) Unlike other frequency sensitive detectors, they have a flat frequency response. These properties make a Ca(2+)-sensitive excitable system nearly ideal for detecting and decoding Ca2+ oscillations. We suggest that Ca2+ oscillations, in concert with these detectors, can act as cellular timekeepers to coordinate related biochemical reactions and enhance their overall efficiency.

Adenylyl cyclases and the interaction between calcium and cAMP signalling

Adenylyl cyclase is the prototypical second messenger generator. Nearly all of the eight cloned adenylyl cyclases are regulated by one or other arm of the phospholipase C pathway. Functional and ultrastructural investigations have shown that adenylyl cyclases are intimately associated with sites of calcium ion entry into the cell. Oscillations in cellular cyclic AMP levels are predicted to arise because of feedback inhibition of adenylyl cyclase by Ca2+. Such findings inextricably intertwine cellular signalling by cAMP and internal Ca2+ and extend the known regulatory modes available to cAMP.

A G protein-based model of adaptation in Dictyostelium discoideum

A new model is proposed based on signal transduction via G proteins for adaptation of the signal relay process in the cellular slime mold Dictyostelium discoideum. The kinetic constants involved in the model are estimated from Dictyostelium discoideum and other systems. A qualitative analysis of the model shows how adaptation arises, and numerical computations show that the model agrees with observations in both perfusion and suspension experiments. Several experiments that can serve to test the model are suggested.

Properties of three different ion channels in the plasma membrane of the slime mold Dictyostelium discoideum

'Patch-clamp' experiments in the cell-attached configuration have shown the existence of three distinct types of ion channels in the plasma membrane of Dictyostelium discoideum. Channels DI (slope conductance 11 pS) and DII (slope conductance 6 pS) promote an outward current at depolarizing voltages. A third ion channel (HI, slope conductance 3 pS) opens preferentially at hyperpolarization and promotes inward current flow. It is suggested that under physiological conditions current through the DI and DII channels is carried by K+, whereas Ca2+ may be the current carrier in the HI channel. The density of these ion channels in the membrane of D. discoideum is low: approx. 0.1/micron 2 for the DI and HI channel and 0.02/micron 2 for the DII channel. The gating properties of the ion channels appear to be complicated because openings are grouped into bursts of activity. The probability of the DI channel being in the open state increases with depolarization. The mean channel life-time is about 20 ms and voltage-independent. The burst duration increases with depolarization whereas the interburst time decreases. The minimal kinetic model accounting for the behaviour of the DI channel is a three-state model with two closed and one open state. A detailed analysis of the gating of the DII and the HI channel was prevented by their low rate of occurrence (DII) or fast inactivation (HI). The formation of a seal resistance greater than or equal to 1 G omega depends critically on the composition of the pipette solution. Examination of a series of monovalent and divalent cations as well as different organic and inorganic anions has shown that 'gigaseals' are formed only in the presence of at least 1 mM Ca2+ or Sr2+, whereas Ba2+, Mg2+ and monovalent cations (Li+, Na+, K+, Rb+, Cs+) do not support the formation of high seal resistances. Anions seem not to affect the seal formation.

Pacemakers in aggregation fields of Dictyostelium discoideum: does a single cell suffice?

In this paper we address the following question: can a single cell of the cellular slime mold Dictyostelium discoideum serve as a pacemaker for the aggregation phase? Whether or not this is possible is determined by the relative importance of cyclic AMP production due to self-stimulation as compared to diffusion of cyclic AMP away from the cell and extracellular degradation. We determine the conditions under which a single cell on an infinite place can emit periodic signals of cyclic AMP using a model developed previously for signal relay and adaptation in Dictyostelium. Elsewhere it has been shown that this model provides an accurate representation of the stimulus-response behavior of Dictyostelium for a variety of experimental conditions.