Frequency encoding in excitable systems with applications to calcium oscillations.

A number of excitable cell types respond to a constant hormonal stimulus with a periodic oscillation in intracellular calcium. The frequency of oscillation is often proportional to the hormonal stimulus, and one says that the stimulus is frequency encoded. Here we develop a theory of frequency encoding in excitable systems and apply it to intracellular calcium oscillations that results from increases in the intracellular level of inositol 1,4,5-triphosphate.

Elevation of intracellular calcium by muscarinic receptor activation induces a block of voltage-activated rat ether-à-go-go channels in a stably transfected cell line.

We have studied the properties of r-eag voltage-activated potassium channels in a stably transfected human embryonic kidney cell line. It was found that r-eag channels are rapidly and reversibly inhibited by a rise in intracellular calcium from 30 to 300 nM. The inhibition does not appear to depend on the activity of calcium-dependent kinases and phosphatases. The effect of calcium on r-eag channel activity was studied in inside-out membrane patches. Calcium inhibited r-eag channel activity with a mean IC50 of 67 nM. Activation of muscarinic receptors, generating calcium oscillations in the transfected cells, induced a synchronous inhibition of r-eag mediated outward currents. This shows that calcium can mediate r-eag current inhibition following muscarinic receptor activation. The data indicate that r-eag channels are calcium-inhibitable voltage-activated potassium channels.

Genetic analysis of calcium spiking responses in nodulation mutants of Medicago truncatula

The symbiotic interaction between Medicago truncatula and Sinorhizobium meliloti results in the formation of nitrogen-fixing nodules on the roots of the host plant. The early stages of nodule formation are induced by bacteria via lipochitooligosaccharide signals known as Nod factors (NFs). These NFs are structurally specific for bacterium–host pairs and are sufficient to cause a range of early responses involved in the host developmental program. Early events in the signal transduction of NFs are not well defined. We have previously reported that Medicago sativa root hairs exposed to NF display sharp oscillations of cytoplasmic calcium ion concentration (calcium spiking). To assess the possible role of calcium spiking in the nodulation response, we analyzed M. truncatula mutants in five complementation groups. Each of the plant mutants is completely Nod− and is blocked at early stages of the symbiosis. We defined two genes, DMI1 and DMI2, required in common for early steps of infection and nodulation and for calcium spiking. Another mutant, altered in the DMI3 gene, has a similar mutant phenotype to dmi1 and dmi2 mutants but displays normal calcium spiking. The calcium behavior thus implies that the DMI3 gene acts either downstream of calcium spiking or downstream of a common branch point for the calcium response and the later nodulation responses. Two additional mutants, altered in the NSP and HCL genes, which show root hair branching in response to NF, are normal for calcium spiking. This system provides an opportunity to use genetics to study ligand-stimulated calcium spiking as a signal transduction event.

Strontium-Induced Repetitive Calcium Spikes in a Unicellular Green Alga1

The divalent cation Sr2+ induced repetitive transient spikes of the cytosolic Ca2+ activity [Ca2+]cy and parallel repetitive transient hyperpolarizations of the plasma membrane in the unicellular green alga Eremosphaera viridis. [Ca2+]cy measurements, membrane potential measurements, and cation analysis of the cells were used to elucidate the mechanism of Sr2+-induced [Ca2+]cy oscillations. Sr2+ was effectively and rapidly compartmentalized within the cell, probably into the vacuole. The [Ca2+]cy oscillations cause membrane potential oscillations, and not the reverse. The endoplasmic reticulum (ER) Ca2+-ATPase blockers 2,5-di-tert-butylhydroquinone and cyclopiazonic acid inhibited Sr2+-induced repetitive [Ca2+]cy spikes, whereas the compartmentalization of Sr2+ was not influenced. A repetitive Ca2+ release and Ca2+ re-uptake by the ER probably generated repetitive [Ca2+]cy spikes in E. viridis in the presence of Sr2+. The inhibitory effect of ruthenium red and ryanodine indicated that the Sr2+-induced Ca2+ release from the ER was mediated by a ryanodine/cyclic ADP-ribose type of Ca2+ channel. The blockage of Sr2+-induced repetitive [Ca2+]cy spikes by La3+ or Gd3+ indicated the necessity of a certain influx of divalent cations for sustained [Ca2+]cy oscillations. Based on these data we present a mathematical model that describes the baseline spiking [Ca2+]cy oscillations in E. viridis.

The generation of oscillations in networks of electrically coupled cells

In several biological systems, the electrical coupling of nonoscillating cells generates synchronized membrane potential oscillations. Because the isolated cell is nonoscillating and electrical coupling tends to equalize the membrane potentials of the coupled cells, the mechanism underlying these oscillations is unclear. Here we present a dynamic mechanism by which the electrical coupling of identical nonoscillating cells can generate synchronous membrane potential oscillations. We demonstrate this mechanism by constructing a biologically feasible model of electrically coupled cells, characterized by an excitable membrane and calcium dynamics. We show that strong electrical coupling in this network generates multiple oscillatory states with different spatio-temporal patterns and discuss their possible role in the cooperative computations performed by the system.

Oxygen-sensitive calcium channels in vascular smooth muscle and their possible role in hypoxic arterial relaxation.

We have investigated the modifications of cytosolic [Ca2+] and the activity of Ca2+ channels in freshly dispersed arterial myocytes to test whether lowering O2 tension (PO2) directly influences Ca2+ homeostasis in these cells. Unclamped cells loaded with fura-2 AM exhibit oscillations of cytosolic Ca2+ whose frequency depends on extracellular Ca2+ influx. Switching from a PO2 of 150 to 20 mmHg leads to a reversible attenuation of the Ca2+ oscillations. In voltage-clamped cells, hypoxia reversibly reduces the influx of Ca2+ through voltage-dependent channels, which can account for the inhibition of the Ca2+ oscillations. Low PO2 selectively inhibits L-type Ca2+ channel activity, whereas the current mediated by T-type channels is unaltered by hypoxia. The effect of low PO2 on the L-type channels is markedly voltage dependent, being more apparent with moderate depolarizations. These findings demonstrate the existence of O2-sensitive, voltage-dependent, Ca2+ channels in vascular smooth muscle that may critically contribute to the local regulation of circulation.