Membrane voltage initiates Ca2+ waves and potentiates Ca2+ increases with abscisic acid in stomatal guard cells

In higher plants changes and oscillations in cytosolic free Ca2+ concentration ([Ca2+]i) are central to hormonal physiology, including that of abscisic acid (ABA), which signals conditions of water stress and alters ion channel activities in guard cells of higher-plant leaves. Such changes in [Ca2+]i are thought to encode for cellular responses to different stimuli, but their origins and functions are poorly understood. Because transients and oscillations in membrane voltage also occur in guard cells and are elicited by hormones, including ABA, we suspected a coupling of [Ca2+]i to voltage and its interaction with ABA. We recorded [Ca2+]i by Fura2 fluorescence ratio imaging and photometry while bringing membrane voltage under experimental control with a two-electrode voltage clamp in intact Vicia guard cells. Free-running oscillations between voltages near −50 mV and −200 mV were associated with oscillations in [Ca2+]i, and, under voltage clamp, equivalent membrane hyperpolarizations caused [Ca2+]i to increase, often in excess of 1 μM, from resting values near 100 nM. Image analysis showed that the voltage stimulus evoked a wave of high [Ca2+]i that spread centripetally from the peripheral cytoplasm within 5–10 s and relaxed over 40–60 s thereafter. The [Ca2+]i increases showed a voltage threshold near −120 mV and were sensitive to external Ca2+ concentration. Substituting Mn2+ for Ca2+ to quench Fura2 fluorescence showed that membrane hyperpolarization triggered a divalent influx. ABA affected the voltage threshold for the [Ca2+]i rise, its amplitude, and its duration. In turn, membrane voltage determined the ability of ABA to raise [Ca2+]i. These results demonstrate a capacity for voltage to evoke [Ca2+]i increases, they point to a dual interaction with ABA in triggering and propagating [Ca2+]i increases, and they implicate a role for voltage in “conditioning” [Ca2+]i signals that regulate ion channels for stomatal function.

Desynchronization of cells on the developmental path triggers the formation of spiral waves of cAMP during Dictyostelium aggregation

Whereas it is relatively easy to account for the formation of concentric (target) waves of cAMP in the course of Dictyostelium discoideum aggregation after starvation, the origin of spiral waves remains obscure. We investigate a physiologically plausible mechanism for the spontaneous formation of spiral waves of cAMP in D. discoideum. The scenario relies on the developmental path associated with the continuous changes in the activity of enzymes such as adenylate cyclase and phosphodiesterase observed during the hours that follow starvation. These changes bring the cells successively from a nonexcitable state to an excitable state in which they relay suprathreshold cAMP pulses, and then to autonomous oscillations of cAMP, before the system returns to an excitable state. By analyzing a model for cAMP signaling based on receptor desensitization, we show that the desynchronization of cells on this developmental path triggers the formation of fully developed spirals of cAMP. Developmental paths that do not correspond to the sequence of dynamic transitions no relay-relay-oscillations-relay are less able or fail to give rise to the formation of spirals.

Visual stimuli induce waves of electrical activity in turtle cortex

The computations involved in the processing of a visual scene invariably involve the interactions among neurons throughout all of visual cortex. One hypothesis is that the timing of neuronal activity, as well as the amplitude of activity, provides a means to encode features of objects. The experimental data from studies on cat [Gray, C. M., Konig, P., Engel, A. K. & Singer, W. (1989) Nature (London) 338, 334–337] support a view in which only synchronous (no phase lags) activity carries information about the visual scene. In contrast, theoretical studies suggest, on the one hand, the utility of multiple phases within a population of neurons as a means to encode independent visual features and, on the other hand, the likely existence of timing differences solely on the basis of network dynamics. Here we use widefield imaging in conjunction with voltage-sensitive dyes to record electrical activity from the virtually intact, unanesthetized turtle brain. Our data consist of single-trial measurements. We analyze our data in the frequency domain to isolate coherent events that lie in different frequency bands. Low frequency oscillations (<5 Hz) are seen in both ongoing activity and activity induced by visual stimuli. These oscillations propagate parallel to the afferent input. Higher frequency activity, with spectral peaks near 10 and 20 Hz, is seen solely in response to stimulation. This activity consists of plane waves and spiral-like waves, as well as more complex patterns. The plane waves have an average phase gradient of ≈π/2 radians/mm and propagate orthogonally to the low frequency waves. Our results show that large-scale differences in neuronal timing are present and persistent during visual processing.

An extracellular signaling component in propagation of astrocytic calcium waves

Focally evoked calcium waves in astrocyte cultures have been thought to propagate by gap-junction-mediated intercellular passage of chemical signal(s). In contrast to this mechanism we observed isolated astrocytes, which had no physical contact with other astrocytes in the culture, participating in a calcium wave. This observation requires an extracellular route of astrocyte signaling. To directly test for extracellular signaling we made cell-free lanes 10–300 μm wide in confluent cultures by deleting astrocytes with a glass pipette. After 4–8 hr of recovery, regions of confluent astrocytes separated by lanes devoid of cells were easily located. Electrical stimulation was used to initiate calcium waves. Waves crossed narrow (<120 μm) cell-free lanes in 15 of 36 cases, but failed to cross lanes wider than 120 μm in eight of eight cases. The probability of crossing narrow lanes was not correlated with the distance from the stimulation site, suggesting that cells along the path of the calcium wave release the extracellular messenger(s). Calculated velocity across the acellular lanes was not significantly different from velocity through regions of confluent astrocytes. Focal superfusion altered both the extent and the direction of calcium waves in confluent regions. These data indicate that extracellular signals may play a role in astrocyte–astrocyte communication in situ.

Fire–diffuse–fire model of dynamics of intracellular calcium waves

When Ca2+ is released from internal stores in living cells, the resulting wave of increased concentration can travel without deformation (continuous propagation) or with burst-like behavior (saltatory propagation). We analyze the “fire–diffuse–fire” model in order to illuminate the differences between these two modes of propagation. We show that the Ca2+ release wave in immature Xenopus oocytes and cardiac myocytes is saltatory, whereas the fertilization wave in the mature oocyte is continuous.

Brain-wave representation of words by superposition of a few sine waves

Data from three previous experiments were analyzed to test the hypothesis that brain waves of spoken or written words can be represented by the superposition of a few sine waves. First, we averaged the data over trials and a set of subjects, and, in one case, over experimental conditions as well. Next we applied a Fourier transform to the averaged data and selected those frequencies with high energy, in no case more than nine in number. The superpositions of these selected sine waves were taken as prototypes. The averaged unfiltered data were the test samples. The prototypes were used to classify the test samples according to a least-squares criterion of fit. The results were seven of seven correct classifications for the first experiment using only three frequencies, six of eight for the second experiment using nine frequencies, and eight of eight for the third experiment using five frequencies.

Selection for spiral waves in the social amoebae Dictyostelium

Starving Dictyostelium amoebae emit pulses of the chemoattractant cAMP that are relayed from cell to cell as circular and spiral waves. We have recently modeled spiral wave formation in Dictyostelium. Our model suggests that a secreted protein inhibitor of an extracellular cAMP phosphodiesterase selects for spirals. Herein we test the essential features of this prediction by comparing wave propagation in wild type and inhibitor mutants. We find that mutants rarely form spirals. The territory size of mutant strains is approximately 50 times smaller than wild type, and the mature fruiting bodies are smaller but otherwise normal. These results identify a mechanism for selecting one wave symmetry over another in an excitable system and suggest that the phosphodiesterase inhibitor may be under selection because it helps regulate territory size.

Do cyanobacteria swim using traveling surface waves?

Bacteria that swim without the benefit of flagella might do so by generating longitudinal or transverse surface waves. For example, swimming speeds of order 25 microns/s are expected for a spherical cell propagating longitudinal waves of 0.2 micron length, 0.02 micron amplitude, and 160 microns/s speed. This problem was solved earlier by mathematicians who were interested in the locomotion of ciliates and who considered the undulations of the envelope swept out by ciliary tips. A new solution is given for spheres propagating sinusoidal waveforms rather than Legendre polynomials. The earlier work is reviewed and possible experimental tests are suggested.

The use of spreading depression waves for acute and long-term monitoring of the penumbra zone of focal ischemic damage in rats.

Slow potential recording was used for long-term monitoring of the penumbra zone surrounding an ischemic region produced by middle cerebral artery (MCA) occlusion in adult hooded rats (n = 32). Four capillary electrodes (El-E4) were chronically implanted at 2-mm intervals from AP -3, L 2 (El) to AP 0, L 5 (E4). Spontaneous or evoked slow potential waves of spreading depression (SD) were recorded during and 4 h after a 1-h MCA occlusion and at 2- to 3-day intervals afterward for 3 weeks. Duration of the initial focal ischemic depolarization was maximal at E4 and decreased with distance from the focus. SD waves in the penumbra zone were high at El and E2, low and prolonged at E3, and almost absent at E4. Amplitude of elicited SD waves was further reduced 3 days later and slowly increased in the following week. Cortical areas displaying marked reduction of SD waves in the first days after MCA occlusion either remained low or showed substantial (60%) recovery, the probability of which decreased with the duration of the initial focal ischemic depolarization and increased with the distance from the focus. It is concluded that the outcome of ischemia monitored by long-term SD recovery in the perifocal region can be partly predicted from the acute signs of MCA occlusion.

Active control of waves in a cochlear model with subpartitions.

Multiscale asymptotic methods developed previously to study macromechanical wave propagation in cochlear models are generalized here to include active control of a cochlear partition having three subpartitions, the basilar membrane, the reticular lamina, and the tectorial membrane. Activation of outer hair cells by stereocilia displacement and/or by lateral wall stretching result in a frequency-dependent force acting between the reticular lamina and basilar membrane. Wavelength-dependent fluid loads are estimated by using the unsteady Stokes' equations, except in the narrow gap between the tectorial membrane and reticular lamina, where lubrication theory is appropriate. The local wavenumber and subpartition amplitude ratios are determined from the zeroth order equations of motion. A solvability relation for the first order equations of motion determines the subpartition amplitudes. The main findings are as follows: The reticular lamina and tectorial membrane move in unison with essentially no squeezing of the gap; an active force level consistent with measurements on isolated outer hair cells can provide a 35-dB amplification and sharpening of subpartition waveforms by delaying dissipation and allowing a greater structural resonance to occur before the wave is cut off; however, previously postulated activity mechanisms for single partition models cannot achieve sharp enough tuning in subpartitioned models.

Origin and evolution of circular waves and spirals in Dictyostelium discoideum territories.

Randomly distributed Dictyostelium discoideum cells form cooperative territories by signaling to each other with cAMP. Cells initiate the process by sending out pulsatile signals, which propagate as waves. With time, circular and spiral patterns form. We show that by adding spatial and temporal noise to the levels of an important regulator of external cAMP levels, the cAMP phosphodiesterase inhibitor, we can explain the natural progression of the system from randomly firing cells to circular waves whose symmetries break to form double- and single- or multi-armed spirals. When phosphodiesterase inhibitor is increased with time, mimicking experimental data, the wavelength of the spirals shortens, and a proportion of them evolve into pairs of connected spirals. We compare these results to recent experiments, finding that the temporal and spatial correspondence between experiment and model is very close.

Temporal fluctuations in coherence of brain waves.

As a measure of dynamical structure, short-term fluctuations of coherence between 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal, and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert, and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within 2-min samples, coherence commonly fluctuates by a factor up to 2-3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15s, either irregularly or quasirhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. In our sampling, we have not found a consistent difference between lobes of the brain, subdural and depth electrodes, or sleeping and waking states. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant nonindependence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging approximately 0.4, falling to approximately 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broad-band events may be the more usual generators. Loci only a few millimeters apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa, and intracortical microelectrodes show still greater coherence fluctuation in space and time. Widely used computations of chaos and dimensionality made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe that measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ.

Three-dimensional scroll waves of cAMP could direct cell movement and gene expression in Dictyostelium slugs.

Complex three-dimensional waves of excitation can explain the observed cell movement pattern in Dictyostelium slugs. Here we show that these three-dimensional waves can be produced by a realistic model for the cAMP relay system [Martiel, J. L. & Goldbeter, A. (1987) Biophys J. 52, 807-828]. The conversion of scroll waves in the prestalk zone of the slug into planar wave fronts in the prespore zone can result from a smaller fraction of relaying cells in the prespore zone. Further, we show that the cAMP concentrations to which cells in a slug are exposed over time display a simple pattern, despite the complex spatial geometry of the waves. This cAMP distribution agrees well with observed patterns of cAMP-regulated cell type-specific gene expression. The core of the spiral, which is a region of low cAMP concentration, might direct expression of stalk-specific genes during culmination.