Analysis of an autonomous phase model for neuronal parabolic bursting

An understanding of the nonlinear dynamics of bursting is fundamental in unraveling structure-function relations in nerve and secretory tissue. Bursting is characterized by alternations between phases of rapid spiking and slowly varying potential. A simple phase model is developed to study endogenous parabolic bursting, a class of burst activity observed experimentally in excitable membrane. The phase model is motivated by Rinzel and Lee's dissection of a model for neuronal parabolic bursting (J. Math. Biol. 25, 653–675 (1987)). Rapid spiking is represented canonically by a one-variable phase equation that is coupled bi-directionally to a two-variable slow system. The model is analyzed in the slow-variable phase plane, using quasi steady-state assumptions and formal averaging. We derive a reduced system to explore where the full model exhibits bursting, steady-states, continuous and modulated spiking. The relative speed of activation and inactivation of the slow variables strongly influences the burst pattern as well as other dynamics. We find conditions of the bistability of solutions between continuous spiking and bursting. Although the phase model is simple, we demonstrate that it captures many dynamical features of more complex biophysical models.This research was partially supported by NSF-JOINT RESEARCH grant 8803573, grant from CONCYT and DGAPA(UNAM) Mexico for H. Carrillo, and for the S. M. Baer NSF DMS-9107538     

Imaging of chlorophyll-a-fluorescence in leaves: Topography of photosynthetic oscillations in leaves of Glechoma hederacea

Images of chlorophyll-a-fluorescence oscillations were recorded using a camera-based fluorescence imaging system. Oscillations with frequencies around 1 per min were initiated by a transient decrease in light intensity during assimilation at an elevated CO₂-concentration. The oscillation was inhomogenously distributed over the leaf. In cells adjacent to minor veins, frequency and damping rate was high, if there was any oscillation. In contrast, the amplitude was highest in cells most distant from phloem elements (maximal distance about 300 m). The appearance of minor veins in oscillation images is explained by a gradient in the metabolic control in the mesophyll between minor veins and by transport of sugar from distant cells to phloem elements. The potential of fluorescence imaging to visualize microscopic source-sink interactions and metabolic domains in the mesophyll is discussed.Abbreviations P_i inorganic phosphate - Fru2,6BP fructose-2,6-bisphosphate - FBPase fructose-1,6-bisphosphatase - SPS sucrose-phosphate synthetase - HP hexosephosphate     

Subcellular calcium oscillators and calcium influx support agonist-induced calcium waves in cultured astrocytes

We have analysed Ca²⁺ waves induced by norepinephrine in rat cortical astrocytes in primary culture using fluorescent indicators fura-2 or fluo-3. The temporal pattern of the average [Ca²⁺]_i responses were heterogeneous from cell to cell and most cells showed an oscillatory response at concentrations of agonist around EC₅₀ (200 nM). Upon receptor activation, [Ca²⁺]_i signals originated from a single cellular locus and propagated throughout the cell as a wave. Wave propagation was supported by specialized regenerative calcium release loci along the length of the cell. The periods of oscillations, amplitudes, and the rates of [Ca²⁺]_i rise of these subcellular oscillators differ from each other. These intrinsic kinetic properties of the regenerative loci support local waves when stimulation is continued over long periods of time. The presence of local waves at specific, invariant cellular sites and their inherent kinetic properties provide for the unique and reproducible pattern of response seen in a given cell. We hypothesize that these loci are local specializations in the endoplasmic reticulum where the magnitude of the regenerative Ca²⁺ release is higher than other regions of the cell. Removal of extracellular Ca²⁺ or blockade of Ca²⁺ channels by inorganic cations (Cd²⁺ and Ni²⁺) during stimulation of adrenergic receptors alter the sustained plateau component of the [Ca²⁺]_i response. In the absence of Ca²⁺ release, due to store depletion with thapsigargin, agonist occupation alone does not induce Ca²⁺ influx in astrocytes. This finding suggests that, under these conditions, receptor-operated Ca²⁺ entry is not operative. Furthermore, our experiments provide evidence for local Ca²⁺ oscillations in cells which can support both wave propagation as well as spatially discrete Ca²⁺ signalling.     

A spatially explicit model of patchy stomatal responses to humidity

Stomata of leaves can exhibit either temporally stable, spatially homogeneous behaviour or complex spatial and temporal dynamics, depending on environmental and physiological conditions. To test the ability of accepted physiological mechanisms to describe these patterns, we developed a simple, spatially explicit model of stomatal responses to humidity that incorporated hydraulic interactions among stomata. Model results showed qualitative agreement with experimental evidence for a number of phenomena: (1) at high humidities, whole-leaf steady-state conductance is a monotonic function of humidity; (2) the initial stomatal response following a perturbation in humidity is in the direction opposite to the final response, and (3) spatial dynamics include patch formation and self-organization similar to that observed in actual leaves. These comparisons do not eliminate other explanations, but do suggest that novel mechanisms need not be invoked to explain the diversity of spatial and temporal patterns of stomatal behaviour in leaves.     

ATP-Induced Oscillations of Cytosolic Ca2+ Activity in Cultured Astrocytes from Rat Brain are Modulated by Medium Osmolarity Indicating a Control of [Ca2+]i Oscillations by Cell Volume

Oscillations of cytosolic Ca²⁺ activity ([Ca²⁺]_i) induced by stimulation with ATP in rat astrocytes in primary cultures were analysed. Astrocytes, prepared from the brains of newborn rats, loaded with the fluorescent Ca²⁺ indicator fura-2/AM, were continuously stimulated with ATP (10 M). ATP caused a large initial [Ca²⁺ peak, followed by regular [Ca²⁺]_i oscillations (frequencies 1–5/min). Astrocytes were identified by glial fibrillary acidic protein staining of cells after [Ca²⁺]_i recording. The oscillations were reversibly blocked by the P₂ purinoceptor antagonist suramin (30 M). Influx of extracellular Ca²⁺ and mobilization of Ca²⁺ from intracellular stores both contributed to the oscillations. The effects of hypertonic and hypotonic superfusion medium on ATP-induced [Ca²⁺]_i oscillations were examined. Hypertonic medium (430 mOsm) reversibly suppressed the ATP-induced oscillations. Hypotonic medium (250 mOsm), in spite of having heterogeneous effects, most frequently induced a rise in [Ca²⁺]_i, or reversibly increased the frequency of the oscillations. Thus, a change in cell volume might be closely connected with [Ca²⁺]_i oscillations in astrocytes indicating that [Ca²⁺]_i oscillations in glial cells play an important role in regulatory volume regulation in the brain.     

Pleistocene diversification in Morocco and recent demographic expansion in the Mediterranean pond turtle Mauremys leprosa

Quaternary climatic oscillations and geographic barriers have strongly influenced the distribution and diversification of thermophilic species occurring in the Mediterranean Basin. The Western Mediterranean pond turtle, Mauremys leprosa, is widely distributed throughout the Iberian Peninsula, southern France and most of the Maghreb region, with two subspecies currently recognized. In this work, we used 566 samples, including 259 new individuals, across the species range, and sequenced two mitochondrial markers (cytochrome b gene and control region; 163 samples in a concatenated mtDNA dataset) and one nuclear intron (R35; 23 samples representing all identified sublineages) to study the evolutionary history of M. leprosa. We combined phylogenetic methods and phylogeographic continuous diffusion models with spatial analysis. Our results (1) show a high level of genetic structure in Morocco originated during the Pleistocene; (2) reveal two independent population expansion waves from Morocco to Tunisia and to southern Europe, which later expanded throughout the Iberian Peninsula, and (3) identify several secondary contact zones in Morocco. Our study also sheds new light on the role of geographical features (Moroccan mountains ranges and the Strait of Gibraltar) and Pleistocene climatic oscillations in shaping genetic diversity and structure of M. leprosa, and underlines the importance of the Maghreb as a differentiation centre harbouring distinct glacial refugia.     

Phylogeography and refugia of the Japanese endemic alpine plant, Phyllodoce nipponica Makino (Ericaceae)

Aim  This study aims to elucidate the phylogeography of the Japanese endemic alpine plant, Phyllodoce nipponica Makino (Ericaceae) and to infer the location of refugia of alpine plants in Japan during climatic oscillations.
Location  Alpine zone in the Japanese archipelago.
Methods  We determined the chloroplast (cp) DNA haplotypes of 155 individuals (22 populations) based on sequence data from the trnL-F and trnT-L intergenic spacers and the trnL intron, whose phylogenetic relationships were analysed using the program tcs . To examine the genetic structure, analysis of molecular variance ( amova ) was carried out and the population differentiation was shown by the parameters G _ST and N _ST.
Results  The haplotype composition and the results of amova showed that populations in the Japanese Central Mountain Region (JCMR) and in the westernmost region were highly divergent (18.8%). The diversity within populations was very high in the JCMR ( h _S = 0.421); less variation was found within populations located in other regions at lower elevations.
Main conclusions  Phyllodoce nipponica survived climatic changes during the Quaternary in the JCMR and the westernmost region. Most of the distribution range was colonized during only one range expansion. The source location from which the range expansion occurred was unclear.     

Arachidonic acid, ARC channels, and Orai proteins

A critical role for arachidonic acid in the regulation of calcium entry during agonist activation of calcium signals has become increasingly apparent in numerous studies over the past 10 years or so. In particular, low concentrations of this fatty acid, generated as a result of physiologically relevant activation of appropriate receptors, induces the activation of a unique, highly calcium-selective conductance now known as the ARC channel. Activation of this channel is specifically dependent on arachidonic acid acting at the intracellular surface of the membrane, and is entirely independent of any depletion of internal calcium stores. Importantly, a specific role of this channel in modulating the frequency of oscillatory calcium signals in various cell types has been described. Recent studies, subsequent to the discovery of STIM1 and the Orai proteins and their role in the store-operated CRAC channels, have revealed that these same proteins are also integral components of the ARC channels and their activation. However, unlike the CRAC channels, activation of the ARC channels depends on the pool of STIM1 that is constitutively resident in the plasma membrane, and the pore of these channels is comprised of both Orai1 and Orai3 subunits. The clear implication is that CRAC channels and ARC channels are closely related, but have evolved to play unique roles in the modulation of calcium signals—largely as a result of their entirely distinct modes of activation. Given this, although the precise details of how arachidonic acid acts to activate the channels remain unclear, it seems likely that the specific molecular features of these channels that distinguish them from the CRAC channels – namely Orai3 and/or plasma membrane STIM1 – will be involved.