Spontaneous calcium transients regulate neuronal plasticity in developing neurons

Calcium ions play critical roles in neuronal differentiation. We have recorded transient, repeated elevations of calcium in embryonic Xenopus spinal neurons over periods of 1 h in vitro and in vivo, confocally imaging fluo 3-loaded cells at 5 s intervals. Calcium spikes and calcium waves are found both in neurons in culture and in the intact spinal cord. Spikes rise rapidly to approximately 400% of baseline fluorescence and have a double exponential decay, whereas waves rise slowly to approximately 200% of baseline fluorescence and decay slowly as well. Imaging of fura 2-loaded neurons indicates that intracellular calcium increases from 50 to 500 nM during spikes. Both spikes and waves are abolished by removal of extracellular calcium. Developmentally, the incidence and frequency of spikes decrease, whereas the incidence and frequency of waves are constant. Spikes are generated by spontaneous calcium-dependent action potentials and also utilize intracellular calcium stores. Waves are produced by a mechanism that does not involve classic voltage-dependent calcium channels. Spikes are required for expression of the transmitter GABA and for potassium channel modulation. Waves in growth cones are likely to regulate neurite extension. The results demonstrate the roles of a novel signaling system in regulating neuronal plasticity, that operates on a time scale 10⁴ times slower than that of action potentials. © 1995 John Wiley & Sons, Inc.     

Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations

In this paper we use a dynamical systems approach to prove the existence of a unique critical value c ^* of the speed c for which the degenerate density-dependent diffusion equation u _ct = [D(u)u _x ] _x + g(u) has: 1. no travelling wave solutions for 0 < c < c ^*, 2. a travelling wave solution u(x, t) = (x - c ^* t) of sharp type satisfying (– ) = 1, () = 0 ^*; '(^*–) = – c ^*/D'(0), '(^*+) = 0 and 3. a continuum of travelling wave solutions of monotone decreasing front type for each c > c ^*. These fronts satisfy the boundary conditions (– ) = 1, '(– ) = (+ ) = '(+ ) = 0. We illustrate our analytical results with some numerical solutions.     

A cross-diffusion model of forest boundary dynamics

A simple mathematical model of mono-species forest with two age classes which takes into account seed production and dispersal is presented in the paper. This reaction — diffusion type model is then reduced by means of an asymptotic procedure to a lower dimensional reaction — cross-diffusion model. The existence of standing and travelling wave front solutions corresponding to the forest boundary is shown for the later model. On the basis of the analysis, possible changes in forest boundary dynamics caused by antropogenic impacts are discussed.     

Effects of Ultrasonic Seed Treatment on Rice Performances under the Seawater Irrigation

Irrigation with desalinated seawater is an effective way to use ocean resources and save freshwater resources. However, seawater irrigation would cause yield loss of rice. In order to explore the effects of ultrasonic seed treatment on rice performances under seawater irrigation, the present study was conducted with three irrigation treatments (fresh water (SW0), ten times diluted seawater (SW1%, 0.34% salinity), and five times diluted seawater (SW2%, 0.68% salinity)) and two seed treatments (ultrasonic treated seeds (UT) and untreated seeds (CK)). Compared with SW0 + CK treatment, SW1 + CK and SW2 + CK treatments significantly decreased grain yield by 56.19% and 66.69%, spikelets per panicle by 30.11% and 55.80%, seed-setting rate by 23.05% and 18.87%, and 1000-grain weight by 4.55% and 14.50%, respectively. Seawater irrigation also significantly increased malonaldehyde (MDA) and proline contents and the activities of superoxide dismutase (SOD) and peroxidase (POD). Ultrasonic seed treatment significantly increased the grain number per panicle, seed-setting rate, and grain yield of rice under seawater irrigation. Compared with CK, UT treatment substantially reduced MDA content, SOD activity, and POD activity in SW1 and SW2 conditions. Furthermore, UT treatment significantly increased proline content and down-regulated proline dehydrogenase activity under seawater irrigation. We deduced that ultrasonic seed treatment enhanced the salinity tolerance of rice by inducing the proline accmulation. Our findings indicated that ultrasonic seed treatment could an effective strategy to promote rice productivity under seawater irrigation.     

Existence and stability of periodic travelling wave solutions to Nagumo's nerve equation

Summary Nagumo's nerve conduction equation has a one-parameter family of spatially periodic travelling wave solutions. First, we prove the existence of these solutions by using a topological method. (There are some exceptional cases in which this method cannot be applied in showing the existence.) A periodic travelling wave solution corresponds to a closed orbit of a third-order dynamical system. The Poincaré index of the closed orbit is determined as a direct consequence of the proof of the existence. Second, we prove that the periodic travelling wave solution is unstable if the Poincaré index of the corresponding closed orbit is + 1. By using this result, together with the result of the author's previous paper, it is concluded that the slow periodic travelling wave solutions are always unstable. Third, we consider the stability of the fast periodic travelling wave solutions. We denote by L(c) the spatial period of the travelling wave solution with the propagation speed c. It is shown that the fast solution is unstable if its period is close to L_min, the minimum of L(c).     

Minimal model for human ventricular action potentials in tissue

Modeling the dynamics of wave propagation in human ventricular tissue and studying wave stability require models that reproduce realistic characteristics in tissue. We present a minimal ventricular (MV) human model that is designed to reproduce important tissue-level characteristics of epicardial, endocardial and midmyocardial cells, including action potential (AP) amplitudes and morphologies, upstroke velocities, steady-state action potential duration (APD) and conduction velocity (CV) restitution curves, minimum APD, and minimum diastolic interval. The model is then compared with three previously published human ventricular cell models, the Priebe and Beuckelmann (PB), the Ten Tusscher–Noble–Noble–Panfilov (TNNP), and the Iyer–Mazhari–Winslow (IMW). For the first time, the stability of reentrant waves for all four models is analyzed, and quantitative comparisons are made among the models in single cells and in tissue. The PB, TNNP, and IMW models exhibit quantitative differences in APD and CV rate adaptation, as well as completely different reentrant wave dynamics of quasi-breakup, stability, and breakup, respectively. All the models have dominant frequencies comparable to clinical values except for the IMW model, which has a large range of frequencies extending beyond the clinical range for both ventricular tachycardia (VT) and ventricular fibrillation (VF). The TNNP and IMW models possess a large degree of short-term memory and we show for the first time the existence of memory in CV restitution. The MV model also can be fitted to reproduce the dynamics of other models and is computationally more efficient: the times required to simulate the MV, TNNP, PB and IMW models follow the ratio 1:31:50:8084.     

What is hidden in the pannexin treasure trove: the sneak peek and the guesswork

Connexins had been considered to be the only class of the vertebrate proteins capable of gap junction formation; however, new candidates for this function with no homology to connexins, termed pannexins were discovered. So far three pannexins were described in rodent and human genomes: Panx1, Panx2 and Panx3. Expressions of pannexins can be detected in numerous brain structures, and now found both in neuronal and glial cells. Hypothetical roles of pannexins in the nervous system include participating in sensory processing, hippocampal plasticity, synchronization between hippocampus and cortex, and propagation of the calcium waves supported by glial cells, which help maintain and modulate neuronal metabolism. Pannexin also may participate in pathological reactions of the neural cells, including their damage after ischemia and subsequent cell death. Recent study revealed non-gap junction function of Panx1 hemichannels in erythrocytes, where they serve as the conduits for the ATP release in response to the osmotic stress. High-throughput studies produced some evidences of the pannexin involvement in the process of tumorigenesis. According to brain cancer gene expression database REMBRANDT, PANX2 expression levels can predict post diagnosis survival for patients with glial tumors. Further investigations are needed to verify or reject hypotheses listed.     

Solitonlike and nonsoliton modes of interaction of taxis waves (illustrated with an example of bacterial population waves)

It was shown earlier that during collisions bacterial population waves may either penetrate one another or stop. In this communication, the mechanism of these two interaction modes is considered in detail. It is shown on the basis of theoretical and experimental results that this interaction is a graphic example confirming one of the characteristic properties of waves in cross-diffusion systems.     

Species coexistence in resource-limited patterned ecosystems is facilitated by the interplay of spatial self-organisation and intraspecific competition

The exploration of mechanisms that enable species coexistence under competition for a sole limiting resource is widespread across ecology. Two examples of such facilitative processes are intraspecific competition and spatial self-organisation. These processes determine the outcome of competitive dynamics in many resource-limited patterned ecosystems, classical examples of which include dryland vegetation patterns, intertidal mussel beds and subalpine ribbon forests. Previous theoretical investigations have explained coexistence within patterned ecosystems by making strong assumptions on the differences between species (e.g. contrasting dispersal behaviours or different functional responses to resource availability). In this paper, I show that the interplay between the detrimental effects of intraspecific competition and the facilitative nature of self-organisation forms a coexistence mechanism that does not rely on species-specific assumptions and captures coexistence across a wide range of the environmental stress gradient. I use a theoretical model that captures the interactions of two generic consumer species with an explicitly modelled resource to show that coexistence relies on a balance between species' colonisation abilities and their local competitiveness, provided intraspecific competition is sufficiently strong. Crucially, the requirements on species' self-limitation for coexistence to occur differ on opposite ends of the resource input spectrum. For low resource levels, coexistence is facilitated by strong intraspecific dynamics of the species superior in its colonisation abilities, but for larger volumes of resource input, strong intraspecific competition of the locally superior species enables coexistence. Results presented in this paper also highlight the importance of hysteresis in understanding tipping points, in particular extinction events. Finally, the theoretical framework provides insights into spatial species distributions within single patches, supporting verbal hypotheses on coexistence of herbaceous and woody species in dryland vegetation patterns and suggesting potential empirical tests in the context of other patterned ecosystems.     

Intercellular calcium waves in primary cultured rat mesenteric smooth muscle cells are mediated by Connexin43

Abstract

Intercellular Ca^{2 +} wave propagation between vascular smooth muscle cells (SMCs) is associated with the propagation of contraction along the vessel. Here, we characterize the involvement of gap junctions (GJs) in Ca^{2 +} wave propagation between SMCs at the cellular level. Gap junctional communication was assessed by the propagation of intercellular Ca^{2 +} waves and the transfer of Lucifer Yellow in A7r5 cells, primary rat mesenteric SMCs (pSMCs), and 6B5N cells, a clone of A7r5 cells expressing higher connexin43 (Cx43) to Cx40 ratio. Mechanical stimulation induced an intracellular Ca^{2 +} wave in pSMC and 6B5N cells that propagated to neighboring cells, whereas Ca^{2 +} waves in A7r5 cells failed to progress to neighboring cells. We demonstrate that Cx43 forms the functional GJs that are involved in mediating intercellular Ca^{2 +} waves and that co-expression of Cx40 with Cx43, depending on their expression ratio, may interfere with Cx43 GJ formation, thus altering junctional communication.