Calcium waves in agarose gel with cell organelles: implications of the velocity curvature relationship

The Plastic Glial-Synaptic Dynamics within the Neuropil: A Self-Organizing System Composed of Polyelectrolytes in Phase Transition

Several explanations have been proposed to account for the mechanisms of neuroglial interactions involved in neural plasticity. We review experimental results addressing plastic nonlinear interactions between glial membranes and synaptic terminals. These results indicate the necessity of elaborating on a model based on the dynamics of hydroionic waves within the neuropil. These waves have been detected in a small scale experimental model of the central nervous system, the in vitro retina. We suggest that the brain, as the heart and kidney, is a system for which the state of water is functional. The use of nonlinear thermodynamics supports experiments at convenient biological spatiotemporal scales, while an understanding of the properties of ions and their interactions with water requires explanations based on quantum theories. In our approach, neural plasticity is seen as part of a larger process that encompasses higher brain functions; in this regard, hydroionic waves within the neuropil are considered to carry both physiological and cognitive functions.

Relevance of excitable media theory and retinal spreading depression experiments in preclinical pharmacological research

In preclinical neuropharmacological research, molecular, cell-based, and systems using animals are well established. On the tissue level the situation is less comfortable, although during the last decades some effort went into establishing such systems, i.e. using slices of the vertebrate brain together with optical and electrophysiological techniques. However, these methods are neither fast, nor can they be automated or upscaled. By contrast, the chicken retina can be used as a suitable model. It is easy accessible and can be kept alive in vitro for hours up to days. Due to its structure, in addition the retina displays remarkable intrinsic optical signals, which can be easily used in experiments. Also to electrophysiological methods the retina is well accessible. In excitable tissue, to which the brain and the retina belong, propagating excitation waves can be expected, and the spreading depression is such a phenomenon. It has been first observed in the forties of the last century. Later, Martins-Ferreira established it in the chicken retina (retinal spreading depression or RSD). The electrophysiological characteristics of it are identical with those of the cortical SD. The metabolic differences are known and can be taken into account. The experimental advantage of the RSD compared to the cortical SD is the pronounced intrinsic optical signal (IOS) associated with the travelling wave. This is due to the maximum transparency of retinal tissue in the functional state; thus any physiological event will change it markedly and therefore can be easily seen even by naked eye. The theory can explain wave spread in one (action potentials), two (RSDs) and three dimensions (one heart beat). In this review we present the experimental and the excitable media context for the data interpretation using as example the cholinergic pharmacology in relation to functional syndromes. We also discuss the intrinsic optical signal and how to use it in pre-clinical research.

Fluorescent hydrogels for studying Ca2+-dependent reaction–diffusion processes

Here, we report a convenient experimental platform to study the diffusion of Ca²⁺ in the presence of a Ca²⁺-binding protein (Calbindin D28k). This work opens up new possibilities to elucidate the physical chemistry of complex Ca²⁺-dependent reaction–diffusion networks that are abundant in living cells.

Ca²⁺ waves in the heart

Ca(2+) waves were probably first observed in the early 1940s. Since then Ca(2+) waves have captured the attention of an eclectic mixture of mathematicians, neuroscientists, muscle physiologists, developmental biologists, and clinical cardiologists. This review discusses the current state of mathematical models of Ca(2+) waves, the normal physiological functions Ca(2+) waves might serve in cardiac cells, as well as how the spatial arrangement of Ca(2+) release channels shape Ca(2+) waves, and we introduce the idea of Ca(2+) phase waves that might provide a useful framework for understanding triggered arrhythmias.

Do calcium buffers always slow down the propagation of calcium waves?

Calcium buffers are large proteins that act as binding sites for free cytosolic calcium. Since a large fraction of cytosolic calcium is bound to calcium buffers, calcium waves are widely observed under the condition that free cytosolic calcium is heavily buffered. In addition, all physiological buffered excitable systems contain multiple buffers with different affinities. It is thus important to understand the properties of waves in excitable systems with the inclusion of buffers. There is an ongoing controversy about whether or not the addition of calcium buffers into the system always slows down the propagation of calcium waves. To solve this controversy, we incorporate the buffering effect into the generic excitable system, the FitzHugh-Nagumo model, to get the buffered FitzHugh-Nagumo model, and then to study the effect of the added buffer with large diffusivity on traveling waves of such a model in one spatial dimension. We can find a critical dissociation constant (K = K(a)) characterized by system excitability parameter a such that calcium buffers can be classified into two types: weak buffers (K ∈ (K(a), ∞)) and strong buffers (K ∈ (0, K(a))). We analytically show that the addition of weak buffers or strong buffers but with its total concentration b(0)(1) below some critical total concentration b(0,c)(1) into the system can generate a traveling wave of the resulting system which propagates faster than that of the origin system, provided that the diffusivity D1 of the added buffers is sufficiently large. Further, the magnitude of the wave speed of traveling waves of the resulting system is proportional to √D1 as D1 --> ∞. In contrast, the addition of strong buffers with the total concentration b(0)(1) > b(0,c)(1) into the system may not be able to support the formation of a biologically acceptable wave provided that the diffusivity D1 of the added buffers is sufficiently large.

Coordination of calcium signals by pituitary endocrine cells in situ

The pulsatile secretion of hormones from the mammalian pituitary gland drives a wide range of homeostatic responses by dynamically altering the functional set-point of effector tissues. To accomplish this, endocrine cell populations residing within the intact pituitary display large-scale changes in coordinated calcium-spiking activity in response to various hypothalamic and peripheral inputs. Although the pituitary gland is structurally compartmentalized into specific and intermingled endocrine cell networks, providing a clear morphological basis for such coordinated activity, the mechanisms which facilitate the timely propagation of information between cells in situ remain largely unexplored. Therefore, the aim of the current review is to highlight the range of signalling modalities known to be employed by endocrine cells to coordinate intracellular calcium rises, and discuss how these mechanisms are integrated at the population level to orchestrate cell function and tissue output.

The synergetic modulation of the excitability of central gray matter by a neuropeptide: two protocols using excitation waves in chick retina

The isolated chick retina provides an in vitro tissue model, in which two protocols were developed to verify the efficacy of a peptide in the excitability control of the central gray matter. In the first, extra-cellular potassium homeostasis is challenged at long intervals and in the second, a wave is trapped in a ring of tissue causing the system to be under self-sustained challenge. Within the neuropil, the extra-cellular potassium transient observed in the first protocol was affected from the initial rising phase to the final concentration at the end of the five-minute pulse. There was no change in the concomitants of excitation waves elicited by the extra-cellular rise of potassium. However, there was an increase on the elicited waves latency and/or a rise in the threshold potassium concentration for these waves to appear. In the second protocol, the wave concomitants and the propagation velocity were affected by the peptide. The results suggest a synergetic action of the peptide on glial and synaptic membranes: by accelerating the glial Na/KATPase and changing the kinetics of the glial potassium channels, with glia tending to accumulate KCl. At the same time, there is an increase in potassium currents through nerve terminals.

Within the cell: analytical techniques for subcellular analysis

This review covers recent developments in the preparation, manipulation, and analyses of subcellular environments. In particular, it highlights approaches for (1) separation and detection of individual organelles, (2) preparation of ultra-pure organelle fractions, and (3) utilization of novel labeling strategies. These approaches, based on innovative technologies such as microfluidics, immunoisolation, mass spectrometry and electrophoresis, suggest that subcellular analyses will soon become as commonplace as single cell and bulk cellular assays.

Disposition of calcium release units in agarose gel for an optimal propagation of Ca2+ signals

Clusters of calcium-loaded sarcoplasmic reticulum (SR) vesicles in agarose gel were previously shown to behave as an excitable medium that propagates calcium waves. In a 3D-hexagonal disposition, the distance between neighboring spheres (which may stand for SR vesicles) is constant and the relationship between distance and vesicular protein concentration is expected to be nonlinear. To obtain a distribution of SR vesicles at different protein concentrations as homogeneous as possible, liquid agarose gels were carefully stirred. Electron micrographs, however, did not confirm the expected relationship between inter-SR vesicle distance and vesicular protein concentration. Light micrographs, to the contrary, resulted in a protein concentration-dependent disposition of clusters of SR vesicles, which is described by a linear function. Stable calcium waves in agarose gel occurred at SR vesicle protein concentrations between 7 and 16 g/l. At lower protein concentrations, local calcium oscillations or abortive waves were observed. The velocities of calcium waves were optimum at approximately 12 g/l and amounted to nearly 60 microm/s. The corresponding distance of neighboring calcium release units was calculated to be approximately 4 microm. The results further show that calcium signaling in the described reaction-diffusion system is optimal in a relatively small range of diffusion lengths. A change by +/-2 microm resulted in a reduction of the propagation velocity by 40%. It would appear that 1), the distance between calcium release units (clusters of ryanodine receptors in cells) is a sensitive parameter concerning propagation of Ca2+ signals; and 2), a dysfunction of the reaction-diffusion system in living cells, however, might have a negative effect on the spreading of intracellular calcium signals, thus on the cell's function.

The velocity of calcium waves is expected to depend non-monotoneously on the density of the calcium release units

In this paper we develop a reaction-diffusion system describing the calcium dynamics in an agarose gel system with resuspended vesicles from the sarcoplasmic reticulum (SR vesicles). We focus on a simple model: compared with living cells (e.g. cardiac myocytes) an important property of the agarose gel system is the absence of the sarcolemma and the spatial separation of the calcium release units (CRUs). Our model includes the kinetics of ryanodine sensitive receptors (RyRs), the activity of the SERCA pumps and the diffusion of free calcium. We describe numerical simulations which show a biphasic relationship between the density of the CRUs and the propagation velocity of spreading waves. The non-monotony can be explained by changes in the amplitude of the local calcium concentration. We formulate implications for the in vitro system which could be verified in future experiments.

On the conservation of fast calcium wave speeds

Calcium waves were first seen about 25 years ago as the giant, 10 micro m/s wave or tsunami which crosses the cytoplasm of an activating medaka fish egg [J Cell Biol 76 (1978) 448]. By 1991, reports of such waves with approximately 10 micro m/s velocities through diverse, activating eggs and with approximately 30 micro m/s velocities through diverse, fully active systems had been compiled to form a class of what are now called fast calcium waves [Proc Natl Acad Sci USA 88 (1991) 9883; Bioessays 21 (1999) 657]. This compilation is now updated to include organisms from algae and sponges up to blowflies, squid and men and organizational levels from mammalian brains and hearts as well as chick embryos down to muscle, nerve, epithelial, blood and cancer cells and even cell-free extracts. Plots of these data confirm the narrow, 2-3-fold ranges of fast wave speeds through activating eggs and 3-4-fold ones through fully active systems at a given temperature. This also indicate Q(10)'s of 2.7-fold per 10 degrees C for both activating eggs and for fully activated cells.Speeds through some ultraflat preparations which are a few-fold above the conserved range are attributed to stretch propagated calcium entry (SPCE) rather than calcium-induced calcium release (CICR).