Modelling and quantification of the thermoregulatory responses of the developing avian embryo: Electrical analogies of a physiological system

Homeothermic animals, including birds, try to keep their body temperature at a constant level within certain boundaries by using thermoregulatory mechanisms. However, during incubation, the thermoregulatory system of the chicken embryo evolves through different stages from a poikilothermic to a homeothermic system. Hence, the thermal response of the fertile egg to changes in ambient temperature is different from one day to another during the embryonic development. The incubated egg can be considered as a physical (thermal) system, which transfers energy (heat) down a potential gradient (temperature difference). The heat flow between the micro-environment and the eggshell under a thermal driving force (temperature difference) has been studied in the past by using the analogy to the flow of electric charge under an electromotive-force. In this work, the thermal-response of incubated eggs to a step-increase in ambient-air temperature is studied and modelled. It is shown that the incubated egg is reacting as a first-order system between embryonic days ED01 and ED13, while, starting from ED14, the egg is reacting as a second-order system. This extends the existing RC (resistor–capacitor) circuit analogue to an RLC (resistor–inductor–capacitor) circuit analogue at the later stage of incubation. The concept of considering the fertile egg and its surrounding environment as an energy-handling device is introduced in this paper. It is suggested that the thermoregulation of the embryo has a thermal induction-like effect starting from ED14 and increasing gradually till hatching.     

Simulation of the cardiovascular system using equivalent electronic system

This paper describes simulation of the cardiovascular system using a complex electronic circuit. In this study we have taken a slightly different approach to the modeling of the system and tried to advance existing electrical models by increasing more segments and parameters. The model consists of 42 segments representing the arterial system. Anatomical and physiological data for circuit parameters have been extracted from medical articles and textbooks. The frequency of heart is 1 Hz and the system operates in steady state condition. Each artery is modeled by one capacitor, resistor and inductor. The left and right ventricles are modeled using AC power suppliers and diodes. The results of the simulation including pressure and volume graphs exhibit operation of the cardiovascular system under normal condition. The results of the simulation have been compared with the relevant experimental observation and are in good agreement with them.     

Directly Writing Resistor,Inductor and Capacitor to Composite Functional Circuits: A Super-Simple Way for Alternative Electronics

Background

The current strategies for making electronic devices are generally time, water, material and energy consuming. Here, the direct writing of composite functional circuits through comprehensive use of GaIn₁₀-based liquid metal inks and matching material is proposed and investigated, which is a rather easy going and cost effective electronics fabrication way compared with the conventional approaches.

Methods

Owing to its excellent adhesion and electrical properties, the liquid metal ink was demonstrated as a generalist in directly making various basic electronic components such as planar resistor, inductor and capacitor or their combination and thus composing circuits with expected electrical functions. For a precise control of the geometric sizes of the writing, a mask with a designed pattern was employed and demonstrated. Mechanisms for justifying the chemical components of the inks and the magnitudes of the target electronic elements so as to compose various practical circuits were disclosed.

Results

Fundamental tests on the electrical components including capacitor and inductor directly written on paper with working time up to 48 h and elevated temperature demonstrated their good stability and potential widespread adaptability especially when used in some high frequency circuits. As the first proof-of-concept experiment, a typical functional oscillating circuit including an integrated chip of 74HC04 with a supply voltage of 5 V, a capacitor of 10 nF and two resistors of 5 kΩ and 1 kΩ respectively was directly composed on paper through integrating specific electrical elements together, which presented an oscillation frequency of 8.8 kHz.

Conclusions

The present method significantly extends the roles of the metal ink in recent works serving as only a single electrical conductor or interconnecting wires. It opens the way for directly writing out complex functional circuits or devices on different substrates. Such circuit composition strategy has generalized purpose and can be extended to more areas, even daily pervasive electronics.     

A PKC wave follows the calcium wave after activation of Xenopus eggs

Calcium waves are well-known hallmarks of egg activation that trigger resumption of the cell cycle and development of the embryo. These waves rapidly and efficiently assure that activation signals are transmitted to all regions of the egg. Although the mechanism by which the calcium wave propagates across an egg as large as that of Xenopus is not known, two models prevail. One model is a wave of calcium-induced calcium release (CICR) and the other is propagation by inositol-induced calcium release (IICR). IICR requires a wave of phosphatidylinositol 4,5-bisphosphate (PIP2) hydrolysis, generating two second messengers, IP3, which then releases calcium and DAG, which activates protein kinase C (PKC). We show here that a wave of PKC-green fluorescent protein travels across the egg immediately following, and at the same velocity as, the calcium wave. This is the first example of a PKC wave in a vertebrate egg and supports the IICR model of wave propagation.     

The part played by inositol trisphosphate and calcium in the propagation of the fertilization wave in sea urchin eggs

Sea urchin egg activation at fertilization is progressive, beginning at the point of sperm entry and moving across the egg with a velocity of 5 microns/s. This activation wave (Kacser, H., 1955, J. Exp. Biol., 32:451-467) has been suggested to be the result of a progressive release of calcium from a store within the egg cytoplasm (Jaffe, L. F., 1983, Dev. Biol., 99:265-276). The progressive release of calcium may be due to the production of inositol trisphosphate (InsP3), a second messenger. We show here that a wave of calcium release crosses the Lytechinus pictus egg; the peak of the wave travels with a velocity of 5 microns/s; microinjection of InsP3 causes the release of calcium within the egg; calcium release (as judged by fertilization envelope elevation) is abolished by prior injection of the calcium chelator EGTA; neomycin, an inhibitor of InsP3 production, does not prevent the release of calcium in response to InsP3 but does abolish the wave of calcium release; the egg cytoplasm rapidly buffers microinjected calcium; the calcium concentration required to cause fertilization membrane elevation when microinjected is very similar to that required to stimulate the production of InsP3 in vitro; and the progressive fertilization membrane elevation seen after microinjection of calcium buffers appears to be due to diffusion of the buffer across the egg cytoplasm rather than to the induction of the activation wave. We conclude that InsP3 diffuses through the egg cytoplasm much more readily than calcium ions and that calcium-stimulated production of InsP3 and InsP3-induced calcium release from an internal store can account for the progressive release of calcium at fertilization.     

The activation wave of calcium in the ascidian egg and its role in ooplasmic segregation

We have studied egg activation and ooplasmic segregation in the ascidian Phallusia mammillata using an imaging system that let us simultaneously monitor egg morphology and calcium-dependent aequorin luminescence. After insemination, a wave of highly elevated free calcium crosses the egg with a peak velocity of 8-9 microns/s. A similar wave is seen in egg fertilized in the absence of external calcium. Artificial activation via incubation with WGA also results in a calcium wave, albeit with different temporal and spatial characteristics than in sperm-activated eggs. In eggs in which movement of the sperm nucleus after entry is blocked with cytochalasin D, the sperm aster is formed at the site where the calcium wave had previously started. This indicates that the calcium wave starts where the sperm enters. In 70% of the eggs, the calcium wave starts in the animal hemisphere, which confirms previous observations that there is a preference for sperm to enter this part of the egg (Speksnijder, J. E., L. F. Jaffe, and C. Sardet. 1989. Dev. Biol. 133:180-184). About 30-40 s after the calcium wave starts, a slower (1.4 microns/s) wave of cortical contraction starts near the animal pole. It carries the subcortical cytoplasm to a contraction pole, which forms away from the side of sperm entry and up to 50 degrees away from the vegetal pole. We propose that the point of sperm entry may affect the direction of ooplasmic segregation by causing it to tilt away from the vegetal pole, presumably via some action of the calcium wave.     

The initiation and propagation of the fertilization wave in sea urchin eggs

Calcium waves sweep across most eggs of the deuterostome lineage at fertilization. The precise timing of the initiation and propagation of a fertilization calcium wave has been best studied in sea urchin embryos, since the rapid depolarization caused by sperm egg fusion can be detected as a calcium influx using confocal imaging of calcium indicator dyes. The time between sperm egg fusion and the first sign of the calcium increase that constitutes the calcium wave is comparable to the time it takes for the wave to sweep across the egg, once initiated. The latency and rise time of the calcium response is sensitive to inhibitors of the InsP3 signalling pathway, as reported previously. Using calcium green dextran and confocal microscopy, we confirm that the propagation time of the calcium wave is lengthened and that initiation of the calcium wave involves activation of calcium release at hot spots that may represent clusters of calcium release channels, as has been seen in other cell types.     

Temporal and spatial correlation of fertilization current, calcium waves and cytoplasmic contraction in eggs of Ciona intestinalis

Eggs of the ascidian Ciona intestinalis were loaded with the calcium indicator fura-2 via whole-cell clamp electrodes and changes in cytoplasmic calcium and cell currents were monitored during fertilization either in separate eggs or simultaneously in the same egg. The first indication of egg activation was the fertilization current; which reached peak values around 1 nA after 30 s. A wave of elevated calcium was detectable between 5 s and 30 s (mean = 21 s) after the start of the fertilization current. This wave spread across the egg increasing cytoplasmic calcium levels to at least 10 microM. When the fertilization current and calcium wave were complete and cytoplasmic calcium levels were decreasing to prefertilization levels, a cortical contraction wave spread across the egg surface. In eggs showing normal fertilization current, the calcium wave and the contraction wave were in the same direction. A region of elevated calcium persisted at the animal pole. Changing cytoplasmic calcium levels locally by local application of ionophore A23187 caused a contraction wave originating at the site of ionophore application. Increasing cytoplasmic calcium uniformly by facilitating calcium entry through voltage-regulated channels did not result in a contraction wave.     

Characteristics of current passage through plant tissue

Plant tissue connected in a d.c. circuit behaves as a capacitor, short-circuited through a resistor. Using a saw-tooth voltage (T = 2 ma, U_max = + 13 V), structural and physiological conditions in a plant tissue can be analyzed on the basis of changes in the current character.     

A calcium‐mediated actin redistribution at egg activation in Drosophila

Egg activation is the essential process in which mature oocytes gain the competency to proceed into embryonic development. Many events of egg activation are conserved, including an initial rise of intracellular calcium. In some species, such as echinoderms and mammals, changes in the actin cytoskeleton occur around the time of fertilization and egg activation. However, the interplay between calcium and actin during egg activation remains unclear. Here, we use imaging, genetics, pharmacological treatment, and physical manipulation to elucidate the relationship between calcium and actin in living Drosophila eggs. We show that, before egg activation, actin is smoothly distributed between ridges in the cortex of the dehydrated mature oocytes. At the onset of egg activation, we observe actin spreading out as the egg swells though the intake of fluid. We show that a relaxed actin cytoskeleton is required for the intracellular rise of calcium to initiate and propagate. Once the swelling is complete and the calcium wave is traversing the egg, it leads to a reorganization of actin in a wavelike manner. After the calcium wave, the actin cytoskeleton has an even distribution of foci at the cortex. Together, our data show that calcium resets the actin cytoskeleton at egg activation, a model that we propose to be likely conserved in other species.     

A free calcium wave traverses the activating egg of the medaka, Oryzias latipes

Aequorin-injected eggs of the medaka (a fresh water fish) show an explosive rise in free calcium during fertilization, which is followed by a slow return to the resting level. Image intensification techniques now show a spreading wave of high free calcium during fertilization. The wave starts at the animal pole (where the sperm enters) and then traverses the egg as a shallow, roughly 20 degrees-wide band which vanishes at the antipode some minutes later. The peak free calcium concentration within this moving band is estimated to be about 30 microM (perhaps 100-1,000 times the resting level). Eggs activated by ionophore A23187 may show multiple initiation sites. The resulting multiple waves never spread through each other; rather, they fuse upon meeting so as to form spreading waves of compound origin. The fertilization wave is nearly independent of extracellular calcium because it is only slightly slowed (by perhaps 15%) in a medium containing 5 mM ethylene glycol-bis[beta-aminoethyl ether]N,N'-tetraacetic acid (EGTA) and no deliberately added calcium. It is also independent of the large cortical vesicles, which may be centrifugally displaced. Normally, however, it distinctly precedes the well-known wave of cortical vesicle exocytosis. We conclude that the fertilization wave in the medaka egg is propagated by calcium-stimulated calcium release, primarily from some internal sources other than the large cortical vesicles. A comparison of the characteristics of the exocytotic wave in the medaka with that in other eggs, particularly in echinoderm eggs, suggests that such a propagated calcium wave is a general feature of egg activation.     

Role of calcium influx during the latent period in sea urchin fertilization

After ∼7–40 s following gamete fusion, a steadily increasing fraction of a sea urchin's zygotes initiate an activating calcium wave. The fertilization membrane then rises, the cell cycle resumes and development begins. This study focuses on the so-called latent period that occurs between the time that gamete fusion occurs and the initiation of the activating calcium wave. We inhibited calcium influx during this period by adding lanthanum or by reducing external calcium with a buffer at various time points after insemination. Both of these treatments blocked the activation of eggs that had not yet started a wave at the time of treatment. This indicates that an influx of calcium is needed during the latent period to induce egg activation. These results support the sperm conduit model of egg activation in the sea urchin, where calcium flows from the sea through the fused sperms' acrosomal process into a cortical region of the eggs' endoplasmic reticulum.     

Cortical activity in vertebrate eggs. I: The activation waves

We present a physical model for the propagation of chemical and mechanical waves on the surface of vertebrate eggs. As a first step we analyzed the propagation of the calcium wave observed to sweep over the surface of the Medaka egg (Gilkey et al., 1978). It has been assumed that this wave is driven by a mechanism of calcium-stimulated-calcium-release. By formulating this hypothesis mathematically we can use the observed wavefront data to obtain a map of cortical reactivity. This map indicates a gradient of reactivity along the egg: highest in the animal hemisphere and tapering off towards the vegetal hemisphere. The cortex of Xenopus eggs is also capable of propagating a calcium wave (Busa & Nuccitelli, 1985). At about the same time a wave of expansion followed by a wave of contraction sweeps across the egg surface (Takeichi et al., 1984). We have proposed a mechanism for this wave pair based on the physical chemistry of actomyosin gels. The calcium wave activates solation factors which sever some of the actin chains which leads to an osmotic swelling of the gel. Calcium also activates the contractile machinery of the actomyosin system which causes the gel to contract. The contraction lags the swelling because of the nature of the kinetics: solation and swelling is a more rapid process than contraction. By writing the equations for gel expansion and contraction we can mimic the mechanical and chemical wave propagation by a computer simulation. If the model is correct this provides a method for using the waves as a diagnostic of the mechanochemical properties of the egg cortex.     

Wave of free calcium at fertilization in the sea urchin egg visualized with fura-2

A wave front of increased free calcium traversing the egg at fertilization is demonstrated in the sea urchin Lytechinus pictus. The use of the fluorescent calcium chelator fura-2 in combination with low-light-level TV microscopy and image processing allows the visualization of the Ca2+ wave front with high spatial and temporal resolution. Such a wave is demonstrated as increased fluorescence after an excitation of 340-nm wavelength and as the reciprocal image in form of a reduced fluorescence when excited at 380 nm. The band-like appearance of the wave resembles the Ca2+ wave described for larger eggs of other species. In a dispermic egg the high resolution of the system used allows us to recognize two waves of Ca2+ originating from the respective points of sperm entry.     

Free calcium wave upon activation in Xenopus eggs

Eggs of Xenopus laevis were preloaded with aequorin and the spatial and temporal pattern of free calcium release in the egg cortex on artificial activation was determined by the aequorin luminescence emitted from the thin cortical layer of naturally opaque eggs. The aequorin luminescence was detected with a photonic microscope system consisting of a light microscope and a two-dimensional photon-counting system with an image processor. A free calcium increase was initiated around the point of prick activation. The state of increased Ca2+ propagated in the cortical cytoplasm of the egg as a wave with a velocity of about 8 micron/sec at 22 degrees C. This wave reached the antipode by 5 to 6 min of prick activation. The spatial pattern of the Ca2+ wave was similar to that of changes in brightness of the egg surface on activation, termed the "activation wave" by K. Hara and P. Tydeman (1979, Wilhelm Roux's Arch. Dev. Biol. 186, 91-94). To examine the temporal correlation between the Ca2+ wave and the activation wave, images of aequorin luminescence and those of the egg cortex taken by incident light illumination were recorded alternately in the same egg. The zone of free calcium increase corresponded to the light (relaxation) zone of the activation wave, where exocytosis of cortical granules and elongation of microvilli were taking place.     

Biochemical fuel cells. Demonstration of an obligatory pathway involving an external circuit for the enzymatically catalyzed aerobic oxidation of glucose.

An in vitro biochemical fuel cell based upon the enzymatically catalyzed aerobic oxidation of glucose is described. The anodic half-reaction employs an electron transfer sequence consisting of the glucose oxidase reductive half-reaction and dichloroindophenol. The cathodic half-reaction involves reduction of molecular oxygen. A high Faradic efficiency for the intact cell approaching 100% has been experimentally demonstrated. The steady state current is exponentially related to the concentration of the terminal electron transfer species in the anodic chamber. The behavior is consistent with application of the Nernst relationship to define the cell potential and a simple resistance circuit. The discharge profile of the cell after complete oxidation of the primary fuel, glucose, can be modeled as a capacitor discharging through a resistor.     

Quasi-Linear Vacancy Dynamics Modeling and Circuit Analysis of the Bipolar Memristor

The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua''s generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis.     

Fertilization Stimulates an Increase in Inositol Trisphosphate and Inositol Lipid Levels inXenopusEggs

Previous experiments from our lab have suggested that the hydrolysis of phosphatidylinositol 4,5-bisphosphate (PIP₂) is required for sperm-induced egg activation inXenopus laevis.Here we measure the endogenous production of both Ins(1,4,5)P₃and PIP₂during the sperm-induced and ionomycin-induced calcium wave in the egg and find that both increase following fertilization. Ins(1,4,5)P₃increases 3.2-fold from an unfertilized egg level of 0.13 pmole per egg (0.29 μM) to a peak of 0.42 pmole per egg (0.93 μM) as the calcium wave reaches the antipode in the fertilized egg. This continuous production of Ins(1,4,5)P₃during the time that the Ca²⁺wave is propagating across the egg suggests the involvement of Ins(1,4,5)P₃in wave propagation. This increase in Ins(1,4,5)P₃is smaller in ionomycin-activated eggs than in sperm-activated eggs, suggesting that the sperm-induced production of Ins(1,4,5)P₃involves a PIP₂hydrolysis pathway that is not simply raising intracellular Ca²⁺. While one might expect PIP₂levels to fall as a result of hydrolysis, we find that PIP₂actually increases 2-fold. The total lipid fraction in unfertilized egg exhibits 0.8 pmole PIP₂per egg and this increases to 1.5 pmole as the calcium wave reaches the antipode. The PIP₂concentration peaks 2 min after the completion of the calcium wave at 1.8 pmole per egg. The amount of PIP₂in the animal and vegetal hemispheres of the egg was also measured by cutting frozen eggs in half. The vegetal hemisphere contained twice the amount of PIP₂as the animal hemisphere but it also contained twice the amount of lipid. Thus, there was an equivalent amount of PIP₂normalized to lipid in each hemisphere. Isolated animal and vegetal hemisphere cortices exhibit similar PIP₂concentrations, suggesting that the 2-fold higher total PIP₂in the vegetal half is not due to a gradient of PIP₂in the plasma membrane, but rather implies that cytoplasmic organelle membranes also contain PIP₂.     

Transcranial Extracellular Impedance Control (tEIC) Modulates Behavioral Performances

Electric brain stimulations such as transcranial direct current stimulation (tDCS), transcranial random noise stimulation (tRNS), and transcranial alternating current stimulation (tACS) electrophysiologically modulate brain activity and as a result sometimes modulate behavioral performances. These stimulations can be viewed from an engineering standpoint as involving an artificial electric source (DC, noise, or AC) attached to an impedance branch of a distributed parameter circuit. The distributed parameter circuit is an approximation of the brain and includes electric sources (neurons) and impedances (volume conductors). Such a brain model is linear, as is often the case with the electroencephalogram (EEG) forward model. Thus, the above-mentioned current stimulations change the current distribution in the brain depending on the locations of the electric sources in the brain. Now, if the attached artificial electric source were to be replaced with a resistor, or even a negative resistor, the resistor would also change the current distribution in the brain. In light of the superposition theorem, which holds for any linear electric circuit, attaching an electric source is different from attaching a resistor; the resistor affects each active electric source in the brain so as to increase (or decrease in some cases of a negative resistor) the current flowing out from each source. From an electrophysiological standpoint, the attached resistor can only control the extracellular impedance and never causes forced stimulation; we call this technique transcranial extracellular impedance control (tEIC). We conducted a behavioral experiment to evaluate tEIC and found evidence that it had real-time enhancement and depression effects on EEGs and a real-time facilitation effect on reaction times. Thus, tEIC could be another technique to modulate behavioral performance.     

A wave of free cytosolic calcium traverses zebrafish eggs on activation.

The activation process in a variety of deuterostome and protostome eggs is accompanied by cytosolic calcium transients that usually take the form of either a single or multiple propagating waves. Here we report that the eggs of zebrafish (Danio rerio) are no exception in that they generate a single activation wave that traverses the egg at a velocity of around 9 microm/s. There appears, however, to be no difference between the calcium-mediated activation response of eggs with regard to the presence or absence of sperm in the spawning medium. This leads us to suggest that these eggs are normally activated when they come in contact with their spawning medium and are then subsequently fertilized. The aspermic wave is initiated at the animal pole in the region of the micropyle, appears to propagate mainly through the yolk-free egg cortex, and then terminates at the vegetal pole. As neither sperm nor external calcium is required for the initiation (or propagation) of the activation wave, this suggests that an alternative wave trigger must be involved.