Mechanical and biochemical modeling of cortical oscillations in spreading cells

Actomyosin-based cortical contractility is a common feature of eukaryotic cells and is involved in cell motility, cell division, and apoptosis. In nonmuscle cells, oscillations in contractility are induced by microtubule depolymerization during cell spreading. We developed an ordinary differential equation model to describe this behavior. The computational model includes 36 parameters. The values for all but two of the model parameters were taken from experimental measurements found in the literature. Using these values, we demonstrate that the model generates oscillatory behavior consistent with current experimental observations. The rhythmic behavior occurs because of the antagonistic effects of calcium-induced contractility and stretch-activated calcium channels. The model makes several experimentally testable predictions: 1), buffering intracellular calcium increases the period and decreases the amplitude of cortical oscillations; 2), increasing the number or activity of stretch activated channels leads to an increase in period and amplitude of cortical oscillations; 3), inhibiting Ca²⁺ pump activity increases the period and amplitude of oscillations; and 4), a threshold exists for the calcium concentration below which oscillations cease.     

Induction of cortical oscillations in spreading cells by depolymerization of microtubules

Actomyosin-based cortical contractility is a common feature of eukaryotic cells but the capability to produce rhythmic contractions is found in only a few types such as cardiomyocytes. Mechanisms responsible for the acquisition of this capability remain largely unknown. Rhythmic contractility can be induced in non-muscle cells by microtubule depolymerization. Spreading epithelial cells and fibroblasts in which microtubules were depolymerized with nocodazole or colcemid underwent rhythmic oscillations of the body that lasted for several hours before the cells acquired a stable, flattened shape. By contrast, control cells spread and flattened into discoid shapes in a smooth and regular manner. Quantitative analysis of the oscillations showed that they have a period of about 50 seconds. The kinase inhibitors, HA 1077 and H7, and the more specific rho-kinase inhibitor, Y 27632, caused the oscillations to immediately cease and the cells to become flat. Transient increases in cytoplasmic calcium preceded the contractile phase of the oscillations. Wrinkle formation by cells plated on elastic substrata indicated that the contractility of colcemid-treated cells increased in comparison to controls but was drastically decreased after HA 1077 addition. These data suggest that an intact microtubular system normally prevents pulsations by moderating excessive rho-mediated actin myosin contractility. Possible mechanistic interactions between rho-mediated and calcium activated contractile pathways that could produce morphological oscillations are discussed.     

In Vitro Dose-Dependent Inhibition of the Intracellular Spontaneous Calcium Oscillations in Developing Hippocampal Neurons by Ketamine

Spatial and temporal abnormalities in the frequency and amplitude of the cytosolic calcium oscillations can impact the normal physiological functions of neuronal cells. Recent studies have shown that ketamine can affect the growth and development and even induce the apoptotic death of neurons. This study used isolated developing hippocampal neurons as its study subjects to observe the effect of ketamine on the intracellular calcium oscillations in developing hippocampal neurons and to further explore its underlying mechanism using Fluo-4-loaded laser scanning confocal microscopy. Using a semi-quantitative method to analyze the spontaneous calcium oscillatory activities, a typical type of calcium oscillation was observed in developing hippocampal neurons. In addition, the administration of NMDA (N-Methyl-D-aspartate) at a concentration of 100 µM increased the calcium oscillation amplitude. The administration of MK801 at a concentration of 40 µM inhibited the amplitude and frequency of the calcium oscillations. Our results demonstrated that an increase in the ketamine concentration, starting from 30 µM, gradually decreased the neuronal calcium oscillation amplitude. The inhibition of the calcium oscillation frequency by 300 µM ketamine was statistically significant, and the neuronal calcium oscillations were completely eliminated with the administration of 3,000 µM Ketamine. The administration of 100, 300, and 1,000 µM NMDA to the 1 mM ketamine-pretreated hippocampal neurons restored the frequency and amplitude of the calcium oscillations in a dose-dependent manner. In fact, a concentration of 1,000 µM NMDA completely reversed the decrease in the calcium oscillation frequency and amplitude that was induced by 1 mM ketamine. This study revealed that ketamine can inhibit the frequency and amplitude of the calcium oscillations in developing hippocampal neurons though the NMDAR (NMDA receptor) in a dose-dependent manner, which might highlight a possible underlying mechanism of ketamine toxicity on the rat hippocampal neurons during development.     

Model for calcium dependent oscillatory growth in pollen tubes

Experiments have shown that pollen tubes grow in an oscillatory mode, the mechanism of which is poorly understood. We propose a theoretical growth model of pollen tubes exhibiting such oscillatory behaviour. The pollen tube and the surrounding medium are represented by two immiscible fluids separated by an interface. The physical variables are pressure, surface tension, density and viscosity, which depend on relevant biological quantities, namely calcium concentration and thickness of the cell wall. The essential features generally believed to control oscillating growth are included in the model, namely a turgor pressure, a viscous cell wall which yields under pressure, stretch-activated calcium channels which transport calcium ions into the cytoplasm and an exocytosis rate dependent on the cytosolic calcium concentration in the apex of the cell. We find that a calcium dependent vesicle recycling mechanism is necessary to obtain an oscillating growth rate in our model. We study the variation in the frequency of the growth rate by changing the extracellular calcium concentration and the density of ion channels in the membrane. We compare the predictions of our model with experimental data on the frequency of oscillation versus growth speed, calcium concentration and density of calcium channels.     

Furrow Constriction in Animal Cell Cytokinesis

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an acto-myosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility. The cortical acto-myosin is identified as the main source of mechanical dissipation and active forces. Thereupon, we propose a viscous active nonlinear membrane theory of the cortex that explicitly includes actin turnover and where the active RhoA signal leads to an equatorial band of myosin overactivity. The resulting cortex deformation is calculated numerically, and reproduces well the features of cytokinesis such as cell shape and cortical flows toward the equator. Our theory gives a physical explanation of the independence of cytokinesis duration on cell size in embryos. It also predicts a critical role of turnover on the rate and success of furrow constriction. Scaling arguments allow for a simple interpretation of the numerical results and unveil the key mechanism that generates the threshold for cytokinesis completion: cytoplasmic incompressibility results in a competition between the furrow line tension and the cell poles’ surface tension.     

Oscillatory reaction of chondroitin sulfate induced by gradual introduction of calcium ion

Rhythm is an important dynamic behavior in biological systems. We have been studying oscillatory reactions of enzymes induced by gradual entry of substances through semipermeable membrane. Not only enzymes but also a few species of substance of living system have been elucidated to cause oscillatory reaction. Here we present the oscillatory reaction by chondroitin sulfate in a system of gradual entry of calcium ion. Introducing calcium ion through dialysis membrane into chondroitin sulfate solution induces an oscillation of free calcium ion concentration in chondroitin sulfate solution. Simultaneously, it is elucidated that oscillation of conformation occurs with permeation of calcium ion. In both measurements, oscillations with 25h period are obtained. The phases of oscillation, however, differ slightly from each other. From these results, it is suggested that autocatalysis exerts in the contraction of chondroitin sulfate conformation. These phenomena are very intriguing for elucidating oscillation in living system.     

Furrow Constriction in Animal Cell Cytokinesis

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an acto-myosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility. The cortical acto-myosin is identified as the main source of mechanical dissipation and active forces. Thereupon, we propose a viscous active nonlinear membrane theory of the cortex that explicitly includes actin turnover and where the active RhoA signal leads to an equatorial band of myosin overactivity. The resulting cortex deformation is calculated numerically, and reproduces well the features of cytokinesis such as cell shape and cortical flows toward the equator. Our theory gives a physical explanation of the independence of cytokinesis duration on cell size in embryos. It also predicts a critical role of turnover on the rate and success of furrow constriction. Scaling arguments allow for a simple interpretation of the numerical results and unveil the key mechanism that generates the threshold for cytokinesis completion: cytoplasmic incompressibility results in a competition between the furrow line tension and the cell poles’ surface tension.     

Brain-derived neurotrophic factor-induced potentiation of Ca(2+) oscillations in developing cortical neurons.

Brain-derived neurotrophic factor (BDNF) has been reported to exert an acute potentiation of synaptic activity. Here we examined the action of BDNF on synchronous spontaneous Ca(2+) oscillations in cultured cerebral cortical neurons prepared from postnatal 2-3-day-old rats. The synchronous spontaneous Ca(2+) oscillations began at approximately DIV 5. It was revealed that voltage-dependent Ca(2+) channels and ionotropic glutamate receptors were involved in the synchronous spontaneous oscillatory activity. BDNF potentiated the frequency of these oscillations. The BDNF-potentiated activity reached 207 +/- 20.1% of basal oscillatory activity. NT-3 and NT-4/5 also induced the potentiation. However, nerve growth factor did not. We examined the correlation between BDNF-induced glutamate release and the BDNF-potentiated oscillatory activity. Both up-regulation of phospholipase C-gamma (PLC-gamma) expression and the BDNF-induced glutamate release occurred at approximately DIV 5 when the BDNF-potentiated oscillations appeared. We confirmed that the BDNF-induced glutamate release occurred through a glutamate transporter that was dependent on the PLC-gamma/IP(3)/Ca(2+) pathway. Transporter inhibitors blocked the BDNF-potentiated oscillations, demonstrating that BDNF enhanced the glutamatergic transmissions in the developing cortical network by inducing glutamate release via a glutamate transporter.     

Feed-forward synchronization: propagation of temporal patterns along the retinothalamocortical pathway

Visual responses in the cortex and lateral geniculate nucleus (LGN) are often associated with synchronous oscillatory patterning. In this short review, we examine the possible relationships between subcortical and cortical synchronization mechanisms. Our results obtained from simultaneous multi-unit recordings show strong synchronization of oscillatory responses between retina, LGN and cortex, indicating that cortical neurons can be synchronized by oscillatory activity relayed through the LGN. This feed-forward synchronization mechanism operating in the 60 to 120 Hz frequency range was observed mostly for static stimuli. In response to moving stimuli, by contrast, cortical synchronization was independent of oscillatory inputs from the LGN, with oscillation frequency in the range of 30 to 60 Hz. The functional implications of synchronization of activity from parallel channels are discussed, in particular its significance for signal transmission and cortical integration processes.     

Effects of caffeine, tetracaine, and ryanodine on calcium-dependent oscillations in sheep cardiac Purkinje fibers

Membrane current and tension were measured in voltage-clamped sheep cardiac Purkinje fibers. Elevating the intracellular calcium concentration ([Ca2+]i) results in oscillations of membrane current and tension both at rest and during stimulation. During stimulation, an oscillatory transient inward current and an after contraction follow repolarization. We have examined the effects on the oscillations of changing the extracellular calcium concentration ([Ca2+]o) and of adding various drugs. In agreement with previous work, high concentrations of drugs that affect the sarcoplasmic reticulum, namely caffeine (10-20 mM), tetracaine (1 mM), and ryanodine (10 microM), abolish the oscillations. However, at lower concentrations, these three drugs have different effects on the oscillations. Caffeine (1-2 mM) decreases the oscillation amplitude but increases the frequency. Tetracaine (100-500 microM) has little effect on the magnitude of the oscillations but decreases their frequency. Ryanodine, at all concentrations used (0.1-10 microM), eventually abolishes the oscillations but, in doing so, decreases the magnitude, leaving the frequency unaffected. When [Ca2+]o was changed in order to vary [Ca2+]i, both the frequency and the magnitude of the oscillations always changed in the same direction. This suggests that these three drugs have effects in addition to just changing [Ca2+]i.     

Cell adhesion and the actin cytoskeleton of the enveloping layer in the zebrafish embryo during epiboly.

As the zebrafish embryo undergoes gastrulation and epiboly, the cells of the enveloping layer (EVL) expand, covering the entire yolk cell. During the epiboly process, the EVL cells move as a coherent layer, remaining tightly attached to each other and to the underlying yolk syncytial layer (YSL). In view of the central role of the actin cytoskeleton, in both cell motility and cell-cell adhesion, we have labeled these cells in situ with fluorescent phalloidin and anti-actin antibodies. We show that, throughout their migration, the EVL cells retain a conspicuous cortical actin cytoskeletal belt coinciding with cell surface cadherins. At the margins approaching the YSL, the EVL cells extend, from their apicolateral domains, actin-rich filopodial protrusions devoid of detectable cadherin. We have studied the role of the actin cytoskeleton in the maintenance of EVL cohesion during epiboly. Cytochalasin treatment of embryos induces EVL dissociation accompanied by general detachment of the rest of the embryonic cells. In the dissociating EVL cells, the cortical actin belt undergoes fragmentation with the formation of actin aggregates; cadherins, on the other hand, remain evenly distributed at the junctional cell surface. Removal of Ca2+ by ethyleneglycolbis (amino-ethyl-ether)-tetraacetic acid (EGTA) treatment also induces cell dissociation without visible disruption of the cortical actin belt. The protein kinase inhibitor (1-isoquinolinylsulfonyl)-2-methyl-piperazine dihydrochloride (H-7), which blocks acto-myosin contractility and disrupts actin cables in cultured cells, also potentiates cytochalasin-induced dissociation and promotes the projection of numerous actin-rich lamellipodial extensions. The fact that EVL cells produce microspike-like structures towards the YSL and are capable of lamellipodial activity lend further support to the suggestion (R.W. Keller and J.P. Trinkaus. 1987. Dev. Biol. 120: 12-24) that the EVL cells are not passively mobilized on the expanding YSL but actively participate in epiboly.     

Actin Microfilament Involved in Regulation of Pacemaking Activity in Cultured Interstitial Cells of Cajal from Murine Intestine

The present study investigated the effect of actin microfilament structure on pacemaker currents and calcium oscillation in cultured murine intestinal interstitial cells of Cajal (ICCs) by whole-cell patch-clamp technique and calcium imaging technique. Cytochalasin B, a disruptor of actin microfilaments, decreased the amplitude and frequency of pacemaker currents from 491.32 ± 160.33 pA and 11.73 ± 0.79 cycles/min to 233.12 ± 92.00 pA and 10.29 ± 0.76 cycles/min. Cytochalasin B also decreased the amplitude and frequency of calcium oscillation from 0.32 ± 0.08 (ΔF/F0) and 2.75 ± 0.17 cycles/min to 0.02 ± 0.01 (ΔF/F0) and 1.20 ± 0.08 cycles/min. Phalloidin, a stabilizer of actin microfilaments, increased the amplitude and frequency of pacemaker currents from 751.79 ± 282.82 pA and 13.93 ± 1.00 cycles/min to 1234.34 ± 607.83 pA and 14.68 ± 1.00 cycles/min. Phalloidin also increased the amplitude and frequency of calcium oscillation from 0.26 ± 0.01 (ΔF/F0) and 2.27 ± 0.18 cycles/min to 0.43 ± 0.03 (ΔF/F0) and 2.87 ± 0.07 cycles/min. 2-Aminoethoxydiphenyl borane (2-APB), an IP₃ receptor blocker, suppressed both pacemaker currents and calcium oscillations. 2-APB also blocked the phalloidin-induced increase in pacemaker currents and calcium oscillation. Ryanodine, an inhibitor of calcium-induced calcium release, did not affect pacemaker current but suppressed calcium oscillations. Ryanodine had no effect on altering phalloidin-induced increases in pacemaker current and calcium oscillation. These results suggest that actin microfilaments regulate pacemaker activity via the IP₃-induced calcium release signaling pathway.     

Role of Calcium Electrogenesis in Apical Dendrites: Generation of Intrinsic Oscillations by an Axial Current

Dendrites are covered with conductances whose function is still mysterious. Using intracellular recording and calcium imaging, we describe an electrogenic band of calcium channels in distal apical dendrites of layer 5 pyramidal neurons (Yuste et al., 1994). We now explore the functional consequences of this distal electrogenic area with multicompartmental numerical simulations. A calcium imaging and electrophysiological database from a single neuron, recorded under blocked sodium and potassium conductances, is replicated by simulations having increased dendritic calcium current. In these models a significant axial current flows from the apical dendrite into the somatic region, activating low-threshold calcium channels and generating oscillations similar to those seen in the electrophysiological data. We propose that the distal electrogenic area in apical dendrites serves to inject current into the soma and produce intrinsic oscillatory dynamics.     

Role of membrane potential in vasomotion of isolated pressurized rat arteries

Vasomotion, the phenomenon of vessel diameter oscillation, regulates blood flow and resistance. The main parameters implicated in vasomotion are particularly the membrane potential and the cytosolic free calcium in smooth muscle cells. In this study, these parameters were measured in rat perfused-pressurized mesenteric artery segments. The application of norepinephrine (NE) caused rhythmic diameter contractions and membrane potential oscillations (amplitude; 5.3 +/- 0.3 mV, frequency; 0.09 +/- 0.01 Hz). Verapamil (1 microM) abolished this vasomotion. During vasomotion, 10(-5) M ouabain (Na(+)-K(+) ATPase inhibitor) decreased the amplitude of the electrical oscillations but not their frequency (amplitude; 3.7 +/- 0.3 mV, frequency; 0.08 +/- 0.002 Hz). Although a high concentration of ouabain (10(-3) M) (which exhibits non-specific effects) abolished both electrical membrane potential oscillations and vasomotion, we conclude that the Na+-K+ ATPase could not be implicated in the generation of the membrane potential oscillations. We conclude that in rat perfused-pressurized mesenteric artery, the slow wave membrane type of potential oscillation by rhythmically gating voltage-dependent calcium channels, is responsible for the oscillation of intracellular calcium and thus vasomotion.     

Complex calcium oscillations and the role of mitochondria and cytosolic proteins

Intracellular calcium oscillations, which are oscillatory changes of cytosolic calcium concentration in response to agonist stimulation, are experimentally well observed in various living cells. Simple calcium oscillations represent the most common pattern and many mathematical models have been published to describe this type of oscillation. On the other hand, relatively few theoretical studies have been proposed to give an explanation of complex intracellular calcium oscillations, such as bursting and chaos. In this paper, we develop a new possible mechanism for complex calcium oscillations based on the interplay between three calcium stores in the cell: the endoplasmic reticulum (ER), mitochondria and cytosolic proteins. The majority ( approximately 80%) of calcium released from the ER is first very quickly sequestered by mitochondria. Afterwards, a much slower release of calcium from the mitochondria serves as the calcium supply for the intermediate calcium exchanges between the ER and the cytosolic proteins causing bursting calcium oscillations. Depending on the permeability of the ER channels and on the kinetic properties of calcium binding to the cytosolic proteins, different patterns of complex calcium oscillations appear. With our model, we are able to explain simple calcium oscillations, bursting and chaos. Chaos is also observed for calcium oscillations in the bursting mode.     

Prolonged Mechanical Stretch Initiates Intracellular Calcium Oscillations in Human Mesenchymal Stem Cells

Mesenchymal stem cells (MSCs) are a promising candidate for cell-based therapy in regenerative medicine. These stem cells can interact with their mechanical microenvironment to control their functions. External mechanical cues can be perceived and transmitted into intracellular calcium dynamics to regulate various cellular processes. Recent studies indicate that human MSCs (hMSCs) exhibit a heterogeneous nature with a subset of hMSCs lacking spontaneous calcium oscillations. In this study, we studied whether and how external mechanical tension can be applied to trigger and restore the intracellular calcium oscillation in these hMSCs lacking spontaneous activities. Utilizing the fluorescence resonance energy transfer (FRET) based calcium biosensor, we found that this subpopulation of hMSCs can respond to a prolonged mechanical stretch (PMS). Further results revealed that the triggering of calcium oscillations in these cells is dependent on the calcium influx across the plasma membrane, as well as on both cytoskeletal supports, myosin light chain kinase (MLCK)-driven actomyosin contractility, and phospholipase C (PLC) activity. Thus, our report confirmed that mechanical tension can govern the intracellular calcium oscillation in hMSCs, possibly via the control of the calcium permeability of channels at the plasma membrane. Our results also provide novel mechanistic insights into how hMSCs sense mechanical environment to regulate cellular functions.     

Two adaptation processes in auditory hair cells together can provide an active amplifier

The hair cells of the vertebrate inner ear convert mechanical stimuli to electrical signals. Two adaptation mechanisms are known to modify the ionic current flowing through the transduction channels of the hair bundles: a rapid process involves Ca(2+) ions binding to the channels; and a slower adaptation is associated with the movement of myosin motors. We present a mathematical model of the hair cell which demonstrates that the combination of these two mechanisms can produce "self-tuned critical oscillations", i.e., maintain the hair bundle at the threshold of an oscillatory instability. The characteristic frequency depends on the geometry of the bundle and on the Ca(2+) dynamics, but is independent of channel kinetics. Poised on the verge of vibrating, the hair bundle acts as an active amplifier. However, if the hair cell is sufficiently perturbed, other dynamical regimes can occur. These include slow relaxation oscillations which resemble the hair bundle motion observed in some experimental preparations.