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The self-similarity of a quadratic, one parameter logistic map was shown. Depending on the value of a constant, four different patterns were obtained and analysed. Only for the chaotic region (R = 4) the obtained patterns were almost independent of the resolution used (the frequency of probing). Some of the analytical operations used as standard tools in investigating the maps properties were also analysed and suitably altered, where necessary.
The whole-cell patch clamp technique was used to record potassium currents in in vitro differentiating myoblasts isolated from healthy and myotonic dystrophy type 1 (DM1) foetuses carrying 2000 CTG repeats. The fusion of the DM1 myoblasts was reduced in comparison to that of the control cells. The dystrophic muscle cells expressed less voltage-activated K+ (delayed rectifier and non-inactivating delayed rectifier) and inward rectifier channels than the age-matched control cells. However, the resting membrane potential was not significantly different between the control and the DM1 cells. After four days in a differentiation medium, the dystrophic cells expressed the fast-inactivating transient outward K+ channels, which were not observed in healthy cells. We suggest that the low level of potassium currents measured in differentiated DM1 cells could be related to their impaired fusion.
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Under the condition of rapid perfusion, the time course of contractile response of single ventricular cells to extracellular calcium (Ca) depletion and repletion identifies „fast” and „slow” cellular Ca pools. ⁴⁵Ca exchange was studied in these cells under the same conditions of on-line rapid perfusion. Four kinetically-defined compartments were distinguished: (1) A „rapid” compartment containing 2.6mmoles Ca/kg dry wt of lanthanum (La) displaceable Ca, t½ < 1 sec.; (2) An „intermediate” compartments) containing 2.1 mmoles, t½ = 3 and 19 sec. Caffeine displaced significant amounts of Ca from this compartment whereas La displaced none; (3) A „slow” compartment containing 1.6 mmoles, t½ = 3.6 min. Addition of inorganic phosphate to the perfusate adds significant amounts of Ca to this compartment; (4) An „inexchangeable” compartment, containing 1.2 mmoles. The „rapid” compartment’s flux is > 300 µmoles Ca/kg wet wt/sec. Its exchange rate indicates that it is the kinetic counterpart of the functionally-defined „fast” pool. Its subcellular locus is undefined. The „intermediate” compartment is best correlated with the „slow” pool and represents Ca in the sarcoplasmic reticulum. The „slow” compartment contains a significant fraction from the mitochondria. The results indicate that > 40% of cellular Ca can turn over within the period of one contraction cycle. These results are consistent with the following sequence: (1) Upon sarcolemmal depolarization, Ca moves through the Ca channel to arrive at the SR and at the myofilaments. (2) Ca induced Ca release occurs via the „feet” at the SR-inner SL region. The Ca diffuses to the myofilaments or is transported across the SL via the Na-Ca exchanger. (3) Ca is pumped into the free or longitudinal SR and diffuses to the cistemae. Ca is pumped across the SL by the SL Ca pump and by the Na-Ca exchanger. (4) Mitochondrial Ca exchange via the Na-Ca exchanger and/or SL Ca pump. (Supported by NHLBI and the Laubisch and Castera Endowments.)
The intergeniculate leaflet (IGL) of the thalamus constitutes a small but important part of the neural network controlling circadian activity in rodents. It appears that IGL integrates photic cues from retina with non-photic information originating from different nonspecific brain systems. Subsequently, this integrated signal is passed to the master biological clock - the suprachiasmatic nuclei (SCN). The common neurotransmitter of biological clock neural structures, the y-amino-butyric acid (GABA) is expressed in many, if not all, IGL and SCN neurons. Whole-cell patch clamp in vitro electrophysiological experiments were performed in order to evaluate GABA's influence on single IGL neurons in rat. Most neurons were hyperpolarized by GABA application and this effect was caused by activation of GABAa as well as GABAb receptors. The presence of GABAB receptors in rat's IGL has been suggested for the first time.
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The inhibitory effect of copper ions on lymphocyte Kv1.3 potassium channels

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We applied the whole-cell patch-clamp technique to study the inhibitory effect of copper ions (Cu) on the activity of Kv1.3 channels expressed in human lymphocytes. Application of Cu reversibly inhibited the currents to about 10% of the control value in a concentration-dependent manner with the half blocking concentration of 5.28±0.5 µM and the Hill's coefficient of 3.83±0.18. The inhibitory effect was saturated at 10 µM concentration. The inhibition was time-dependent and it was correlated in time with a significant slowing of the current activation rate. In contrast the voltage dependence of activation was not changed by Cu as well as the inativation kinetics. The inhibitory effect of Cu was voltage-independent. It was also unaffected by changing the extracellular pH in the range from 6.4 to 8.4, raising the extracellular potassium concentration to 150 mM and by changing the holding potential from -90 to -60 mV. The inhibitiory effect of Cu was not changed in the presence of an equivalent concentration of Zn. Altogether, obtained data suggest that Cu inhibits Kv1.3 channels by a different mechanism than Zn and that Cu and Zn act on different binding sites. The inhibitory effect of Cu was probably due to a specific binding of Cu on binding sites on the channels. Possible physiological significance of the Cu-induced inhibition of Kv1.3 channels is discussed.
We applied the whole-cell patch-clamp technique to study the influence of zinc ions (Zn2+) and extracellular protons at acidic pH (pHo) on voltage-gated potassium currents in cultured rat hippocampal neurons. The first goal of the study was to estimate whether Kv1.3 currents significantly contributed to voltage-gated potassium currents in examined cells. Then, the influence of both ions on the activity of other voltage-gated potassium currents in the neurons was examined. We examined both the total current and the delayed - rectifier component. Results obtained in both cases were not significantly different from each other. Available data argued against any significant contribution of Kv1.3 currents to the recorded currents. Nevertheless, application of Zn2+ in the concentration range from 100 µM to 5 mM reversibly modulated the recorded currents. The activation midpoint was shifted by about 40 mV (total current) and 30 mV (delayed-rectifier current) towards positive membrane potentials and the activation kinetics were slowed significantly (2 - 3 fold) upon application of Zn2+. The inactivation midpoint was also shifted towards positive membrane potentials, but less significantly (about 14 mV). The current amplitudes were reduced in a concentration-dependent manner to about 0.5 of the control value. The effects of Zn2+ were saturated at the concentration of 1 mM. Raising extracellular proton concentration by lowering the pHo from 7.35 to 6.4 did not affect significantly the currents. Possible mechanisms underlying the observed phenomena and their possible physiological significance are discussed.
The ion current through individual etched ion tracks (diameter ≈50 nm, length ≈12 µm) in a poly (ethylene terephthalate) membrane is recorded at pH 7 as function of applied voltage (-5V to +5V) across the membrane. With increasing voltage, the ion current changes abruptly from random oscillations to structured fluctuations. The power spectrum and the generalized entropy of the recorded current reminds of the potassium channel of a locust muscle cell.
Patch clamp data of PETP track-etched membranes have been analysed by the crowd model based on three i.e. regular, exponential and delayed maps of the logistic family. The same data were worked out for all equations, indicating expressive difference between theoretical predictions of the models with constant coefficients and experimental data. The differences disappeared for suitably chosen time dependent coefficients. Some possibilities of relating the functional forms of the logistic coefficients to the "dynamical structure" of a membrane as well as "the memory" of a system have also been discussed.
The nonlinear, pseudo-periodic current of potassium ions through a high conductance locust K+ channel (BK channel) has been modelled by a two-parameter logistic map (“crowd model”). Data obtained by the patch clamp for different values of potential difference has been correlated with a mechanism of transport incorporating dynamical structure and morphology of pores in a membrane. The ordering influence of applied voltage upon ionic current behaviour has been found and explained within the “crowd model”.
In the present study we applied the whole-cell patch-clamp technique to study the influence of extracellular pH (pHo) on the modulatory effect exerted by zinc ions (Zn2+) on voltage-gated potassium channels Kv1.3 expressed in human lymphocytes. Obtained data provide evidence that lowering of pHo from the 7.35 to 6.4 slowed significantly the current activation rate, shifted the activation midpoint by about 16 mV towards positive membrane potentials and reduced the current amplitude to about 0.55 of the control value. In contrast, raising the pHo from 7.35 to 8.4 did not affect significantly the activation midpoint and current amplitude. Application of Zn2+ in the concentration range from 100 µM to 1 mM at pHo=6.4 slowed additionally the activation rate, shifted the activation midpoint by about 20 mV towards positive membrane potentials and reduced the current amplitude in a concentration-dependent manner. The total effect exerted by Zn2+ and protons at pHo = 6.4 was more significant than the effect exerted by Zn alone. Both the magnitude of the shift and the degree of current inhibition by Zn2+ were independent on pHo in the range from 6.4 to 8.4. The data might suggest that the effects exerted by protons and zinc ions occur independently on each other and probably involve different mechanisms. Changing the holding potential from -90 mV to -60 mV at pHo=7.35 abolished the Zn2+-induced inhibition of the current amplitudes at concentrations below 300 µM. At pHo=6.4 the total inhibition caused by Zn2+ and protons was also diminished, however, a significant reduction was observed at 100 µM concentration. In contrast, changing the holding potential did not change the Zn2+- and proton-induced shift of the activation midpoint. Altogether, obtained data suggest that extracellular protons exert the modulatory effects that are additive to the effects exerted by Zn2+ on the channels. Possible physiological significance of these additive effects is discussed.
Acute hippocampal slices and primary neuronal cultures are often used with a tacit assumption that basic characteristics of the two models closely resemble each other. The use of the cell cultures, however, may raise controversies because of non-physiological conditions resulting from e.g. glial cells deficit, random neuronal sprouting, lack of specificity in the synaptic connections, impaired homeostasis, etc. Importantly, alteration in neuronal environment, especially when occurring over a prolonged period of time, may give rise to a profound homeostatic modulation. In the present study we have compared the properties of GABAergic and glutamatergic (non-NMDA) currents in pyramidal neurons from hippocampal slices and neuronal cell culture. We show that, most strikingly, amplitude ratio of currents elicited by ultrafast applications of saturating GABA and glutamate was nearly one order of magnitude larger in cultured neurons than that in slices. Miniature IPSCs and EPSCs also showed substantial differences between these two models. In particular, mEPSC amplitudes were larger and more frequent in cultured neurons but their time duration was longer in slices. Miniature IPSCs did not show differences in amplitude when comparing slices and cultures but their time duration was faster and occurrence more frequent in slices. In conclusion, we provide evidence that expression pattern of GABAA and glutamate receptors as well as synaptic current properties in the neuronal cell culture show profound differences with respect to that in the physiological conditions.
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