A cation channel for K+ and Ca2+ from Tetrahymena cilia in planar lipid bilayers

The single-channel properties for monovalent and divalent cations of a voltage-independent cation channel from Tetrahymena cilia were studied in planar lipid bilayers. The single-channel conductance reached a maximum value as the K+ concentration was increased in symmetrical solutions of K+. The concentration dependence of the conductance was approximated to a simple saturation curve (a single-ion channel model) with an apparent Michaelis constant of 16.3 mM and a maximum conductance of 354 pS. Divalent cations (Ca2+, Ba2+, Sr2+, and Mg2+) also permeated this channel. The sequence of permeability determined by zero current potentials at high ionic concentrations was Ba2+ greater than or equal to K+ greater than or equal to Sr2+ greater than Mg2+ greater than Ca2+. Single-channel conductances for Ca2+ were nearly constant (13.9 pS-20.5 pS) in the concentrations between 0.5 mM and 50 mM Ca-gluconate. In the experiments with mixed solutions of K+ and Ca2+, a maximum conductance of Ca2+ (gamma Camax) and an apparent Michaelis constant of Ca2+ (K Cam) were obtained by assuming a simple competitive relation between the cations. Gamma Camax and K Cam were 14.0 pS and 0.160 mM, respectively. Single-channel conductances in mixed solutions were well-fitted to this competitive model supporting that this cation channel behaves as a single-ion channel. This channel had relatively high-affinity Ca2+-binding sites.     

Physiological studies of cortical spreading depression

Cortical spreading depression (CSD) produces propagating waves of transient neuronal hyperexcitability followed by depression. CSD is initiated by K+ release following neuronal firing or electrical, mechanical or chemical stimuli. A triphasic (30-50 s) cortical potential transient accompanies localized transmembrane redistributions of K+, glutamate, Ca2+, Na+, Cl- and H+. Accumulated K+ in the restricted interstitial space can cause both further neuronal depolarisation and inward movement of K+ into astrocytes that buffers this increased extracellular K+ concentration ([K+])o. However, astrocyte interconnections may then propagate the CSD wave by K+ liberation through an opening of remote K+ channels by volume, Ca2+ or N-methyl-D-aspartate receptor activation. Changes in cerebral blood volume and in apparent water diffusion co-efficient (ADC) accompanying CSD were first studied using magnetic resonance imaging (MRI) in whole lissencephalic brains. Diffusion-weighted echoplanar imaging in gyrencephalic brains went on to demonstrate CSD features that paralleled classical migraine aura. The ADC activity persisted minutes/hours post KCl stimulus. Pixelwise analyses distinguished single primary events and multiple, spatially restricted, slower propagating, secondary events whose detailed features varied with the nature of the originating stimulus. These ADC changes varied reciprocally with T2*-weighted (i.e. referring to spin-spin relaxation times) waveforms reflecting local blood flow. There followed prolonged decreases in cerebral blood flow culminating in late cerebrovascular changes blocked by the antimigraine agent sumatriptan. CSD phenomena have possible translational significance for human migraine aura and other cerebral pathologies such as the peri-infarct depolarisation events that follow ischaemia and brain injury.     

Ionic currents of channels that are permeable to monovalent and divalent cations.

The cation-selective channel from Tetrahymena cilia is permeable to both monovalent and divalent cations. The single channel conductance in mixed solutions of K+ and Ca2+ was determined by the Gibbs-Donnan ratio of K+ and Ca2+, and the binding sites of this channel were considered to be always occupied by two potassium ions or by one calcium ion under the experimental conditions: 5-90 mM K+ and 0.5-35 mM Ca2+ (Oosawa and Kasai, 1988). A two-barrier model for the channel was introduced and the values of Michaelis-Menten constants and maximum currents carried by K+ and Ca2+ were calculated using this model. Single channel current amplitudes and reversal potentials were calculated from these values. The calculated single-channel currents were compared with those obtained experimentally. The calculated reversal potentials were compared with the resting potentials of Tetrahymena measured in various concentrations of extracellular K+ and Ca2+. The method of calculation of ionic currents and reversal potentials presented here is helpful for understanding the properties of the channels permeable to both monovalent and divalent cations.     

The Ca2+-sensitive K+-conductance of the human red cell membrane is strongly dependent on cellular pH

The conductance of the Ca2+-sensitive K+-channels in human red cell membranes has been determined as a function of the intracellular pH. A sudden increase in the intracellular concentration of ionized calcium was established by addition of ionophore A23187 to a suspension of cells in buffer-free, Ca2+-containing salt solution. At the various cellular pH-values cellular concentrations of ionized Ca, saturating with respect to activation of the Ca2+-sensitive K+-conductance, were obtained by the use of varied concentrations of extracellular Ca2+ and added ionophore A23187. Changes in membrane potential was monitored as CCCP-mediated changes in extracellular pH. Initial net effluxes of K+, cellular K+ contents and the K+ Nernst equilibrium potentials were calculated from flame photometric measurements. Cellular Ca-contents were determined by aid of 45Ca. With cellular Ca2+ at the saturating level with respect to activation of the K+-channel the K+-conductance calculated from these data was independent of extracellular pH and a steep function of cellular pH with a half maximal conductance of 31 microSeconds/cm2 at a cellular pH of 6.1. The K+-conductance is not a simple function of cellular pH (pHc). From pHc = 6.5 and down to pHc = 6.0 a Hill-coefficient of 2.5 was found, indicating cooperativity between at least two sites regulating the conductance. Below pHc = 6.0 an extremely high Hill-coefficient of 11 was found, probably indicating that the additional titration of the channel protein leads to an increased cooperativity. The importance, as a physiological regulatory mechanism, of a K+-conductance increasing from zero to maximal conductance within less than one unit of pH, is discussed.     

Effect of curare on responses to different putative neurotransmitters in Aplysia neurons.

We have studied the effects of curare on responses resulting from iontophoretic application of several putative neurotransmitters onto Aplysia neurons. These neurons have specific receptors for acetylcholine (ACh), dopamine, octopamine, phenylethanolamine, histamine, gamma-aminobutyric acid (GABA), aspartic acid, and glutamic acid. Each of these substances may on different specific neurons elicit at least three types of response, caused by a fast depolarizing Na+, a fast hyperpolarizing Cl-, or a slow hyperpolarizing K+ conductance increase. All responses resulting from either Na+ or Cl- conductance increases, irrespective of which putative transmitter activated the response, were sensitive to curare. Most were totally blocked by less than or equal to 10-4 M curare. GABA responses were less sensitive and were often only depressed by 10-3 M curare. K+ conductance responses, irrespective of the transmitter, were not curare sensitive. These results are consistent with a model of receptor organization in which one neurotransmitter receptor may be associated with any of at least three ionophores, mediating conductance increase responses to Na+, Cl-, and K+, respectively. In Aplysia nervous tissue, curare appears not to be a specific antagonist for the nicotinic ACh receptor, but rather to be a specific blocking agent for a class of receptor-activated Na+ and Cl- responses.     

Differences in presynaptic action of 4-aminopyridine and tetraethylammonium at frog neuromuscular junction

4-Aminopyridine markedly potentiates transmitter release at the frog pectoris neuromuscular junction by increasing the quantal content even when applied at low concentrations (5-20 microM). This enhancement of transmitter release is associated with greater minimum synaptic latency, but the dispersion of the synaptic latencies does not appear much affected. This is in contrast with the action of tetraethylammonium (0.2-0.5 mM) in which case similar enhancement of transmitter release results not only in larger minimum synaptic latency but also in greater dispersion of the synaptic latencies. The time course of transmitter release associated with enhanced transmitter output is hence much more prolonged in the presence of tetraethylammonium than 4-aminopyridine, at least for low concentrations of 4-aminopyridine (5-20 microM). This indicates that their presynaptic actions differ significantly. This conclusion is further strengthened by the finding that unlike tetraethylammonium, 4-aminopyridine induces bursts of release, presumably by producing multiple action potentials in the nerve terminal. Tetraethylammonium probably acts by blocking the delayed potassium conductance, but the blockade of Ca2+-activated K+ conductance cannot be excluded. 4-Aminopyridine, however, probably blocks the fast inactivating (IA) K+ current, but it also may be acting directly on the voltage-dependent Ca2+ conductance or on the intracellular Ca2+ buffering.     

Retinal spreading depression and the extracellular milieu

We used isolated chick retina in vitro to study the participation of the extracellular milieu in the occurrence and propagation of spreading depression. The propagation was followed by visual observation or microphotometry and the ionic changes in the extracellular compartment were recorded with double-barreled ion-selective microelectrodes. The front of the spreading wave is accompanied by increased light scattering in the tissue and by decrease of Cl-, Na+, and Ca2+, increase of K+, and an alkaline-acid shift in the extracellular space, concomitant with the slow voltage changes characteristic of the wave. As the spread is related to the chemical steady-state of the extracellular milieu, the velocity of propagation is influenced by a balanced interplay of the chemical constituents of the superfusing solution, e.g., K+, HCO-3, and glucose facilitate, while Cl- and Mg2+ hinder the wave. Steady-state alterations induced by physical factors (temperature) or related to experimental conditions (speed and direction of superfusate flow) change markedly the velocity of propagation. Generally the procedures that cause increase of velocity augment the susceptibility of the preparation to the reaction and eventually may trigger it. Propagated spreading depression is considered as a chemical diffusion reaction pervading more intensively the inner plexiform layer of the retina.     

Calcium-activated chloride conductance of lactotrophs: Comparison of activation in normal and tumoral cells during thyrotropin-releasing-hormone stimulation

We studied a chloride (Cl-) conductance activated by calcium (Ca2+) in normal rat lactotrophs and compared its activation during TRH stimulation in normal rat lactotrophs and in GH3 tumoral lactosomatotrophs cells, using the whole-cell configuration of the patch-clamp technique. The Cl- specificity of the conductance was assessed by manipulation of internal and external Cl- concentrations. The reversal potentials were in agreement with those predicted by the Nernst equation. Ca2+ ionophore A23187 and membrane depolarizations activated the Cl- conductance. However, a feedback effect of Cl- gradient modifications on Ca2+ movements was also observed in normal lactotrophs. In the latter, TRH (100 nM) mobilization of intracellular Ca2+ activated this Cl- conductance together with the potassium (K+) conductance when both ions were present in the intracellular medium (IM) or alone when K+ was absent. Chloride conductance was not activated in the GH3 cells, where mobilization of intracellular Ca2+ by TRH (100 nM) activated only Ca2(+)-dependent K+ conductance. It seems likely that the activation of Cl- conductance in these two different cell types involves different mechanisms.     

Temporal relationship between neurotransmitter release and ion flux during spreading depression and anoxia

Brain ion homeostasis is severely perturbed during spreading depression of Leao and during anoxia. The ionic composition of the extracellular space changes abruptly and approaches the intracellular concentrations owing to an increase in cell permeability. In spreading depression, synchronous transmitter efflux caused by a depolarization of the presynaptic terminals has been implicated as a possible mechanism that would explain the concomitant movement of ions. Anoxia, having many features in common with spreading depression, may follow the same mechanism. We have measured the concentrations of extracellular potassium with ion-selective microelectrodes and dopamine by in vivo voltammetry with carbon fiber microelectrodes during spreading depression and anoxia to compare the temporal relationship between the release of dopamine and ion movements in the striatum. There is a pronounced release of dopamine during both spreading depression and anoxia. In spreading depression, the sharp increase of potassium concentration that follows an initial smaller and slower increase of potassium is accompanied by the release of dopamine. In anoxia, the dopamine release clearly precedes the fast rise of extracellular potassium concentration. We conclude that in striatum, there is a pronounced dopamine release during spreading depression and anoxia, but that the relationships between ionic changes and transmitter release for these two phenomena are different and probably reflect different mechanisms.     

Saltatory propagation of Ca2+ waves by Ca2+ sparks.

Punctate releases of Ca2+, called Ca2+ sparks, originate at the regular array of t-tubules in cardiac myocytes and skeletal muscle. During Ca2+ overload sparks serve as sites for the initiation and propagation of Ca2+ waves in myocytes. Computer simulations of spark-mediated waves are performed with model release sites that reproduce the adaptive Ca2+ release observed for the ryanodine receptor. The speed of these waves is proportional to the diffusion constant of Ca2+, D, rather than D, as is true for reaction-diffusion equations in a continuous excitable medium. A simplified "fire-diffuse-fire" model that mimics the properties of Ca2+-induced Ca2+ release (CICR) from isolated sites is used to explain this saltatory mode of wave propagation. Saltatory and continuous wave propagation can be differentiated by the temperature and Ca2+ buffer dependence of wave speed.     

The Role of Cell Volume in the Dynamics of Seizure,Spreading Depression,and Anoxic Depolarization

Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics. We here performed the first detailed study of the effects of cell volume on neuronal dynamics. By incorporating cell swelling together with dynamic ion concentrations and oxygen supply into Hodgkin-Huxley type spiking dynamics, we demonstrate the spontaneous transition between epileptic seizure and spreading depression states as the cell swells and contracts in response to changes in osmotic pressure. Our use of volume as an order parameter further revealed a dynamical definition for the experimentally described physiological ceiling that separates seizure from spreading depression, as well as predicted a second ceiling that demarcates spreading depression from anoxic depolarization. Our model highlights the neuroprotective role of glial K buffering against seizures and spreading depression, and provides novel insights into anoxic depolarization and the relevant cell swelling during ischemia. We argue that the dynamics of seizures, spreading depression, and anoxic depolarization lie along a continuum of the repertoire of the neuron membrane that can be understood only when the dynamic ion concentrations, oxygen homeostasis,and cell swelling in response to osmotic pressure are taken into consideration. Our results demonstrate the feasibility of a unified framework for a wide range of neuronal behaviors that may be of substantial importance in the understanding of and potentially developing universal intervention strategies for these pathological states.     

Multi-ion conduction and selectivity in the high-conductance Ca++-activated K+ channel from skeletal muscle.

Open-channel ion permeation properties were investigated for Ca++-activated K+ (CaK) channels in solutions of K+ and its analogues T1+, Rb+, and NH4+. Single CaK channels were inserted into planar lipid bilayers composed of neutral phospholipids, and open-channel current-voltage (I-V) relations were measured in symmetrical and asymmetrical solutions of each of these individual ions. For all concentrations studied, the zero-voltage conductance falls in the sequence K+ greater than T1+ greater than NH4+ greater than Rb+. The shape of the I-V curve in symmetrical solutions of a single permeant ion is non-ohmic and is species-dependent. The I-V shape is sublinear for K+ and T1+ and superlinear for Rb+ and NH4+. As judged by reversal potentials under bi-ionic conditions with K+ on one side of the bilayer and the test cation on the other, the permeability sequence is T1+ greater than K+ greater than Rb+ greater than NH4+ at 300 mM, which differs from the conductance sequence. Symmetrical mixtures of K+ or NH4+ with Rb+ show a striking anomalous mole fraction behavior, i.e., a minimum in single-channel conductance when the composition of a two-ion mixture is varied at constant total ion concentration. This result is incompatible with present models that consider the CaK channel a single-ion pore. In total, the results show that the CaK channel finely discriminates among K+-like ions, exhibiting different energy profiles among these species, and that several such ions can reside simultaneously within the conduction pathway.     

Multiple actions of cadmium on transmitter release at the mouse neuromuscular junction

The action of cadmium ions on transmitter release was studied at the neuromuscular junction in mouse diaphragm. In the presence of raised K+, Cd2+ caused a parallel shift to the right of the graph of transmitter release rate (frequency of miniature end-plate potentials, fmepp) versus log [Ca2+], with no change in maximum or slope, indicating a competitive mode of action of Cd2+. The apparent dissociation constant for Cd2+ was 3 microM. In calcium-free solutions containing 15 mM K+, Cd2+ caused a rise in the fmepp, which subsequently slowly declined despite the continued presence of Cd2+. The rise in fmepp caused by Cd2+ could be interrupted, but not reversed, by washing out the Cd2+ with EDTA. Exposure of the preparation to 100 microM Cd2+ for 15 min or more resulted in a raised fmepp that persisted despite the removal of Cd2+ and exposure to 200 microM EDTA. Following such treatment, the graph of fmepp versus log [Ca2+] continued to be shifted to the right. The interaction of Ca2+ with the residual effect of Cd2+ indicates that Cd2+, in addition to its action to block Ca2+ entry into the terminal, may act as a competitor and perhaps as a partial agonist at intracellular sites that normally bind Ca2+ and govern transmitter release. If this is the case, then it must be supposed that, in raised K+, quantal release of transmitter represents intermittent intense activation of release sites with local high levels of Ca2+ rather than continuous low level activation.     

Protons resolve dual effects of calcium on miniature end-plate potential frequency at frog neuromuscular junctions

Inhibition of transmitter release by protons (H+) was studied at the frog neuromuscular junction at various extracellular concentrations of calcium ([Ca++]o) and potassium ([K+]o) by recording miniature end-plate potential (MEPP) frequency with the intracellular microelectrode. H+ decreased K+ -stimulated MEPP frequency. A double logarithmic graph of MEPP frequency at 7.5 mM K+ vs. [H+]o yielded a straight line with negative slope. At 10 mM K+, there was a parallel shift to the right of the graph. According to the surface charge model, K+ acts solely to depolarize the prejunctional membrane in accordance with the Nernst equation. By decreasing the prejunctional negative surface charge, H+ decreases K+ -stimulated MEPP frequency by decreasing [Ca++]o at the Ca++ channel. An estimated pKa of 4.20 may represent an acidic site at the Ca++ channel associated with Ca++ influx. As [Ca++]o increased above 1 mM for pH 7.40 and 10 mM K+, MEPP frequency decreased, i.e., the inhibitory component of dual effects of Ca++ occurred. At pH 6.40, the inhibitory component was abolished, unmasking the stimulatory effect of Ca++ on MEPP frequency. Reversal of Ca++ action by H+ could not be explained by surface charge theory alone. A double logarithmic graph of MEPP frequency vs. [K+]o at 8.5-10.5 mM was linear with a slope of 4. There were parallel shifts to the right of this graph for changes in pH from 7.40 to 6.90 and in [Ca++]o from 1 to 2.5 mM. These results are explained on the hypothesis that K+ also acts at an acidic prejunctional site to increase Ca++ -dependent quantal transmitter release. This action of K+ was inhibited by H+ and raised Ca++. Based on kinetic theory, the estimated pKa of the acidic prejunctional K+ site was 6.31. Based on free energy calculations, its cation preference was H+ greater than K+ greater than Ca++.     

Localization of the K+ lock-In and the Ba2+ binding sites in a voltage-gated calcium-modulated channel. Implications for survival of K+ permeability.

Using Ba2+ as a probe, we performed a detailed characterization of an external K+ binding site located in the pore of a large conductance Ca2+-activated K+ (BKCa) channel from skeletal muscle incorporated into planar lipid bilayers. Internal Ba2+ blocks BKCa channels and decreasing external K+ using a K+ chelator, (+)-18-Crown-6-tetracarboxylic acid, dramatically reduces the duration of the Ba2+-blocked events. Average Ba2+ dwell time changes from 10 s at 10 mM external K+ to 100 ms in the limit of very low [K+]. Using a model where external K+ binds to a site hindering the exit of Ba2+ toward the external side (Neyton, J., and C. Miller. 1988. J. Gen. Physiol. 92:549-568), we calculated a dissociation constant of 2.7 mircoM for K) at this lock-in site. We also found that BK(Ca) channels enter into a long-lasting nonconductive state when the external [K+] is reduced below 4 microM using the crown ether. Channel activity can be recovered by adding K+, Rb+, Cs+, or NH4+ to the external solution. These results suggest that the BK(Ca) channel stability in solutions of very low [K+] is due to K+ binding to a site having a very high affinity. Occupancy of this site by K+ avoids the channel conductance collapse and the exit of Ba2+ toward the external side. External tetraethylammonium also reduced the Ba2+ off rate and impeded the channel from entering into the long-lasting nonconductive state. This effect requires the presence of external K+. It is explained in terms of a model in which the conduction pore contains Ba2+, K+, and tetraethylammonium simultaneously, with the K+ binding site located internal to the tetraethylammonium site. Altogether, these results and the known potassium channel structure (Doyle, D.A., J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, and R. MacKinnon. 1998. Science. 280:69-77) imply that the lock-in site and the Ba2+ sites are the external and internal ion sites of the selectivity filter, respectively.     

Leptinotarsin-D, a neurotoxic protein, evokes neurotransmitter release from, and calcium flux into, isolated electric organ nerve terminals

Previous work has demonstrated that the neurotoxin leptinotarsin elicits release of neurotransmitter from mammalian nerve terminals, and it has been suggested that the toxin may act either as a direct agonist of voltage-sensitive calcium channels in these terminals (Crosland et al., 1984) or as a calcium ionophore (Madeddu et al., 1985a,b). Preliminary studies (Yeager et al., 1987) demonstrated that leptinotarsin also evokes transmitter release from isolated elasmobranch electric organ nerve terminals. We now report further investigations of the effects of leptinotarsin in this system. The action of the toxin is saturable, releasing about the same small fraction of total transmitter as that released by depolarization. An upper limit for the concentration for half maximal release is estimated to be 4 nM. Leptinotarsin-evoked transmitter release exhibits behavior very similar to depolarization-evoked release with respect to dependence on Ca2+, Ba2+, and Sr2+ and blockade by Co2+, Cd2+, and trifluoperazine. Leptinotarsin also promotes the uptake of calcium into synaptosomes to a degree similar to that caused by depolarization by K+. The binding of leptinotarsin to nerve terminals is probably Ca2+ dependent and receptor mediated. Taken together with the behavior of leptinotarsin-evoked release in other preparations, these results are consistent with the hypothesis that this toxin acts by opening a presynaptic calcium channel. However, the possibility that leptinotarsin is a calcium ionophore cannot be excluded.     

Characterization of the cyclic AMP-independent actions of somatostatin in GH cells. I. An increase in potassium conductance is responsible for both the hyperpolarization and the decrease in intracellular free calcium produced by somatostatin

The neuropeptide somatostatin causes membrane hyperpolarization and reduces the intracellular free calcium ion concentration ([Ca2+]i) in GH pituitary cells. In this study, we have used the fluorescent dyes bisoxonol (bis,-(1,3-diethylthiobarbiturate)-trimethineoxonol) and quin2 to elucidate the mechanisms by which these ionic effects are triggered. Addition of 100 nM somatostatin to GH4C1 cells caused a 3.4 mV hyperpolarization and a 26% decrease in [Ca2+]i within 30 s. These effects were not accompanied by changes in intracellular cAMP concentrations and occurred in cells containing either basal or maximally elevated cAMP levels. To determine which of the major permeant ions were involved in these actions of somatostatin, we examined its ability to elicit changes in the membrane potential and the [Ca2+]i when the transmembrane concentration gradients for Na+, Cl-, Ca2+, and K+ were individually altered. Substitution of impermeant organic ions for Na+ or Cl- did not block either the hyperpolarization or the decrease in [Ca2+]i induced by somatostatin. Decreasing extracellular Ca2+ from 1 mM to 250 nM abolished the reduction in [Ca2+]i but did not prevent the hyperpolarization response. These results show that hyperpolarization was not primarily due to changes in the conductances of Na+, Cl-, or Ca2+. Although the somatostatin-induced decrease in [Ca2+]i did require Ca2+ influx, it was independent of changes in Na+ or Cl- conductance. In contrast, elevating the extracellular [K+] from 4.6 to 50 mM completely blocked both the somatostatin-induced hyperpolarization and the reduction in [Ca2+]i. Furthermore, hyperpolarization of the cells with gramicidin mimicked the effect of somatostatin to decrease the [Ca2+]i and prevented any additional effect by the hormone. These results indicate that somatostatin increases a K+ conductance, which hyperpolarizes GH4C1 cells, and thereby secondarily decreases Ca2+ influx. Since the somatostatin-induced decrease in [Ca2+]i is independent of changes in intracellular cAMP levels, it may be responsible for somatostatin inhibition of hormone secretion by its cAMP-independent mechanism.     

Ionophore-induced oscillations in erythrocytes. A kinetic model

The kinetic model for K+, H+, Ca2+ concentrational self-oscillations in erythrocytes induced by A23187 and FCCP ionophores are considered. The model is based on the experimental data available and contains the minimal number of essential variables. The model was analysed by the method based on the graph representation of kinetic equations. The critical graph fragments provoking self-oscillatory trajectories in the system were revealed. It is shown that self-oscillatory behaviour is basically induced by conjugated processes produced by A23187. The parameter domain for self-oscillations is estimated including parameters of Ca2+-induced (through K+-channels) proton transport with FCCP participation. Numerical integration of kinetic equations was performed. The results obtained are in a good qualitative agreement with experimental data.     

根表面养分吸收通量和根围溶质浓度的近似解析解

该文用Nye-Tinker-Barber模型来研究植物根系表面的养分吸收通量和根围溶质浓度的近似解析解。将根围区域分为远场区域和近场区域, 在远场用相似变量, 在近场用尺度变换, 将远场解在根表面展开并与近场解进行待定函数的匹配, 从而获得对流扩散方程根表面通量和浓度的一阶近似解析解, 该解能够简化到扩散方程的解的形式。对氮、钾、硫、磷、镁、钙的养分吸收通量和氮、钾的浓度分别进行数值模拟, 比较模型的数值解、Roose的近似解析解和该文的近似解析解。结果表明: 在扩散方程中, 6种元素通量的解析解与Roose解析解相近, 但均高于数值解, 钾和磷的通量在短时间内迅速衰减; 钾和氮浓度的全局近似解析解与Roose解析解接近, 并与数值解的变化趋势一致。在对流扩散方程中, 除氮外的5种元素通量的近似解较Roose的解析解更接近于数值解, 且没有奇性。     

Calmodulin mediates calcium-dependent activation of the intermediate conductance KCa channel, IKCa1

Small and intermediate conductance Ca2+-activated K+ channels play a crucial role in hyperpolarizing the membrane potential of excitable and nonexcitable cells. These channels are exquisitely sensitive to cytoplasmic Ca2+, yet their protein-coding regions do not contain consensus Ca2+-binding motifs. We investigated the involvement of an accessory protein in the Ca2+-dependent gating of hIKCa1, a human intermediate conductance channel expressed in peripheral tissues. Cal- modulin was found to interact strongly with the cytoplasmic carboxyl (C)-tail of hIKCa1 in a yeast two-hybrid system. Deletion analyses defined a requirement for the first 62 amino acids of the C-tail, and the binding of calmodulin to this region did not require Ca2+. The C-tail of hSKCa3, a human neuronal small conductance channel, also bound calmodulin, whereas that of a voltage-gated K+ channel, mKv1.3, did not. Calmodulin co-precipitated with the channel in cell lines transfected with hIKCa1, but not with mKv1. 3-transfected lines. A mutant calmodulin, defective in Ca2+ sensing but retaining binding to the channel, dramatically reduced current amplitudes when co-expressed with hIKCa1 in mammalian cells. Co-expression with varying amounts of wild-type and mutant calmodulin resulted in a dominant-negative suppression of current, consistent with four calmodulin molecules being associated with the channel. Taken together, our results suggest that Ca2+-calmodulin-induced conformational changes in all four subunits are necessary for the channel to open.