Theoretical simulation of the calcium action potential in squid giant synapse: Repetitive stimulation

A biophysical model of the experimentally observed calcium action potential (CAP) in squid giant synapse is proposed. Whereas the inclusion of the inward calcium current in the Hodgkin-Huxley model can generate the rising phase of CAP, to account for the observed termination of the action potential, a repolarizing process needs to be introduced. Adding a term representing Ca-activated K current, the observed features of CAP can be reproduced. However, one feature of CAP, namely the gradual shortening of the plateau duration on repetitive stimulation, cannot be simulated by this model. In this paper, it is proved that both the termination of the action potential and the gradual shortening of the plateau cannot be accounted for by inclusion of a single repolarizing process. One more repolarizing process, namely a slow voltage-dependent Ca-inactivation, is therefore proposed to account for all the observed features of CAP.     

Calcium-activated conductance in skate electroreceptors: current clamp experiments

When current clamped, skate electroreceptor epithelium produces large action potentials in response to stimuli that depolarize the lumenal faces of the receptor cells. With increasing stimulus strength these action potentials become prolonged. When the peak voltage exceeds about 140 mV the repolarizing phase is blocked until the end of the stimulus. Perfusion experiments show that the rising phase of the action potential results from an increase in calcium permeability in the lumenal membranes. Perfusion of the lumen with cobalt or with a zero calcium solution containing EGTA blocks the action potential. Perfusion of the lumen with a solution containing 10 mM Ca and 20 mM EGTA initially slows the repolarizing process at all voltages and lowers the potential at which it is blocked. With prolonged perfusion, repolarization is blocked at all voltages. When excitability is abolished by perfusion with cobalt, or with a zero calcium solution containing EGTA, no delayed rectification occurs. We suggest that repolarization during the action potential depends on an influx of calcium into the cytoplasm, and that the rate of repolarization depends on the magnitude of the inward calcium current. Increasingly large stimuli reduce the rate of repolarization by reducing the driving force for calcium, and then block repolarization by causing the lumenal membrane potential to exceed ECa. Changes in extracellular calcium affect repolarization in a manner consistent with the resulting change in ECa.     

Propagated repolarization in heart muscle

The effect of current flow on the transmembrane action potential of single fibers of ventricular muscle has been examined. Pulses of repolarizing current applied during the plateau of the action potential displace membrane potential much more than do pulses of depolarizing current. The application of sufficiently strong pulses of repolarizing current initiates sustained repolarization which persists after the end of the pulse. This sustained repolarization appears to propagate throughout the length of the fiber. Demonstration of propagated repolarization is made difficult by appearance of break excitation at the end of the repolarizing pulse. The thresholds for sustained repolarization and break excitation are separated by reducing the concentration of Ca⁺⁺ in the environment of the fiber. In fibers in such an environment it is easier to demonstrate apparently propagated repolarization and also, by further increase of the strength of the repolarizing current, to demonstrate graded break excitation.     

Electrotropic acetylcholine action on the mammalian auricle by means of the "phase plane" trajectories of the action potential

A single sucrose gap techniques has been used to study action potentials and phase plane trajectories of them in atrial trabeculae of the rabbit. Using polynomial representations of current-voltage relationships a model of membrane action potential of atrial myocardial fibres is described and allows an interpretation of recording data from the phase plane trajectories. Our findings show: 1. Increasing extracellular calcium concentration increases a potassium conductivity of the atrial membrane. 2. An anomalous rectification concerning repolarizing currents in atrial fibres decreases with increasing extracellular calcium. 3. Acetylcholine (3.10(-4) g.cm-3) abolishes the anomalous rectification. These results are discussed in relation to previous electrophysiological studies of negative electrotropic effects of acetylcholine in cardiac muscle.     

Action potentials of the mollusk giant neuron with changes in extracellular concentrations of sodium and calcium ions

The action potential (AP) of the giant neuron of the molluskPlanorbis corneus exhibits an increased sensitivity of the spike overshoot to external sodium concentration in solutions containing a significantly lowered concentration of calcium. These results suggest that during the AP both sodium and calcium ions may act as carriers of the inward-directed current. During repeated responses the role of calcium ions in AP generation increases while that of sodium decreases. A delay in repolarization can occasionally be observed at the beginning of the falling phase of the AP. This delay is considered to be a result of a decrease in efficiency of the repolarizing action of the outward potassium current due to competition from a current entering the cell at the time of the falling phase. Results suggest that the carrier of this inward current is calcium.A. A. Bogomolets' Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 1, No. 1, pp. 109–117, July–August, 1969.     

A Nonlinear Cable Framework for Bidirectional Synaptic Plasticity

Finding the rules underlying how axons of cortical neurons form neural circuits and modify their corresponding synaptic strength is the still subject of intense research. Experiments have shown that internal calcium concentration, and both the precise timing and temporal order of pre and postsynaptic action potentials, are important constituents governing whether the strength of a synapse located on the dendrite is increased or decreased. In particular, previous investigations focusing on spike timing-dependent plasticity (STDP) have typically observed an asymmetric temporal window governing changes in synaptic efficacy. Such a temporal window emphasizes that if a presynaptic spike, arriving at the synaptic terminal, precedes the generation of a postsynaptic action potential, then the synapse is potentiated; however if the temporal order is reversed, then depression occurs. Furthermore, recent experimental studies have now demonstrated that the temporal window also depends on the dendritic location of the synapse. Specifically, it was shown that in distal regions of the apical dendrite, the magnitude of potentiation was smaller and the window for depression was broader, when compared to observations from the proximal region of the dendrite. To date, the underlying mechanism(s) for such a distance-dependent effect is (are) currently unknown. Here, using the ionic cable theory framework in conjunction with the standard calcium based plasticity model, we show for the first time that such distance-dependent inhomogeneities in the temporal learning window for STDP can be largely explained by both the spatial and active properties of the dendrite.     

Voltage dependence of calcium current deactivation in the somatic membrane of mouse sensory neurons

Voltage dependence of the deactivation kinetics of calcium inward currents was investigated in the somatic membrane of murine spinal ganglia neurons. It was found that deactivation of high threshold calcium current has a slower component (=0.80–0.85 msec at a repolarizing potential of –80 mV) as well as the principal transient exponential component (130 sec at the same potential repolarizing level). A dissimilar relationship exists between amplitudes of the transient and slower exponential components, describing deactivation of high threshold calcium current and degree of activation of the depolarizing shift in membrane potential; the former dependence is expressed by a sigmoid and the latter by a V-shaped curve. The slower component of deactivation of high threshold current was inhibited substantially by perfusing the cell with a Tris-PO₄-containing solution. Low-threshold calcium tail current undergoes slower deactivation (=1.1–1.2 msec) at a repolarizing potential of –160 mV. A relationship between the time constant of low threshold current deactivation and the type of penetrating cation used was observed. A kinetic model of calcium current deactivation is suggested, taking account of the three different types of calcium channels, (one low and two high threshold) present in the somatic membrane.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 20, No. 2, pp. 185–193, March–April, 1988.     

Electrophysiological characterization of the hERG R56Q LQTS variant and targeted rescue by the activator RPR260243

Human Ether-à-go-go (hERG) channels contribute to cardiac repolarization, and inherited variants or drug block are associated with long QT syndrome type 2 (LQTS2) and arrhythmia. Therefore, hERG activator compounds present a therapeutic opportunity for targeted treatment of LQTS. However, a limiting concern is over-activation of hERG resurgent current during the action potential and abbreviated repolarization. Activators that slow deactivation gating (type I), such as RPR260243, may enhance repolarizing hERG current during the refractory period, thus ameliorating arrhythmogenicity with reduced early repolarization risk. Here, we show that, at physiological temperature, RPR260243 enhances hERG channel repolarizing currents conducted in the refractory period in response to premature depolarizations. This occurs with little effect on the resurgent hERG current during the action potential. The effects of RPR260243 were particularly evident in LQTS2-associated R56Q mutant channels, whereby RPR260243 restored WT-like repolarizing drive in the early refractory period and diastolic interval, combating attenuated protective currents. In silico kinetic modeling of channel gating predicted little effect of the R56Q mutation on hERG current conducted during the action potential and a reduced repolarizing protection against afterdepolarizations in the refractory period and diastolic interval, particularly at higher pacing rates. These simulations predicted partial rescue from the arrhythmic effects of R56Q by RPR260243 without risk of early repolarization. Our findings demonstrate that the pathogenicity of some hERG variants may result from reduced repolarizing protection during the refractory period and diastolic interval with limited effect on action potential duration, and that the hERG channel activator RPR260243 may provide targeted antiarrhythmic potential in these cases.     

Bilateral processing in chemical synapses with electrical 'ephaptic' feedback: a theoretical model

I have developed a detailed biophysical model of the chemical synapse which hosts voltage-dependent presynaptic ion channels and takes into account the capacitance of synaptic membranes. I find that at synapses with a relatively large cleft resistance (e.g., mossy fiber or giant calyx synapse) the rising postsynaptic current could activate, within the synaptic cleft, electrochemical phenomena that induce rapid widening of the presynaptic action potential (AP). This mechanism could boost fast Ca(2+) entry into the terminal thus increasing the probability of subsequent synaptic releases. The predicted difference in the AP waveforms generated inside and outside the synapse can explain the previously unexplained fast capacitance transient recorded in the postsynaptic cell at the giant calyx synapse. I propose therefore the mechanism of positive ephaptic feedback that acts between the postsynaptic and presynaptic cell contributing to the basal synaptic transmission at large central synapses. This mechanism could also explain the supralinear voltage dependence of EPSCs recorded at hyperpolarizing membrane potentials in low extracellular calcium concentration.     

Spine calcium transients induced by synaptically-evoked action potentials can predict synapse location and establish synaptic democracy

CA1 pyramidal neurons receive hundreds of synaptic inputs at different distances from the soma. Distance-dependent synaptic scaling enables distal and proximal synapses to influence the somatic membrane equally, a phenomenon called "synaptic democracy". How this is established is unclear. The backpropagating action potential (BAP) is hypothesised to provide distance-dependent information to synapses, allowing synaptic strengths to scale accordingly. Experimental measurements show that a BAP evoked by current injection at the soma causes calcium currents in the apical shaft whose amplitudes decay with distance from the soma. However, in vivo action potentials are not induced by somatic current injection but by synaptic inputs along the dendrites, which creates a different excitable state of the dendrites. Due to technical limitations, it is not possible to study experimentally whether distance information can also be provided by synaptically-evoked BAPs. Therefore we adapted a realistic morphological and electrophysiological model to measure BAP-induced voltage and calcium signals in spines after Schaffer collateral synapse stimulation. We show that peak calcium concentration is highly correlated with soma-synapse distance under a number of physiologically-realistic suprathreshold stimulation regimes and for a range of dendritic morphologies. Peak calcium levels also predicted the attenuation of the EPSP across the dendritic tree. Furthermore, we show that peak calcium can be used to set up a synaptic democracy in a homeostatic manner, whereby synapses regulate their synaptic strength on the basis of the difference between peak calcium and a uniform target value. We conclude that information derived from synaptically-generated BAPs can indicate synapse location and can subsequently be utilised to implement a synaptic democracy.     

The role of cyclic AMP in the modulation of synaptic efficacy.

1. Heterosynaptic facilitation (modification of synaptic transmission by a neuron influencing the terminals of the presynaptic neuron) was studied in the pleural ganglion of Aplysia. Among several identified synapses, heterosynaptic facilitation was observed only in one type (EIPSP synapses) when repetitive stimulation was applied to the tentacular nerve or to a particular identified neuron. 2. Serotonin was shown to increase the amplitude of the EIPSP at this synapse; this facilitatory effect was prolonged in the presence of theophylline and mimicked by cyclic AMP. 3. When transmission was abolished by calcium-free solution, calcium injected in the region of the synapse caused partial recovery of the EIPSP; when calcium injection was preceded by serotonin injection near the same terminal, the EIPSP was much larger than with calcium injection alone. 4. It was concluded that the activation of one neuron (the heterosynaptic neuron) caused it to release serotonin, which activated an adenylate cyclase in the pre-synaptic terminals of another neuron. Consequent accumulation of cyclic AMP in these terminals is supposed to have increased their voltage-dependent calcium conductance and hence the amount of transmitter released during an action potential.     

Effect of changes in action potential shape on calcium currents and transmitter release in a calyx-type synapse of the rat auditory brainstem

We studied the relation between the size of presynaptic calcium influx and transmitter release by making simultaneous voltage clamp recordings from presynaptic terminals, the calyces of Held and postsynaptic cells, the principal cells of the medical nucleus of the trapezoid body, in slices of the rat brainstem. Calyces were voltage clamped with different action potential waveforms. The amplitude of the excitatory postsynaptic currents depended supralinearly on the size of the calcium influx, in the absence of changes in the time-course of the calcium influx. This result is in agreement with the view that at this synapse most vesicles are released by the combined action of multiple calcium channels.     

Calcium-activated chloride channels (CaCCs) regulate action potential and synaptic response in hippocampal neurons

Central neurons respond to synaptic inputs from other neurons by generating synaptic potentials. Once the summated synaptic potentials reach threshold for action potential firing, the signal propagates leading to transmitter release at the synapse. The calcium influx accompanying such signaling opens calcium-activated ion channels for feedback regulation. Here, we report a mechanism for modulating hippocampal neuronal signaling that involves calcium-activated chloride channels (CaCCs). We present evidence that CaCCs reside in hippocampal neurons and are in close proximity of calcium channels and NMDA receptors to shorten action potential duration, dampen excitatory synaptic potentials, impede temporal summation, and raise the threshold for action potential generation by synaptic potential. Having recently identified TMEM16A and TMEM16B as CaCCs, we further show that TMEM16B but not TMEM16A is important for hippocampal CaCC, laying the groundwork for deciphering the dynamic CaCC modulation of neuronal signaling in neurons important for learning and memory.     

The dependence of calcium-activated potassium currents on membrane potential.

Previous experiments on cholinergic synapses in chick cochlear hair cells have shown that calcium entering through acetylcholine-activated synaptic channels in turn activates calcium-dependent potassium currents, resulting in synaptic inhibition. In voltage-clamp experiments such currents would be expected to increase with depolarization (as the driving force for potassium entry is increased) and then decrease towards zero as the membrane approaches the calcium equilibrium potential (when calcium entry is suppressed). In the hair cells, however, such currents approached zero at about +20 mV, more than 170 mV negative to the calcium equilibrium potential. Another feature of the synapse is its post-junctional morphology: a uniform 20 nm cleft is formed between the postsynaptic membrane and the outermost membrane of an underlying cisterna. Here we present a model in which synaptic activation results in calcium influx into the subsynaptic cleft and thence into the bulk of the cytoplasm. The model suggests that the voltage dependence of the calcium-activated potassium current can be accounted for by only two basic assumptions: (i) entry of calcium through the activated synaptic channels by simple diffusion; and (ii) activation of the potassium channels by the cooperative action of four calcium ions. In addition, the model suggests that during activation the calcium concentration in the restricted subsynaptic space can reach levels adequate to activate the potassium channels, without requiring additional, more complicated, considerations (for example, secondary calcium release from the cisterna).     

Exocytotic dynamics and calcium cooperativity effects in the calyx of Held synapse: a modelling study

A stochastic computational approach to the study of secretory processes at the calyx of Held synapse is presented in this paper. The calyx of Held is a giant synapse located in the brainstem which is widely used for experimental recording of neurotransmitter release. We focus on the study of the exocytotic dynamics for a pool of readily releasable vesicles using a Monte Carlo simulation scheme that includes models for the P-type calcium channels, the kinetic reactions of endogenous and exogenous (mobile) buffers, the kinetic reactions for the secretory vesicles, as well as the microscopic diffusion of mobile buffers and calcium ions. The simulations are performed in a 3-D orthogonal grid which approximates a cylindrical domain representing an active zone of the presynaptic terminal of the calyx. For this domain, we quantify the release rates related to calcium currents in response to depolarizing voltage pulses. The influence on simulated pulse/action potential depolarization protocols of the kinetic scheme for the calcium sensor of vesicles and the geometry of calcium channels for the kinetic cooperativity for release, is analyzed at a microdomain level. Among other aspects, our results suggest that the spatial organization of Ca ^2 + channels could have measurable effects in the kinetic cooperativity which could reflect developing changes in the calyx of Held synapse.     

Calcium and the tonic release of transmitter at a non-impulsive synapse in the crab

Depolarization-transmitter release coupling was studied in the promotor stretch receptor/motoneuron synapse of the crab. Callinectes sapidus, a preparation in which presynaptic action potentials do not occur. Intracellular microelectrode recordings were made from the presynaptic terminal and from the somata of postsynaptic motoneurons while injecting current pulses into the peripheral stretch receptor dendrite with the aid of the sucrose-gap. 1. For short current pulses, the relationship between presynaptic potential and postsynaptic response was found to be similar to that demonstrated in the giant synapse of the squid stellate ganglion, indicating a common reliance on the properties of voltage-dependent calcium channels. 2. The crab synapse was found to be capable of continuous transmission in the range of seconds and minutes without the pronounced depletion of transmitter seen in the squid, and without inactivation of the release process (i.e., the calcium conductance is non-inactivating). 3. A graded, transient response to depolarising current in the presynaptic fibre was found to be calcium-dependent, and probably to reflect the presence of a separate, inactivating calcium conductance. 4. It was concluded that the graded response of the presynaptic membrane could function in helping to compensate for capacitative distortion of receptor potentials decrementally conducted in the sensory dendrite, and was therefore a specialisation for non-impulsive transmission.     

Control of action potential duration by calcium ions in cardiac Purkinje fibers

It is well known that cardiac action potentials are shortened by increasing the external calcium concentration (Cao). The shortening is puzzling since Ca ions are thought to carry inward current during the plateau. We therefore studied the effects of Cao on action potentials and membrane currents in short Purkinje fiber preparations. Two factors favor the earlier repolarization. First, calcium-rich solutions generally raise the plateau voltage; in turn, the higher plateau level accelerates time- and voltage-dependent current changes which trigger repolarization. Increases in plateau height imposed by depolarizing current consistently produced shortening of the action potential. The second factor in the action of Ca ions involves iK1, the background K current (inward rectifier). Raising Cao enhances iK1 and thus favors faster repolarization. The Ca-sensitive current change was identified as an increase in iK1 by virtue of its dependence on membrane potential and Ko. A possible third factor was considered and ruled out: unlike epinephrine, calcium-rich solutions do not enhance slow outward plateau current, ikappa. These results are surprising in showing that calcium ions and epinephrine act quite differently on repolarizing currents, even though they share similar effects on the height and duration of the action potential.     

Calcium-activated conductance in skate electroreceptors: voltage clamp experiments

Voltage clamp experiments allow further characterization of the calcium-dependent repolarizing process in skate electroreceptor epithelium. Four current components are described: a prolonged capacity current, a leakage current, an early active current which flows inward across the lumenal membranes of the receptor cells, and a late current which flows outward. The leakage and capacity currents are linear and may be substracted from the total current, giving net active currents. The early active current is carried by calcium and does not undergo inactivation for at least several seconds. When large stimuli exceed the reversal potential for the early calcium current, the late current is suppressed. Reduction of the ionized calcium concentration in the lumen lowers the reversal potential for the early current and the suppression potential for the late current by the same amount. We conclude that the late current is initiated by a calcium influx into the cytoplasm. During pulses of moderate duration, activation of the late current does not begin until a fixed amount of calcium has entered the receptor cells. The required amount of calcium is reduced if a recent calcium influx has occurred. We suggest that the calcium-activated outward current is mediated by a distinct macromolecule that is insensitive to voltage. Such macromolecules are likely to have an important role in the regulation of electrical activity in excitable cells.     

Modeling synaptic transmission of the tripartite synapse

The tripartite synapse denotes the junction of a pre- and postsynaptic neuron modulated by a synaptic astrocyte. Enhanced transmission probability and frequency of the postsynaptic current-events are among the significant effects of the astrocyte on the synapse as experimentally characterized by several groups. In this paper we provide a mathematical framework for the relevant synaptic interactions between neurons and astrocytes that can account quantitatively for both the astrocytic effects on the synaptic transmission and the spontaneous postsynaptic events. Inferred from experiments, the model assumes that glutamate released by the astrocytes in response to synaptic activity regulates store-operated calcium in the presynaptic terminal. This source of calcium is distinct from voltage-gated calcium influx and accounts for the long timescale of facilitation at the synapse seen in correlation with calcium activity in the astrocytes. Our model predicts the inter-event interval distribution of spontaneous current activity mediated by a synaptic astrocyte and provides an additional insight into a novel mechanism for plasticity in which a low fidelity synapse gets transformed into a high fidelity synapse via astrocytic coupling.     

Effect of ouabain on mechanical and electrical properties of rat and guinea pig hearts at 180 C.

The effects of ouabain 10(-6) M on rat and guinea pig hearts have been studied at 18 degrees C, in order to reduce almost fully both the Na+, K+-dependent ATPase activity and the ouabain induced inhibition of this enzyme. In isolated guinea pig hearts the positive inotropic response to ouabain obtained at 32 degrees C disappeared at 18 degrees C. On the contrary, the contractile strength of rat hearts was slightly reduced by ouabain and in the same manner at both temperatures. Current and voltage clamp experiments carried out at 18 degrees C in ventricular fibres revealed that ouabain 10(-6) M decreased both the action potential overshoot and the fast sodium current in rat and guinea pig, by reduction of the membrane sodium conductance. Ouabain did not change the calcium current in guinea pig preparations, whereas in rat heart muscle this current was reduced. The effects of ouabain on both the action potential plateau and outward repolarizing current indicated some inconsistencies from preparation to preparation and cannot therefore be considered as significant. The persistence of the ouabain induced alterations of g Na (in rat and guinea pig) and calcium current (in rat) at 18 degrees C supports the hypothesis of two ouabain cell receptors in heart muscle.