Mathematical modelling of intra- and extracellular potentials generated by active structures: effects of a step change in structure diameter

A mathematical model developed in our laboratory is used to estimate and analyse extracellular potentials generated in a volume conductor by a geometrically inhomogeneous structure with a step increase or a step decrease in its diameter. The transmembrane potentials were calculated using the model of Hodgkin and Huxley (1952) and the method of Joyner et al. (1978). Variations in waveforms of the transmembrane and extracellular potentials were described and discussed. Differences in waveforms of the extracellular potentials and in declines of their components are due to changes in the source which generates these potentials. In case of a propagation block the peak-to-peak amplitude of the extracellular potentials calculated over the area of the block may be higher than that over the area of propagation of action potentials. The possible applications of the results to the analysis of extracellular potentials recorded around actual motoneurons during their orthodromic or antidromic activation are discussed.     

Mathematical modelling of intra- and extracellular potentials generated by active structures with short regions of increased diameter

The Hodgkin-Huxley (1952) model was used to calculate intracellular potentials by the method of Joyner et al. (1978). Extracellular potentials were estimated on the basis of a mathematical model proposed by us. It has shown that, irrespective of practical isopotentiality of the membrane of a local inhomogeneity, the latter affects extracellular potentials in two ways: 1) through changes in the potential profile in the region of the structure before the inhomogeneity; 2) through its own potential profile. The first effect is considerably greater than the second one, but the second is greater than the effect of the equal portion of the thin fibre. Increase in the diameter or length of an inhomogeneity is combined with such changes in the potential profile, that the effect of the inhomogeneity on the extracellular potential amplitude is practically independent of its actual size. The extracellular potential waveform substantially depends on the ratio of the diameters of the two parts of the structure and on the position of the inhomogeneity in relation to the sealed structure end. Registration of the positive-negative potentials having a large positive phase should not be considered as an indication of passive properties of the structure.     

Unique roles of SK and Kv4.2 potassium channels in dendritic integration

Focal activation of glutamate receptors in distal dendrites of hippocampal pyramidal cells triggers voltage-dependent Ca(2+) channel-mediated plateau potentials that are confined to the stimulated dendrite. We examined the role of dendritic K(+) conductances in determining the amplitude, duration, and spatial compartmentalization of plateau potentials. Manipulations that blocked SK-type Ca(2+)-activated K(+) channels, including apamin and BAPTA dialysis, increased the duration of plateau potentials without affecting their amplitude or compartmentalization. Manipulations that blocked Kv4.2 A-type K(+) channels, including a dominant-negative Kv4.2 construct and 4-aminopyridine, increased the amplitude of plateau potentials by allowing them to recruit neighboring dendrites. Prolongation of plateau potentials or block of Kv4.2 channels at branch points facilitated the ability of dendritic excitation to trigger fast action potentials. SK channels thus underlie repolarization of dendritic plateau potentials, whereas Kv4.2 channels confine these potentials to single dendritic branches, and both act in concert to regulate synaptic integration.     

Extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor

The extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor were studied. The spatial distribution of the transmembrane potential was obtained by integrating the system of partial differential equations characterizing the electric processes in the active myelinated nerve fiber. The spatial distribution of the extracellular potentials at various radial distances in the volume conductor were calculated using the line source model. Up to a certain radial distance (500 m) the discontinuity of the action potential propagation is reflected in the extracellular potentials, while further in the volume conductor the potentials are smooth. The effect of the fiber diameter and the internodal distance on the volume conductor potentials as well as the changes in the magnitude of the extracellular potential (in the time domain) between two adjacent nodes at various radial distances were studied. The radial decline of the peak-to-peak amplitude of the extracellular potential depends on the radial coordinater of the field point and increases with the increase ofr.     

Transmembrane outward hydrogen current in intracellularly perfused neurones of the snail Helix pomatia

The ionic nature and pharmacological properties of the outward current activated by membrane depolarization were studied on isolated neurones of the snail Helix pomatia, placed in Na+- and Ca2+-free extracellular solutions and intracellularly perfused with K+-free solution ("nonspecific outward current"). It was shown that the amplitude and reversal potential of this current (estimated from instantaneous current-voltage characteristics) are determined mainly by the transmembrane gradient for H+ ions. Lowering of pHi induced an increase in the current amplitude and a shift of the reversal potential to more negative values; the shift magnitude was comparable with that predicted for the hydrogen electrode. Raising pHi, as well as lowering pHo, induced a decrease in the current amplitude and a displacement of the current activation curve to more positive potentials. Addition of EGTA (8 mmol/l) to the intracellular perfusate did not affect the current amplitude. Extracellular 4-aminopyridine (10 mmol/l), verapamil (0.25 mmol/l) or Cd2+ (0.5 mmol/l) blocked the current. It is concluded that the current studied is carried mainly by H+ ions. In the same neurones the nature of the fast decay of the calcium inward current was also studied (in the presence of extracellular Ca2+ ions). This decay considerably slowed when pHi was raised or pHo was lowered, and it became less pronounced upon extracellular application of 4-aminopyridine or upon intracellular introduction of phenobarbital (4 mmol/l) and tolbutamide (3 mmol/l). It is suggested that the fast decay of the calcium inward current is due to activation of a Ca-sensitive component of the hydrogen current which depends on accumulation of Ca2+ ions. The possible physiological role of the transmembrane hydrogen currents is discussed.     

The transmembrane segment S6 determines cation versus anion selectivity of TRPM2 and TRPM8

TRPM2 and TRPM8, closely related members of the transient receptor potential (TRP) family, are cation channels activated by quite different mechanisms. Their transmembrane segments S5 and S6 are highly conserved. To identify common structures in S5 and S6 that govern interaction with the pore, we created a chimera in which the S5-pore-S6 region of TRPM8 was inserted into TRPM2, along with a lysine at each transition site. Currents through this chimera were induced by ADP-ribose (ADPR) in cooperation with Ca(2+). In contrast to wild-type TRPM2 channels, currents through the chimera were carried by Cl(-), as demonstrated in ion substitution experiments using the cation N-methyl-D-glucamine (NMDG) and the anion glutamate. Extracellular NMDG had no effects. The substitution of either intracellular or extracellular Cl(-) with glutamate shifted the reversal potential, decreased the current amplitude and induced a voltage-dependent block relieved by depolarization. The lysine in S6 was responsible for the anion selectivity; insertion of a lysine into corresponding sites within S6 of either TRPM2 or TRPM8 created anion channels that were activated by ADPR (TRPM2 I1045K) or by cold temperatures (TRPM8 V976K). The positive charge of the lysine was decisive for the glutamate block because the mutant TRPM2 I1045H displayed cation currents that were blocked at acidic but not alkaline intracellular pH values. We conclude that the distal part of S6 is crucial for the discrimination of charge. Because of the high homology of S6 in the whole TRP family, this new role of S6 may apply to further TRP channels.     

Action Potentials in Lupinus angustifolius L. Shoots: VI. PROPAGATION OF ACTION POTENTIAL IN THE STEM AFTER THE APPLICATION OF MECHANICAL BLOCK

The action potential (AP) in Lupinus stem was produced by electricalstimulation. The block was accomplished by tightening a nylonthread looped around the stem. The character of tissue damagein the blocked area was observed in microscopic sections. Itwas found that the AP propagation in the block and beyond dependedon the degree of compression, i. e. on the extent of damageto stem tissues within the block. With a slight tightening onlyAP ‘retardation’ occurs within the block. With astrong tightening, in which tissue damage reaches the externallayers of phloemcells, there is a total extinction or arrestof the AP in the block. Beyond the block there occur extrinsicpotentials (EPs) which have the character of electrotonic potentials.Under certain conditions the excitation may pass through sucha block. Then the AP propagation beyond the block reveals acomplex character. It may be assumed that AP propagation inthe Lupinus stem occurs on the principle of electrotonic currentswith the participation of many (probably all) cells of the primarycortex.     

Active electric properties of cardiac muscle

A model of electrical activity in the heart has been developed that treats the intracellular domain and the extracellular domain as electrical syncytia with anisotropic resistivities (bi-syncytial model). At the microscopic level, propagation is assumed to proceed primarily along the axes of individual cells. Considerations at the macroscopic level relate the transmembrane current to the intracellular and extracellular resistivity and the transmembrane potential. The result is a relationship between instantaneous extracellular potentials and cardiac action potentials.     

Voltage-dependent block of cardiac inward-rectifying potassium current by monovalent cations

The inward-rectifying K+ current (IK1) in cat ventricular myocytes, like inward-rectifying K+ currents in many other preparations, exhibited a negative slope conductance region at hyperpolarized membrane potentials that was time-dependent. This was evident as an inactivation of inward current elicited by hyperpolarizing voltage-clamp pulses resulting in a negative slope region of the steady-state current-voltage relationship at potentials negative to -140 mV. Removing extracellular Na+ prevented the development of the negative slope in this voltage region, suggesting that Na+ can block IK1 channels in a time- and voltage-dependent manner. The time and voltage dependence of Cs+-induced block of IK1 was also examined. Cs+ blocked inward current in a manner similar to that of Na+, but the former was much more potent. The fraction of current blocked by Cs+ in the presence of Na+ was reduced in a time- and voltage-dependent manner, which suggested that these blocking ions compete for a common or at least similar site of action. In the absence of Na+, inactivation of IK1 could also be induced by both Cs+ and Li+. However, Li+ was less potent than Na+ in this respect. Calculation of the voltage sensitivity of current block by each of these ions suggests that the mechanism of block by each is similar.     

Voltage-dependent block of the cystic fibrosis transmembrane conductance regulator Cl- channel by two closely related arylaminobenzoates

The gene defective in cystic fibrosis encodes a Cl- channel, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is blocked by diphenylamine-2-carboxylate (DPC) when applied extracellularly at millimolar concentrations. We studied the block of CFTR expressed in Xenopus oocytes by DPC or by a closely related molecule, flufenamic acid (FFA). Block of whole-cell CFTR currents by bath-applied DPC or by FFA, both at 200 microM, requires several minutes to reach full effect. Blockade is voltage dependent, suggesting open-channel block: currents at positive potentials are not affected but currents at negative potentials are reduced. The binding site for both drugs senses approximately 40% of the electric field across the membrane, measured from the inside. In single-channel recordings from excised patches without blockers, the conductance was 8.0 +/- 0.4 pS in symmetric 150 mM Cl-. A subconductance state, measuring approximately 60% of the main conductance, was often observed. Bursts to the full open state lasting up to tens of seconds were uninterrupted at depolarizing membrane voltages. At hyperpolarizing voltages, bursts were interrupted by brief closures. Either DPC or FFA (50 microM) applied to the cytoplasmic or extracellular face of the channel led to an increase in flicker at Vm = -100 mV and not at Vm = +100 mV, in agreement with whole-cell experiments. DPC induced a higher frequency of flickers from the cytoplasmic side than the extracellular side. FFA produced longer closures than DPC; the FFA closed time was roughly equal (approximately 1.2 ms) at -100 mV with application from either side. In cell-attached patch recordings with DPC or FFA applied to the bath, there was flickery block at Vm = -100 mV, confirming that the drugs permeate through the membrane to reach the binding site. The data are consistent with the presence of a single binding site for both drugs, reached from either end of the channel. Open-channel block by DPC or FFA may offer tools for use with site-directed mutagenesis to describe the permeation pathway.     

Non-Decaying postsynaptics potentials and delayed spikes in hippocampal pyramidal neurons generated by a zero slope conductance created by the persistent Na+ current

The negative slope conductance created by the persistent sodium current (I_NaP) prolongs the decay phase of excitatory postsynaptic potentials (EPSPs). In a recent study, we demonstrated that this effect was due to an increase of the membrane time constant. When the negative slope conductance opposes completely the positive slope conductances of the other currents it creates a zero slope conductance region. In this region the membrane time constant is infinite and the decay phase of the EPSPs is virtually absent. Here we show that non-decaying EPSPs are present in CA1 hippocampal pyramidal cells in the zero slope conductance region, in the suprathreshold range of membrane potential. Na⁺ channel block with tetrodotoxin abolishes the non-decaying EPSPs. Interestingly, the non-decaying EPSPs are observed only in response to artificial excitatory postsynaptic currents (aEPSCs) of small amplitude, and not in response to aEPSCs of big amplitude. We also observed concomitantly delayed spikes with long latencies and high variability only in response to small amplitude aEPSCs. Our results showed that in CA1 pyramidal neurons I_NaP creates non-decaying EPSPs and delayed spikes in the subthreshold range of membrane potentials, which could potentiate synaptic integration of synaptic potentials coming from distal regions of the dendritic tree.     

The effects of cations upon the action potentials recorded from neurohaemal tissue of the stick insect

Summary The ionic requirement for the action potentials recorded from the neurohaemal tissue on the lateral branch of the median nerve inCarausius morosus has been studied using extracellular electrodes. Sodium-free, magnesium-free, or calcium-free salines produce irreversible block of the action potentials following prolonged exposure to the nerves. Reducing the sodium concentration to 4 mM has little effect on the amplitude of the action potentials, whilst increasing the sodium concentration to 100 mM reduces the amplitude by 50%. Neither tetrodotoxin nor procaine has any effect on these action potentials.Reducing the magnesium concentration to 1 mM increases the amplitude of the action potentials, whilst increasing the concentration of magnesium reduces the amplitude.The amplitude of the action potentials is linearly related to the log of the external calcium concentration, and the action potentials are blocked by both cobalt ions and lanthanum ions.It is concluded that calcium is the major charge carrier of the inward current in these neurosecretory axons which is the first report of calcium dependent action potentials in a nerve axon. Furthermore, small amounts of sodium and magnesium are necessary to maintain electrical activity. Magnesium is a competitive inhibitor of the calcium currents.We are grateful to the Science Research Council for financial support, and to Mrs. J. Birch for the printing of the electron micrographs.     

Spermine and arcaine block and permeate N-methyl-D-aspartate receptor channels.

Polyamines such as spermine are thought to be endogenous regulators of NMDA (N-methyl-D-aspartate)-type glutamate receptors. Polyamine block of NMDA receptors was studied in excised outside-out patches from rat hippocampal neurons and Xenopus oocytes expressing recombinant receptors. Extracellular spermine and arcaine reduced NMDA single-channel conductance in a voltage-dependent manner, with partial relief of block evident at large inside negative membrane potentials. Reducing extracellular Na+ concentration increased the apparent affinities for spermine and arcaine, indicating strong interaction between spermine and permeant ions. Internal spermine also blocked NMDA channels in a voltage-dependent manner, with relief of block evident at large inside positive potentials. The Woodhull model of channel block by an impermeant ion adequately described the actions of external spermine from -60 to +60 mV, but failed for more negative potentials. Eyring rate theory for a permeable blocker with two barriers and one binding site adequately described the voltage-dependent block and relief from block by both external and internal spermine over the range of -120 to +60 mV. These findings indicate that polyamines block and permeate neuronal NMDA receptor channels from the extracellular and intracellular sides, although sensitivity to internal spermine is probably too low to be physiologically relevant.     

Sodium and calcium currents in action potentials of rat somatotrophs: their possible functions in growth hormone secretion

We report that both Na+ and Ca2+ currents are involved in the action potentials and in the hormone release from rat somatotrophs in primary culture. Single somatotrophs were identified by reverse hemolytic plaque assay (RHPA) and transmembrane voltage and currents were recorded using the whole-cell mode of the patch-clamp technique. Somatotrophs displayed a mean resting potential of -80mV and an average input resistance of 5.7G omega. Most of the cells showed spontaneous or evoked action potentials. Single action potentials or the initial spike in a burst were characterized by their high amplitude and short duration. Tetrodotoxin (TTX, 1 microM) blocked single action potentials and the initial spikes in a burst, whereas action potentials of long duration and low amplitude persisted. Cobalt (2 mM) plus TTX (1 microM) blocked all the action potentials. Voltage-clamp experiments confirmed the presence of both a TTX-sensitive Na+ current and Co2(+)-sensitive Ca2+ currents. TTX or Na(+)-free medium slightly decreased the basal release of GH but did not markedly modify hGRF-stimulated GH release. However, Co2+ (2 mM), which partially decreased the basal release, totally blocked hGRF-stimulated release. We conclude that (1) Na+ currents which initiate rapid action potentials may participate in spontaneous GH release; (2) Ca2+ currents, which give rise to long duration action potentials and membrane voltage fluctuation, are probably involved in both basal and hGRF-stimulated GH releases.     

Characterization of impulse propagation at the microscopic level across geometrically defined expansions of excitable tissue: multiple site optical recording of transmembrane voltage (MSORTV) in patterned growth heart cell cultures

Impulse propagation across sudden expansions of excitable tissue has been shown to exhibit various forms of conduction disturbance on a macroscopic scale, ranging from small delays to unidirectional or complete conduction block. With the present study, we attempted to characterize systematically the dependence of impulse propagation on the geometry of the underlying excitable tissue on a microscopic scale by investigating the spatio-temporal pattern of transmembrane voltage changes associated with impulse propagation from a narrow cell strand to a large cell area using multiple site optical recording of transmembrane voltage (MSORTV) in conjunction with patterned growth of neonatal rat heart cells in culture. While action potential propagation was smooth in the case of funneled expansions, delays of variable size occurred during propagation into rectangular or incised expansions. Close to the abrupt expansion, which functionally represented an increased electrical load to the narrow cell strand, the delays were accompanied by marked distortions of the action potential upstroke, exhibiting, in extreme cases, an initial depolarization to 50% followed by a delayed secondary depolarization to 100% of the full-signal amplitude. These distortions, which were based on bidirectional electrotonic interactions across the transition, were maximal immediately downstream from the expansion. The maximal slowing of impulse conduction across abrupt expansions was, in agreement with recently published results obtained from two-dimensional computer simulations, always situated in the expanded region. At high stimulation rates, the delays sometimes turned into intermittent unidirectional blocks, as revealed by reverse stimulation. These blocks were always characterized by a marked abbreviation of the action potentials upstream from the region causing the block which might, in an appropriate network, facilitate reentry because of the associated shortening of the refractory period. Because the patterns were composed of cells having identical membrane properties, the results show that the local action potential shape can be modulated profoundly by the two- dimensional architecture of the underlying cell ensemble alone.     

Hypertonicity triggers RhoA-dependent assembly of myosin-containing striated polygonal actin networks in endothelial cells

Electrical slow waves determine the timing and force of peristaltic contractions in the stomach. Slow waves originate from a dominant pacemaker in the orad corpus and propagate actively around and down the stomach to the pylorus. The mechanism of slow-wave propagation is controversial. We tested whether Ca(2+) entry via a voltage-dependent, dihydropyridine-resistant Ca(2+) conductance is necessary for active propagation in canine gastric antral muscles. Muscle strips cut parallel to the circular muscle were studied with intracellular electrophysiological techniques using a partitioned-chamber apparatus. Slow-wave upstroke velocity and plateau amplitude decreased from the greater to the lesser curvature, and this corresponded to a decrease in the density of interstitial cells of Cajal in the lesser curvature. Slow-wave propagation velocity between electrodes impaling cells in two regions of muscle and slow-wave upstroke and plateau were measured in response to experimental conditions that reduce the driving force for Ca(2+) entry or block voltage-dependent Ca(2+) currents. Nicardipine (0.1-1 microM) did not affect slow-wave upstroke or propagation velocities. Upstroke velocity, amplitude, and propagation velocity were reduced in a concentration-dependent manner by Ni(2+) (1-100 microM), mibefradil (10-30 microM), and reduced extracellular Ca(2+) (0.5-1.5 mM). Depolarization (by 10-15 mM K(+)) or hyperpolarization (10 microM pinacidil) also reduced upstroke and propagation velocities. The higher concentrations (or lowest Ca(2+)) of these drugs and ionic conditions tested blocked slow-wave propagation. Treatment with cyclopiazonic acid to empty Ca(2+) stores did not affect propagation. These experiments show that voltage-dependent Ca(2+) entry is obligatory for the upstroke phase of slow waves and active propagation.     

Sodium currents in toad cardiac pacemaker cells

Cells in the pacemaker region of toad (Bufo marinus) sinus venosus had spontaneous rhythmic action potentials. The rate of firing of action potentials, the rate of diastolic depolarization and the maximum rate of rise of action potentials were reduced by TTX (10 nm to 1 m). Currents were recorded with the whole cell, tight seal technique from cells enzymatically dissociated from this region. Cells studied were identified as pacemaker cells by their characteristic morphology, spontaneous rhythmic action potential activity that could be blocked by cobalt but not by TTX and lack of inward rectification. When calcium, potassium and nonselective cation currents (I_f) activated by hyperpolarization were blocked, depolarization was seen to generate transient and persistent inward currents. Both were sodium currents: they were abolished by tetrodotoxin (10 to 100 nm), their reversal potential was close to the sodium equilibrium potential and their amplitude and reversal potential were influenced as expected for sodium currents when extracellular sodium ions were replaced with choline ions. The transient sodium current was activated at potentials more positive than –40 mV while the persistent sodium current was obvious at more negative potentials. It was concluded that, in toad pacemaker cells, TTX-sensitive sodium currents contributing both to the upstroke of action potentials and to diastolic depolarization may play an important role in setting heart rate.We thank the Australian National Heart Foundation for their support. D.A.S. is an NHMRC Senior Research Officer.     

Electrophysiological interaction through the interstitial space between adjacent unmyelinated parallel fibers.

The influence of interstitial or extracellular potentials on propagation usually has been ignored, often through assuming these potentials to be insignificantly different from zero, presumably because both measurements and calculations become much more complex when interstitial interactions are included. This study arose primarily from an interest in cardiac muscle, where it has been well established that substantial interstitial potentials occur in tightly packed structures, e.g., tens of millivolts within the ventricular wall. We analyzed the electrophysiological interaction between two adjacent unmyelinated fibers within a restricted extracellular space. Numerical evaluations made use of two linked core-conductor models and Hodgkin-Huxley membrane properties. Changes in transmembrane potentials induced in the second fiber ranged from nonexistent with large intervening volumes to large enough to initiate excitation when fibers were coupled by interstitial currents through a small interstitial space. With equal interstitial and intracellular longitudinal conductivities and close coupling, the interaction was large enough (induced Vm approximately 20 mV peak-to-peak) that action potentials from one fiber initiated excitation in the other, for the 40-microns radius evaluated. With close coupling but no change in structure, propagation velocity in the first fiber varied from 1.66 mm/ms (when both fibers were simultaneously stimulated) to 2.84 mm/ms (when the second fiber remained passive). Although normal propagation through interstitial interaction is unlikely, the magnitudes of the electrotonic interactions were large and may have a substantial modulating effect on function.     

Action potentials in human macrophages are calcium spikes

Transmembrane resting and action potentials measured with single and double microelectrode impalements of human monocyte-derived macrophages reveal that repetitive action potentials induced by depolarizing current pulses are sodium insensitive and calcium dependent. Neither amplitude, frequency of spiking, threshold nor rate of rise of the action potentials is altered by different levels of extracellular sodium, substitution of choline for sodium, or exposure to tetrodotoxin. Spiking activity is enhanced in high calcium, diminished in frequency and amplitude by lowered extracellular calcium and is blocked by cobalt and verapamil.