Time Constants and Electrotonic Length of Membrane Cylinders and Neurons

A theoretical basis is provided for the estimation of the electrotonic length of a membrane cylinder, or the effective electrotonic length of a whole neuron, from electrophysiological experiments. It depends upon the several time constants present in passive decay of membrane potential from an initially nonuniform distribution over the length. In addition to the well known passive membrane time constant, τ_m = R_mC_m, observed in the decay of a uniform membrane potential, there exist many smaller time constants that govern rapid equalization of membrane potential over the length. These time constants are present also in the transient response to a current step applied across the membrane at one location, such as the neuron soma. Similar time constants are derived when a lumped soma is coupled to one or more cylinders representing one or more dendritic trees. Different time constants are derived when a voltage clamp is applied at one location; the effects of both leaky and short-circuited termination are also derived. All of these time constants are demonstrated as consequences of mathematical boundary value problems. These results not only provide a basis for estimating electrotonic length, L = [unk]/λ, but also provide a new basis for estimating the steady-state ratio, ρ, of cylinder input conductance to soma membrane conductance.     

Electrotonic measurements by electric field-induced polarization in neurons: theory and experimental estimation

We present a theory for estimation of the dendritic electrotonic length constant and the membrane time constant from the transmembrane potential (TMP) induced by an applied electric field. The theory is adapted to morphologically defined neurons with homogeneous passive electric properties. Frequency characteristics and transients at the onset and offset of the DC field are considered. Two relations are useful for estimating the electrotonic parameters: 1) steady-state polarization versus the dendritic electrotonic length constant; 2) membrane time constant versus length constant. These relations are monotonic and may provide a unique estimate of the electrotonic parameters for 3D-reconstructed neurons. Equivalent tip-to-tip electrotonic length of the dendritic tree was estimated by measuring the equalization time of the field-induced TMP. For 11 turtle spinal motoneurons, the electrotonic length from tip to tip of the dendrites was in the range of 1-2.5 lambda, whereas classical estimation using injection of current pulses gave an average dendrite length of 0.9-1.1 lambda. For seven ventral horn interneurons, the estimates were 0.7-2.6 lambda and 0.6-0.9 lambda, respectively. The measurements of the field-induced polarization promise to be a useful addition to the conventional methods using microelectrode stimulation.     

Functional diversity of motoneuron dendrites: by accident or design?

The distribution and geometry of the dendritic trees of spinal motoneurons obey several well-established rules. Some of these rules are based on systematic relationships between quantitative geometrical features (e.g. total dendritic length) and the three-dimensional trajectory followed by dendrites from their origin to their termination. Since dendritic geometry partially determines the transmission of current and voltage signals generated by synapses on the dendritic tree, our goal was to compare the efficacy of signal transmission by dendritic trajectories that followed different directions. To achieve this goal, we constructed detailed compartmental models of the dendritic trees of intracellularly stained neck motoneurons and calculated the electrotonic properties of each soma-to-terminal trajectory. These properties displayed a high degree of variability. To determine if this variability was due, in part, to the orientation (e.g. rostral, rostral-dorsal-lateral) of the trajectory, each trajectory was classified according to its orientation. The attenuation of current and voltage signals en route to the soma were strongly related to trajectory orientation. Trajectories with similar attenuation factors formed functional subunits that were arranged in distinct domains within the ventral horn. The difference in the efficacy of signal transmission between subunits was increased by activation of neighbouring synapses due to trajectory-related differences in non-linear summation. These results indicate that the input-output properties of motoneurons depend on the direction of the path taken by dendrites from their origin at the cell body to their terminals.     

The somatic shunt cable model for neurons.

The derivation of the equations for an electrical model of nerve cells is presented. The model consists of an equivalent cylinder, a lumped somatic impedance, and a variable shunt at the soma. This shunt was introduced to take into account the fast voltage decays observed following the injections of current pulses in some motoneurons and hippocampal granule cells that could not be explained by existing models. The shunt can be interpreted either by penetration damage with the electrode or by a lower membrane specific resistance at the soma than in the dendrites. A solution of the model equations is presented that allows the estimation of the electrotonic length L, the membrane time constant tau m, the dendritic dominance ratio rho, and the shunt parameter epsilon, based only on the measurement of the first two coefficients and time constants in the multiexponential voltage response to injected current pulses.     

Voltage Clamp of Cardiac Muscle in a Double Sucrose Gap: A Feasibility Study

A method of stabilizing the membrane potential of a small area of cardiac muscle membrane and the limitations of this method are described. Tiny bundles or strands, approximately 80 μm in diameter, of electrically interconnected fibers from the ventricles of rabbit hearts were used in a double sucrose gap. Current records associated with step changes in voltage were complicated by two capacitive surges of current of nodal and nonnodal origin and large “leakage” currents of nonnodal origin resulting mainly from the multifibered nature of the preparation and emphasized by the method. The transient, inward membrane currents in response to moderate depolarizing steps in command potential had the same duration as the upstroke of the action potential. In good runs, currents were smooth and free from notches. These initial currents behaved qualitatively like the initial sodium currents in squid axon and in other excitable membranes. A fraction of the initial sodium current persisted at least as long as 300 ms. The relationship between peak initial current and voltage was graded and linear in the positive direction. In the negative region the relationship was often very steep, indicating insufficient voltage control of all the membranes despite the squareness of the voltage record. Other indications of inadequacy of control could occur and thus even with this optimum preparation of cardiac muscle it was not feasible to analyze quantitatively either the initial or the prolonged sodium currents.     

Dynamic modification of dendritic cable properties and synaptic transmission by voltage-gated potassium channels

Computer simulations of a dendrite possessing voltage-sensitive potassium conductances were used to determine the effects of these conductances on synaptic transmission and on the propagation of synaptic signals within the dendritic tree. Potassium conductances had two principal effects on voltage transients generated by current injections or synaptic conductances. Locally (near the source of the transient), voltage-gated potassium channels produced a potassium shunt current that reduced the amplitude of voltage transients generated by depolarizing currents. This shunt current increased as the amplitude of the depolarizing transient increased and so acted to prevent large synaptic transients from reaching levels that would saturate due to a reduction in driving force. In the presence of rapidly activating potassium currents, excitatory synapses produced larger synaptic currents that were more linearly related to synaptic conductance, but these produced smaller voltage transients. The maximum amplitudes of the voltage transients were limited by the voltage sensitivity of the K⁺ conductance and the rate at which it could activate. Sufficiently rapid synaptic currents could outrun the K⁺ conductance and thus achieve high local peak amplitudes. These effects of K⁺ conductances were unrelated to whether they were located on dendrites or not, being related only to their proximity to the source of synaptic current. The second class of effects of K⁺ conductances depended on their alteration of the electrotonic structure of the postsynaptic cell and so were observed only when they were located on postsynaptic dendrites. Voltage-gated K⁺ conductances produced voltage-dependent electrotonic expansion of depolarized dendrites, which had the effect of isolating synaptic inputs on depolarized dendrites from events on the rest of the neuron. Thus, synapses on the same dendrite interacted destructively to a degree much greater than that expected from the classical driving force nonlinearity. Synapses located proximally to a depolarized dendritic region were less effected than those located distally, and the range of the nonlinear interaction between synapses was dependent on the kinetics of activation and deactivation of the conductance. When present in conjunction with rapidly activating dendritic sodium conductance, the potassium conductance sharpened the requirement for spatial and temporal coincidence to produce synaptic boosting by inward currents, and suppressed out-of-synchrony synaptic inputs.     

Voltage-Driven Translocation of DNA through a High Throughput Conical Solid-State Nanopore

Nanopores have become an important tool for molecule detection at single molecular level. With the development of fabrication technology, synthesized solid-state membranes are promising candidate substrates in respect of their exceptional robustness and controllable size and shape. Here, a 30–60 (tip-base) nm conical nanopore fabricated in 100 nm thick silicon nitride (Si₃N₄) membrane by focused ion beam (FIB) has been employed for the analysis of λ-DNA translocations at different voltage biases from 200 to 450 mV. The distributions of translocation time and current blockage, as well as the events frequencies as a function of voltage are investigated. Similar to previously published work, the presence and configurations of λ-DNA molecules are characterized, also, we find that greater applied voltages markedly increase the events rate, and stretch the coiled λ-DNA molecules into linear form. However, compared to 6–30 nm ultrathin solid-state nanopores, a threshold voltage of 181 mV is found to be necessary to drive DNA molecules through the nanopore due to conical shape and length of the pore. The speed is slowed down ∼5 times, while the capture radius is ∼2 fold larger. The results show that the large nanopore in thick membrane with an improved stability and throughput also has the ability to detect the molecules at a single molecular level, as well as slows down the velocity of molecules passing through the pore. This work will provide more motivations for the development of nanopores as a Multi-functional sensor for a wide range of biopolymers and nano materials.     

Voltage and Current Clamp Transients with Membrane Dielectric Loss

Transient responses of a space-clamped squid axon membrane to step changes of voltage or current are often approximated by exponential functions of time, corresponding to a series resistance and a membrane capacity of 1.0 μF/cm². Curtis and Cole (1938, J. Gen. Physiol. 21:757) found, however, that the membrane had a constant phase angle impedance z = z₁(jωτ)^-α, with a mean α = 0.85. (α = 1.0 for an ideal capacitor; α < 1.0 may represent dielectric loss.) This result is supported by more recently published experimental data. For comparison with experiments, we have computed functions expressing voltage and current transients with constant phase angle capacitance, a parallel leakage conductance, and a series resistance, at nine values of α from 0.5 to 1.0. A series in powers of t^α provided a good approximation for short times; one in powers of t^-α, for long times; for intermediate times, a rational approximation matching both series for a finite number of terms was used. These computations may help in determining experimental series resistances and parallel leakage conductances from membrane voltage or current clamp data.     

A minimal,compartmental model for a dendritic origin of bistability of motoneuron firing patterns

Various nonlinear regenerative responses, including plateau potentials and bistable repetitive firing modes, have been observed in motoneurons under certain conditions. Our simulation results support the hypothesis that these responses are due to plateau-generating currents in the dendrites, consistent with a major role for a noninactivating calcium L-type current as suggested by experiments. Bistability as observed in the soma of low- and higher-frequency spiking or, under TTX, of near resting and depolarized plateau potentials, occurs because the dendrites can be in a near resting or depolarized stable steady state. We formulate and study a two-compartment minimal model of a motoneuron that segregates currents for fast spiking into a soma-like compartment and currents responsible for plateau potentials into a dendrite-like compartment. Current flows between compartments through a coupling conductance, mimicking electrotonic spread. We use bifurcation techniques to illuminate how the coupling strength affects somatic behavior. We look closely at the case of weak coupling strength to gain insight into the development of bistable patterns. Robust somatic bistability depends on the electrical separation since it occurs only for weak to moderate coupling conductance. We also illustrate that hysteresis of the two spiking states is a natural consequence of the plateau behavior in the dendrite compartment.     

Dendritic analysis of lobster stretch receptor neurons: Electrotonic properties with single and distributed inputs

Using steady-state cable analysis as derived by Rall, electrotonic properties of the dendritic trees of the tonic stretch receptor neuron of the spiny lobster, Panulirus interruptus,have been examined. By directly measuring the somatic input resistance and by visualizing the dendritic trees of this neuron by backfilling the axon with cobalt, the electrotonic properties of the dendritic trees have been derived. The calculated membrane resistivity is 800-3600 -cm ². Voltage and current transfer functions were calculated for (a) single dendritic tips the size observed in the cobalt preparations and (b) for processes 2 µm or smaller, as observed in electron microscopy. Current transfer to the soma was high in both cases (greater than 80%). Voltage transfer was 22% for large and 4% for small dendrites. When a more natural simultaneous conductance change at the tips of all major dendrites was modeled, voltage transfer was 84% and current transfer 56%. But the dynamic range of the cell (rheobase to saturation) is well-predicted by varying the simultaneous inputs, not by scaling up a single input, thus illustrating that convenient indices of electrotonic properties may not prove useful in appreciating the integrative properties of a neuron.     

Voltage-imaging and simulation of effects of voltage- and agonist-activated conductances on soma-dendritic voltage coupling in cerebellar Purkinje cells

We investigated the spread of membrane voltage changes from the soma into the dendrites of cerebellar Purkinje cells by using voltage-imaging techniques in combination with intracellular recordings and by performing computer simulations using a detailed compartmental model of a cerebellar Purkinje cell. Fluorescence signals from single Purkinje cells in cerebellar cultures stained with the styryl dye di-4-ANEPPS were detected with a 10 × 10 photodiode array and a charge coupled device (CCD). Fluorescence intensity decreased and increased with membrane depolarization and hyperpolarization, respectively. The relation between fractional fluorescence change (F/F) and membrane potential could be described by a linear function with a slope of up to – 3%/100 mV. Hyperpolarizing and depolarizing voltage jumps applied to Purkinje cells voltage-clamped with an intrasomatic recording electrode induced dendritic dye signals, demonstrating that these voltage transients invaded the dendrites. Dye signals induced by depolarizing somatic voltage jumps were weaker in the dendrites, when compared with those induced by hyperpolarizing voltage jumps. Dendritic responses to hyperpolarizing voltage steps applied at the soma were attenuated when membrane conductance was increased by muscimol, an agonist for GABA_Areceptors.Corresponding experimental protocols were applied to a previously developed detailed compartmental model of a Purkinje cell. In the model, as in the electrophysiological recordings, voltage attenuation from soma to dendrites increased under conditions where membrane conductance is increased by depolarization or by activation of GABA_A receptors, respectively.We discuss how these results affect voltage clamp studies of synaptic currents and synaptic integration in Purkinje cells.     

Time-dependent Outward Currents through the Inward Rectifier Potassium Channel IRK1 : The Role of Weak Blocking Molecules

Outward currents through the inward rectifier K⁺ channel contribute to repolarization of the cardiac action potential. The properties of the IRK1 channel expressed in murine fibroblast (L) cells closely resemble those of the native cardiac inward rectifier. In this study, we added Mg²⁺ (0.44–1.1 mM) or putrescine (∼0.4 mM) to the intracellular milieu where endogenous polyamines remained, and then examined outward IRK1 currents using the whole-cell patch-clamp method at 5.4 mM external K⁺. Without internal Mg²⁺, small outward currents flowed only at potentials between −80 (the reversal potential) and ∼−40 mV during voltage steps applied from −110 mV. The strong inward rectification was mainly caused by the closed state of the activation gating, which was recently reinterpreted as the endogenous-spermine blocked state. With internal Mg²⁺, small outward currents flowed over a wider range of potentials during the voltage steps. The outward currents at potentials between −40 and 0 mV were concurrent with the contribution of Mg²⁺ to blocking channels at these potentials, judging from instantaneous inward currents in the following hyperpolarization. Furthermore, when the membrane was repolarized to −50 mV after short depolarizing steps (>0 mV), a transient increase appeared in outward currents at −50 mV. Since the peak amplitude depended on the fraction of Mg²⁺-blocked channels in the preceding depolarization, the transient increase was attributed to the relief of Mg²⁺ block, followed by a re-block of channels by spermine. Shift in the holding potential (−110 to −80 mV), or prolongation of depolarization, increased the number of spermine-blocked channels and decreased that of Mg²⁺-blocked channels in depolarization, which in turn decreased outward currents in the subsequent repolarization. Putrescine caused the same effects as Mg²⁺. When both spermine (1 μM, an estimated free spermine level during whole-cell recordings) and putrescine (300 μM) were applied to the inside-out patch membrane, the findings in whole-cell IRK1 were reproduced. Our study indicates that blockage of IRK1 by molecules with distinct affinities, spermine and Mg²⁺ (putrescine), elicits a transient increase in the outward IRK1, which may contribute to repolarization of the cardiac action potential.     

Regulation of the Epithelial Na+ Channel by Membrane Tension

The sensitivity of αβγ rat epithelial Na⁺ channel (rENaC) to osmotically or mechanically induced changes of membrane tension was investigated in the Xenopus oocyte expression system, using both dual electrode voltage clamp and cell-attached patch clamp methodologies. ENaC whole-cell currents were insensitive to mechanical cell swelling caused by direct injection of 90 or 180 nl of 100-mM KCl. Similarly, ENaC whole-cell currents were insensitive to osmotic cell swelling caused by a 33% decrease of bathing solution osmolarity. The lack of an effect of cell swelling on ENaC was independent of the status of the actin cytoskeleton, as ENaC remained insensitive to osmotic and mechanical cell swelling in oocytes pretreated with cytochalasin B for 2–5 h. This apparent insensitivity of ENaC to increased cell volume and changes of membrane tension was also observed at the single channel level in membrane patches subjected to negative or positive pressures of 5 or 10 in. of water. However, and contrary to the lack of an effect of cell swelling, ENaC currents were inhibited by cell shrinking. A 45-min incubation in a 260-mosmol solution (a 25% increase of solution osmolarity) caused a decrease of ENaC currents (at −100 mV) from −3.42 ± 0.34 to −2.02 ± 0.23 μA (n = 6). This decrease of current with cell shrinking was completely blocked by pretreatment of oocytes with cytochalasin B, indicating that these changes of current are not likely related to a direct effect of cell shrinking. We conclude that αβγ rENaC is not directly mechanosensitive when expressed in a system that can produce a channel with identical properties to those found in native epithelia.     

Phe-Met-Arg-Phe-amide Activates a Novel Voltage-dependent K+ Current through a Lipoxygenase Pathway in Molluscan Neurones

The neuropeptide Phe-Met-Arg-Phe-amide (FMRFa) dose dependently (ED₅₀ = 23 nM) activated a K⁺ current in the peptidergic caudodorsal neurones that regulate egg laying in the mollusc Lymnaea stagnalis. Under standard conditions ([K⁺]_o = 1.7 mM), only outward current responses occurred. In high K⁺ salines ([K⁺]_o = 20 or 57 mM), current reversal occurred close to the theoretical reversal potential for K⁺. In both salines, no responses were measured below −120 mV. Between −120 mV and the K⁺ reversal potential, currents were inward with maximal amplitudes at ∼−60 mV. Thus, U-shaped current–voltage relations were obtained, implying that the response is voltage dependent. The conductance depended both on membrane potential and extracellular K⁺ concentration. The voltage sensitivity was characterized by an e-fold change in conductance per ∼14 mV at all [K⁺]_o. Since this result was also obtained in nearly symmetrical K⁺ conditions, it is concluded that channel gating is voltage dependent. In addition, outward rectification occurs in asymmetric K⁺ concentrations. Onset kinetics of the response were slow (rise time ∼650 ms at −40 mV). However, when FMRFa was applied while holding the cell at −120 mV, to prevent activation of the current but allow activation of the signal transduction pathway, a subsequent step to −40 mV revealed a much more rapid current onset. Thus, onset kinetics are largely determined by steps preceding channel activation. With FMRFa applied at −120 mV, the time constant of activation during the subsequent test pulse decreased from ∼36 ms at −60 mV to ∼13 ms at −30 mV, confirming that channel opening is voltage dependent. The current inactivated voltage dependently. The rate and degree of inactivation progressively increased from −120 to −50 mV. The current is blocked by internal tetraethylammonium and by bath- applied 4-aminopyridine, tetraethylammonium, Ba²⁺, and, partially, Cd²⁺ and Cs⁺. The response to FMRFa was affected by intracellular GTPγS. The response was inhibited by blockers of phospholipase A₂ and lipoxygenases, but not by a cyclo-oxygenase blocker. Bath-applied arachidonic acid induced a slow outward current and occluded the response to FMRFa. These results suggest that the FMRFa receptor couples via a G-protein to the lipoxygenase pathway of arachidonic acid metabolism. The biophysical and pharmacological properties of this transmitter operated, but voltage-dependent K⁺ current distinguish it from other receptor-driven K⁺ currents such as the S-current- and G-protein-dependent inward rectifiers.     

Synaptic interaction between single motoneurons in the isolated frog spinal cord

The nature of synaptic interaction between two neighboring motoneurons in the isolated frog spinal cord was studied by parallel insertion of two separate micro-electrodes into the cells. In 82 of 89 motoneurons tested transmission through synapses between the motoneurons was electrical in nature, as shown by the absence or short duration of the latent period of elementary intermotoneuronal EPSPs, stability of their amplitude, and preservation of responses in Ca⁺⁺-free solution containing 2 mM Mn⁺⁺. Direct electrotonic interaction was demonstrated in both directions: artificial de- and hyperpolarization of one motoneuron led to corresponding shifts of membrane potential in the neighboring motoneuron. The time constant of rise and decay of this potential was appreciably greater than the time constant of the membrane of the two interconnected motoneurons. Blockade of the SD-component of the action potential in the "triggering" motoneuron led to a decrease in the elementary EPSP in the neighboring motoneuron. These facts suggest that electrotonic interaction takes place through dendro-dendritic junctions. Absence of rectification was demonstrated in electrical synapses between motoneurons. In four cases elementary EPSPs were chemical in nature, for they appeared 1.3–3.3 msec after the beginning of the action potential in the "triggering" motoneuron, and were blocked in Ca⁺⁺-free solution containing Mn⁺⁺; fluctuations of their amplitude approximated closely to a Poisson or binomial distribution. Such responses are evidently generated by synapses formed by recurrent axon collaterals of one motoneuron on the neighboring motoneurons. In three cases elementary intermotoneuronal EPSPs consisted of two components, the first electrical and the second chemical in nature. Morphological structures which may be responsible for generation of 2-component EPSPs are examined.Deceased.I. M. Sechenov Institute of Evolutionary Physiology and Biochemistry, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 16, No. 5, pp. 619–630, September–October, 1984.     

Quantification of Transmembrane Currents during Action Potential Propagation in the Heart

The measurement, quantitative analysis, theory, and mathematical modeling of transmembrane potential and currents have been an integral part of the field of electrophysiology since its inception. Biophysical modeling of action potential propagation begins with detailed ionic current models for a patch of membrane within a distributed cable model. Voltage-clamp techniques have revolutionized clinical electrophysiology via the characterization of the transmembrane current gating variables; however, this kinetic information alone is insufficient to accurately represent propagation. Other factors, including channel density, membrane area, surface/volume ratio, axial conductivities, etc., are also crucial determinants of transmembrane currents in multicellular tissue but are extremely difficult to measure. Here, we provide, to our knowledge, a novel analytical approach to compute transmembrane currents directly from experimental data, which involves high-temporal (200 kHz) recordings of intra- and extracellular potential with glass microelectrodes from the epicardial surface of isolated rabbit hearts during propagation. We show for the first time, to our knowledge, that during stable planar propagation the biphasic total transmembrane current (I_m) dipole density during depolarization was ∼0.25 ms in duration and asymmetric in amplitude (peak outward current was ∼95 μA/cm² and peak inward current was ∼140 μA/cm²), and the peak inward ionic current (I_ion) during depolarization was ∼260 μA/cm² with duration of ∼1.0 ms. Simulations of stable propagation using the ionic current versus transmembrane potential relationship fit from the experimental data reproduced these values better than traditional ionic models. During ventricular fibrillation, peak I_m was decreased by 50% and peak I_ion was decreased by 70%. Our results provide, to our knowledge, novel quantitative information that complements voltage- and patch-clamp data.     

The Structure of Mytilus Smooth Muscle and the Electrical Constants of the Resting Muscle

The individual muscle fibers of the anterior byssus retractor muscle (ABRM) of Mytilus edulis L. are uninucleate, 1.2–1.8 mm in length, 5 µm in diameter, and organized into bundles 100–200 µm in diameter, surrounded by connective tissue. Some bundles run the length of the whole muscle. Adjacent muscle cell membranes are interconnected by nexuses at frequent intervals. Specialized attachments exist between muscle fibers and connective tissue. Electrical constants of the resting muscle membrane were measured with intracellular recording electrodes and both extracellular and intracellular current-passing electrodes. With an intracellular current-passing electrode, the time constant τ, was 4.3 ± 1.5 ms. With current delivered via an extracellular electrode τ was 68.3 ± 15 ms. The space constant, λ, was 1.8 mm ± 0.4. The membrane input resistance, R_eff, ranged from 23 to 51 MΩ. The observations that values of τ depend on the method of passing current, and that the value of λ is large relative to fiber length and diameter are considered evidence that the individual muscle fibers are electrically interconnected within bundles in a three-dimensional network. Estimations are made of the membrane resistance, R_m, to compare the values to fast and slow striated muscle fibers and mammalian smooth muscles. The implications of this study in reinterpreting previous mechanical and electrical studies are discussed.     

Changes in membrane characteristics of heart muscle during inhibition

Membrane characteristics were studied in isolated muscle strands from auricles of frogs using the "square pulse" technique. Changes in the time course and spatial spread of subthreshold electrotonic potentials were measured. If acetylcholine is applied in concentrations which cause slowing or stoppage of the heart beat, the following changes are produced: (a) the length constant (λ) of the membrane is reduced, (b) the time constant is shortened. The effects are reversible and increase with acetylcholine concentration. The membrane changes caused by acetylcholine dimmish with time. It is concluded that during acetylcholine inhibition, as well as during vagal inhibition, the conductance of the muscle membrane is increased. Appreciable changes in the resting membrane potential need not accompany inhibition.     

A two-compartment model for the dependence of a postsynaptic potential on a postsynaptic current, measured by the patch-clamp method

As known, the dependence of a postsynaptic potential (PSP)1 on a postsynaptic current (PSC) is not satisfactorily approximated by simple Ohm's law due to a significant role of electrotonic propagation of currents along dendrites. The present work shows that a two-compartment model of a neuron, conjointly solving the two problems of voltage and current clamping, gives quite precisely the PSP-on-PSC dependence, in spite of inaccurate reconstruction of currents on dendritic terminals. The two-compartment model is compared with the neuron model consisting of a distributed cylindrical dendrite and a concentrated soma.     

Opiate-Induced Suppression of Rat Hypoglossal Motoneuron Activity and Its Reversal by Ampakine Therapy

Background

Hypoglossal (XII) motoneurons innervate tongue muscles and are vital for maintaining upper-airway patency during inspiration. Depression of XII nerve activity by opioid analgesics is a significant clinical problem, but underlying mechanisms are poorly understood. Currently there are no suitable pharmacological approaches to counter opiate-induced suppression of XII nerve activity while maintaining analgesia. Ampakines accentuate α-amino-3-hydroxyl-5-methyl-4-isoxazole-propionate (AMPA) receptor responses. The AMPA family of glutamate receptors mediate excitatory transmission to XII motoneurons. Therefore the objectives were to determine whether the depressant actions of μ-opioid receptor activation on inspiratory activity includes a direct inhibitory action at the inspiratory premotoneuron to XII motoneuron synapse, and to identify underlying mechanism(s). We then examined whether ampakines counteract opioid-induced depression of XII motoneuron activity.

Methodology/Principal Findings

A medullary slice preparation from neonatal rat that produces inspiratory-related output in vitro was used. Measurements of inspiratory burst amplitude and frequency were made from XII nerve roots. Whole-cell patch recordings from XII motoneurons were used to measure membrane currents and synaptic events. Application of the μ-opioid receptor agonist, DAMGO, to the XII nucleus depressed the output of inspiratory XII motoneurons via presynaptic inhibition of excitatory glutamatergic transmission. Ampakines (CX614 and CX717) alleviated DAMGO-induced depression of XII MN activity through postsynaptic actions on XII motoneurons.

Conclusions/Significance

The inspiratory-depressant actions of opioid analgesics include presynaptic inhibition of XII motoneuron output. Ampakines counteract μ-opioid receptor-mediated depression of XII motoneuron inspiratory activity. These results suggest that ampakines may be beneficial in countering opiate-induced suppression of XII motoneuron activity and resultant impairment of airway patency.