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Subthreshold inactivation of voltage-gated K+ channels modulates action potentials in neocortical bitufted interneurones from rats
http://www.100md.com 《生理学报》 2005年第2期
     1 Abteilung Zellphysiologie, Max-Planck-Institut für Medizinische Forschung, Jahnstrasse 29, D-69120 Heidelberg, Germany

    2 Faculty of Life Sciences and The Leslie and Susan Gonda Interdisciplinary Brain Research Centre, Bar-Ilan University, Ramat-Gan 52900, Israel

    3 Department of Neuroscience, Karolinska Institute, Retzius vg. 8, B2-2, S-17177 Stockholm, Sweden

    Abstract
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    Voltage-gated K+ channels perform many functions in integration of synaptic input and action potential (AP) generation. In this study we show that in bitufted interneurones from layer 2/3 of the somatosensory cortex, the height and width of APs recorded at the soma are sensitive to changes in the resting membrane potential, suggesting subthreshold activity of voltage-gated conductances. Attributes of K+ currents examined in nucleated patches revealed a fast subthreshold-inactivating K+ conductance (Kf) and a slow suprathreshold-inactivating K+ conductance (Ks). Simulations of these K+ conductances, incorporated into a Hodgkin–Huxley-type model, suggested that during a single AP or during low frequency trains of APs, subthreshold inactivation of Kf was the primary modulator of AP shape, whereas during trains of APs the shape was governed to a larger degree by Ks resulting in the generation of smaller and broader APs. Utilizing the facilitating function of unitary pyramidal-to-bitufted cell synaptic transmission, single back-propagating APs were initiated in a bitufted interneurone by repeated stimulation of a presynaptic pyramidal cell. Ca2+ imaging and dendritic whole-cell recordings revealed that modulation of APs, which also affect the shape of back-propagating APs, resulted in a change in dendritic Ca2+ influx. Compartmental simulation of the back-propagating AP suggested a mechanism for the modulation of the back-propagating AP height and width by subthreshold activation of Kf. We speculate that this signal may modulate retrograde GABA release and consequently depression of synaptic efficacy of excitatory input from neighbouring pyramidal neurones.
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    Introduction

    During the last decade, a number of studies revealed the functional importance of back-propagating APs (b-APs) in central nervous system neurones (for reviews see Stuart et al. 1997, 1999). Specifically, that an increase in volume-averaged dendritic Ca2+ concentration induced by b-APs underlies their role in different types of synaptic plasticity. For instance, a coincidence of b-APs with synaptic activity initiated long-term changes in efficacy of excitatory and inhibitory synaptic transmission (Magee & Johnston, 1997; Markram et al. 1997; Holmgren & Zilberter, 2001). It was also found that short-term synaptic plasticity mediated by dendritic release of retrograde messengers could be triggered by trains of b-APs (Zilberter et al. 1999, 2000). Recently, measurements of Ca2+ dynamics in individual excitatory synapses between pyramidal cells and bitufted interneurones in L2/3 of the neocortex showed (Kaiser et al. 2004) that even a single b-AP induced by unitary EPSPs provides sufficient Ca2+ enhancement for the initiation of retrograde messenger (GABA) release (Zilberter et al. 1999). Given that b-APs mediate feedback between neurone outputs and its synaptic inputs, modulation of the shape of b-APs may have a direct effect on synaptic input.
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    Bitufted interneurones that are GABAergic and somatostatin-positive are target cells for axon collaterals of pyramidal neurones within the same layer (Reyes et al. 1998). A characteristic of these interneurones is frequency-dependent facilitation of EPSPs (Reyes et al. 1998) that provides a unique opportunity to initiate an AP during unitary synaptic activity (Kaiser et al. 2004). It has previously been shown that a single b-AP generated Ca2+ transients of similar amplitude throughout the dendritic tree of bitufted interneurones (Kaiser et al. 2001) indicating effective backpropagation of APs in their dendrites. Trains of APs from 1 to 50 Hz generated dendritic Ca2+ transients that were a linear function of the number of action potentials and their frequency (Kaiser et al. 2001). However at higher frequencies, Ca2+ accumulation in the dendrite was sublinear to the number of APs. This behaviour is similar to the apical dendrite of pyramidal neurones in the CA1 region of the hippocampus, where the amplitude of b-APs decreases during a train (Spruston et al. 1995).
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    In the present study, we investigated the role of voltage-gated channels in the modulation of AP waveform in bitufted interneurones. We show that subthreshold depolarization induces inactivation of voltage-gated K+ conductance resulting in broadening of somatic APs. Dendritic whole-cell and Ca2+-imaging experiments suggest that the broadening of the somatic AP is echoed by changes in the b-AP inducing a larger dendritic Ca2+ influx. We hypothesize that this mechanism provides a dendritic retrograde signal that encodes the duration of synaptic integration and fine-tunes retrograde GABA release by b-AP (Kaiser et al. 2004).
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    Methods

    Slices (sagittal, 300 μm thick) were prepared from the somatosensory cortex of Wistar rats (13–15 days old) that were killed by rapid decapitation, in accordance with the guidelines of the Max-Planck Institute or Bar-Ilan University animal welfare committees, as previously described (Korngreen & Sakmann, 2000). Cortical slices were perfused throughout the experiment with a solution containing (mM): NaCl 125, NaHCO3 25, KCl 2.5, NaH2PO4 1.25, MgCl2 1, CaCl2 2 and glucose 25; pH 7.4 with 5% CO2, 310 mosmol kg–1 and heated to 32–35°C. Neurones were visually identified using infrared differential interference contrast (IR-DIC) videomicroscopy. The pipette solution contained (mM): potassium gluconate 125, KCl 20, Hepes 10, MgATP 4, sodium phosphocreatine 10, EGTA 0.5 and GTP 0.3; pH 7.2 with KOH, 312 mosmol kg–1. In experiments with high concentrations (>3 mM) of 4-aminopyridine (4-AP; Merck) and tetraethylammonium (TEA; Sigma) the equivalent amount of NaCl was removed from the bath solution. Tetrodotoxin (TTX; Tocris Cookson, Bristol, UK), dendrotoxin- (DTX-; Peptide Institute, Japan), mast cell degranulating (MCD)-peptide (MCD-P; Peptide Institute), tityustoxin K (TsTx-K; Peptide Institute), margatoxin (MgTx; Peptide Institute), stychodactyla toxin (ShTx; Peptide Institute) and agitoxin (AgTx; Alomone Laboratories, Jerusalem, Israel) were stored at –20°C as stock solutions in doubly distilled water. The bath solution was supplemented with bovine serum albumin (0.1 mg ml–1) to prevent non-specific binding.
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    Nucleated outside-out patches were extracted from the soma of bitufted interneurones as previously described (Sather et al. 1992; Korngreen & Sakmann, 2000). Measurements from nucleated patches were performed using fire-polished Sylgard- (General Electric) coated pipettes (5–8 M) with an Axopatch-200B (Axon Instruments, Foster City, CA, USA) amplifier. Linear leak and capacitative currents were subtracted off-line by scaling average traces recorded at hyperpolarized voltages. Simultaneous whole-cell recordings from the soma and dendrites of bitufted interneurones were performed with two Axoclamp-2B amplifiers. A third amplifier was used in the whole-cell configuration to stimulate presynaptic pyramidal neurones in layer 2/3. Due to the high resistance of the electrodes used for dendritic recordings (15–20 M), the whole-cell configuration was established using hyperpolarizing current steps instead of suction pulses.
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    Ca2+ imaging

    Dendritic Ca2+ transients were recorded as previously described (Kaiser et al. 2001). Briefly, bitufted interneurones were filled with fura-2 (250 μM; Molecular Probes, Eugene, OR, USA), via the somatic patch pipette, at least 10 min before recording. Fluorescence excitation was achieved with a monochromatic light source (T.I.L.L. Phototonics, Planegg, Germany) at the Ca2+-dependent and independent wavelengths of 380 nm and 350 nm, respectively. Fluorescence was imaged with a water immersion lens (x 60; Olympus, Tokyo, Japan) mounted on an upright microscope (Axioskop 2FS, Zeiss, Jena, Germany). A back-illuminated, frame-transfer CCD camera (Princeton Instruments, Trenton, NJ, USA) was used to record Ca2+ transients at a frequency of 100 Hz with 12-bit resolution. Transients were averaged on-line (3–5 sweeps) and smoothed with a binominal filter. Data were then converted to Ca2+ concentrations using the standard conversion formula (Grynkiewicz et al. 1985). Peak Ca2+ amplitudes were determined by fitting a single exponential to the Ca2+ transients. In Ca2+-imaging experiments, the pipette solution also contained 0.2% biocytin. After imaging, the slices were fixed with 4% formaldehyde, and later stained to reveal morphology.
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    Two-photon excitation Ca2+ imaging

    The experimental procedure was similar to that described by Kaiser et al. (2004). Bitufted interneurones were filled with 200 μM Oregon-Green-Bapta-1 (OGB-1) for at least 15 min before imaging began. The two-photon setup was assembled from a Scan-Microscope (Leica, Germany) fitted with x 40 objective. Fluorescence transients were recorded in the line scan mode with a time resolution of 250 Hz. The emission light from OGB-1 was averaged from two photomultiplier tubes (PMTs), one at the epifluorescence and one at the condenser output port.
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    Analysis and simulations

    All off-line data analysis, including curve fitting, was carried out with IGOR (WaveMetrics, Lake Oswego, NY, USA) on a Macintosh computer. Experimental results were obtained with cells from two or more animals, and thus were pooled and depicted as mean ±S.E.M. Groups were compared with two-way ANOVA or paired t test. Current traces were analysed assuming a Hodgkin–Huxley like model (Hodgkin & Huxley, 1952). The activation and deactivation current traces were fitted to the general equation:
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    where t is time, I is the steady-state current, Io is the current at t= 0, is the time constant of the exponential relaxation, and n is the number of gates in the model. Since Io is negligibly different from zero at hyperpolarized holding potentials the above equation simplifies to:

    Correspondingly, tail currents were fitted to:

    The normalized conductance was fitted to a Boltzmann equation:

, http://www.100md.com     Where G/Gmax is the conductance normalized to its maximal value, V is membrane potential, V is the voltage at which the conductance is activated to half its maximal value (for a single gate, n= 1) and k is the slope factor. To allow comparison between V and k-values obtained in different sections of the paper the values are reported throughout the text for a fit to eqn (4) with one gate (n= 1). When the currents were analysed according to a higher order Hodgkin–Huxley model the results of the fit to eqn (4) with more gates are given in the figure legends. All modelling was carried out using NEURON 5.4 on a PC with SuSE Linux 7.1. More details of the simulations are given in the Supplementary Material.
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    Results

    Dependence of AP shape on membrane potential

    Early in the course of the research we observed that the height and width of APs recorded at the soma of bitufted interneurones were dependent on the resting membrane potential (RMP, –59.2 ± 3.0 mV, n= 27). Figure 1A displays a comparison between APs recorded at several RMPs following a square current injection into the soma of the same interneurone. The RMP was changed by constant current injection via the whole-cell pipette. Action potential amplitude ranged from 69 ± 4 mV at RMP of –90 mV to 84 ± 3 mV at –60 mV (n= 6). Above –60 mV, AP amplitude decreased to 77 ± 2 mV at –55 mV (Fig. 1B, n= 6). The AP half-width increased from 0.45 ± 0.03 ms at –90 mV to 0.73 ± 0.05 ms at –60 mV (Fig. 1C, n= 6). The observed decrease in AP amplitude at –55 mV is probably due to inactivation of voltage-gated Na+ channels.
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    A, changes in the width and height of APs as a result of changes in RMP caused by a constant current injection. The membrane potential at the soma was set at –80 mV, –70 mV, –60 mV and –55 mV. B, average changes in the amplitude of AP as a function of RMP when the membrane potential was set as in A(n= 6). The AP amplitude was measured from the threshold. C, changes in the AP half-width as the membrane potential was set to several levels (n= 6). D, changes in AP following transient changes in RMP. The membrane potential was hyperpolarized to various durations by negative current injection, prior to the initiation of AP by a 10-ms depolarizing current pulse. The horizontal line corresponds to the amplitude of the first AP that was not subjected to the current prepulse. E, the net changes in the amplitude of AP. F, changes in the half-width of AP. The changes were calculated versus the amplitude of an AP that was initiated without the current prepulse. The changes in the AP amplitude were measured after a prepulse of 40 pA that depolarized the membrane () and two levels of current injection that hyperpolarized the membrane, –40 pA () and –80 pA (), respectively.
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    The AP height and width were also sensitive to dynamic changes of the membrane potential in the vicinity of the RMP. To allow comparison between cells the RMP was set to –60 mV using constant current injection. Injecting a negative pulse of current, via the whole-cell pipette, to the soma prior to AP initiation by a positive current pulse decreased AP amplitude and width contingent on the length of negative prepulse (Fig. 1D). In six additional cells, AP amplitude (Fig. 1E) and half-width (Fig. 1F) displayed an exponential-like dependence on the length of the prepulse. When a positive prepulse was injected the height and width of APs increased and when a negative prepulse was injected they decreased (Fig. 1E and F). Injecting a larger negative current, resulting in a larger hyperpolarization, further decreased the AP height and width (Fig. 1E and F).
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    Somatic voltage-gated K+ currents

    Based on the above findings, we hypothesized that subthreshold inactivation of voltage-gated K+ channels caused AP modulation. This hypothesis was tested by measuring the properties of voltage-gated K+ channels in nucleated outside-out somatic patches from bitufted interneurones. Several selection criteria were applied in order to limit the investigation to a single type of interneurone out of the large variety of cortical interneurones (Gupta et al. 2000; Wang et al. 2002). For the experiments described in Fig. 2, neurones were initially selected based on their spindle-like somatic morphology and characteristic firing pattern (Reyes et al. 1998; Cauli et al. 2000). In four such cells, unitary EPSPs induced by paired-pulse stimulation of layer 2/3 pyramidal neurones were recorded, confirming the facilitating behaviour of synaptic connections (Reyes et al. 1998; Cauli et al. 2000). Finally, a nucleated patch was extracted from the soma of these interneurones and 100 nM TTX was added to the bath solution to block voltage-gated Na+ channels. In subsequent experiments, synaptic properties of pyramid-to-interneurone connections were not tested and cells were selected based on their shape, firing pattern and K+ currents in nucleated patches.
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    A, outward currents evoked by a series of voltage-clamp steps. The voltage was stepped to –110 mV for 500 ms to remove inactivation (truncated to facilitate display of outward currents), then stepped from –80 mV in steps of 10 mV for 400 ms, and finally stepped back to the holding voltage. Only every second step is displayed. Scale bar applies also to D and E. B, steady-state inactivation of bitufted interneurones was measured by stepping up the holding potential for periods of 15 s (truncated) in steps of 5 mV (every second step displayed) from –110 mV. The voltage was then stepped to +80 mV for 300 ms and then to –100 mV for 1 s to remove inactivation (truncated). Filtered at 5 kHz and sampled at 10 kHz. C, the peak current at +80 mV following a given voltage step was normalized to the maximal current at +80 mV following a step from –110 mV. The resulting curve was fitted with a double Boltzmann function to give V, –75 ± 3 mV; k, –11 ± 1 mV with a relative contribution of 80%, and V, –18 ± 4 mV; k, –11 ± 3 mV with a relative contribution of 20%. D, similar voltage protocol, applied to the same patch; however, with a 50 ms prepulse to –50 mV inserted after the –110 mV pulse. During the –50 mV prepulse, the fast component was completely inactivated, thus only a slow component was left. E, subtraction of the current evoked in D from currents evoked in C isolated the fast component. F, the separation protocol (C–E) generated steady-state activation curves for the two separated currents. Conductance (G) was calculated by dividing the maximal amplitude of current at a given pulse by the driving force calculated with a Nernst equation. The conductance was divided by the maximal conductance obtained from a series of voltage clamp steps. The activation curve of the fast current () was fitted with a Boltzmann function to yield V, –13 ± 3 mV; k, 18 ± 3 mV (n= 5). Similarly, the activation curve of the slow current () yielded V, –15 ± 2 mV; k, 11 ± 1 mV (n= 6).
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    Figure 2A displays a family of K+ currents recorded from a nucleated patch in the voltage-clamp mode, following a series of depolarizing voltage commands. These outward K+ currents displayed bi-exponential inactivation suggesting that at least two types of K+ channels contributed to the currents in nucleated patches. To delineate which of these current components inactivated at subthreshold voltages, their steady-state inactivation was measured (Fig. 2B). Following 15-s conditioning prepulses to potentials from –110 to 0 mV, the voltage was stepped to +80 mV and the maximal current amplitude was recorded. Afterwards, the voltage was stepped to –100 mV for 1 s to allow K+ channels to recover from inactivation. The amplitude of the fast decaying current component inactivated at more negative potentials than the slower current component (Fig. 2B). Figure 2C plots the normalized maximal current amplitude from six additional experiments as a function of the prepulse potential. This steady-state inactivation curve could be fitted with a sum of two Boltzmann functions (Fig. 2C). The fast inactivating component of the current had V and k of –75 ± 3 mV and –11 ± 1 mV (n= 7), respectively; the slower inactivating current component had V and k of –18 ± 4 mV and –11 ± 3 mV (n= 7), respectively.
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    The large difference between the steady-state inactivation V of the current components was used to kinetically separate them. The fast-inactivating current component (Kf) was inactivated by a 60-ms voltage step to –50 mV that was inserted after the –110 mV prepulse leaving only the slow inactivating current component (Ks, Fig. 2D). Subtraction revealed the fast inactivating current (Fig. 2E). The normalized average peak conductances (calculated by dividing the maximal current amplitude at each command voltage by the driving force calculated from the Nernst equation), were fitted to a one-gate Boltzmann function (eqn (4), Fig. 2F) to yield for Ks: V, –15 ± 2 mV; k, 11 ± 1 mV; conductance, 2.6 ± 1.5 nS (Fig. 2F, n= 6) and for Kf: V, –13 ± 3 mV; k, 18 ± 3 mV; conductance, 6.7 ± 2.2 nS (Fig. 2F, n= 5). The Boltzmann function was fitted to the activation curve of Ks only up to 30 mV because the conductance decreased above this potential. The diameter of the nucleated patches, calculated from video pictures taken during the experiments, was 5.5 ± 1.5 μm (n= 5). The conductance density was therefore calculated to be 27 ± 14 pS μm–2 for Ks and 70 ± 20 pS μm–2 for Kf.
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    The inactivation curve displayed in Fig. 2C indicated that Kf would be more inactivated than Ks at voltages around RMP (–59.2 ± 3.0 mV, n= 27). To further characterize Kf, its inactivation time constant was measured as a function of the membrane potential (Fig. 3). The rate of recovery from inactivation in the potential range of –110 to –80 mV was measured by a modified double-voltage protocol (Fig. 3A); to fully inactivate Kf the patch was first depolarized for 400 ms to +60 mV, and then hyperpolarized to –110 mV for varying durations, with the relative recovery from inactivation measured by a second step to +60 mV. The rate of recovery from inactivation was well approximated by a mono-exponential fit to the maximal current amplitude obtained during the second step to +60 mV, providing a value of 43 ms for the experiment displayed in Fig. 3A and an average of 46 ± 2 ms (n= 5). The rate of inactivation between –70 mV and –40 mV was measured by stepping the voltage for 500 ms to –110 mV to relieve channels from inactivation, followed by a step to the test potential (–60 mV in the experiment shown in Fig. 3B) for varying duration, and then to +60 mV to measure the current amplitude. As in Fig. 3A, the rate of inactivation was calculated by mono-exponential fits to the maximal current amplitude at +60 mV providing a value of 14 ms for the experiment displayed in Fig. 3B and an average of 15 ± 1 ms (n= 6). Above –40 mV the time constant of inactivation was measured by mono-exponential fits to the decay phase of Kf (Fig. 3C) after subtraction of Ks as described in Fig. 2. The inactivation time constant obtained from the aforementioned voltage protocols displayed a bell shaped dependence on voltage (Fig. 3D).
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    A, recovery from inactivation of K+ current in nucleated patches at –100 mV. The double-pulse protocol was used. Kf was inactivated by depolarizing the patch for 400 ms to +60 mV following a 500 ms pulse to –110 mV (truncated). The patch was then hyperpolarized to –110 mV for varying durations, and the relative recovery from inactivation was measured by a second step to +60 mV. Data sampled at 5 kHz and filtered at 2 kHz. Leak and capacitative currents are not subtracted. B, time constant of inactivation at –60 mV measured by a pulse protocol. Following 500-ms prepulse to –110 mV, the patch was stepped to –60 mV for various durations, and then to 60 mV to measure the current. Pre-pulse truncated to facilitate display. C, fitting of single exponentials to a decay phase of Kf for obtaining the rate of inactivation. Voltage steps (20 mV) from –40 mV depicted. D, time constant of inactivation from recovery protocols (, n= 4), prepulse protocols (, n= 5), and exponential fits (, n= 5) plotted as a function of voltage. Below –80 mV the inactivation time constant was fitted by 956 + 16.6Vm+ 0.076Vm2 and above –80 mV it was fitted by 6.5 + 0.0008exp(– 0.147Vm).
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    For further characterization of the conductances in nucleated patches the activation time constants of Kf and Ks were measured by fitting eqn (1) to traces of channel activation and deactivation. In order to increase the amplitude of the deactivation traces the bath K+ concentration was increased to 7.5 mM. As shown in Fig. 4Aa the resulting total outward and tail currents were larger in amplitude when a prepulse to –50 mV was not used. Insertion of 60-ms prepulse to –50 mV inactivated Kf. The residual current (Ks) was fitted with a one-gate Hodgkin–Huxley equation (eqn (1)) to give a time constant of 0.74 ms at +60 mV for the displayed trace. Similarly, fitting the tail current of Ks gave a time constant of 0.3 ms at –120 mV for the displayed trace. Subtraction of Ks from the total current gave outward and tail currents that were attributable to activation and deactivation of Kf (Fig. 4Ab). The activation of Kf was best fitted by a fourth-order Hodgkin–Huxley equation (eqn (1)) to give a time constant of 0.15 ms at +60 mV for the displayed trace. Likewise, fitting the tail current of Kf gave a time constant of 0.26 ms at –120 mV for the displayed trace. The average activation and deactivation time constants for Ks and Kf over the voltage range of –120 mV to +70 mV from seven nucleated patches are shown in Fig. 4B and C, respectively.
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    A, representative traces showing the activation and deactivation kinetics of Kf and Ks. Currents were filtered at 10 kHz and sampled at 50 kHz. The bath K+ concentration was increased from 2.5 mM to 7.5 mM to increase the size of tail currents at negative potentials. The total K+ current was measured after a 400 ms prepulse to –100 mV (Aa) and Ks with a similar protocol with addition of a 60 ms pulse to –50 mV (Aa). Following this the voltage was stepped to +60 mV and then to –120 mV in the displayed traces. The activation and deactivation of Ks were fitted to a single-gate Hodgkin–Huxley model (thick lines). The activation and deactivation of Kf were fitted to the difference current (Ab) of the two traces shown in Aa. B, the activation () and deactivation () time constants of Ks displayed a bell-shaped dependence on the membrane potential that was fitted to 0.31 + 1492/((V+ 23.5)2+ 565). C, the activation () and deactivation () time constants of Kf displayed a bell shaped-like dependence on the membrane potential that was fitted to 0.1 + 1.64/(1 + exp(– (V+ 16.9)/9)) below –40 mV, and to 0.096 + 0.18 exp(–V/50) above –40 mV.
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    Subsequently, the sensitivity of Kf and Ks to several K+ channel blockers was tested. Tetraethyl ammonium (TEA; 3 mM) reduced the amplitude of Ks by 50 ± 5%(n= 4) without affecting that of Kf and 20 mM TEA blocked 90 ± 5%(n= 4) of Ks also without affecting Kf. 4-aminopyridine (4-AP; 3 mM) reduced the amplitude of both currents by 40 ± 10%(n= 3). Several selective K+ channel toxins were also tested. Dendrotoxin- (DTX-; 250 nM) reduced the amplitude of Ks by 30 ± 5% (n= 3, data not shown); while MCD-peptide (MCD-P; 1 mM, n= 4), blood depressing substance (BDS-I; 100 nM, n= 3), tityustoxin K (TsTx-K; 200 nM, n= 3), margatoxin (MgTx; 300 nM, n= 3), stychodactyla toxin (StTx; 300 nM, n= 3) and agitoxin (AgTx; 60 nM, n= 3) all had little or no effect on either currents.
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    Simulation of somatic conductance activation by AP waveforms

    The equations describing the activation and inactivation of Ks and Kf obtained in the previous sections were transformed into a Hodgkin–Huxley-like model (Hodgkin & Huxley, 1952) using the numerical simulation environment NEURON (for details of the model see Supplementary Material). An ideal voltage clamp was simulated in a single compartment containing the model channels. The membrane potential was clamped to a waveform of an experimentally recorded AP in bitufted interneurones. We had observed that the AP waveform was sensitive to changes in the membrane potential (Fig. 1). Therefore, three AP waveforms were used for the simulations (Fig. 5A). One waveform was of an AP generated by current injection into the soma from RMP; the other two waveforms were of APs generated by the same current injection after a 600-ms current prepulse, that deflected the membrane potential by 5 mV to depolarized or hyperpolarized potentials. The full voltage traces are shown in the inset to Fig. 5A and the APs are enlarged in Fig. 5A, displaying the effect of membrane potential on the height and width of APs as in Fig. 1. As expected from its steady-state activation curve and time constants, Kf activated both during the voltage prepulse and during the upstroke of AP (Fig. 5B). Due to smaller inactivation at more negative potentials, Kf activated to a larger degree after AP initiation. Conversely, Ks displayed almost no activation around the RMP and during the upstroke of the AP (Fig. 5C) but displayed larger activation as the AP waveform was taller and broader (Fig. 5C).
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    A, three APs recorded from the soma of bitufted interneurone following current injection via the patch pipette. The entire recording is shown in the inset and APs are enlarged for displaying changes in the width and amplitude. One AP was preceded by a 600-ms negative current prepulse that hyperpolarized the membrane potential by 5 mV (dashed line), one AP was preceded by a 600-ms positive current prepulse that depolarized the membrane potential by 5 mV (dotted line), and one AP was not preceded by a current prepulse (continuous line). The APs were aligned to threshold in order to enable clear display of the changes in amplitude and width. Changes in the conductance of Kf (B), Ks (C) and Na+ (D) were simulated using three APs from A as voltage-clamp waveforms in NEURON.
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    The recorded AP waveforms were also employed to investigate the conductance changes of voltage-gated Na+ channels during the AP. Voltage-gated Na+ channels were not measured in bitufted interneurones therefore a Hodgkin–Huxley model of this current that was based on recordings from nucleated patches extracted out of layer 5 pyramidal neurones of the somatosensory cortex was employed (A. Korngreen & B. Sakmann, unpublished data). As seen in Fig. 5D, subthreshold depolarization inactivated Na+ channels that consequently activated less at suprathreshold voltages. Thus, the activation of Kf during the upstroke of the AP causes the AP to be smaller despite a larger Na+ channel activation. In the hippocampus it was shown that the properties of Na+ channels differed between interneurones and pyramidal neurones (Martina & Jonas, 1997). To investigate the possibility that the Na+ conductance model we derived from pyramidal neurones might not be appropriate for the simulation of the Na+ conductance in interneurones, a published model of this conductance from hippocampal interneurones was used (Saraga et al. 2003). While there were differences between the activation of the cortical and hippocampal Na+ conductances by the three AP waveforms, the overall pattern of activation was qualitatively similar (Fig. 1 of Supplementary Material). Modulation of AP height that effects the activation of Ks is therefore predicted by the simulations to be the result of the interplay between Kf and Na+ conductances. Moreover, the rate of repolarization and the AP width are controlled by the total K+ conductance activation.
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    The function of Kf and Ks during AP trains was simulated using experimental AP trains as voltage-clamp waveforms. Experimental AP trains at 40 Hz and 66 Hz are shown in Fig. 6A and B, respectively. Both AP trains display, to a varying degree, characteristic attenuation of AP amplitude during the train and an increase of the afterhyperpolarization. Kf recovers from inactivation between APs in the train to a greater extent at 40 Hz than at 66 Hz. Conversely, Ks fully deactivates, after each AP, at 40 Hz while at 66 Hz it does not. This interplay between the activation of Ks and Kf projects on the membrane potential between APs in the train, leading to a smaller activation of the Na+ conductance, and subsequently to a decrease in AP amplitude during the train. Qualitatively similar results were obtained when the simulation was repeated with a Na+ conductance model of hippocampal interneurones (Fig. 2 of Supplementary Material). This analysis was repeated using AP trains of 5, 20, 40, 66 and 100 Hz. The maximal activation of the Kf, Ks and Na conductances during each AP in the train is shown in Fig. 7. At 5Hz the activation of the three conductances was similar for each AP in the train. As the frequency of the train increased, the activation of the Kf (Fig. 7A) and Na+ (Fig. 7C) conductances decreased and the activation of Ks increased (Fig. 7B). Thus, during a single AP or during low frequency trains of APs the subthreshold activation of Kf is the primary modulator of the shape of the AP; during a train of APs at frequencies higher than 20 Hz, Kf does not fully recover from inactivation and the AP shape is regulated to a larger degree by Ks, resulting in the generation of smaller APs.
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    Two experimental AP trains at 40 Hz (A) and 66 Hz (B) recorded from the bitufted interneurone soma were used as voltage-clamp command waveforms in simulations. Electrode capacitance artefacts were manually removed from the traces. The simulated changes in the conductance of Kf, Ks and Na+ during two trains are shown below the corresponding train. The resting values of the membrane potential, the conductance of Kf and the conductance of Ks are indicated by dotted lines to enable better observation of the changes to these variables during the trains.The simulations were carried out in a single compartment model.
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    The maximal activation of Kf (A) Ks (B) and Na (C) conductances during each of the first 10 APs in trains of varying frequency. The maximal conductance activated by each AP was normalized to the maximal conductance inserted into the model to obtain the relative activation of each conductance. The frequency of the AP train is indicated next to the appropriate curve. As the frequency of the train increased, Kf and Na activated to a smaller degree while Ks activated to a larger degree.
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    Dendritic recordings

    The experiments shown in Fig. 1D–F were repeated while performing dendritic Ca2+ imaging, in order to investigate whether the changes in the AP waveform recorded at the soma back-propagated into the dendrite. When a 400-ms negative current injection was used to generate a hyperpolarizing prepulse prior to the initiation of the AP, [Ca2+]i transients in the dendrite decreased (Fig. 8A). This effect was observed in three more experiments providing an average of 92 ± 8%(n= 4) of the Ca2+ transient recorded without a prepulse (Fig. 8C). When a 400-ms positive current injection was used to generate a depolarizing prepulse prior to the initiation of AP, [Ca2+]i transients in the dendrite increased (Fig. 8B). This effect was observed in three more experiments providing an average of 109 ± 11%(n= 4) of the Ca2+ transient recorded without a prepulse (Fig. 8C) – which was significantly different than the result obtained after a negative prepulse (P < 0.05, paired t test).
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    A, fluorescence traces recorded from the dendrite of bitufted interneurone using two-photon scanning laser microscope. The left trace represents Ca2+ transient in response to a b-AP generated by current injection into the interneurone soma. The amplitude of Ca2+ transient decreased (right trace) when a 400-ms prepulse of hyperpolarizing current (deflecting the membrane potential by –10 mV) was injected into the soma. B, the amplitude of Ca2+ transient became larger when the same experiment was repeated with a current prepulse depolarizing the membrane by 10 mV (right trace). D, summary of four experiments showing the change in F/F, normalized to control, following a positive prepulse and a negative prepulse. Error bars are S.E.M.
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    In order to obtain a direct measurement of b-APs, whole-cell voltage recordings were performed along the dendrite of bitufted interneurones. The facilitating behaviour of pyramidal-to-bitufted cell synapses was employed, allowing initiation of APs in this interneurone by repetitive stimulations of a presynaptic pyramidal cell (Kaiser et al. 2004). Thus, pyramidal-bitufted cell triple recordings were performed, in which APs in the soma and dendrite of the interneurone were measured simultaneously up to a distance of 55 μm. For example, the membrane potential was measured 31 μm away from the soma (Fig. 9A), and APs were initiated either by somatic square-pulse current injections or by trains of facilitating EPSPs generated by stimulation of a pyramidal cell (not shown in the field of view in Fig. 9A). In these experiments, a train of presynaptic APs resulted in summation of EPSPs that triggered an AP in the interneurone (Fig. 9B). This AP, recorded in the interneurone soma, was broader than that initiated at the same RMP (set to –60 mV by constant current injection) by an injection of a square-pulse somatic current (Fig. 9C). APs initiated by synaptic stimulation and by somatic current injection had half-widths of 0.65 ± 0.05 ms (n= 5) and 0.56 ± 0.05 ms (n= 5, P < 0.01, paired t test), respectively. Furthermore, synaptically induced APs had larger amplitudes than somatically induced APs (synaptically induced: 86 ± 3 mV, n= 5: somatically induced: 83 ± 3 mV, n= 5; P < 0.05, paired t test). b-APs (Fig. 9D) were also broader following the EPSP trains. Since the amplitude of b-APs varied as a function of distance from the soma, the half-width of the synaptically evoked AP was normalized to the one generated by the somatic current injection. The normalized half-width of the synaptically evoked AP was larger by 28 ± 5% (n= 5, P < 0.05, paired t test) than that evoked by a somatic current injection. In three of the recordings, the amplitudes of the b-APs recorded after trains of facilitating EPSPs were bigger than those recorded after somatic square-pulse current injections. In the other two recordings, the back-propagating AP recorded after trains of facilitating EPSPs was smaller and delayed compared to the back-propagating AP recorded after somatic current injection. One of these recordings is shown in Fig. 9D.
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    A, an infrared differential interference contrast (IR-DIC) image of a simultaneous recording of a b-AP in a bitufted interneurone. The distance between the electrodes was 30 μm. EPSPs were evoked in the bitufted interneurone by stimulation (in whole-cell mode) of a layer 2/3 pyramidal neurone by a third electrode (not in field of view). B, dual recording from a pyramidal neurone and a bitufted interneurone in layer 2/3. A 50-Hz train of APs (Vpre) was initiated by current injection (Ipre) in the pyramidal neurone, which generated a facilitating train of EPSPs (Vpost) in the bitufted interneurone that culminated in the initiation of an AP (truncated to facilitate displaying the EPSP train). C, APs recorded by the somatic electrode following a train of EPSPs (dashed line) and one generated by a somatic square current injection (solid line, 200 pA, 20 ms). D, APs recorded by the dendritic electrode following a train of EPSPs (dashed line) and one generated by a somatic square current injection (solid line).
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    Waveform modulations of synaptically induced b-APs were further investigated by measuring Ca2+ signalling in the dendrites of interneurones during dual pyramidal–bitufted cell recordings (Fig. 10A). After loading an interneurone with the Ca2+ indicator fura-2 (250 μM), APs were evoked either by stimulation of the presynaptic pyramidal neurone or by current injections into the soma of the interneurone. In both stimulation protocols, APs back-propagated into the dendrites and gave rise to a dendritic Ca2+ influx (Fig. 10A). The peak amplitudes of dendritic Ca2+ transients evoked by synaptic stimulations were 74 ± 41 nM (134 regions of 23 neurones), which are larger than those generated by somatic square-pulse current injections (51 ± 29 nM, P < 0.05). The correlation between the peak amplitudes of Ca2+ transients evoked by synaptically and somatically induced APs was linear with a slope of 1.37 ± 0.03 (Fig. 10B). This behaviour was consistent throughout the apical and basal dendritic tree, independent of distance from the soma.
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    A, fluorescence Ca2+ imaging of a bitufted interneurone synaptically connected to a neighbouring pyramidal neurone (not shown); rectangles mark dendritic regions selected for imaging. Ca2+ transients caused in response to a single AP evoked by either somatic current injection into the interneurone (left) or unitary synaptic stimulation (right). Six sweeps were averaged. B, relationship between Ca2+ transients evoked by somatically initiated and synaptically initiated b-APs. Data from 134 dendritic regions of 23 interneurones. Data fitted by linear regression with a slope of 1.37 ± 0.03. Ca2+ amplitude was 2.5-fold larger when corrected for the presence of exogenous Ca2+ buffer (Fura-2) (Kaiser et al. 2001).
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    Simulation of the back-propagating action potential

    The dendritic whole-cell voltage recordings and imaging experiments indicated that changes in the height and width of the AP recorded at the soma were echoed by changes to the b-AP. To extend our understanding of this process we performed simulations of the b-AP using a reconstructed neurone (Fig. 11) and a compartmental model in the simulation environment NEURON (see the Supplementary Material for details). To avoid assumptions regarding the axonal site for AP generation, the soma of neurone used in the simulations was voltage-clamped to recorded APs and the back-propagation of these APs was simulated along the dendrite. We have shown that the b-AP invaded the entire dendritic tree suggesting contribution of voltage-gated Na+ channels (Kaiser et al. 2001, 2004). Therefore, the first step in adjusting the parameters of the model was to investigate various densities of voltage-gated Na+ conductance along the dendrite. When the dendritic Na+ conductance density was set to 50 pS μm–2 throughout the dendritic tree, the b-AP failed to actively invade the dendrites (Fig. 3 in Supplementary material). Active back-propagation could be simulated when Na+ conductance density was set to 100 pS μm–2 and to 200 S μm–2 (Fig. 3 in Supplementary material).
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    Compartmental simulations of the b-AP were carried out in a 185-compartment model of the bitufted interneurone shown on the left. A, simulated b-APs recorded at 100 μm along the basal dendrite of the interneurone. The same APs used in as voltage-clamp commands in a single compartment model were used as somatic voltage-clamp commands in the displayed simulations. One AP was preceded by a 600-ms negative current prepulse that hyperpolarized the membrane potential by 5 mV (dashed line), one AP was preceded by a 600 ms positive current prepulse that depolarized the membrane potential by 5 mV (dotted line), and one AP was not preceded by a current prepulse (continuous line). B, the b-AP recorded at 200 μm along the basal dendrite following a somatic voltage-clamp command to the AP waveforms described above. C, changes to the half-width of the simulated b-AP as a function of the distance from the soma were calculated by subtracting the half-width of the b-AP, simulated when the somatic AP was generated from the RMP, from the half-width of the b-AP simulated when the somatic AP was generated following a hyperpolarizing () or depolarizing current prepulse (). D, changes to the amplitude of the simulated b-AP as a function of the distance from the soma were calculated by subtracting the amplitude of the b-AP, simulated when the somatic AP was generated from the RMP, from the amplitude of the b-AP simulated when the somatic AP was generated following a hyperpolarizing () or depolarizing current prepulse ().
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    To investigate whether the compartmental model reproduced the experimental results, the soma was voltage-clamped to three AP waveforms used for the simulations in the single compartment model (Fig. 5A). One waveform was of an AP generated by current injection into the soma from the RMP; the other two waveforms were of APs generated by the same current injection after a 600-ms current prepulse, that hyperpolarized or depolarized the membrane potential by 5 mV (Fig. 5A inset). Both at 100 μm (Fig. 11A) and 200 μm (Fig. 11B) away from the soma, the b-AP, simulated following a depolarizing current prepulse at the soma, was broader than the b-AP simulated when the somatic AP was generated from the RMP. The b-AP, simulated when the somatic AP was generated from the RMP, was broader than the b-AP simulated when the somatic AP was generated following a hyperpolarizing current prepulse. Throughout the dendritic tree the half-width of the simulated b-AP displayed similar behaviour (Fig. 11C). Changes to the half-width of the simulated b-AP were calculated by subtracting the half-width of the b-AP, simulated when the somatic AP was generated from the RMP, from the half-width of the b-AP simulated when the somatic AP was generated following a hyperpolarizing or depolarizing current prepulse (Fig. 11C).
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    While the simulation predicted that changes to the half-width of the somatic AP would be echoed by changes to the b-AP half-width, the amplitude of the simulated b-AP did not show a similar behaviour. The amplitude of the b-AP simulated when the somatic AP was generated following a depolarizing current prepulse was smaller than the b-AP amplitude simulated when the somatic AP was initiated from the RMP (Fig. 11A and B). In addition, the amplitude of the b-AP simulated when the somatic AP was generated following a depolarizing current prepulse was delayed compared to the b-AP amplitude simulated when the somatic AP was initiated from the RMP (Fig. 11A and B). A similar situation was observed in part of our dendritic whole-cell recordings (Fig. 9D). At 200 μm (Fig. 11B) and throughout the more distant dendritic tree (Fig. 11D) the amplitude of the b-AP simulated when the somatic AP was generated following a hyperpolarizing current prepulse was bigger than the b-AP amplitude simulated when the somatic AP that was initiated from the RMP.
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    Discussion

    The functional characteristics of APs in bitufted interneurones from neocortical layer 2/3 were investigated in acute brain slices. The height and width of the AP were observed to be a function of the RMP suggesting modulation by activity of voltage-gated channels. Two classes of K+ conductances were kinetically separated in nucleated patches from such neurones: slow inactivating (Ks) and fast inactivating (Kf). Simulations suggested that inactivation of Kf during subthreshold synaptic activity was related to changes in the width and height of APs; that is, during a single AP or a low frequency train of APs, subthreshold activation of Kf is a primary modulator of the AP shape. However, during a train of APs at frequencies higher than 20 Hz, Kf does not fully recover from inactivation between APs and the residual activation of Ks potentials results in the generation of smaller APs. Broadening of APs was echoed by broadening of b-APs, which resulted in a larger influx of Ca2+ into dendrites.
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    Subthreshold inactivation of K+ channels differentially affects firing of various neurones (Llinás, 1988; Geiger & Jonas, 2000). Additionally, fast inactivating voltage-gated K+ channels have been implicated in the response of neurones to graded levels of current by increasing their firing frequencies (Connor & Stevens, 1971a,b). Moreover, cumulative K+ channel inactivation is responsible for AP broadening in molluscan neurones (Aldrich et al. 1979; Aldrich, 1981). Furthermore, a slow inactivating K+ current controls the onset of firing in hippocampal pyramidal neurones (Storm, 1988). Finally, attenuation of b-APs in the dendrites of CA1 hippocampal pyramidal neurones is induced by fast inactivating voltage-gated K+ channels (Hoffman et al. 1997; Migliore et al. 1999).
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    In this study we observed that the height and width of an AP are sensitive to dynamic changes in the resting membrane potential (Fig. 1). This observation led to a working hypothesis suggesting a role for subthreshold inactivation of voltage-gated K+ conductances in the modulation of APs. Voltage-clamp recordings, from nucleated outside-out patches, confirmed that K+ conductance inactivating at subthreshold potentials is expressed in bitufted interneurones (Fig. 2). The kinetics of the two conductances (Figs 2–4) were described by a Hodgkin–Huxley-type model. This kinetic model was used to suggest a mechanism by which interplay between the activation of Kf and Ks could cause changes in the amplitude and width of single APs or during low frequency trains at the soma (Figs 5–7). According to the model, an increase in AP amplitude is due to a decrease in Kf activation at AP threshold following subthreshold depolarization. An increase in AP width results from a decrease in Kf activation (Fig. 5B) and a slight increase in Ks activation (Fig. 5C). During AP trains partial recovery from inactivation of Kf dictates a frequency-dependent reduction in the activation of Kf by each AP in the train. Therefore, the shape of the APs during a train is probably controlled to a larger degree by Ks, leading to smaller and broader APs.
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    Dendritic whole-cell (Fig. 9) and Ca2+ imaging (Figs 8 and 10) revealed that the modulation of the shape of the AP recorded at the soma was echoed by changes to the shape of the b-AP and to dendritic Ca2+ transients. There are several possible explanations for the modulation of Ca2+ transients in the apical dendrite. We have shown that the AP shape at the soma is modulated by the inactivation of Kf (Fig. 5); it is therefore possible to hypothesize that the shape of the AP is set at the soma and then back propagates into the dendrite, causing variable Ca2+ influx. Another possible mechanism is that Kf is expressed in the dendrite and that dendritic depolarization will result in inactivation of this current leading to broadening of the b-AP along the dendrite. In pyramidal neurones of the CA1 region of the hippocampus the density of a fast inactivating K+ conductance increase along the apical dendrite (Hoffman et al. 1997). A similar gradient of Kf in bitufted interneurones will add considerable functionality to the dendritic compartment enabling modulation of the height and width of the b-AP as it travels along the dendrite. Yet another possible mechanism is direct action of the membrane potential on other types of voltage-gated channels in the dendrite (such as Ca2+ or Na+). However, at present our ability to obtain first-hand recordings of ion channels in dendrites is limited to a small set of dendrites that can be approached with a patch pipette. Unfortunately, the dendrites of bitufted interneurones become too thin to attach a patch pipette within the first 50 μm after leaving the soma; this distance is too short to allow valid investigations of dendritic gradients of voltage-gated ion channels. To try and sort out one of the above hypotheses we simulated the b-AP in a compartmental model of a bitufted interneurone (Fig. 11). This simple simulation, using a homogenous conductance density of Kf, Ks and Na+ conductances, reproduced several of our experimental observations. The simulation indicated that the width of the AP set at the soma was echoed by changes to the b-AP (Fig. 11). However, the amplitude of the b-AP in the simulations did not display similar behaviour as that observed at the soma. Larger somatic APs were filtered to a greater extent than smaller somatic APs (Fig. 11) an effect that could be observed in a sub set of our dendritic whole-cell voltage recordings (Fig. 9D). The possible mechanism for this effect resides in the subthreshold activity of Kf. When the membrane potential at the soma is depolarized by a current injection or a train of EPSPs it causes activation of Kf (Fig. 5B). The somatic depolarization passively propagates into the dendrite causing activation of dendritic Kf. This subthreshold activation of dendritic Kf increases dendritic shunting which subsequently filters taller b-AP. The opposite applies to a hyperpolarizing current pulse at the soma that decreases the activation of dendritic Kf reducing the amount of dendritic shunting. Thus, the compartmental model favoured the working hypothesis that Kf is expressed in the dendrite and suggested a functional role for this current during propagation of subthreshold events into the dendrite. It is clear that in its present form the model is highly limited because we cannot constrain a model for the site for AP initiation in the axon. The model is also limited by the lack of information on the density gradients of the voltage-gated conductances observed in this study along the dendrites of bitufted interneurones.
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    In pyramidal neurones of the CA1 region of the hippocampus an A-type K+ conductance is responsible for the modulation of b-AP amplitude (Hoffman et al. 1997). Thus, it is interesting to compare the properties of Kf to the A-type K+ conductance found in CA1 hippocampal pyramidal neurones. The A-type conductance from CA1 activates and inactivates at potentials approximately 20 mV more depolarized than Kf. The inactivation V for the hippocampal A-type conductance is –56 mV (Hoffman et al. 1997) versus–75 mV for Kf. Similarly, the activation V for the hippocampal A-type conductance is 11 mV (Hoffman et al. 1997) versus–13 mV for Kf. Furthermore, a simple calculation, assuming one gate for activation and inactivation, shows that at a RMP of –60 mV the activation gate of the hippocampal A-type is 0.02 and the inactivation gate is 0.62, while at the same resting membrane potential the activation gate of Kf is 0.07 and the inactivation gate is 0.2. Additionally, the product of activation and inactivation at –60 mV is similar for both conductances providing an estimated activity of 1% of the total conductance. However, due to the high inactivation at –60 mV, the relative instantaneous current activated by rapid depolarization will be smaller for Kf than for the hippocampal A-type conductance. It is therefore possible to predict that Kf will probably have a smaller effect on the amplitude of the b-AP, modulating mostly the width of the AP.
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    Dendritic Ca2+ signalling is shown to be sensitive to changes in the width of a single AP (Figs 8 and 10). Thus, b-APs convey, to the dendrite, information about the duration of EPSP/IPSP integration. This ‘extra’ information is coded as variations in dendritic Ca2+ concentration, which is regulated by the frequency of b-APs (Helmchen et al. 1996; Kaiser et al. 2001). Coincidence of b-APs with incoming synaptic input contributes to long-term changes in synaptic efficacy (Magee & Johnston, 1997; Markram et al. 1997; Holmgren & Zilberter, 2001), while coincidence of a b-AP with a large synaptic input generates a Ca2+ spike in dendrites of layer 5 pyramidal neurones (Larkum et al. 1999); additionally, broadening of APs contributes to long-term potentiation in hippocampal mossy fibres (Mellor et al. 2002). In these examples, the informational content of b-APs was discrete, with trains of APs providing supplementary information. It has recently been demonstrated that retrograde release of GABA from dendrites of bitufted interneurones is triggered by an increase in dendritic [Ca2+]i (Zilberter et al. 1999). Moreover, even a single b-AP provides enhancement of [Ca2+]i in the individual synaptic contact sufficient for the initiation of retrograde signalling (Kaiser et al. 2004). Modulation of the b-AP waveform will affect dendritic Ca2+ levels resulting in a change in synaptic efficacy of excitatory input from neighbouring pyramidal neurones. Thus, information on the duration of synaptic integration is used to vary the gain of excitatory input onto the interneurone. In combination with retrograde GABA release this may provide a novel way to fine-tune the input/output function of bitufted interneurones.
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    Supplementary material

    The online version of this paper can be accessed at:

    DOI: 10.1113/jphysiol.2004.077032

    http://jp.physoc.org/cgi/content/full/jphysiol.2004.077032/DC1

    and contains supplementary material describing the compartmental model.

    This material can be also found at:

    http://www.blackwellpublishing.com/products/journals/suppmat/tjp/tjp662/tjp662sm.htm
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