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REPORT

Current- and Voltage-Clamp Recordings and Computer Simulations of Kenyon Cells in the Honeybee

¹Department of Neurobiology and Anatomy, Center for Computational Biomedicine, The University of Texas–Houston Medical School, Houston, Texas 77030; and ²Institut für Biologie, Neurobiologie, Freie Universität Berlin, D-14 195 Berlin, Germany

Submitted 23 December 2003; accepted in final form 3 June 2004

	ABSTRACT

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The mushroom body of the insect brain is an important locus for olfactory information processing and associative learning. The present study investigated the biophysical properties of Kenyon cells, which form the mushroom body. Current- and voltage-clamp analyses were performed on cultured Kenyon cells from honeybees. Current-clamp analyses indicated that Kenyon cells did not spike spontaneously in vitro. However, spikes could be elicited by current injection in approximately 85% of the cells. Of the cells that produced spikes during a 1-s depolarizing current pulse, approximately 60% exhibited repetitive spiking, whereas the remaining approximately 40% fired a single spike. Cells that spiked repetitively showed little frequency adaptation. However, spikes consistently became broader and smaller during repetitive activity. Voltage-clamp analyses characterized a fast transient Na⁺ current (I_Na), a delayed rectifier K⁺ current (I_K,V), and a fast transient K⁺ current (I_K,A). Using the neurosimulator SNNAP, a Hodgkin–Huxley-type model was developed and used to investigate the roles of the different currents during spiking. The model led to the prediction of a slow transient outward current (I_K,ST) that was subsequently identified by reevaluating the voltage-clamp data. Simulations indicated that the primary currents that underlie spiking are I_Na and I_K,V, whereas I_K,A and I_K,ST primarily determined the responsiveness of the model to stimuli such as constant or oscillatory injections of current.

	INTRODUCTION

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The mushroom bodies are bilaterally symmetrical regions of the insect brain that play critical roles in associative learning and memory (de Belle and Heisenberg 1994; Erber et al. 1980; Heisenberg et al. 1985; Menzel et al. 1974; for reviews see Davis 1993; Heisenberg 2003; Menzel 2001) and olfactory and multimodal processing (Faber and Menzel 2001; Laurent and Naraghi 1994; Perez-Orive et al. 2002; Wang et al. 2001). Kenyon cells are the intrinsic cells that constitute the mushroom bodies. Thus characterizing the biophysical properties of Kenyon cells is an important step toward understanding the cellular basis of complex behaviors such as learning. The voltage-gated currents expressed in Kenyon cells have been described in several species and in various levels of detail (Acheta domesticus: Cayre et al. 1998; Apis melifera: Grünewald 2003; Pelz et al. 1999; Schäfer et al. 1994; Drosophila melanogaster: Wright and Zhong 1995). However, little is known about the spiking characteristics of Kenyon cells (Laurent and Naraghi 1994; Perez-Orive et al. 2002), and no study has yet investigated both the spiking characteristics and the underlying ionic currents in a single preparation. Some studies have attempted to use the voltage-clamp data to draw conclusions about the current-clamp behavior of Kenyon cells (Ikeno and Usui 1999; Pelz et al. 1999), but these studies were compromised because of an incomplete knowledge of the underlying currents.

Previous studies examined some of the ionic currents that are expressed by Kenyon cells in cell culture. Kenyon cells express several voltage-gated inward and outward currents. The inward currents include a tetrodotoxin (TTX)-sensitive fast transient Na⁺ current (I_Na) and at least 2 Ca²⁺ currents (I_Ca) (Grünewald 2003; Schäfer et al. 1994). The outward currents include a fast, transient A-type K⁺ current (I_K,A) and a delayed, noninactivating K⁺ current (I_K,V) (Cayre et al. 1998; Pelz et al. 1999; Schäfer et al. 1994; Wright and Zhong 1995). In one study, a Ca²⁺-dependent K⁺ current was described (Schäfer et al. 1994). The most complete set of voltage-clamp data are available for the honeybee Kenyon cells in which Schäfer et al. (1994) provided a comprehensive description of I_Na and Pelz et al. (1999) analyzed the properties of I_K,A.

In the present study, current-clamp recordings from cultured honeybee Kenyon cells were performed to examine their spiking characteristics. The in vitro preparation ensured a degree of control over experimental conditions that cannot be achieved in vivo. Therefore cell culture is well suited to analyze the electrical properties of Kenyon cells. The experimental setup allowed for switching between current- and voltage-clamp recordings. Thus the action potentials and the contributing currents were measured in the same cells. The impact of blocking certain currents on the spiking properties was also examined. To build a realistic conductance-based model, data from previous studies (Pelz et al. 1999; Schäfer et al. 1994) together with current- and voltage-clamp from the present study provided the basis for the development of Hodgkin–Huxley-type descriptions of the voltage-gated currents. The mathematical descriptions of the currents were then used to implement a model. The model consisted of a fast, transient Na⁺ current (I_Na); a fast, transient A-type K⁺ current (I_K,A); and a delayed, noninactivating K⁺ current (I_K,V). However, the 3-membrane current model was inadequate to describe the total current that was measured in voltage-clamp experiments. Therefore the existence of a slow transient outward current (I_K,ST) was postulated. This modification to the model led us to reexamine the empirical data, and I_K,ST was identified in the voltage-clamp records. The model that included the 4 currents was able to qualitatively reproduce the spiking behavior of the Kenyon cells.

	METHODS

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Animals and cell preparation

Honeybee (Apis mellifera) pupae were collected from the comb between days 4 and 6 of pupal development, which lasts 9 days under natural conditions. Kenyon cells were dissected and cultured following a modified protocol published previously (Kreissl and Bicker 1992). Brains were removed from the head capsule in a Leibovitz L15 medium (GIBCO BRL) supplemented with sucrose, glucose, fructose, and praline, 42.0, 4.0, 2.5, and 3.3 g l^–1, respectively (500 mOsmol pH 7.2). The glial sheath was removed and the mushroom bodies were dissected out of the brains. After incubation (10 min) in a Ca²⁺-free saline to loosen cell adhesion (pH 7.2, in mM: 130 NaCl, 5 KCl, 10 MgCl₂, 25 glucose, 180 sucrose, 10 HEPES), mushroom bodies were transferred back to L15 preparation medium (2 mushroom bodies per 100 µl) and dissociated by gentle trituration with a 100 µl Eppendorf pipette. Cells were then plated in aliquots of 10 µl on polylysine (polylysine-L-hydrobromide MW 150–300 kDa; Sigma, St. Louis, MO) coated Falcon plastic dishes and allowed to settle and adhere to the substrate for 10 min. Thereafter, the dishes were filled with approximately 2.5 ml of culture medium [13% (vol/vol) heat-inactivated fetal calf serum (Sigma), 1.3% (vol/vol) yeast hydrolysate (Sigma), 12.5% (wt/vol) L15 powder medium (GIBCO BRL), 18.9 mM glucose, 11.6 mM fructose, 3.3 mM proline, 93.5 mM sucrose; adjusted to pH 6.7 with NaOH; 500 mOsmol] and were kept at high humidity in an incubator at 26°C. Recordings were made from cells that had been in culture for between 3 and 7 days. The processes of those cells chosen for recordings did not overlap with neighboring neurites.

Electrophysiological techniques

Whole cell recordings were performed at room temperature (22°C). Recordings were made using an EPC9 amplifier (HEKA Elektronik Dr. Schulz GmbH, Lamprecht, Germany). Pulse generation, data acquisition, and analysis were carried out using PULSE and PULSE-FIT (version 8.53, HEKA) software and the Windows NT4 operating system. Currents were low-pass filtered with a 4-pole Bessel filter at 3 kHz and sampled at 20 kHz for K⁺ currents or 40 kHz for Na⁺ currents. Patch-electrode offset potentials were nulled before seal formation. Leakage currents were not subtracted. Series resistances ranged from 5 to 20 M and were compensated at approximately 80%. Electrodes were pulled from borosilicate glass capillaries (1.5 mm OD, 0.8 mm ID, GB150-8P, Science Products, Hofheim, Germany) with a horizontal puller (DMZ-Universal Puller, Zeitz-Instrumente, Munich, Germany) and had tip resistances between 5 and 10 M in standard external solution (see following text). Before breaking through the membrane to establish the whole cell configuration, the seal resistance was in all cases >10 G (in most cases >20 G), which is the largest value the amplifier could accurately measure. Only large Kenyon cells with a soma diameter of approximately 10 µm and with no or only very short visible processes were examined. The holding potential was –80 mV throughout. After establishing the whole cell configuration, it was possible to switch between voltage- and current-clamp recordings. Short (40-ms) or long (1-s) depolarizing current pulses were used to evoke either single or trains of spikes, respectively.

Data were analyzed using IGOR Pro (version 3.15; Wavemetrics, Lake Oswego, OR). Origin (version 7; OriginLab, Northampton, MA), PulseFit (version 8.53; HEKA), and Matlab (version 3.1; The MathWorks, Natick, MA).

Solutions

The bath was continuously perfused at flow rates of about 2 ml min^–1 with a standard external solution that consisted of (in mM): 130 NaCl, 6 KCl, 4 MgCl₂, 5 CaCl₂, 160 sucrose, 25 glucose, 10 Hepes–NaOH. The external saline was adjusted to pH 6.7 and 520 mOsmol. To record currents through K⁺ channels, TTX (100 nM) was added to the saline to block voltage-gated Na⁺ currents. Some experiments were performed with 50 µM CdCl₂ in the solution to block Ca²⁺ currents. In some experiments, fast transient K⁺ currents were blocked with 5 mM 4-aminopyridine (4-AP) in the external saline. The internal solution contained (in mM): 115 potassium gluconate, 40 KF, 20 KCl, 3 MgCl₂, 5 K-BAPTA, 3 Na₂ATP, 0.1 Mg-GTP, 3 glutathione, 120 sucrose, and 10 HEPES-bis-tris; pH 6.7, 490 mOsmol.

To record currents through Na⁺ channels, K⁺ ions in the micropipette solution were replaced by TEA or Cs²⁺; Cs-gluconate, TEA-Cl, Cs-EGTA, and CsF replaced the corresponding K⁺ salts (in mM: 20 TEA-Cl, 83 Cs-gluconate, 3 Na₂-ATP, 0.2 CaCl₂, 3 MgCl₂, 10 Cs-EGTA, 3 glutathione, 0.1 Mg-GTP, 10 HEPES-bis-tris, 120 sucrose, 40 CsF). All chemicals were purchased from Sigma.

Calcium currents were not examined in the present study. Two factors influenced the decision not to examine Ca²⁺ currents. First, previous studies found that Ca²⁺ currents vary considerably both in kinetics and amplitude among Kenyon cells (Grünewald 2003; Schäfer et al. 1994). The variability in kinetics appears to be attributable to the existence of at least 2 components in the Ca²⁺ currents. Unfortunately, these 2 components cannot be adequately separated for detailed analysis. Second, a pilot study examined the contribution of Ca²⁺ currents to the waveform of the action potential. Blocking Ca²⁺ currents with CdCl₂ had no visible effect on the waveform of the action potential (see following text). Taken together, these data suggested that Ca²⁺ currents played only a minor role in the spiking, and thus Ca²⁺ currents were not examined in the present study nor were they included in the model (see DISCUSSION).

Data analyses and model development

To simulate voltage-gated currents, equations predicting the values for the activation and inactivation of the current were developed. The voltage-dependent steady-state activation and inactivation were denoted as m and h, respectively. The corresponding voltage-dependent time constants were denoted as _m and _h, respectively. These empirical functions were derived from new data and from previously published data. Data from cells that were inadequately space clamped were discarded from quantitative analysis. Poor space clamp was indicated when fast Na⁺-like currents appeared suddenly during stepwise depolarizations in voltage-clamp protocols.

The voltage-dependent steady-state activation (m) and inactivation (h) were described by Boltzmann equations

(1a)

(1b)

where V_h is the membrane potential at which the current is half (in)activated, s is a shape parameter that describes the steepness of the curve, and N is a power.

The activation was derived from the current–voltage (I–V) curves of the currents. The ratio of g/g_max was used as a measure of the activation. Membrane currents were described by Ohm's law

(2)

where g_max is the maximum conductance, E_m is the membrane potential, E_rev is the reversal potential for the current, and g(E_m, t) is the voltage- and time-dependent ionic conductance.

The maximum current and time constants for activation and inactivation at a given membrane potential were estimated by fitting the data to the following equation

(3)

where _m and _h are the activation and inactivation time constants, respectively. I_max is the theoretical maximum of current possible (i.e., in the absence of inactivation).

The time constants were then plotted versus the command potential and fit with Boltzmann equations

(4)

or

(5)

where _max and _min are the maximal and the minimal time constants, respectively.

Similar expressions were used for _h. The currents were computed by multiplying the maximal conductance with the numerically determined solutions of the differential equations

(6)

for the activation and

(7)

for the inactivation of a given current.

The model was implemented and the simulations were performed by the neurosimulator SNNAP (version 8; Hayes et al. 2003; Ziv et al. 1994; http://snnap.uth.tmc.edu/). The input files that were used for these studies are available from the SNNAP website and from the Model DB section of the Senselab database (http://senselab.med.yale.edu).

	RESULTS

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Current-clamp data

Data collection began in voltage-clamp mode with cells voltage-clamped at a holding potential of –80 mV (see following text). When the amplifier was switched into the current-clamp mode, a constant current was injected, which maintained the cells at –80 mV in the moment the switching occurred. The holding current was then removed and the resting potential determined. Membrane potentials at 0 pA holding current varied considerably from –140 to –54 mV, with an average resting potential of –84.7 ± 4.6 mV (means ± SE, n = 25) (see Table 1). Studies of Kenyon cells in vivo found resting potentials of –70 to –60 mV (Laurent and Naraghi 1994). The average input resistance, which was calculated from the slopes of current–voltage relationships (Fig. 1B) for subthreshold potentials, was 3.8 ± 0.7 G (n = 25). Input resistances 1 G also were observed during intracellular recordings from Kenyon cells in vivo (Laurent and Naraghi 1994; Perez-Orive et al. 2002). There was no correlation between the resting potential and the membrane resistance (r = –0.56, n = 20, data not shown). The mean membrane capacitance was derived from the capacitance compensation routine of the PULSE software and the average membrane capacitance was 4 ± 0.3 pF (n = 19).

View larger version (21K): [in this window] [in a new window]   FIG. 1. Characterization of the intrinsic firing properties of a Kenyon cell in vitro. A: voltage responses to hyperpolarizing and depolarizing current steps from a membrane potential of –70 mV (protocol drawn below voltage traces). Here and in subsequent illustrations, the dashed line indicates a membrane potential of 0 mV. Above threshold, the cell responded with spikes that broaden and whose amplitudes decreased during the train. Voltage recordings were responses to current steps that were incremented from –17.5 to 14.5 pA in steps of 4 pA. To hold the cell at –70 mV, a hyperpolarizing current of –2.5 nA was applied. B: corresponding current–voltage (I–V) curve of the same cell. Input resistance was linear for hyperpolarizing and weak depolarizing currents. An input resistance of 3.5 G was calculated from the linear range of the I–V curve.

Although Kenyon cells generally are considered to be a relatively homogeneous population, the distinctive spiking characteristics that were observed in vitro suggested the possibility that different subpopulations of Kenyon cells may exist. To investigate this possibility, Kenyon cells were categorized into 3 groups based on their spiking characteristics (i.e., repetitive spiking, single spikes, and silent) and several biophysical parameters were examined in an attempt to identify systematic differences among the 3 groups. For the 3 groups, the average resting potentials were –88.6 ± 9.2 mV for cells that spiked repetitively, –79.3 ± 3.5 mV for cells that produced a single spike, and –85.2 ± 2.5 mV for cells that were silent. A single-factor ANOVA indicated that these differences were not significant [F_(2,22) = 0.41, P = 0.67]. (Note, here and elsewhere, statistical analysis indicated that the data were normally distributed, and thus parametric analyses were justified.) Similarly, no statistically significant differences were found among the input resistances of the 3 groups [4.2 ± 1.2 G for cells that spiked repetitively; 2.2 ± 0.3 G for cells that produced a single spike; and 6 ± 2.5 G for cells that were silent; F_(2,22) = 1.72, P = 0.2]. Although the ANOVA suggested a significant difference among the membrane capacitances of the 3 groups [4.8 ± 0.4 pF for cells that spiked repetitively; 3.6 ± 0.3 pF for cells that produced a single spike; and 3.2 ± 0.8 pF for cells that were silent; F_(2,22) = 3.73, P = 0.05], post hoc, pairwise comparisons (Tukey) failed to find a significant difference (q₃ = 2.806). Thus no significant differences were identified among the 3 groups of cells, which had distinctive spiking characteristics. The possibility that differences existed in the membrane conductances of these 3 groups is considered below.

The responses of those Kenyon cells that fired repetitively during sustained depolarization revealed several characteristic properties (Fig. 2). First, cells that fired repetitively during sustained depolarization showed little or no frequency adaptation during the spike train. A similar lack of frequency adaptation was observed previously during intracellular recordings from Kenyon cells in vivo (Laurent and Naraghi 1994; Perez-Orive et al. 2002). Second, the instantaneous spiking frequency did not change substantially as the stimulus intensity was increased. Third, with smaller depolarizing currents, cells showed a long delay between the start of the current pulse and the onset of firing. The average delay during a just suprathreshold stimulus was 377 ± 45 ms. This delay decreased when the injection current increased. Fourth, during the spike train, action potentials progressively had smaller amplitudes and increased durations. To ensure that the decreasing amplitude of action potentials during repetitive spiking was not the result of a rundown phenomenon, we repeated the depolarization protocol that led to the spike train and compared the amplitudes of the first spikes in the 2 trains. The average interval between the 2 stimuli was 208 ± 29 s. The average amplitude of the first spike during the first stimulus was 20.7 ± 3.8 mV (n = 9), and the average amplitude of the first spike during the second stimulus was 24.2 ± 4.7 mV. This small increase was not significant (t₈ = –1.767, P = 0.12), which indicated that rundown was not a likely explanation for the observed changes in spike waveform during repetitive activity. Finally, in many cases, the induced spike train terminated before the termination of the current pulse, especially when the depolarizing current was large.

View larger version (35K): [in this window] [in a new window]   FIG. 2. Response of a repetitively spiking Kenyon cell to depolarizing current pulses of increasing magnitude. A1: increasing the current magnitude beyond threshold (12 pA in this example) led to an increasing number of spikes and a slightly higher frequency of spiking. Increasing current magnitude also led to broader action potentials with decreasing amplitudes. Ultimately, high current magnitudes led only to oscillations in membrane voltage without producing action potentials. Examples of the instantaneous frequency in repetitive spiking in 3 cells are illustrated in the right column (A2, B, C). Data in A1 and A2 are from the same cell. Instantaneous frequency was calculated as the inverse of the interval between 2 given spikes in a train. Although greater intensity stimuli slightly increased the frequency of firing, the spike rate showed no sign of frequency adaptation.

Single-action potentials were initiated by using a brief (40-ms) depolarizing current pulse. Because it was necessary to quickly depolarize the cells to threshold, pulses used to elicit single-action potentials were greater than those used for sustained depolarization. Spikes were followed by an afterhyperpolarization (AHP). Action potentials were abolished by bath-applied TTX, which blocked the fast transient inward current (Fig. 3A, n = 5). Addition of 4-AP, a blocker of A-type K⁺ channels, blocked the transient component of the whole cell outward current and led to a larger and broader action potential (Fig. 3B1, n = 3). To evaluate the contribution of Ca²⁺ currents to the action potential waveform, spikes were elicited in the presence of Cd²⁺, which blocks Ca²⁺ currents in Kenyon cells (Grünewald 2003; Schäfer et al. 1994). The presence of Cd²⁺ had no visible effect on the shape of the action potential (Fig. 3C, n = 3) and only a relatively small effect on the whole cell current. From these results we conclude that Ca²⁺ currents play only a minor role in the generation of action potentials in cultured Kenyon cells.

View larger version (31K): [in this window] [in a new window]   FIG. 3. Pharmacological properties of the action potential. Leftmost column illustrates current-clamp data. Middle 2 columns illustrate voltage-clamp data from the same cell before (control) and after (treatment) application of a pharmacological agent that blocks a specific membrane current. Right-hand column illustrates the difference currents that resulted from subtracting control and treatment data. In current-clamp experiments (leftmost column), cells were depolarized by 40-ms current pulses (bars). Current-clamp responses are illustrated as solid (control) and dashed (treatment) lines. In voltage-clamp experiments (2 middle columns), cells were held at –80 mV and then depolarized stepwise to command potentials between –80 and +80 mV after a conditioning prepulse to –120 mV. A1: action potentials were eliminated by 100 nM tetrodotoxin (TTX). A3: illustrates that TTX blocked the fast inward current seen in A2. Current that was blocked by TTX (i.e., the difference current) is illustrated in the right-hand column. B1: 5 mM 4-aminopyridine (4-AP) broadened the action potential, increased the peak amplitude of the spike, and lowered the threshold, as indicated by the earlier onset of the action potential in the presence of 4-AP. This behavior corresponded to a lack of the fast transient outward compound as seen in whole cell current recordings in B3 vs. B2. Current that was blocked by 4-AP (i.e., the difference current) is illustrated in the right-hand column. C1: 50 µM CdCl2 did not substantially alter the shape of the spike. Correspondingly, the voltage-clamp traces showed little difference between control conditions (C2) and a solution containing 50 µM CdCl2 (C3) except for a slightly smaller inward current and a larger outward current in C3 compared with C2 resulting from the blocked Ca2+ current. A2–A3, B2–B3, and C2–C3 illustrate the difference currents between the voltage-clamp traces under control conditions and under the influence of TTX, 4-AP, and Cd2+, respectively. Note change in scale in the difference currents. TTX blocked a fast transient inward current, 4-AP blocked a transient outward current, and Cd2+ blocked a slow transient inward current.

To construct the model, it was necessary to extend previous characterizations of I_Na and I_K,V (Schäfer et al. 1994). In addition, the original voltage-clamp data from Pelz et al. (1999) were used to refine the description of I_K,A.

Sodium current (I_Na)

In 3 separate experiments, I_Na was isolated by blocking voltage-gated Ca²⁺ and K⁺ currents. Voltage-gated Ca²⁺ currents were blocked by adding 50 µM CdCl₂ to the bath solution and K⁺ currents were blocked by substituting Cs²⁺ (133 mM) for K⁺ and adding 20 mM TEA to the pipette solution (Fig. 4A1). I_Na activated at voltages more depolarized than –40 mV and peaked at about –10 mV. The reversal potential of the I_Na was approximately 58 mV (Fig. 4, A and B). The steady-state activation curve, fit with a 3rd-order Boltzmann function (i.e., n = 3 in Eq. 1a), had a V_h = –30.1 mV and a slope value of s = 6.65 (Fig. 4C). The inactivation curve was taken from Schäfer et al. (1994) where steady-state inactivation data were fit with a 1st-order Boltzmann function (Eq. 1b). The function had a V_h = –51.4 mV and a slope value of s = 5.9 (Fig. 4C, dashed line). To determine the time constants of activation and inactivation, individual recordings of I_Na at the different command potentials were normalized to the peak current value and the traces were then averaged. An initial analysis indicated that I_Na could not be adequately fit by Eq. 3. Rather, the best fit was obtained by assuming I_Na had 2 components (i.e., the current was fit with a sum of 2 currents because the voltage dependency of the inactivation time constants followed a double-exponential function). The 2 currents (I_NaF and I_NaS) differed only in their inactivation time constants. Our fits gave an activation time constant between 0.83 and 0.09 ms. The 2 exponentials of the inactivation kinetics were fit with the time constants _h1 (I_NaF) varying between 1.66 and 0.21 ms and _h2 (I_NaS) varying between 12.24 and 1.9 ms (Eq. 4). The parameters that were used to model the voltage dependency of the Na⁺ current time constants are given in Table 2. The ratio of the fast to the slow component for the averaged current was 87:13. A small sustained Na⁺ component (<1% of the total I_Na) also was identified. Because of its small amplitude, the sustained component of I_Na was not characterized further, and it was not included in the model.

View larger version (33K): [in this window] [in a new window]   FIG. 4. Fast transient Na+ current (INa). A: empirical voltage-clamp recordings (A1) and simulations (A2) of INa. Simulations used the parameters of Table 2. Voltage-clamp experiment was performed with 50 mM CdCl2 in the external solution to block Ca2+ currents and 5 mM Ba2+ instead of Ca2+ in the external solution and Cs+ instead of K+ ions in the pipette to block potassium currents. Cell was depolarized for 10 ms to various command potentials and then stepped back to –80 mV. B: I–V curve of INa obtained from experiments similar to the one illustrated in A1 (n = 3). For each cell, INa was normalized to the peak current value and the traces were then averaged. Solid line plots the I–V curve resulting from the simulation illustrated in A2. C: steady-state activation and inactivation. Boltzmann functions (solid lines) were fit to the values of the activating INa (see text). Dashed curve in C represents the inactivation function from Schäfer et al. (1994). D: examples of INa from 3 separate experiments were normalized and averaged and were used to determine voltage dependency of the time constants for activation and inactivation. Inactivation was best fit using 2 time constants (h1 and h2).

In 5 separate experiments, the properties of I_K,V were characterized. To record I_K,V, inward currents were blocked by adding 50 µM CdCl₂ and 100 nM TTX to the bath solution (Fig. 5). By analyzing tail currents, a reversal potential for I_K,V of –59.8 ± 4.4 mV (n = 5, data not shown) was determined, whereas the calculated equilibrium potential for K⁺ was –81 mV. Thus it appears that ions other than K⁺ also contribute to the current. To inactivate I_K,A, cells were held at –20 mV for 1 s before switching to various command potentials from –100 to 90 mV and then back to the holding potential of –80 mV. The steady-state activation curve was fit with a 4th-order Boltzmann function (n = 4, Eq. 1a) (Fig. 5C). The current did not inactivate during the voltage pulse (100 ms). The activation time constant was slightly voltage dependent and ranged between 3.53 ms at membrane potentials more negative than 0 mV and 1.85 ms at membrane potentials more positive than 60 mV. The simulated current closely matched the measured current (Fig. 5, A1 and A2), which is also demonstrated by the fact that the experimental I–V curve is well fit by the simulation (Fig. 5B).

View larger version (31K): [in this window] [in a new window]   FIG. 5. Voltage-dependent activation of delayed, noninactivating K+ current (IK,V). A1: IK,V recorded from a Kenyon cell in vitro. INa was blocked with 100 nM TTX in the bath solution. To block a fast, transient A-type K+ current (IK,A), the cell was clamped to –20 mV for 1 s and then stepped to various command potentials from –70 to +60 mV and then back to –80 mV, as illustrated in the voltage protocol. A2: same protocol in a simulated cell. Simulations used the parameters of Table 2. B: I–V curve derived from 5 separate experiments (current normalized to current at +50 mV). Solid line indicates the values obtained from the simulation. C: steady-state activation curve derived from measurements on 8 Kenyon cells. Curve was fit by a Boltzmann function (solid line, see text). D: time constants of the activation. A Boltzmann function was fit to the values (solid line).

The description of I_K,A was based on data published by Pelz et al. (1999). Although Pelz et al. provided a Hodgkin–Huxley-type description of the current, the parameters of this model were not published and are no longer available. Therefore it was necessary to reexamine these data and derive a description of I_K,A. To fit the steady-state activation, a 3rd-order Boltzmann function was used that had a half-maximal activation of V_h = –20.1 mV and a slope factor of s = 16.1. The steady-state inactivation was fit with a 1st-order Boltzmann function with a half-maximal inactivation at V_h = –74.7 mV and a slope factor of s = 7. Activation and inactivation time constants followed a bell-shaped curve and were therefore fit using Eq. 5 (for parameter values see Table 2). An example of the Kenyon cell I_K,A and its simulation is shown in Fig. 6.

View larger version (17K): [in this window] [in a new window]   FIG. 6. Examples and simulations of IK,A from Pelz et al. (1999). A1: isolated IK,A. Inward currents were blocked by adding 100 nM TTX and 50 µM CdCl2 and IK,V was blocked by adding 200 µM quinidine to the bath solution. Traces illustrate the result from a subtraction protocol to isolate the A-type current. Cell was stepped to command voltages from –55 mV to +45 mV after a 1-s prepulse to either –120 or –20 mV. Prepulse either completely removed inactivation (–120 mV) of IK,A or completely inactivated (–20 mV) IK,A. Current traces illustrate the difference of the resulting currents (data from Pelz et al. 1999). A2: simulation of IK,A with the parameters of Table 2. B: normalized I–V curve of IK,A from 7 cells. Solid line is the I–V curve of the simulated current.

Whole cell K⁺ currents were simulated using the initial models composed of only I_K,A and I_K,V. However, the shape of the simulated total outward current differed from that obtained from the voltage-clamp recordings (Fig. 7, A and B). The simulated I_K appeared to inactivate faster than the empirical data. Thus we hypothesized that the total outward current included an additional component that has yet to be described. Pelz et al. (1999) noted that I_K,A in Kenyon cells is not completely blocked by 5 mM 4-AP and therefore empirical experiments were conducted to analyze the 4-AP–resistant transient current component. In 2 separate experiments, inward currents were blocked by adding 100 nM TTX and 50 µM CdCl₂ to the bath solution and I_K,A was blocked by adding 5 mM 4-AP. Under these conditions, I_K,V was unaffected. To separate the remaining transient current from I_K,V, a subtraction technique was used. The subtraction technique used 2 voltage-clamp protocols. First, data were collected using a protocol in which the command potential was preceded by a –120 mV prepulse of 1-s duration to completely remove inactivation of the putative transient current (Fig. 7C1). Second, the prepulse was set to –20 mV to inactivate the transient current (Fig. 7C2). Subtraction of the current traces recorded with these 2 protocols yielded a slow transient current, designated I_K,ST. I_K,ST activated faster than I_K,V and inactivated more slowly than I_K,A (Fig. 7C3). Although I_K,ST was not characterized in great detail, an additional outward current was incorporated into the simulation. The new outward current had features similar to those illustrated in Fig. 7C3. The steady-state activation and inactivation parameters of I_K,A were used for I_K,ST, but the kinetics of I_K,ST were slower (Fig. 7D; for parameters see Table 2). With I_K,ST included, the simulation of the total outward currents more faithfully reproduced the empirical data (Fig. 7E).

View larger version (27K): [in this window] [in a new window]   FIG. 7. Slow transient outward current (IK,ST). A: typical example of a whole cell current recording. Inward currents were blocked by 100 nM TTX and 50 µM CdCl2. To remove inactivation of currents, a 1-s prepulse of –120 mV was applied before stepping to various command potentials from –65 to +55 mV (increments of 10 mV). B: simulation of the whole cell current that included only IK,A and IK,V (parameters were from Table 2). C: subtraction protocol used to isolate a transient component from IK,V. To block IK,A, 5 mM 4-AP was added to the bath. Voltage protocol in C1 was the same as in A; in C2 the 1-s prepulse was –20 mV, which inactivated the transient current. C3: subtraction of C2 from C1 revealed a slowly inactivating current. D: simulation of a slow transient outward current modeled after C3 (see text for details). E: whole cell current simulation with IK,A, IK,V, and the newly modeled IK,ST.

The voltage-clamp simulations presented above were combined to implement a model cell that was based on conductance ratios and capacitance estimates from currents of individual cells that spiked repetitively in response to injection of constant depolarizing current. The model had an input resistance of 2.6 G. The reversal potential for the leakage conductance was adjusted to yield a resting membrane potential of –65 mV and the membrane capacitance was set to 4 pF, which was in agreement with empirical data (see Table 1). As in cultured Kenyon cells, the model cell did not generate spontaneous action potentials. To closely match the biological spiking behavior, it was necessary to assume an approximately 5-fold higher Na⁺ conductance (the total g_Na was 152 nS in the model vs. 30 nS in the cell) than was measured empirically. The simulated cell generated spike activity on depolarization. The threshold for eliciting a spike was about –25 mV, and the spike shape was similar to that of Kenyon cell action potentials. By switching off I_K,A in the simulation, the model mimicked the spike broadening that occurs in Kenyon cells when I_K,A is blocked by 4-AP. In the absence of I_K,A, however, the simulated spike was followed by an AHP, a phenomenon that was not observed empirically (Fig. 8). The AHP in the simulated spike was attributed to the fast inactivation of I_Na, whereas the K⁺ currents remained active.

View larger version (12K): [in this window] [in a new window]   FIG. 8. Current-clamp recordings (A) and simulations (B) of a Kenyon cell action potential and effects of 4-AP. A: spike initiated by a depolarizing current pulse under control conditions (solid line) and with 5 mM 4-AP in the bath (dashed line). B: depolarization induced a spike in the model with (solid line) and without (dashed line) IK,A. In the absence of IK,A spike amplitudes are greater and spike durations are longer. Bars under the voltage traces indicate the duration of the current pulses. For the simulations illustrated in Figs. 8, 9, and 10, the parameters are given in Table 2.

View larger version (22K): [in this window] [in a new window]   FIG. 9. Comparison of simulated (A) and empirical (B) responses to sustained depolarizing current pulses. A: on depolarization, the simulated cell slowly depolarizes until the first spike was elicited. Cell then fires repetitively with constant frequency. Increasing the injected current (A2) led to an increased firing frequency and a decrease in the delay between the onset of the stimulus and the first spike. B: similar firing properties were recorded experimentally. Cells fired after a delay that depended on the magnitude of the depolarizing current pulse. Increasing the current magnitude led to a slight increase in firing frequency. Repetitive firing in many cases also led to decreasing spike amplitudes and longer spike durations during the spike train. Bars indicate the duration of the current pulse.

View larger version (28K): [in this window] [in a new window]   FIG. 10. Properties of the Kenyon cell model and roles of the individual conductances. A: current waveforms of individual ionic currents during action potentials in the simulated Kenyon cell. Primary currents that contributed to the spike were INa and IK,V, whereas the 2 other outward currents are relatively small. B: model was depolarized by a stimulus slightly above threshold. B1: cell illustrated a delay between the depolarization and the onset of spiking. B2: when IK,ST was removed from the model, the delay was substantially reduced. B3: without IK,ST and IK,A, no delay was observed. C: instantaneous frequencies of the first 8 action potentials of the spike train are presented. Spiking frequency of the model showed no sign of frequency adaptation. Inset: instantaneous firing frequency was averaged over the first 8 spikes during responses to stimuli, ranging from 12 to 16 nA, illustrating the dependency of the firing frequency on the stimulus strength.

To test for the robustness of the model, single conductances were individually varied over a range of values or removed completely to examine its influence on the behavior of the model. I_Na and I_K,V were essential for spiking behavior in that their presence was both necessary and sufficient for spike generation. Repetitive spiking was possible over a wide range of ratios between I_Na and I_K,V. The simulated cell spiked repetitively from ratios of 54:1 (220:5 nS) to about 4:1 (154:60 nS). [Estimated empirical ratios of I_Na and I_K,V ranged between 2.3:1 and 4.7:1 (3.6 ± 0.8:1) in spiking cells and 1.5:1 and 3.9:1 (2.6 ± 1.2:1) in nonspiking cells.] At the same time, a minimal amount of I_Na was needed for repetitive spiking (0.088 nS I_Na:0.005 nS I_K,V). Greater I_Na conductances increased the frequency of spiking, lowered the threshold of the cell, and increased the amplitude of the spike, whereas greater I_K,V generally reduced the frequency, increased the threshold, and reduced the amplitude of the spike.

Simulations also investigated the ways in which the model might be altered so as to change the spiking characteristic of the model. In vitro, Kenyon cells responded to prolonged depolarizing stimuli by either firing repetitively, firing a single spike, or remaining silent. Using the parameters of Table 2, the model cell spiked repetitively during a prolonged stimulus (e.g., Figs. 9 and 10). Simulations indicated that the spiking characteristics of the model could be changed by piecewise adjustments to the membrane conductances. For example, the repetitively spiking model could be transformed into a model that produced a single spike by either decreasing g_Na or/and increasing g_K. When g_Na in the model was high enough for spiking, but the ratio between g_Na and g_K,V was lower than about 4:1, only one spike could be elicited. Thus the full range of spiking properties that were observed in vitro could be simulated by the model, which suggested that the present model is a canonical representation of Kenyon cells.

Moreover, these simulations suggested that a systematic difference in biophysical properties of Kenyon cells was not necessary to explain the different spiking characteristics. The spiking characteristics of the model could be altered by any combinations of values for g_Na and g_K that matched the 4:1 ratio. This result suggested that the different spiking characteristics in vitro may represent random differences in the membrane conductances of the cells rather than subpopulations of Kenyon cells with distinct biophysical properties. If this hypothesis is correct, it may not be possible to detect a correlation between the spiking characteristics and the biophysical properties of Kenyon cells. To examine this hypothesis, Kenyon cells were categorized based on their spiking characteristics, and the maximum outward and inward membrane conductances of the 3 groups were compared. (To control for different sizes of the cells, the membrane capacitance of each cell was used to normalize the individual membrane conductances.) For the 3 groups, the average maximum outward conductances were 53 ± 18 nS for cells that spiked repetitively, 30 ± 6 nS for cells that produced a single spike, and 40 ± 8 nS for cells that were silent. An ANOVA indicated a significant difference among the 3 groups [F_(2,15) = 3.98; P = 0.04]. Post hoc, pairwise comparisons indicated a significant difference between cells that spike repetitively and cells that fired a single spike (q₃ = 3.98, P = 0.03). However, there was no significant difference between repetitively spiking cells and silent cells (q₃ = 1.49), or between silent cells and cells that fired a single spike (q₃ = 1.03). The average maximum inward conductances were 67 ± 23 nS for cells that spiked repetitively, 35 ± 3 nS for cells that produced a single spike, and 38 ± 6 nS µS for cells that were silent. An ANOVA indicated a significant difference among the 3 groups [F_(2,16) = 7.5; P = 0.005]. Post hoc, pairwise comparisons indicated a significant difference between cells that spiked repetitively and cells that fired a single spike (q₃ = 5.33, P = 0.005). However, there was no significant difference between repetitively spiking cells and silent cells (q₃ = 2.91), or between silent cells and cells that fired a single spike (q₃ = 0.37). These data do not indicate that the different spiking characteristics of Kenyon cells in vitro represented distinct subpopulations.

Finally, simulations were also used to analyze the contributions of the different currents to the action potential and spiking characteristics of Kenyon cells (Fig. 10, A and B). Action potentials could be generated solely by I_Na and I_K,V, whereas I_K,A and I_K,ST modulated the spike shape and the characteristics of cellular responses to stimuli. I_K,A and I_K,ST could be omitted from the cell model without affecting the general ability to spike repetitively. The lack of I_K,A led to broader spikes, as was expected from experiments where the A-current was blocked by 4-AP (Fig. 3A1, Fig. 8). Greater I_K,A also led to a higher threshold of the model cell. I_K,ST had a similar influence on the threshold of the model. Addition of I_K,ST also could recover repetitive spiking when the amount of I_K,V was just insufficient to sustain spiking. I_K,ST was also the main current responsible for the long delays between the start of the current and the onset of firing (Fig. 10B). If g_K,ST was increased, the duration of the delay also increased. Because Kenyon cells appear to receive oscillatory inputs in vivo (e.g., Laurent and Naraghi 1994), we also examined the response of the model to sinusoidal stimuli. Using the parameters of Table 2, the model failed to spike consistently in response to large-amplitude (17 to 24 nA) sinusoidal inputs (2 to 10 Hz) (data not shown). However, if g_K,ST was removed, the model fired spikes, or brief bursts of spikes, in phase with the sinusoidal input. These results indicated that Kenyon cells were not intrinsically "tuned" to respond to oscillatory inputs, but their responses to oscillatory inputs could be enhanced by modulation of g_K,ST.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Current-clamp data

The recordings presented here are the first examples of spike activity in cultured honeybee Kenyon cells. In the present study, the majority of the recorded cells generated spikes on depolarization and most of them spiked repetitively. The variability in spike amplitude, spike duration, threshold, and firing frequency is probably attributable to the variability of current densities in the different cells, as is also suggested by simulations. The morphological variability of the cells should be negligible because cells were selected with as few outgrown processes as possible (see METHODS). Because data on the electrophysiological properties of honeybee Kenyon cells in vivo are limited, it is difficult to judge whether the variability in cultured cells reflects physiological variability in vivo or is the result of cell culture conditions. Much of the present data are in good agreement with the results that have been reported from mushroom body recordings (Laurent and Naraghi 1994; Perez-Orive et al. 2002). In these studies, Kenyon cells were found to have resting potentials of about –70 mV, input resistances in excess of 1 G, little or no spontaneous activity, and no intrinsic bursting behavior. These findings suggest that in vivo Kenyon cells are either constantly inhibited or inactive at resting potential, as they are in culture. According to the hypothesis presented by Perez-Orive et al. (2002), Kenyon cells may act as coincidence detectors for simultaneous activity in projection neurons converging on the same Kenyon cells. Sustained presentation of an odor can lead to repetitive spiking in some Kenyon cells at the same frequency as the projection neurons (20 Hz) (Laurent and Naraghi 1994). The spike frequencies (5–60 Hz) observed in cultured Kenyon cells on depolarization fall within the same frequency range. Moreover, Kenyon cells in vitro express an array of functional transmitter receptors, which are similar to those observed in vivo (e.g., Bicker 1996; Bicker and Kreissl 1994; Cayre et al. 1999; Su and O'Dowd 2003). Thus the currently available data suggest that Kenyon cells in vitro are a useful model of the in vivo preparation.

Although some studies suggest the existence of different subpopulations of mushroom body cells (Strausfeld et al. 2000; Yang et al. 1995), it is not known whether these differences translate into electrophysiological variability. In the present study, Kenyon cells exhibited diverse spiking characteristics in vitro. However, several lines of evidence suggest that the variability in spiking characteristic do not represent distinct subpopulations of Kenyon cells. First, no consistently significant differences were found in the resting membrane potential, input resistance, membrane capacitance, or maximum outward or inward membrane conductances of the 3 groups of cells (i.e., cells that spiked repetitively, fired a single spike, or were silent). Second, simulations indicated that the spiking characteristics of the model could be changed by simple piecewise adjustments to the membrane conductances. For example, the repetitively spiking model could be transformed into a model that produced a single spike by altering the ratio of g_Na to g_K (see also Goldman et al. 2001). Thus the present study failed to detect subpopulations of Kenyon cells with distinct biophysical properties, which supports the hypothesis that random differences in membrane conductances may underlie the spiking characteristics of Kenyon cells in vitro.

Voltage-clamp data and simulations

Voltage-gated currents in cultured insect cells have been characterized in neurons of various species (Apis mellifera: Kloppenburg et al. 1999; Laurent et al. 2002; Drosophila melanogaster: Dubin and Harris 1997; O'Dowd 1995; O'Dowd and Aldrich 1988; Schmidt et al. 2000; Gryllus bimaculatus: Kloppenburg and Hörner 1998; Mamestra brassicae: Lucas and Shimahara 2002; Manduca sexta: Christensen et al. 1988; Hayashi and Levine 1992; Mercer et al. 1996; Zufall et al. 1991; Periplaneta americana: Grolleau and Lapied 1995, 2000; Schistocerca gregaria/americana: Laurent 1991; for a review see Wicher et al. 2001). Kenyon cells in particular have been the focus of several studies (Acheta domesticus: Cayre et al. 1998; Apis mellifera: Grünewald 2003; Pelz et al. 1999; Schäfer et al. 1994; Drosophila melanogaster: Wright and Zhong 1995).

Several different types of currents have been described in cultured Kenyon cells. At least 3 different types of outward currents have been found, including slowly inactivating currents of the delayed rectifier type (Cayre et al. 1998; Schäfer et al. 1994; Wright and Zhong 1995) Ca²⁺-dependent outward currents (Cayre et al. 1998; Schäfer et al. 1994), and transient K⁺ currents (Pelz et al. 1999; Schäfer et al. 1994; Wright and Zhong 1995). In the honeybee, only a fast transient, 4-AP–sensitive A-type current has been described until now (Pelz et al. 1999; Schäfer et al. 1994), but in Drosophila, a somewhat slower transient outward current has been found that was insensitive to 4-AP (Wright and Zhong 1995). Inward currents so far have been described only in honeybee Kenyon cells. These constitute a fast TTX-sensitive Na⁺ current (Schäfer et al. 1994), a small persistent Na⁺ current (Schäfer et al. 1994), and a Ca²⁺ current that possibly encompasses 2 components (Grünewald 2003; Schäfer et al. 1994).

I_Na

I_Na in Kenyon cells is a fast transient Na⁺ current and is similar to I_Na in other insect neurons (Kloppenburg and Hörner 1998; Kloppenburg et al. 1999; Laurent et al. 2002; Lucas and Shimahara 2002; O'Dowd 1995; O'Dowd and Aldrich 1988; Wicher 2001; Zufall et al. 1991; for a review see Wicher et al. 2001). The activation steady-state parameters of our description of I_Na are very similar to the parameters provided in a previous study (Schäfer et al. 1994) and the parameters for the inactivation in our simulation were taken directly from the latter.

The time constants of I_Na have not been determined previously and were described best with a single time constant for activation and 2 time constants for inactivation, which in the simulation leads to 2 Na⁺ conductances, I_NaF and I_NaS. The fact that the best fit for the inactivation was with 2 time constants does not necessarily imply the presence of different types of Na⁺ channels. A possible interpretation of this phenomenon would be the existence of several states of the Na⁺ channel. I_Na has been found to be modulated by PKA- and PKC-dependent phosphorylation in mammals (Conley 1999) and insects (Wicher 2001), which changes its dynamics. It seems unlikely that the double-exponential inactivation results from inadequate space clamp because care was taken to choose cells with no neurite outgrowth. In addition, cells that showed inadequate space clamp were discarded from quantitative analysis of voltage-clamp data.

I_K,V

The delayed rectifier in honeybee Kenyon cells has not been described in detail previously. However, similar currents have been described in other insects (Acheta domesticus: Cayre et al. 1998; Apis mellifera: antenna motoneurons: Kloppenburg et al. 1999; olfactory receptor neurons: Laurent et al. 2002; Manduca sexta: Hayashi and Levine 1992; Zufall et al. 1991; Gryllus bimaculatus: Kloppenburg and Hörner 1998; Calliphora erythrocephala: Haag et al. 1997; Hardie and Weckström 1990; Drosophila melanogaster: O'Dowd 1995; Wright and Zhong 1995; Mamestra brassicae: Lucas and Shimahara 2002; Periplaneta americana: Grolleau and Lapied 1995; Schistocerca gregaria/americana: Laurent 1991; reviews: Grolleau and Lapied 2000; Wicher et al. 2001). In general, these currents show little or no inactivation. Similarly, I_K,V in the present study showed no inactivation. The V_h determined in the present study was within range of values described in other insect preparations. Although I_K,V can activate at voltages more negative than the –40 mV reported here (Laurent 1991), other cases are known where activation occurs until about 10 mV (Lucas and Shimahara 2002).

I_K,A

The data of Pelz et al. (1999) on I_K,A were reexamined and the quality of the fit was improved by setting the half-maximal steady-state inactivation to V_h = –74.7 mV instead of the –54.7 mV, which was used in the previous study. In addition, the activation parameters differed because in the present model the steady-state activation was fit to a 3rd-order Boltzmann function rather than to a 1st-order function.

I_K,ST

The simulations indicated that a previously unidentified slow transient component (I_K,ST) contributed to the total outward current in Kenyon cells. Unlike I_K,A, I_K,ST is not sensitive to 4-AP. The properties of this component are yet to be fully determined, but it appears to activate slower than I_K,A and faster than I_K,V. I_K,ST also shows a slow inactivation with an estimated time constant of about 200 ms. Although further analysis will be necessary, it is probable that K⁺ is the main charge carrier of I_K,ST. Slowly inactivating potassium currents have been described in many cell types (e.g., Huguenard and Prince 1991; Laurent 1991; McCormick and Huguenard 1992; Wright and Zhong 1995; Zufall et al. 1991). Interestingly, Wright and Zhong (1995) described 2 transient outward currents in cultured Drosophila Kenyon cells, one of which was insensitive to 4-AP and might therefore correspond to the newly identified component in honeybee Kenyon cells. Although such a current has not been explicitly described in the honeybee before, Pelz et al. (1999) reported that only about 50% of I_K,A was blocked by 5 mM 4-AP. The nonsensitive part may represent I_K,ST. In Drosophila, currents with similar properties are based on genes of the shab-family (Tsunoda and Salkoff 1995; Wicher et al. 2001). The presence of I_K,ST had profound effects on the spiking characteristics of the model. I_K,ST was the primary determinant of the delayed spiking responses during constant current stimuli, and I_K,ST prevented the model from responding to oscillatory stimuli. These results suggest that the spiking characteristic of Kenyon cells in vivo could be profoundly altered by the modulation of I_K,ST.

The model

Hodgkin–Huxley-type cell models based on voltage-clamp data have been constructed in many cases to investigate the interplay of the different conductances involved in spiking, to simulate complex spike patterns, and to investigate the influence of plasticity on cell behavior (e.g., Baxter et al. 1999; Byrne 1980; Canavier et al. 1993; Connor and Stevens 1971; De Schutter and Bower 1994; Haag et al. 1997; Hodgkin and Huxley 1952; Huguenard and McCormick 1992; McCormick and Huguenard 1992). In all these cases, mathematical models proved to be powerful tools to understand the mechanisms that lead to a specific electrophysiological behavior. Previously, two attempts were made to construct a Kenyon cell model based on voltage-clamp data (Ikeno and Usui 1999; Pelz et al. 1999). The model presented by Pelz et al. (1999)