Current- and Voltage-Clamp Recordings and Computer...

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

Daniel G. Wustenberg,1 Milena Boytcheva,2 Bernd Grunewald,2 John H. Byrne,1 Randolf Menzel,2

and Douglas A. Baxter1

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

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

Wustenberg, Daniel G., Milena Boytcheva, Bernd Grunewald,John H. Byrne, Randolf Menzel, and Douglas A. Baxter. Current-and voltage-clamp recordings and computer simulations of Kenyoncells in the honeybee. J Neurophysiol 92: 2589–2603, 2004. Firstpublished June 9, 2004; 10.1152/jn.01259.2003. The mushroom bodyof the insect brain is an important locus for olfactory informationprocessing and associative learning. The present study investigatedthe biophysical properties of Kenyon cells, which form the mushroombody. Current- and voltage-clamp analyses were performed on cul-tured Kenyon cells from honeybees. Current-clamp analyses indicatedthat Kenyon cells did not spike spontaneously in vitro. However,spikes could be elicited by current injection in approximately 85% ofthe cells. Of the cells that produced spikes during a 1-s depolarizingcurrent pulse, approximately 60% exhibited repetitive spiking,whereas the remaining approximately 40% fired a single spike. Cellsthat spiked repetitively showed little frequency adaptation. However,spikes consistently became broader and smaller during repetitiveactivity. Voltage-clamp analyses characterized a fast transient Na�

current (INa), a delayed rectifier K� current (IK,V), and a fast transientK� current (IK,A). Using the neurosimulator SNNAP, a Hodgkin–Huxley-type model was developed and used to investigate the roles ofthe different currents during spiking. The model led to the predictionof a slow transient outward current (IK,ST) that was subsequentlyidentified by reevaluating the voltage-clamp data. Simulations indi-cated that the primary currents that underlie spiking are INa and IK,V,whereas IK,A and IK,ST primarily determined the responsiveness of themodel to stimuli such as constant or oscillatory injections of current.

I N T R O D U C T I O N

The mushroom bodies are bilaterally symmetrical regions ofthe insect brain that play critical roles in associative learningand memory (de Belle and Heisenberg 1994; Erber et al. 1980;Heisenberg et al. 1985; Menzel et al. 1974; for reviews seeDavis 1993; Heisenberg 2003; Menzel 2001) and olfactory andmultimodal processing (Faber and Menzel 2001; Laurent andNaraghi 1994; Perez-Orive et al. 2002; Wang et al. 2001).Kenyon cells are the intrinsic cells that constitute the mush-room bodies. Thus characterizing the biophysical properties ofKenyon cells is an important step toward understanding thecellular basis of complex behaviors such as learning. Thevoltage-gated currents expressed in Kenyon cells have beendescribed in several species and in various levels of detail(Acheta domesticus: Cayre et al. 1998; Apis melifera:Grunewald 2003; Pelz et al. 1999; Schafer et al. 1994; Dro-sophila 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 nostudy has yet investigated both the spiking characteristics andthe underlying ionic currents in a single preparation. Somestudies have attempted to use the voltage-clamp data to drawconclusions about the current-clamp behavior of Kenyon cells(Ikeno and Usui 1999; Pelz et al. 1999), but these studies werecompromised because of an incomplete knowledge of theunderlying currents.

Previous studies examined some of the ionic currents thatare expressed by Kenyon cells in cell culture. Kenyon cellsexpress several voltage-gated inward and outward currents.The inward currents include a tetrodotoxin (TTX)-sensitivefast transient Na� current (INa) and at least 2 Ca2� currents(ICa) (Grunewald 2003; Schafer et al. 1994). The outwardcurrents include a fast, transient A-type K� current (IK,A) anda delayed, noninactivating K� current (IK,V) (Cayre et al. 1998;Pelz et al. 1999; Schafer et al. 1994; Wright and Zhong 1995).In one study, a Ca2�-dependent K� current was described(Schafer et al. 1994). The most complete set of voltage-clampdata are available for the honeybee Kenyon cells in whichSchafer et al. (1994) provided a comprehensive description ofINa and Pelz et al. (1999) analyzed the properties of IK,A.

In the present study, current-clamp recordings from culturedhoneybee Kenyon cells were performed to examine their spik-ing characteristics. The in vitro preparation ensured a degree ofcontrol over experimental conditions that cannot be achieved invivo. Therefore cell culture is well suited to analyze theelectrical properties of Kenyon cells. The experimental setupallowed for switching between current- and voltage-clamprecordings. Thus the action potentials and the contributingcurrents were measured in the same cells. The impact ofblocking certain currents on the spiking properties was alsoexamined. To build a realistic conductance-based model, datafrom previous studies (Pelz et al. 1999; Schafer et al. 1994)together with current- and voltage-clamp from the presentstudy provided the basis for the development of Hodgkin–Huxley-type descriptions of the voltage-gated currents. Themathematical descriptions of the currents were then used toimplement a model. The model consisted of a fast, transientNa� current (INa); a fast, transient A-type K� current (IK,A);and a delayed, noninactivating K� current (IK,V). However, the3-membrane current model was inadequate to describe the totalcurrent that was measured in voltage-clamp experiments.

Address for reprint requests and other correspondence: D. A. Baxter,Department of Neurobiology and Anatomy, The University of Texas–HoustonMedical School, Houston, TX 77030 (E-mail: [email protected]).

The costs of publication of this article were defrayed in part by the paymentof page charges. The article must therefore be hereby marked “advertisement”in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

J Neurophysiol 92: 2589–2603, 2004.First published June 9, 2004; 10.1152/jn.01259.2003.

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Therefore the existence of a slow transient outward current(IK,ST) was postulated. This modification to the model led us toreexamine the empirical data, and IK,ST was identified in thevoltage-clamp records. The model that included the 4 currentswas able to qualitatively reproduce the spiking behavior of theKenyon cells.

M E T H O D S

Animals and cell preparation

Honeybee (Apis mellifera) pupae were collected from the combbetween days 4 and 6 of pupal development, which lasts 9 days undernatural conditions. Kenyon cells were dissected and cultured follow-ing a modified protocol published previously (Kreissl and Bicker1992). Brains were removed from the head capsule in a Leibovitz L15medium (GIBCO BRL) supplemented with sucrose, glucose, fructose,and praline, 42.0, 4.0, 2.5, and 3.3 g l�1, respectively (500 mOsmolpH 7.2). The glial sheath was removed and the mushroom bodies weredissected out of the brains. After incubation (10 min) in a Ca2�-freesaline to loosen cell adhesion (pH 7.2, in mM: 130 NaCl, 5 KCl, 10MgCl2, 25 glucose, 180 sucrose, 10 HEPES), mushroom bodies weretransferred back to L15 preparation medium (2 mushroom bodies per100 �l) and dissociated by gentle trituration with a 100 �l Eppendorfpipette. Cells were then plated in aliquots of 10 �l on polylysine(polylysine-L-hydrobromide MW 150–300 kDa; Sigma, St. Louis,MO) coated Falcon plastic dishes and allowed to settle and adhere tothe substrate for �10 min. Thereafter, the dishes were filled withapproximately 2.5 ml of culture medium [13% (vol/vol) heat-inacti-vated fetal calf serum (Sigma), 1.3% (vol/vol) yeast hydrolysate(Sigma), 12.5% (wt/vol) L15 powder medium (GIBCO BRL), 18.9mM 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 highhumidity in an incubator at 26°C. Recordings were made from cellsthat had been in culture for between 3 and 7 days. The processes ofthose cells chosen for recordings did not overlap with neighboringneurites.

Electrophysiological techniques

Whole cell recordings were performed at room temperature(�22°C). Recordings were made using an EPC9 amplifier (HEKAElektronik Dr. Schulz GmbH, Lamprecht, Germany). Pulse genera-tion, data acquisition, and analysis were carried out using PULSE andPULSE-FIT (version 8.53, HEKA) software and the Windows NT4operating system. Currents were low-pass filtered with a 4-pole Besselfilter at 3 kHz and sampled at 20 kHz for K� currents or 40 kHz forNa� currents. Patch-electrode offset potentials were nulled before sealformation. Leakage currents were not subtracted. Series resistancesranged from 5 to 20 M� and were compensated at approximately80%. Electrodes were pulled from borosilicate glass capillaries (1.5mm OD, 0.8 mm ID, GB150-8P, Science Products, Hofheim, Ger-many) with a horizontal puller (DMZ-Universal Puller, Zeitz-Instru-mente, Munich, Germany) and had tip resistances between 5 and 10M� in standard external solution (see following text). Before break-ing 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�m and with no or only very short visible processes were examined.The holding potential was �80 mV throughout. After establishing thewhole cell configuration, it was possible to switch between voltage-and current-clamp recordings. Short (40-ms) or long (1-s) depolariz-ing 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; TheMathWorks, Natick, MA).

Solutions

The bath was continuously perfused at flow rates of about 2 mlmin�1 with a standard external solution that consisted of (in mM): 130NaCl, 6 KCl, 4 MgCl2, 5 CaCl2, 160 sucrose, 25 glucose, 10Hepes–NaOH. The external saline was adjusted to pH 6.7 and 520mOsmol. To record currents through K� channels, TTX (100 nM)was added to the saline to block voltage-gated Na� currents. Someexperiments were performed with 50 �M CdCl2 in the solution toblock Ca2� currents. In some experiments, fast transient K� currentswere blocked with 5 mM 4-aminopyridine (4-AP) in the externalsaline. The internal solution contained (in mM): 115 potassiumgluconate, 40 KF, 20 KCl, 3 MgCl2, 5 K-BAPTA, 3 Na2ATP, 0.1Mg-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 micropi-pette solution were replaced by TEA or Cs2�; Cs-gluconate, TEA-Cl,Cs-EGTA, and CsF replaced the corresponding K� salts (in mM: 20TEA-Cl, 83 Cs-gluconate, 3 Na2-ATP, 0.2 CaCl2, 3 MgCl2, 10Cs-EGTA, 3 glutathione, 0.1 Mg-GTP, 10 HEPES-bis-tris, 120 su-crose, 40 CsF). All chemicals were purchased from Sigma.

Calcium currents were not examined in the present study. Twofactors influenced the decision not to examine Ca2� currents. First,previous studies found that Ca2� currents vary considerably both inkinetics and amplitude among Kenyon cells (Grunewald 2003; Scha-fer et al. 1994). The variability in kinetics appears to be attributable tothe existence of at least 2 components in the Ca2� currents. Unfor-tunately, these 2 components cannot be adequately separated fordetailed analysis. Second, a pilot study examined the contribution ofCa2� currents to the waveform of the action potential. Blocking Ca2�

currents with CdCl2 had no visible effect on the waveform of theaction potential (see following text). Taken together, these datasuggested that Ca2� currents played only a minor role in the spiking,and thus Ca2� currents were not examined in the present study norwere they included in the model (see DISCUSSION).

Data analyses and model development

To simulate voltage-gated currents, equations predicting the valuesfor the activation and inactivation of the current were developed. Thevoltage-dependent steady-state activation and inactivation were de-noted as m� and h�, respectively. The corresponding voltage-depen-dent time constants were denoted as �m and �h, respectively. Theseempirical functions were derived from new data and from previouslypublished data. Data from cells that were inadequately space clampedwere discarded from quantitative analysis. Poor space clamp wasindicated when fast Na�-like currents appeared suddenly duringstepwise depolarizations in voltage-clamp protocols.

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

m� �1

�1 � e�Vh�V�/s�N (1a)

h� �1

�1 � e�V�Vh�/s�N (1b)

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

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

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2590 WUSTENBERG ET AL.

J Neurophysiol • VOL 92 • OCTOBER 2004 • www.jn.org

I � g�Em, t�gmax�Em � Erev� (2)

where gmax is the maximum conductance, Em is the membranepotential, Erev is the reversal potential for the current, and g(Em, t) isthe voltage- and time-dependent ionic conductance.

The maximum current and time constants for activation and inac-tivation at a given membrane potential were estimated by fitting thedata to the following equation

I � Imax�1 � e��t/�m��Ne��t/�h� (3)

where �m and �h are the activation and inactivation time constants,respectively. Imax is the theoretical maximum of current possible (i.e.,in the absence of inactivation).

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

�m ��max � �min

�1 � e�V�Vh�/s�� min (4)

or

�m ��max � �min

�1 � e�V�Vh1�/s1��1 � e�V�Vh2�/s2�� min (5)

where �max and �min are the maximal and the minimal time constants,respectively.

Similar expressions were used for �h. The currents were computedby multiplying the maximal conductance with the numerically deter-mined solutions of the differential equations

dm

dt�

m�Em�� m

�m

(6)

for the activation and

dh

dt�

h�Em�� h

�h

(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 forthese studies are available from the SNNAP website and from theModel DB section of the Senselab database (http://senselab.med.yale.edu).

R E S U L T S

Current-clamp data

Data collection began in voltage-clamp mode with cellsvoltage-clamped at a holding potential of �80 mV (see fol-lowing text). When the amplifier was switched into the current-clamp mode, a constant current was injected, which maintainedthe cells at �80 mV in the moment the switching occurred.The holding current was then removed and the resting potentialdetermined. Membrane potentials at 0 pA holding currentvaried considerably from �140 to �54 mV, with an averageresting potential of �84.7 4.6 mV (means SE, n 25)(see Table 1). Studies of Kenyon cells in vivo found restingpotentials of �70 to �60 mV (Laurent and Naraghi 1994). Theaverage input resistance, which was calculated from the slopesof current–voltage relationships (Fig. 1B) for subthresholdpotentials, was 3.8 0.7 G� (n 25). Input resistances �1G� also were observed during intracellular recordings fromKenyon cells in vivo (Laurent and Naraghi 1994; Perez-Oriveet 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 derivedfrom the capacitance compensation routine of the PULSEsoftware and the average membrane capacitance was 4 0.3pF (n 19).

Spontaneous spike activity was never observed in vitro, andKenyon cells in vitro showed no intrinsic bursting behavior. Asimilar lack of spontaneous and/or bursting activity was ob-served previously during intracellular recordings from Kenyoncells in vivo (Laurent and Naraghi 1994; Perez-Orive et al.2002). Most Kenyon cells (21 of 25 cells) responded to aprolonged (1-s) extrinsic depolarizing stimulus by firing atleast one action potential. The remaining 4 cells failed togenerate action potentials. Of the 21 cells that exhibited spik-ing, 12 of the cells spiked repetitively when depolarized with a1-s constant-current pulse (Fig. 1A), whereas the remaining 9cells fired only a single spike in response to a 1-s suprathresh-old depolarization. The threshold for eliciting an action poten-tial, defined as the inflection point of the first action potential,varied from �31 to �17 mV (�25.8 1 mV). Actionpotentials were normally overshooting but otherwise variedconsiderably in amplitude and duration among different cells.The amplitudes, measured from threshold to the peak of thefirst elicited spike, ranged from 22 to 61 mV. The durations ofthe first spike, measured at half-maximal amplitude, rangedgenerally between 0.7 and 2.5 ms (2.1 0.4 ms, n 18).However, in 2 cells values of 3.8 and 7 ms were observed. Anoverview of the electrophysiological parameters is given inTable 1.

Although Kenyon cells generally are considered to be arelatively homogeneous population, the distinctive spikingcharacteristics that were observed in vitro suggested the pos-sibility that different subpopulations of Kenyon cells mayexist. To investigate this possibility, Kenyon cells were cate-gorized into 3 groups based on their spiking characteristics(i.e., repetitive spiking, single spikes, and silent) and severalbiophysical parameters were examined in an attempt to identifysystematic differences among the 3 groups. For the 3 groups,the average resting potentials were �88.6 9.2 mV for cellsthat spiked repetitively, �79.3 3.5 mV for cells that pro-duced a single spike, and �85.2 2.5 mV for cells that weresilent. A single-factor ANOVA indicated that these differenceswere not significant [F(2,22) 0.41, P 0.67]. (Note, here andelsewhere, statistical analysis indicated that the data werenormally distributed, and thus parametric analyses were justi-fied.) Similarly, no statistically significant differences werefound among the input resistances of the 3 groups [4.2 1.2G� for cells that spiked repetitively; 2.2 0.3 G� for cells

TABLE 1. Empirically determined parameters of culturedKenyon cells

Mean SE n

Vm, mV �84.7 4.6 25Rm, G� 3.8 0.7 25Cm, pF 4 0.3 19Threshold, mV �25.8 1 21Spike duration, ms 2.1 0.4 18

Vm is the resting membrane potential; Rm is the input resistance; Cm is themembrane capacitance. Threshold was defined as the inflection point of thefirst spike and spike duration was measured at half-maximal spike amplitude.

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2591RECORDINGS AND COMPUTER SIMULATIONS OF KENYON CELLS


that produced a single spike; and 6 2.5 G� for cells thatwere silent; F(2,22) 1.72, P 0.2]. Although the ANOVAsuggested a significant difference among the membrane capac-itances of the 3 groups [4.8 0.4 pF for cells that spikedrepetitively; 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 asignificant difference (q3 2.806). Thus no significant differ-ences were identified among the 3 groups of cells, which haddistinctive spiking characteristics. The possibility that differ-ences existed in the membrane conductances of these 3 groupsis considered below.

The responses of those Kenyon cells that fired repetitivelyduring sustained depolarization revealed several characteristicproperties (Fig. 2). First, cells that fired repetitively duringsustained depolarization showed little or no frequency adapta-

tion during the spike train. A similar lack of frequency adap-tation was observed previously during intracellular recordingsfrom Kenyon cells in vivo (Laurent and Naraghi 1994; Perez-Orive et al. 2002). Second, the instantaneous spiking frequencydid not change substantially as the stimulus intensity wasincreased. Third, with smaller depolarizing currents, cellsshowed a long delay between the start of the current pulse andthe onset of firing. The average delay during a just supra-threshold stimulus was 377 45 ms. This delay decreasedwhen the injection current increased. Fourth, during the spiketrain, action potentials progressively had smaller amplitudesand increased durations. To ensure that the decreasing ampli-tude of action potentials during repetitive spiking was not theresult of a rundown phenomenon, we repeated the depolariza-tion protocol that led to the spike train and compared theamplitudes of the first spikes in the 2 trains. The averageinterval between the 2 stimuli was 208 29 s. The averageamplitude of the first spike during the first stimulus was 20.7 3.8 mV (n 9), and the average amplitude of the first spikeduring the second stimulus was 24.2 4.7 mV. This smallincrease was not significant (t8 �1.767, P 0.12), whichindicated that rundown was not a likely explanation for theobserved changes in spike waveform during repetitive activity.Finally, in many cases, the induced spike train terminatedbefore the termination of the current pulse, especially when thedepolarizing current was large.

Pharmacology

Single-action potentials were initiated by using a brief (40-ms) depolarizing current pulse. Because it was necessary toquickly depolarize the cells to threshold, pulses used to elicitsingle-action potentials were greater than those used for sus-tained depolarization. Spikes were followed by an afterhyper-polarization (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 celloutward 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 elicitedin the presence of Cd2�, which blocks Ca2� currents inKenyon cells (Grunewald 2003; Schafer et al. 1994). Thepresence of Cd2� had no visible effect on the shape of theaction potential (Fig. 3C, n 3) and only a relatively smalleffect on the whole cell current. From these results we con-clude that Ca2� currents play only a minor role in the gener-ation of action potentials in cultured Kenyon cells.

Voltage-clamp data

To construct the model, it was necessary to extend previouscharacterizations of INa and IK,V (Schafer et al. 1994). Inaddition, the original voltage-clamp data from Pelz et al.(1999) were used to refine the description of IK,A.

Sodium current (INa)

In 3 separate experiments, INa was isolated by blockingvoltage-gated Ca2� and K� currents. Voltage-gated Ca2� cur-rents were blocked by adding 50 �M CdCl2 to the bath solutionand K� currents were blocked by substituting Cs2� (133 mM)

FIG. 1. Characterization of the intrinsic firing properties of a Kenyon cell invitro. A: voltage responses to hyperpolarizing and depolarizing current stepsfrom a membrane potential of �70 mV (protocol drawn below voltage traces).Here and in subsequent illustrations, the dashed line indicates a membranepotential of 0 mV. Above threshold, the cell responded with spikes thatbroaden and whose amplitudes decreased during the train. Voltage recordingswere responses to current steps that were incremented from �17.5 to 14.5 pAin steps of 4 pA. To hold the cell at �70 mV, a hyperpolarizing current of �2.5nA 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–Vcurve.

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for K� and adding 20 mM TEA to the pipette solution (Fig.4A1). INa activated at voltages more depolarized than �40mV and peaked at about �10 mV. The reversal potential ofthe INa was approximately 58 mV (Fig. 4, A and B). Thesteady-state activation curve, fit with a 3rd-order Boltzmannfunction (i.e., n 3 in Eq. 1a), had a Vh �30.1 mV anda slope value of s 6.65 (Fig. 4C). The inactivation curvewas taken from Schafer et al. (1994) where steady-stateinactivation data were fit with a 1st-order Boltzmann func-tion (Eq. 1b). The function had a Vh �51.4 mV and aslope value of s 5.9 (Fig. 4C, dashed line). To determinethe time constants of activation and inactivation, individualrecordings of INa at the different command potentials werenormalized to the peak current value and the traces werethen averaged. An initial analysis indicated that INa couldnot be adequately fit by Eq. 3. Rather, the best fit wasobtained by assuming INa had 2 components (i.e., the currentwas fit with a sum of 2 currents because the voltagedependency of the inactivation time constants followed adouble-exponential function). The 2 currents (INaF and INaS)differed only in their inactivation time constants. Our fitsgave an activation time constant between 0.83 and 0.09 ms.The 2 exponentials of the inactivation kinetics were fit withthe time constants �h1 (INaF) varying between 1.66 and 0.21ms and �h2 (INaS) varying between 12.24 and 1.9 ms (Eq. 4).The parameters that were used to model the voltage depen-dency of the Na� current time constants are given in Table2. The ratio of the fast to the slow component for theaveraged current was 87:13. A small sustained Na� com-ponent (�1% of the total INa) also was identified. Becauseof its small amplitude, the sustained component of INa wasnot characterized further, and it was not included in themodel.

Delayed rectifier current (IK,V)

In 5 separate experiments, the properties of IK,V were char-acterized. To record IK,V, inward currents were blocked byadding 50 �M CdCl2 and 100 nM TTX to the bath solution(Fig. 5). By analyzing tail currents, a reversal potential for IK,Vof �59.8 4.4 mV (n 5, data not shown) was determined,whereas the calculated equilibrium potential for K� was �81mV. Thus it appears that ions other than K� also contribute tothe current. To inactivate IK,A, cells were held at �20 mV for1 s before switching to various command potentials from �100to 90 mV and then back to the holding potential of �80 mV.The steady-state activation curve was fit with a 4th-orderBoltzmann function (n 4, Eq. 1a) (Fig. 5C). The current didnot inactivate during the voltage pulse (100 ms). The activationtime constant was slightly voltage dependent and ranged be-tween 3.53 ms at membrane potentials more negative than 0mV and 1.85 ms at membrane potentials more positive than 60mV. The simulated current closely matched the measuredcurrent (Fig. 5, A1 and A2), which is also demonstrated by thefact that the experimental I–V curve is well fit by the simulation(Fig. 5B).

Fast transient potassium current (IK,A)

The description of IK,A was based on data published by Pelzet al. (1999). Although Pelz et al. provided a Hodgkin–Huxley-type description of the current, the parameters of this modelwere not published and are no longer available. Therefore itwas necessary to reexamine these data and derive a descriptionof IK,A. To fit the steady-state activation, a 3rd-order Boltz-mann function was used that had a half-maximal activation ofVh �20.1 mV and a slope factor of s 16.1. The steady-

FIG. 2. Response of a repetitively spiking Kenyon cell todepolarizing current pulses of increasing magnitude. A1: in-creasing the current magnitude beyond threshold (12 pA in thisexample) led to an increasing number of spikes and a slightlyhigher frequency of spiking. Increasing current magnitude alsoled to broader action potentials with decreasing amplitudes.Ultimately, high current magnitudes led only to oscillations inmembrane voltage without producing action potentials. Exam-ples of the instantaneous frequency in repetitive spiking in 3cells are illustrated in the right column (A2, B, C). Data in A1and A2 are from the same cell. Instantaneous frequency wascalculated as the inverse of the interval between 2 given spikesin a train. Although greater intensity stimuli slightly increasedthe frequency of firing, the spike rate showed no sign offrequency adaptation.

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state inactivation was fit with a 1st-order Boltzmann functionwith a half-maximal inactivation at Vh �74.7 mV and aslope factor of s 7. Activation and inactivation time con-stants followed a bell-shaped curve and were therefore fit usingEq. 5 (for parameter values see Table 2). An example of theKenyon cell IK,A and its simulation is shown in Fig. 6.

Slow transient outward current (IK,ST)

Whole cell K� currents were simulated using the initialmodels composed of only IK,A and IK,V. However, the shape ofthe simulated total outward current differed from that obtainedfrom the voltage-clamp recordings (Fig. 7, A and B). Thesimulated IK appeared to inactivate faster than the empiricaldata. Thus we hypothesized that the total outward currentincluded an additional component that has yet to be described.Pelz et al. (1999) noted that IK,A in Kenyon cells is notcompletely blocked by 5 mM 4-AP and therefore empiricalexperiments were conducted to analyze the 4-AP–resistanttransient current component. In 2 separate experiments, inwardcurrents were blocked by adding 100 nM TTX and 50 �M

CdCl2 to the bath solution and IK,A was blocked by adding 5mM 4-AP. Under these conditions, IK,V was unaffected. Toseparate the remaining transient current from IK,V, a subtrac-tion technique was used. The subtraction technique used 2voltage-clamp protocols. First, data were collected using aprotocol in which the command potential was preceded by a�120 mV prepulse of 1-s duration to completely removeinactivation of the putative transient current (Fig. 7C1). Sec-ond, the prepulse was set to �20 mV to inactivate the transientcurrent (Fig. 7C2). Subtraction of the current traces recordedwith these 2 protocols yielded a slow transient current, desig-nated IK,ST. IK,ST activated faster than IK,V and inactivatedmore slowly than IK,A (Fig. 7C3). Although IK,ST was notcharacterized in great detail, an additional outward current wasincorporated into the simulation. The new outward current hadfeatures similar to those illustrated in Fig. 7C3. The steady-state activation and inactivation parameters of IK,A were usedfor IK,ST, but the kinetics of IK,ST were slower (Fig. 7D; forparameters see Table 2). With IK,ST included, the simulation ofthe total outward currents more faithfully reproduced the em-pirical data (Fig. 7E).

FIG. 3. Pharmacological properties of the action potential. Leftmost column illustrates current-clamp data. Middle 2 columnsillustrate voltage-clamp data from the same cell before (control) and after (treatment) application of a pharmacological agent thatblocks a specific membrane current. Right-hand column illustrates the difference currents that resulted from subtracting control andtreatment 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 conditioningprepulse to �120 mV. A1: action potentials were eliminated by 100 nM tetrodotoxin (TTX). A3: illustrates that TTX blocked thefast 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 thethreshold, as indicated by the earlier onset of the action potential in the presence of 4-AP. This behavior corresponded to a lackof 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 �M CdCl2 did not substantially alter the shape of thespike. Correspondingly, the voltage-clamp traces showed little difference between control conditions (C2) and a solution containing50 �M CdCl2 (C3) except for a slightly smaller inward current and a larger outward current in C3 compared with C2 resulting fromthe blocked Ca2� current. A2–A3, B2–B3, and C2–C3 illustrate the difference currents between the voltage-clamp traces undercontrol 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 inwardcurrent.

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Current-clamp simulations

The voltage-clamp simulations presented above were com-bined to implement a model cell that was based on conductanceratios and capacitance estimates from currents of individualcells that spiked repetitively in response to injection of constantdepolarizing current. The model had an input resistance of 2.6G�. The reversal potential for the leakage conductance wasadjusted to yield a resting membrane potential of �65 mV andthe membrane capacitance was set to 4 pF, which was inagreement with empirical data (see Table 1). As in cultured

Kenyon cells, the model cell did not generate spontaneousaction potentials. To closely match the biological spikingbehavior, it was necessary to assume an approximately 5-foldhigher Na� conductance (the total gNa was 152 nS in the modelvs. 30 nS in the cell) than was measured empirically. Thesimulated cell generated spike activity on depolarization. Thethreshold for eliciting a spike was about �25 mV, and thespike shape was similar to that of Kenyon cell action poten-tials. By switching off IK,A in the simulation, the modelmimicked the spike broadening that occurs in Kenyon cells

FIG. 4. Fast transient Na� current (INa). A: empirical volt-age-clamp recordings (A1) and simulations (A2) of INa. Simu-lations used the parameters of Table 2. Voltage-clamp exper-iment was performed with 50 mM CdCl2 in the externalsolution to block Ca2� currents and 5 mM Ba2� instead ofCa2� in the external solution and Cs� instead of K� ions in thepipette to block potassium currents. Cell was depolarized for10 ms to various command potentials and then stepped back to�80 mV. B: I–V curve of INa obtained from experimentssimilar to the one illustrated in A1 (n 3). For each cell, INa

was normalized to the peak current value and the traces werethen averaged. Solid line plots the I–V curve resulting from thesimulation illustrated in A2. C: steady-state activation andinactivation. Boltzmann functions (solid lines) were fit to thevalues of the activating INa (see text). Dashed curve in Crepresents the inactivation function from Schafer et al. (1994).D: examples of INa from 3 separate experiments were normal-ized and averaged and were used to determine voltage depen-dency of the time constants for activation and inactivation.Inactivation was best fit using 2 time constants (�h1 and �h2).

TABLE 2. Parameters used in the simulations of a repetitively spiking Kenyon cell in vitro

E, mV g, nS �max, ms �min, ms Vh1, mV s1 Vh2, mV s2 N

INa m� �30.1 6.65 3�m 0.83 0.093 �20.3 6.45

INaF† 58 140 h� �51.4 5.9 1�h 1.66 0.12 �8.03 8.69

INaS† 58 12 h� �51.4 5.9 1�h 12.24 1.9 �32.6 8

IK,V �81 6 m� �37.6 27.24 4�m 3.53 1.85 45 13.71

IK,A �81 58.1 m� �20.1 16.1 3�m‡ 1.65 0.35 �70 �4 �20 12h� �74.7 7 1�h‡ 90 2.5 �60 �25 �62 16

IK,ST �81 8.11 m� �20.1 16.1 3�m 5.0 0.5 20 20h� �74.7 7 1�h 200 150 52 15

E, equilibrium potential; m�, steady-state activation; h�, steady-state inactivation; �m, activation time constant; �h, inactivation time constant; N, exponent inEqs. 1a, 1b, and 3. The leakage conductance was 0.39 nS and leakage equilibrium potential was �65 mV. The parameters correspond to the equations used todescribe the steady-state dynamics and the time constants as presented in METHODS. †The activation of both INa,F and INa,S was described by the same algebraicexpressions, and the parameters for these equations are listed in the rows labeled INa (i.e., m� and �m). ‡The time constants for activation and inactivation ofIK,A were described by Eq. 5.

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when IK,A is blocked by 4-AP. In the absence of IK,A, however,the simulated spike was followed by an AHP, a phenomenonthat was not observed empirically (Fig. 8). The AHP in thesimulated spike was attributed to the fast inactivation of INa,whereas the K� currents remained active.

Although the simulated cell spiked at a constant frequencyon sustained depolarization [i.e., similar to Kenyon cells itshowed no frequency adaptation (Fig. 9)], differences betweenthe simulated and empirical current-clamp data were observed.For example, the simulated cell tended to spike at higherfrequencies than did Kenyon cells (see Fig. 2, A2, B, and C andFig. 10C for a typical range of firing frequencies in Kenyon

cells and the simulation, respectively). When depolarized overa sustained period of time, the simulated cell spiked at fre-quencies �20 Hz, whereas most Kenyon cells fired at frequen-cies between 5 and 20 Hz. However, in the empirical study 2cells did have spike frequencies of 40 and 60 Hz. The modelcell also showed a more pronounced effect of stimulus mag-nitude on frequency, whereas Kenyon cells spike at relativelyconstant frequency regardless of the stimulus amplitude (Fig.10C and Fig. 2). The example model cell fires at a frequencyof about 25 Hz in response to a 13.5-pA stimulus and at about45 Hz during an 18-pA stimulus. At higher stimulus intensitiesthe model cell showed an initial spike followed by fading

FIG. 5. Voltage-dependent activation of delayed, noninacti-vating K� current (IK,V). A1: IK,V recorded from a Kenyon cell invitro. INa was blocked with 100 nM TTX in the bath solution. Toblock a fast, transient A-type K� current (IK,A), the cell wasclamped to �20 mV for 1 s and then stepped to various commandpotentials from �70 to �60 mV and then back to �80 mV, asillustrated in the voltage protocol. A2: same protocol in a simu-lated cell. Simulations used the parameters of Table 2. B: I–Vcurve derived from 5 separate experiments (current normalized tocurrent at �50 mV). Solid line indicates the values obtained fromthe simulation. C: steady-state activation curve derived frommeasurements on 8 Kenyon cells. Curve was fit by a Boltzmannfunction (solid line, see text). D: time constants of the activation.A Boltzmann function was fit to the values (solid line).

FIG. 6. Examples and simulations of IK,A from Pelz et al.(1999). A1: isolated IK,A. Inward currents were blocked byadding 100 nM TTX and 50 �M CdCl2 and IK,V was blockedby adding 200 �M quinidine to the bath solution. Tracesillustrate the result from a subtraction protocol to isolate theA-type current. Cell was stepped to command voltages from�55 mV to �45 mV after a 1-s prepulse to either �120 or �20mV. Prepulse either completely removed inactivation (�120mV) of IK,A or completely inactivated (�20 mV) IK,A. Currenttraces illustrate the difference of the resulting currents (datafrom Pelz et al. 1999). A2: simulation of IK,A with the param-eters 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.

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membrane oscillations (�60 Hz at 21 pA). In addition, themodel did not emulate the frequently observed decrement ofspike amplitude and spike broadening during the course of anelicited spike train.

Robustness of the model and role of currents

To test for the robustness of the model, single conductanceswere individually varied over a range of values or removedcompletely to examine its influence on the behavior of themodel. INa and IK,V were essential for spiking behavior in thattheir presence was both necessary and sufficient for spikegeneration. Repetitive spiking was possible over a wide rangeof ratios between INa and IK,V. The simulated cell spikedrepetitively from ratios of 54:1 (220:5 nS) to about 4:1 (154:60nS). [Estimated empirical ratios of INa and IK,V ranged between2.3:1 and 4.7:1 (3.6 0.8:1) in spiking cells and 1.5:1 and3.9:1 (2.6 1.2:1) in nonspiking cells.] At the same time, aminimal amount of INa was needed for repetitive spiking(0.088 nS INa:0.005 nS IK,V). Greater INa conductances in-creased the frequency of spiking, lowered the threshold of thecell, and increased the amplitude of the spike, whereas greaterIK,V generally reduced the frequency, increased the threshold,and reduced the amplitude of the spike.

Simulations also investigated the ways in which the modelmight be altered so as to change the spiking characteristic ofthe model. In vitro, Kenyon cells responded to prolongeddepolarizing stimuli by either firing repetitively, firing a singlespike, or remaining silent. Using the parameters of Table 2, themodel cell spiked repetitively during a prolonged stimulus(e.g., Figs. 9 and 10). Simulations indicated that the spikingcharacteristics of the model could be changed by piecewiseadjustments to the membrane conductances. For example, therepetitively spiking model could be transformed into a modelthat produced a single spike by either decreasing gNa or/and

increasing gK. When gNa in the model was high enough forspiking, but the ratio between gNa and gK,V was lower thanabout 4:1, only one spike could be elicited. Thus the full rangeof spiking properties that were observed in vitro could besimulated by the model, which suggested that the presentmodel is a canonical representation of Kenyon cells.

Moreover, these simulations suggested that a systematicdifference in biophysical properties of Kenyon cells was notnecessary to explain the different spiking characteristics. Thespiking characteristics of the model could be altered by anycombinations of values for gNa and gK that matched the 4:1ratio. This result suggested that the different spiking charac-teristics in vitro may represent random differences in themembrane conductances of the cells rather than subpopulationsof Kenyon cells with distinct biophysical properties. If thishypothesis is correct, it may not be possible to detect acorrelation between the spiking characteristics and the bio-physical properties of Kenyon cells. To examine this hypoth-esis, Kenyon cells were categorized based on their spikingcharacteristics, and the maximum outward and inward mem-brane conductances of the 3 groups were compared. (Tocontrol for different sizes of the cells, the membrane capaci-tance of each cell was used to normalize the individual mem-brane conductances.) For the 3 groups, the average maximumoutward conductances were 53 18 nS for cells that spikedrepetitively, 30 6 nS for cells that produced a single spike,and 40 8 nS for cells that were silent. An ANOVA indicateda significant difference among the 3 groups [F(2,15) 3.98;P 0.04]. Post hoc, pairwise comparisons indicated a signif-icant difference between cells that spike repetitively and cellsthat fired a single spike (q3 3.98, P 0.03). However, therewas no significant difference between repetitively spiking cellsand silent cells (q3 1.49), or between silent cells and cellsthat fired a single spike (q3 1.03). The average maximum

FIG. 7. Slow transient outward current (IK,ST). A: typicalexample of a whole cell current recording. Inward currents wereblocked by 100 nM TTX and 50 �M CdCl2. To remove inacti-vation of currents, a 1-s prepulse of �120 mV was appliedbefore stepping to various command potentials from �65 to �55mV (increments of 10 mV). B: simulation of the whole cellcurrent that included only IK,A and IK,V (parameters were fromTable 2). C: subtraction protocol used to isolate a transientcomponent from IK,V. To block IK,A, 5 mM 4-AP was added tothe bath. Voltage protocol in C1 was the same as in A; in C2 the1-s prepulse was �20 mV, which inactivated the transientcurrent. C3: subtraction of C2 from C1 revealed a slowlyinactivating current. D: simulation of a slow transient outwardcurrent modeled after C3 (see text for details). E: whole cellcurrent simulation with IK,A, IK,V, and the newly modeled IK,ST.

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inward conductances were 67 23 nS for cells that spikedrepetitively, 35 3 nS for cells that produced a single spike,and 38 6 nS �S for cells that were silent. An ANOVAindicated a significant difference among the 3 groups [F(2,16) 7.5; P 0.005]. Post hoc, pairwise comparisons indicated asignificant difference between cells that spiked repetitively andcells that fired a single spike (q3 5.33, P 0.005). However,there was no significant difference between repetitively spikingcells and silent cells (q3 2.91), or between silent cells andcells that fired a single spike (q3 0.37). These data do notindicate that the different spiking characteristics of Kenyoncells in vitro represented distinct subpopulations.

Finally, simulations were also used to analyze the contribu-tions of the different currents to the action potential and spikingcharacteristics of Kenyon cells (Fig. 10, A and B). Actionpotentials could be generated solely by INa and IK,V, whereasIK,A and IK,ST modulated the spike shape and the characteristicsof cellular responses to stimuli. IK,A and IK,ST could be omittedfrom the cell model without affecting the general ability tospike repetitively. The lack of IK,A led to broader spikes, as wasexpected from experiments where the A-current was blockedby 4-AP (Fig. 3A1, Fig. 8). Greater IK,A also led to a higherthreshold of the model cell. IK,ST had a similar influence on thethreshold of the model. Addition of IK,ST also could recoverrepetitive spiking when the amount of IK,V was just insufficientto sustain spiking. IK,ST was also the main current responsiblefor the long delays between the start of the current and theonset of firing (Fig. 10B). If gK,ST was increased, the durationof the delay also increased. Because Kenyon cells appear toreceive oscillatory inputs in vivo (e.g., Laurent and Naraghi1994), we also examined the response of the model to sinu-soidal stimuli. Using the parameters of Table 2, the modelfailed to spike consistently in response to large-amplitude (17to 24 nA) sinusoidal inputs (2 to 10 Hz) (data not shown).However, if gK,ST was removed, the model fired spikes, or briefbursts of spikes, in phase with the sinusoidal input. Theseresults indicated that Kenyon cells were not intrinsically“tuned” to respond to oscillatory inputs, but their responses tooscillatory inputs could be enhanced by modulation of gK,ST.

FIG. 8. Current-clamp recordings (A) and simulations (B) of a Kenyon cellaction potential and effects of 4-AP. A: spike initiated by a depolarizing currentpulse 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 aregreater and spike durations are longer. Bars under the voltage traces indicatethe duration of the current pulses. For the simulations illustrated in Figs. 8, 9,and 10, the parameters are given in Table 2.

FIG. 9. Comparison of simulated (A) and empirical (B)responses to sustained depolarizing current pulses. A: ondepolarization, the simulated cell slowly depolarizes untilthe first spike was elicited. Cell then fires repetitively withconstant frequency. Increasing the injected current (A2)led to an increased firing frequency and a decrease in thedelay 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 ofthe depolarizing current pulse. Increasing the current mag-nitude led to a slight increase in firing frequency. Repet-itive firing in many cases also led to decreasing spikeamplitudes and longer spike durations during the spiketrain. Bars indicate the duration of the current pulse.

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D I S C U S S I O N

Current-clamp data

The recordings presented here are the first examples of spikeactivity in cultured honeybee Kenyon cells. In the presentstudy, the majority of the recorded cells generated spikes ondepolarization and most of them spiked repetitively. The vari-ability in spike amplitude, spike duration, threshold, and firingfrequency is probably attributable to the variability of currentdensities in the different cells, as is also suggested by simula-tions. The morphological variability of the cells should benegligible because cells were selected with as few outgrownprocesses as possible (see METHODS). Because data on theelectrophysiological properties of honeybee Kenyon cells invivo are limited, it is difficult to judge whether the variabilityin cultured cells reflects physiological variability in vivo or isthe result of cell culture conditions. Much of the present dataare in good agreement with the results that have been reportedfrom mushroom body recordings (Laurent and Naraghi 1994;Perez-Orive et al. 2002). In these studies, Kenyon cells werefound to have resting potentials of about �70 mV, inputresistances in excess of 1 G�, little or no spontaneous activity,and no intrinsic bursting behavior. These findings suggest thatin vivo Kenyon cells are either constantly inhibited or inactive

at resting potential, as they are in culture. According to thehypothesis presented by Perez-Orive et al. (2002), Kenyoncells may act as coincidence detectors for simultaneous activityin projection neurons converging on the same Kenyon cells.Sustained presentation of an odor can lead to repetitive spikingin some Kenyon cells at the same frequency as the projectionneurons (�20 Hz) (Laurent and Naraghi 1994). The spikefrequencies (5–60 Hz) observed in cultured Kenyon cells ondepolarization fall within the same frequency range. Moreover,Kenyon cells in vitro express an array of functional transmitterreceptors, which are similar to those observed in vivo (e.g.,Bicker 1996; Bicker and Kreissl 1994; Cayre et al. 1999; Suand O’Dowd 2003). Thus the currently available data suggestthat Kenyon cells in vitro are a useful model of the in vivopreparation.

Although some studies suggest the existence of differentsubpopulations of mushroom body cells (Strausfeld et al. 2000;Yang et al. 1995), it is not known whether these differencestranslate into electrophysiological variability. In the presentstudy, Kenyon cells exhibited diverse spiking characteristics invitro. However, several lines of evidence suggest that thevariability in spiking characteristic do not represent distinctsubpopulations of Kenyon cells. First, no consistently signifi-

FIG. 10. Properties of the Kenyon cell model androles of the individual conductances. A: current wave-forms of individual ionic currents during action poten-tials in the simulated Kenyon cell. Primary currents thatcontributed to the spike were INa and IK,V, whereas the2 other outward currents are relatively small. B: modelwas depolarized by a stimulus slightly above threshold.B1: cell illustrated a delay between the depolarizationand the onset of spiking. B2: when IK,ST was removedfrom 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 potentialsof the spike train are presented. Spiking frequency ofthe model showed no sign of frequency adaptation.Inset: instantaneous firing frequency was averaged overthe first 8 spikes during responses to stimuli, rangingfrom 12 to 16 nA, illustrating the dependency of thefiring frequency on the stimulus strength.

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cant differences were found in the resting membrane potential,input resistance, membrane capacitance, or maximum outwardor inward membrane conductances of the 3 groups of cells (i.e.,cells that spiked repetitively, fired a single spike, or weresilent). Second, simulations indicated that the spiking charac-teristics of the model could be changed by simple piecewiseadjustments to the membrane conductances. For example, therepetitively spiking model could be transformed into a modelthat produced a single spike by altering the ratio of gNa to gK(see also Goldman et al. 2001). Thus the present study failed todetect subpopulations of Kenyon cells with distinct biophysicalproperties, which supports the hypothesis that random differ-ences in membrane conductances may underlie the spikingcharacteristics of Kenyon cells in vitro.

Voltage-clamp data and simulations

Voltage-gated currents in cultured insect cells have beencharacterized in neurons of various species (Apis mellifera:Kloppenburg et al. 1999; Laurent et al. 2002; Drosophilamelanogaster: Dubin and Harris 1997; O’Dowd 1995;O’Dowd and Aldrich 1988; Schmidt et al. 2000; Gryllusbimaculatus: Kloppenburg and Horner 1998; Mamestra bras-sicae: Lucas and Shimahara 2002; Manduca sexta: Christensenet al. 1988; Hayashi and Levine 1992; Mercer et al. 1996;Zufall et al. 1991; Periplaneta americana: Grolleau and Lapied1995, 2000; Schistocerca gregaria/americana: Laurent 1991;for a review see Wicher et al. 2001). Kenyon cells in particularhave been the focus of several studies (Acheta domesticus:Cayre et al. 1998; Apis mellifera: Grunewald 2003; Pelz et al.1999; Schafer et al. 1994; Drosophila melanogaster: Wrightand Zhong 1995).

Several different types of currents have been described incultured Kenyon cells. At least 3 different types of outwardcurrents have been found, including slowly inactivating cur-rents of the delayed rectifier type (Cayre et al. 1998; Schafer etal. 1994; Wright and Zhong 1995) Ca2�-dependent outwardcurrents (Cayre et al. 1998; Schafer et al. 1994), and transientK� currents (Pelz et al. 1999; Schafer et al. 1994; Wright andZhong 1995). In the honeybee, only a fast transient, 4-AP–sensitive A-type current has been described until now (Pelz etal. 1999; Schafer et al. 1994), but in Drosophila, a somewhatslower transient outward current has been found that wasinsensitive to 4-AP (Wright and Zhong 1995). Inward currentsso far have been described only in honeybee Kenyon cells.These constitute a fast TTX-sensitive Na� current (Schafer etal. 1994), a small persistent Na� current (Schafer et al. 1994),and a Ca2� current that possibly encompasses 2 components(Grunewald 2003; Schafer et al. 1994).

INa

INa in Kenyon cells is a fast transient Na� current and issimilar to INa in other insect neurons (Kloppenburg and Horner1998; Kloppenburg et al. 1999; Laurent et al. 2002; Lucas andShimahara 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 descrip-tion of INa are very similar to the parameters provided in aprevious study (Schafer et al. 1994) and the parameters for theinactivation in our simulation were taken directly from thelatter.

The time constants of INa have not been determined previ-ously and were described best with a single time constant foractivation and 2 time constants for inactivation, which in thesimulation leads to 2 Na� conductances, INaF and INaS. The factthat the best fit for the inactivation was with 2 time constantsdoes not necessarily imply the presence of different types ofNa� channels. A possible interpretation of this phenomenonwould be the existence of several states of the Na� channel. INahas been found to be modulated by PKA- and PKC-dependentphosphorylation in mammals (Conley 1999) and insects(Wicher 2001), which changes its dynamics. It seems unlikelythat the double-exponential inactivation results from inade-quate space clamp because care was taken to choose cells withno neurite outgrowth. In addition, cells that showed inadequatespace clamp were discarded from quantitative analysis ofvoltage-clamp data.

IK,V

The delayed rectifier in honeybee Kenyon cells has not beendescribed in detail previously. However, similar currents havebeen 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 Horner 1998; Calli-phora erythrocephala: Haag et al. 1997; Hardie and Weck-strom 1990; Drosophila melanogaster: O’Dowd 1995; Wrightand Zhong 1995; Mamestra brassicae: Lucas and Shimahara2002; 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, IK,V inthe present study showed no inactivation. The Vh determined inthe present study was within range of values described in otherinsect preparations. Although IK,V can activate at voltagesmore negative than the �40 mV reported here (Laurent 1991),other cases are known where activation occurs until about 10mV (Lucas and Shimahara 2002).

IK,A

The data of Pelz et al. (1999) on IK,A were reexamined andthe quality of the fit was improved by setting the half-maximalsteady-state inactivation to Vh �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 modelthe steady-state activation was fit to a 3rd-order Boltzmannfunction rather than to a 1st-order function.

IK,ST

The simulations indicated that a previously unidentified slowtransient component (IK,ST) contributed to the total outwardcurrent in Kenyon cells. Unlike IK,A, IK,ST is not sensitive to4-AP. The properties of this component are yet to be fullydetermined, but it appears to activate slower than IK,A andfaster than IK,V. IK,ST also shows a slow inactivation with anestimated time constant of about 200 ms. Although furtheranalysis will be necessary, it is probable that K� is the maincharge carrier of IK,ST. Slowly inactivating potassium currentshave been described in many cell types (e.g., Huguenard and

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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 cur-rents in cultured Drosophila Kenyon cells, one of which wasinsensitive to 4-AP and might therefore correspond to thenewly identified component in honeybee Kenyon cells. Al-though such a current has not been explicitly described in thehoneybee before, Pelz et al. (1999) reported that only about50% of IK,A was blocked by 5 mM 4-AP. The nonsensitive partmay represent IK,ST. In Drosophila, currents with similar prop-erties are based on genes of the shab-family (Tsunoda andSalkoff 1995; Wicher et al. 2001). The presence of IK,ST hadprofound effects on the spiking characteristics of the model.IK,ST was the primary determinant of the delayed spikingresponses during constant current stimuli, and IK,ST preventedthe model from responding to oscillatory stimuli. These resultssuggest that the spiking characteristic of Kenyon cells in vivocould be profoundly altered by the modulation of IK,ST.

The model

Hodgkin–Huxley-type cell models based on voltage-clampdata have been constructed in many cases to investigate theinterplay of the different conductances involved in spiking, tosimulate complex spike patterns, and to investigate the influ-ence 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 andHuxley 1952; Huguenard and McCormick 1992; McCormickand Huguenard 1992). In all these cases, mathematical modelsproved to be powerful tools to understand the mechanisms thatlead to a specific electrophysiological behavior. Previously,two attempts were made to construct a Kenyon cell modelbased on voltage-clamp data (Ikeno and Usui 1999; Pelz et al.1999). The model presented by Pelz et al. (1999) is basedmainly on an analysis of the A-current. In addition to IK,A, Pelzet al. (1999) completed the model by adding 2 generic currents,a fast transient INa, based on steady-state data of Schafer et al.(1994) and IK,V. This simple model is surprisingly close to themodel of the present study in that the values of INa and IK,V thatwe determined experimentally are similar to the parametersassumed in the earlier study. However, the Pelz et al. modelcould not reproduce repetitive spiking. In contrast to thepresent study, Pelz et al. (1999) suggested that IK,A was themain current to repolarize the cell and IK,V played only a minorrole during a single-action potential. Although IK,A makes animportant contribution to the repolarizing the spike (e.g., Fig.8), spiking activity persisted in the absence of IK,A, whichindicates that IK,V made a substantial contribution to spikeactivity.

The Kenyon cell model published by Ikeno and Usui (1999)is based on data published by Schafer et al. (1994). The modelspiked repetitively on depolarization. The spike shape, how-ever, was clearly different from the spike shape observed inKenyon cells, both in vivo and in vitro. The Ikeno and Usuimodel implemented a Ca2� current, a fast transient Na�

current, a delayed rectifier, 2 types of fast transient K� cur-rents, and a Ca2�-dependent K� current. INa in the model ofIkeno and Usui (1999) is very close to the one presented here,whereas the other currents differ. In particular, the activationtime constant for IK,V in their model is much slower than

indicated by the empirical data presented here. Many of thedifferences may be attributable to the incorporation of a Ca2�-dependent K� current in the Ikeno and Usui model. NeitherPelz et al. (1999) nor the present study observed a Ca2�-dependent K� current in Kenyon cells.

The present model is a single-compartment model. This wasdeemed sufficient because the data were derived from Kenyoncells that showed little or no neurite outgrowth. Thus it wasassumed that most channels were localized in the soma. Themodel reproduced many aspects of the electrophysiologicalproperties of Kenyon cells. It generated spike trains withconstant frequency on depolarization and showed a spikingbehavior close to that observed in Kenyon cells in vivo. Themodel also suggested that the role of IK,A is to regulate theduration of the action potential and to regulate the threshold,whereas the main repolarizing current is IK,V. IK,ST regulatesthe threshold of the cell and can supplement IK,V in supportingrepetitive spiking of the cell to some extent. In addition, IK,STleads to a typical delay between stimulation and the onset ofrepetitive spiking that was similarly observed in cultured Ke-nyon cells.

However, there were some differences between the modeland Kenyon cells in vivo. Specifically, the value of gNa in themodel was greater than the empirical measurements. Thisincrease was necessary to construct a model with “realistic”spiking properties. It might be that INa in vivo is mainly foundin neurites. Under the conditions of the cell culture, sodiumchannels might concentrate in patches of the soma membrane.This would lead to a nonuniform distribution of the channels inthe cultured cell. Such hotspots would require less voltagechange to reach the spike threshold than if the channels wereevenly distributed in the membrane (Shen et al. 1999). Aone-compartment model had to compensate for this nonuni-form current density by a higher overall current density of INa(Johnson and Thompson 1989). Hints that INa is indeed notlocalized in the soma come from Schafer et al. (1994). Theyreport that freshly isolated Kenyon cell soma show no INa andthat INa appears only later during culture. A possible interpre-tation of this observation is that the cells lost INa with itsneurites and the current reappears only when enough newlysynthesized Na� channels have been inserted in the membrane.Similar results come from Drosophila where INa could not bemeasured in acutely isolated Kenyon cells (Wright and Zhong1995).

A difference between the empirical data and the model thatcould not be readily explained is the generally higher firingfrequencies of the model compared with Kenyon cells in vitro.In addition, the model showed a marked frequency increase onincreased depolarization, whereas the Kenyon cells in vitro didnot. Some of the differences between the neuron and the modelmight be attributable to inaccuracies of the current fits. Inparticular, the parameters used for IK,ST were only a roughestimation and this current plays an important role in deter-mining the spike threshold and the firing frequency. It will beimportant to further characterize this new current. There wasalso some uncertainty in the description of IK,A. Although IK,Adisplays 2 inactivation constants, only the fast one was mod-eled. A possible slow inactivation (� � 400–800 ms at mem-brane potentials below �70 mV) was described in Pelz et al.(1999). It is known that A-type currents can undergo 2 differ-ent and independent inactivation processes (Iverson and Rudy

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1990). A slow inactivation that accumulates over repeatedactivation of the current may underlie the spike broadeningobserved over the course of experimentally recorded spiketrains. The model did not contain a slow inactivation timeconstant and was not able to reproduce such spike broadening.Although the model did show spike broadening in the absenceof IK,A, it still produced an AHP under these conditions, abehavior that was not observed empirically (Fig. 8). The AHPin the model was ascribed to the inactivation of INa. Clearly,more work is needed to explain why 4-AP causes the AHP todisappear. One possibility would be that other inward currentslike ICa can compensate for the inactivated INa. Moreover, themodel did not implement an ICa. Ca2� currents in Kenyon cellsinclude at least 2 different components that cannot be separatedpharmacologically or by voltage protocols (Grunewald 2003).Because of this uncertainty about the exact characteristics ofICa, because ICa had little effect on the spike (Fig. 3C), andbecause no Ca2�-activated K� currents could be found incultured Kenyon cells, ICa was omitted from the final model.However, we did tentatively include a generic ICa [with a slowinactivation as is found in Kenyon cells (Grunewald 2003)] insome preliminary simulations and found that ICa might beresponsible for the decrease in spike amplitude during inducedspike trains by reducing the repolarization of the cell after anspike. The same effect could help terminate a spike train. Bothphenomena can be observed in Kenyon cells but are notmimicked by the model. These results indicate that additionalempirical analyses of ICa are warranted. Finally there was nosustained Na� current in the model. Although a sustained Na�

current has been identified in Kenyon cells (Schafer et al.1994) (its existence could be confirmed in the experimentspresented here), it has not been characterized and attempts toinclude an independent sustained sodium conductance in themodel led either to nonphysiological behavior (i.e., permanentdepolarization) or to sustained spiking after a current stimulus(persistent Na� conductance �0.1% of total Na� conductance)or to a small effect on the spike threshold. Therefore a sus-tained Na� current was not included in the model until moreempirical analyses are available.

In conclusion, the work presented here extended the descrip-tion of voltage-dependent currents in honeybee Kenyon cells.A model, which was built based on the present data and on datafrom previous studies, helped to identify a new outward com-ponent of the current (IK,ST) that has not yet been described andnow awaits a closer characterization. Even though not allknown currents could be included, the model was able to matchmany of the spiking properties that were found in Kenyoncells. Moreover, the spiking characteristics of the model couldbe changed by simple piecewise adjustments to the membraneconductances. Thus the full range of spiking properties thatwere observed in vitro could be simulated by the model, whichsuggested that the present model is a canonical representationof Kenyon cells and confirms the validity of the electrophysi-ological data about the individual currents. Future investiga-tions of the roles of Kenyon cells in information processingmay benefit from the physiological knowledge gained by thismodel.

A C K N O W L E D G M E N T S

We thank Dr. C. Pelz for providing original current traces of IK,A and M.Ganz for technical assistance with cell culture techniques.

G R A N T S

This work was supported by National Institute of Neurological Disordersand Stroke Grant P01NS-38310, National Center for Research ResourcesGrant ROIRR-11626, and the Deutsche Forschungsgemeinschaft SFB 515/C5.

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