Frequency-selective transmission of graded signals in large monopolar neurons of blowfly Calliphora vicina compound eye

Abstract

The functional roles of voltage-gated K⁺ (K_v) channels in visual system interneurons remain poorly studied. We have addressed this problem in the large monopolar cells (LMCs) of the blowfly Calliphora vicina, using intracellular recordings and mathematical modeling methods. Intracellular recordings were performed in two cellular compartments: the synaptic zone, which receives input from photoreceptors, and the axon, which provides graded potential output to the third-order visual neurons. Biophysical properties of K_v conductances in the physiological voltage range were examined in the dark with injections of current in the discontinuous current-clamp mode. Putative LMC types 1/2 and 3 (L1/2 and L3, respectively) had dissimilar K_v channelomes: L1/2 displayed a prominent inactivating K_v conductance in the axon, while L3 cells were characterized by a sustained delayed-rectifier K_v conductance. To study the propagation of voltage signals, the data were incorporated into the previously developed mathematical model. We demonstrate that the complex interaction between the passive membrane properties, K_v conductances, and the neuronal geometry leads to a resonance-like filtering of signals with peak frequencies of transmission near 15 and 40 Hz for L3 and L1/2, respectively. These results point to distinct physiological roles of different types of LMCs.

visual systems need to capture environmental information with adequate detail over a large dynamic range of light intensities. On the part of photoreceptors and first interneurons, this usually requires large information capacity with information transmission by means of graded potentials instead of action potentials. However, information capacities of individual neurons are necessarily limited. Their operational voltage ranges typically span from resting potentials to equilibrium (Nernst) potentials for synaptic conductances. Thus to compress the information encoded in the often enormous intensity changes of the environmental stimuli into the restricted operational range of sensory neurons and to transmit it with minimal losses, visual systems utilize numerous adaptation mechanisms (reviewed in Cronin et al. 2014). Specifically, at the level of first- and second-order visual neurons, prevention of signal saturation involves adjustment of absolute sensitivity and membrane gain.

In the widely studied blowfly (Calliphora vicina) compound eye, adaptation mechanisms adjust the sensitivity of the visual system according to the mean light intensity. In addition to processes in photoreceptors, signal transmission is modified by adaptation at the level of the first visual synapse between the photoreceptor and the large monopolar cell (LMC) (Laughlin 1989; Laughlin and Hardie 1978). It was previously shown that the synapse plays a crucial role in adaptation of LMCs (Juusola et al. 1995b; Laughlin et al. 1987), operating like a low-pass filter in dim light and like a band- or high-pass filter in bright light. This mechanism maximizes information transmission within the system (van Hateren 1992). While the processes underlying adaptive filtering are well known for photoreceptors (Hardie and Postma 2009; Juusola et al. 1995a; Weckström et al. 1992), these mechanisms in the postsynaptic LMC neurons are known only as far as the photoreceptor transmitter (histamine)-gated channels are concerned, although the properties of network adaptation have been investigated in the Drosophila visual system (Nikolaev et al. 2009; Zheng et al. 2006, 2009).

In the first optic ganglion of the blowfly, the lamina, three large parallel first-order interneurons [LMC types 1 (L1), 2 (L2), and 3 (L3)] receive synaptic input directly from several photoreceptors sharing the same receptive field in different ommatidia, according to the neural superposition configuration (Kirschfeld 1967). LMCs integrate photoreceptors' outputs and transmit the resulting graded potentials to the terminals in the second visual ganglion, the medulla (Shaw 1984). LMC signals are crucial for computing the motion of the visual field (L1/2) and for feature-detection tasks (L3) (Joesch et al. 2010; Rister et al. 2007; Silies et al. 2013). LMCs are 250- to 1,100-μm-long elongated cells with three distinct compartments: a high-resistance cell body, an ∼50-μm-long low-resistance synaptic zone, and a 250- to 1,000-μm-long high-resistance axon (Fig. 1). The diameter of the synaptic zone and the axon is ∼2.5–3 μm. Photoreceptor-LMC synapses are constantly active (Juusola et al. 1996; Uusitalo et al. 1995a; Uusitalo and Weckström 2000), which causes the average membrane resistance of synaptic zone to be very low (Nicol and Meinertzhagen 1982; Strausfeld 1976; van Hateren and Laughlin 1990). The high-resistance cell body does not receive synapses and is not involved in signal generation (van Hateren and Laughlin 1990).

Fig. 1.

The “ball-and-stick” model of a large monopolar cell (LMC). The model consists of 2 equal-diameter (2.7 μm) compartments: a 50-μm-long low-resistance synaptic zone and a 1,000-μm-long high-resistance axon.

In this work we performed experimental and modeling analyses of transmission properties of LMC neurons in the blowfly and investigated how signals are shaped by dynamic filtering dependent on two types of voltage-gated K⁺ (K_v) conductances.

MATERIALS AND METHODS

Intracellular Recordings

All experiments were performed in the blowfly C. vicina with the well-established intracellular recording method as described previously (Laughlin and Hardie 1978; Uusitalo et al. 1995b). Both female and male flies were used. Briefly, borosilicate microelectrodes were filled with a solution containing 2 M potassium acetate; pH was adjusted to 6.8 with a solution containing 5% KH₂PO₄ and 5% KCl. Electrode resistance was between 100 and 200 MΩ; higher-impedance electrodes were used to record from axons. All recordings were performed with an NPI SEC-05L amplifier (NPI), in the discontinuous current-clamp mode (Brennecke and Lindemann 1974; Wilson and Goldner 1975), from two regions of LMCs, the synaptic region in the lamina and the axon in the chiasm between the lamina and medulla. Electrodes were lowered to the lamina via a small hole made in the back of the head capsule. By alteration of the angle of the electrodes they were guided into either the lamina or the chiasm under visual control. Recordings were performed at room temperature. Only the recordings with resting potential of −30 mV and lower and with maximal light-induced hyperpolarization no less than 20 mV were included in analysis. All data are presented as means ± SD.

Mathematical Modeling of LMC Neurons

LMC neurons were modeled as 1,050-μm-long cylinders with a diameter of 2.7 μm, consisting of two compartments with different electrophysiological properties: a 50-μm-long synaptic zone and a 1,000-μm axon (Fig. 1). Such “ball and stick” models were built with NEURON 7.2 software. The synaptic zone is highly folded because of multiple dendritic spines, with a total membrane area of ∼900-1,000 μm² (Nicol and Meinertzhagen 1982). Therefore, by modeling the synaptic zone as a simple cylinder (l = 50 μm, d = 2.7 μm) the membrane area in the model was rendered 2.0–2.4 times smaller than in the real cells. This was compensated by obtaining higher fitted membrane capacitance and conductance values in the synaptic zone than in the axon. This also agrees with the concept of constantly active input synapses, resulting in high conductance values. Fourteen cells were used for fitting to the model: six L3 cells (3 axonal and 3 synaptic recordings) and seven L1/2 cells (3 axonal and 4 synaptic recordings). Tables 1 and 2 summarize parameter values obtained from the fitting.

Table 1.

Fitted parameter values for L3 cells

	Epas-Vr, mV	gpas, S/cm2 (×10−3)	EK, mV	gmax Ka, S/cm2	gmax Kd, S/cm2 (×10−4)	Vshift Ka, mV	Vshift Kd, mV	τinact Ka, ms	cm, μF/cm2
Synaptic zone (3)	0.1 ± 1.8	5.1 ± 0.2	−71.2 ± 10.6	0	92 ± 37	—	19.6 ± 3.4	—	1.82 ± 0.31
Axon (3)	3.6 ± 7.1	0.064 ± 0.01	−68.2 ± 7.7	0	3.42 ± 1.88	—	20.6 ± 3.3	—	1*

Values are means ± SD for number of cells in parentheses. Parameter marked with an asterisk was kept constant.

Table 2.

Fitted parameter values for L1/2 cells

	Epas-Vr, mV	gpas,S/cm2 (×10−3)	EK, mV	gmax Ka, S/cm2	gmax Kd, S/cm2 (×10−4)	Vshift Ka, mV	Vshift Kd, mV	τinact Ka, ms	cm, μF/cm2
Synaptic zone (4)	0.6 ± 1.7	8.3 ± 2.5	−64.6 ± 4.3	0	62 ± 23	—	20.4 ± 5.9	—	2.00 ± 0.44
Axon (3)	10.3 ± 2.9	97 ± 37	−67.2 ± 4.5	3.5 ± 2.3	1.51 ± 0.74	48.3 ± 3	16.8 ± 4.3	22.9 ± 5.2	1*

Values are means ± SD for number of cells in parentheses. Parameter marked with an asterisk was kept constant.

Model Parameters and Procedures

Electrophysiological parameters describing the model are listed below. Ranges for parameter values were derived from the previous studies and changed whenever needed.

Shunt conductance.

Shunt conductance (g_shunt) is a nonselective conductance caused by the piercing of the membrane with the recording electrode. The maximal g_shunt is likely to be <10 nS (Ince et al. 1986); however, it cannot be estimated reliably in intracellular recordings. The value of g_shunt used in the model was 2 nS, except from the modeling of transfer ratios and signal propagation, where g_shunt was set to 0. The value of E_shunt, the reversal potential for g_shunt, was set to 0 mV.

Membrane leak conductance.

Membrane leak conductance (g_pas) consists of the postsynaptic Cl⁻ current, which is present even in darkness (Juusola et al. 1996; Uusitalo et al. 1995a; Uusitalo and Weckström 2000) and dramatically reduces the input resistance of the synaptic zone compared with the axon (Laughlin and Osorio 1989; van Hateren and Laughlin 1990). Leak conductance also includes a Na⁺ conductance and a Cl⁻ countercurrent (Uusitalo et al. 1995a). Because leak conductances are poorly studied, membrane leak was modeled as a single background conductance, g_pas. According to previous studies, the specific membrane conductance is in the range of 3.3–6.7 mS/cm² in the synaptic zone and 0.01–0.1 mS/cm² in the axon (Guy and Srinivasan 1988; van Hateren and Laughlin 1990). However, taking into account the cell-to-cell variation in the shunt conductance and the fact that the membrane area in the model's synaptic zone was smaller than in the real cell, wider ranges for g_pas values were stipulated in the model: from 0.001 to 0.1 mS/cm² in the axon and from 2 to 8 mS/cm² in the synaptic zone. E_pas, the reversal potential for the g_pas, is not known experimentally; it was allowed to vary by ±30 mV in respect to the resting potential.

Specific membrane capacitance.

To compensate for the smaller membrane area in the model, the specific membrane capacitance (C_m) was allowed to vary between 1 and 3 μF/cm² in the synaptic zone. A standard value of 1 μF/cm² was used for the axon region.

Cytoplasmic resistivity.

Values for cytoplasmic resistivity (R_i) in the range from 80 to 100 Ω·cm were used in LMC models developed previously (van Hateren 1986; van Hateren and Laughlin 1990). Here we have chosen an intermediate value of 90 Ω·cm.

A-type and delayed-rectifier K⁺ current conductances.

A HH-type voltage-dependent current can be described as (Koch 1999)

$$I_k=g_{\text{max},k}\cdot m\cdot h\cdot \left(V-E_k\right)$$ (1)

where g_max,k is the maximal conductance of the ion channel k, E_k is the reversal potential, and m and h are the activation and inactivation variables, respectively.

m and h can described as

$$m=\text{1}/\left\{\text{1}+\text{exp}\left[\left(V-V_{50m}\right)/s_m\right]\right\}$$ (2)

$$h=\text{1}/\left\{\text{1}+\text{exp}\left[\left(V-V_{50h}\right)/s_h\right]\right\}$$ (3)

where s is the slope factor and V₅₀ is the half-activation or inactivation parameter (V_50m or V_50h, respectively). Parameters for Eqs. 1 and 2 were adopted from previous work (Hardie and Weckström 1990). Activation time constant τ_m was derived by fitting the Boltzmann function (Eq. 4) to the activation time constant values from the same publication.

$${\tau }_m=\left(a_1-a_2\right)/\left[1+\exp \left(V-V_{50}\right)/d_V\right]+a_2$$ (4)

Inactivation time constants were previously reported not to be dependent on voltage; τ_{inact Kd} was in the range from 1,000 to 3,000 ms, and τ_{inact Ka} was in the range from 7 to 35 ms (Hardie and Weckström 1990).

Since the results of the previous patch-clamp study of dissociated LMC neurons (Hardie and Weckström 1990) were obtained from isolated neurons, based on a disrupted lamina preparation, recorded activation/inactivation voltages of K⁺ currents might be different from those when recordings are made in vivo with sharp electrodes. Typically, the recorded membrane potential tends to be less negative and the membrane resistance smaller when sharp intracellular electrodes are used (Li et al. 2004; Staley et al. 1992). Therefore, an additional parameter V_shift was applied to the activation/inactivation and τ_m functions (Eqs. 1–3) to allow shifting of the voltage dependencies of the K_v currents. The resulting equations for A-type K⁺ (K_a) current were

$$m=1/\left(1+\exp \left\{\left[V-\left(-78mV+V_{\mathrm{shift}\mathrm{Ka}}\right)\right]/-2.8\right\}\right)$$ (5)

$$h=1/\left(1+\exp \left\{\left[V-\left(-101mV+V_{\mathrm{shift}\mathrm{Ka}}\right)\right]/-5.6\right\}\right)$$ (6)

$${\tau }_m=\left(6.2ms-1.1ms\right)/\left\{1+\exp \left[V-(-77.1mV+V_{\mathrm{shift}\mathrm{Ka}})/4.1\right]\right\}+1.1ms$$ (7)

The equations for delayed-rectifier K⁺ (K_d) current were

$$m=1/\left(1+\exp \left\{\left[V-(-60mV+V_{\mathrm{shift}\mathrm{Kd}})\right]/-5.5\right\}\right)$$ (8)

$$h=1/\left(1+\exp \left\{\left[V-(-84mV+V_{\mathrm{shift}\mathrm{Kd}})\right]/-8.7\right\}\right)$$ (9)

$${\tau }_m=\left(35.6ms-4.2ms\right)/\left\{1+\exp \left[V-\left(-62.6mV+V_{\mathrm{shift}\mathrm{Kd}}\right)/3.4\right]\right\}+4.2ms$$ (10)

Data fitting.

Parameters were obtained by fitting the model to experimental voltage responses evoked by current pulses. Current pulses were injected into the model via an ideal current clamp (IClamp point process). g_shunt was applied to the stimulation point. The resulting voltage responses were allowed to change in accordance with the experimental results by altering the free parameters of the model (Tables 3 and 4). Fitting was performed with NEURON's Multiple Run Fitter, a tool for computation and minimization of the error between the simulation results and recorded data.

Table 3.

Constant and free parameters of the model: ranges of passive and structural parameters

	d, μm	l, μm	Ri, Ω·cm	ek, mV	gpas,S/cm2	epas, mV	cm, μF/cm2
Description	Diameter	Length	Cytoplasmic resistivity	K channel reversal potential	Leak conductance	Leak channel reversal potential	Membrane capacitance
Synaptic zone	2.7*	50*	90*	−100 mV–Vr		Vr ± 25 mV	1–3
Axon	2.7*	1,000*	90*	−100 mV–Vr	0.5–10 × 10−5	Vr ± 25 mV	1*

Parameters marked with an asterisk were kept constant. All other parameters were allowed to vary within the ranges shown.

Table 4.

Constant and free parameters of the model: ranges of K_a and K_d channel parameters

	gmax Ka, S/cm2	gmax Kd, S/cm2	Vshift Ka, mV	Vshift Kd, mV	τinact Ka, ms	τinact Kd, ms
Description	Ka channel maximum conductance	Kd channel maximum conductance	Voltage dependence of Ka window current	Voltage dependence of Kd window current	Ka inactivation time constant	Kd inactivation time constant
Synaptic zone	0–0.02	0–0.02	−50 to 50	−50 to 50	7–35	1,000–3,000
Axon	0–0.02	0–0.02	−50 to 50	−50 to 50	7–35	1,000–3,000

Parameters were allowed to vary within the ranges shown.

Passive parameters.

At the first stage, the passive membrane parameters g_pas, C_m, and E_pas were fitted. Parameters for the synaptic region were obtained first, as the high-resistance axon has only a small effect on the responses in the synaptic region. While fitting the passive parameters for the synaptic region, the axon was assumed to be a passive cable characterized by the same parameters as described earlier: C_m = 1 μF and g_pas = 1 × 10⁻⁵ S/cm² (van Hateren and Laughlin 1990). Recordings were assumed to be obtained at the synaptic zone midpoint. The passive parameters (g_pas, C_m, and E_pas) were obtained by fitting small (5–12 mV) depolarizing voltage responses recorded from LMCs hyperpolarized by constant current (less than −30 mV), in the apparent absence of voltage-gated currents.

In a long, elongated cell like the LMC, input resistance and therefore conductance depend critically on the place of recording (Guy and Srinivasan 1988). Since we did not know the exact recording position in our experiments, we assumed for modeling purposes that the recordings were performed from the midpoint of the axon (at 550 μm from the distal end of the cell). This is not likely to be very far from the actual recording locations, because the electrode track was aimed toward the middle of the chiasm between the lamina and medulla.

Voltage-dependent conductances.

Next, voltage-dependent parameters were obtained. For each cell, fitting was performed for 6–10 voltage responses, ranging from −65 mV to +55 mV relative to the resting potential. The g_pas and E_pas values obtained at the previous stage were used as initial guesses. However, since K_v conductances contribute to both resting potential and input resistance, E_pas and g_pas were allowed to vary while fitting the voltage-dependent parameters. Voltage-dependent conductances were obtained initially for the synaptic region and then for the recordings from axons. First, an appropriate synaptic model was selected according to the putative type of the LMC as deduced on the basis of the axonal recording. At this stage, the previously obtained synaptic g_pas and g_{max k} values were kept constant. All other parameters—E_pas, E_k, g_{max Kd axon}, g_{max Ka axon}, V_{shift Ka}, V_{shift Kd}, t_{inact Kd}, and t_{inact Kd}—were refitted. The procedure was repeated several times with different combinations of initial synaptic g_pas and g_{max k} values. However, this had a small effect on the fitted values; a greater effect was exerted by the overall synaptic resistance, which was found to be quite consistent within each LMC class.

Modeling the signal transmission.

In the models for studying impedance transfer and signal transmission between different compartments of LMCs, g_shunt was set to zero as to reflect the in vivo situation. In the model this led to small changes, including hyperpolarization of the resting potential by 3.6 mV and an increase in input resistance by 2.8 MΩ in the synaptic zone and by 8.9 MΩ in the axon.

RESULTS

Large Monopolar Cells

Although L1 and L2 neurons terminate in different layers of the second optical ganglion (Strausfeld 1971), they have similar morphology and electrophysiological properties and cannot be reliably separated with the methods used here. However, L3 cells are anatomically different, have more negative resting potential and higher input impedance, and are often characterized by a light response with a pronounced off-spike after the end of stimulus and by greater sustained hyperpolarization during stimulation by light (Laughlin and Hardie 1978; Uusitalo et al. 1995b; Weckström and Laughlin 2010). Therefore, in this study LMCs were separated into two groups, L1/2 and L3, based on input impedance, resting potential, and the character of light response.

The synaptic and axon recordings were distinguished on the basis of electrode insertion angle, the presence (in the lamina) or absence (in the axons) of alternating penetrations of depolarizing photoreceptor responses, and differences in the input resistance and in the magnitude of changes in the receptive field of the cells over the course of successive impalements, which are large for the axon recordings because of a peculiar arrangement of the axons in the chiasm. In addition, high input resistance can be considered a very reliable indication of axonal recording (Guy and Srinivasan 1988; van Hateren and Laughlin 1990). However, in some cases off-spike responses typical for L3 were observed in cells that could otherwise be identified as L1/2 cells. Since in these cases there was no maintained hyperpolarization during light responses (Fig. 2D) and high input resistance (>45 MΩ) was observed, these recordings were classified as L1/2 axonal recordings. Of 27 cells used for analysis, 18 were recordings from the lamina and 9 from the axons. Among the lamina recordings, 7 cells were identified as L3 and the other 11 as L1/2. Among the axon recordings, 4 cells were identified as L3 and 5 as L1/2.

Fig. 2.

Responses of LMC neurons to light. A: typical LMC type 3 (L3) response to a 250-ms steady light stimulus (horizontal black bar) is characterized by maintained hyperpolarization during the response with a pronounced light-off spike at the end (arrow); resting potentials of individual cells are shown on left. B: LMC type 1/2 (L1/2) response was characterized by a more depolarized resting potential and faster decay of the response toward the resting level than in the L3 cell in A. C and D: responses of L3 and L1/2 neurons as recorded from the axons.

The resting potential was −38.4 ± 3.2 mV (n = 15) in L1/2 cells and −49.3 ± 6.5 mV (n = 11) in L3 cells. Passive and voltage-dependent membrane properties were studied in the current-clamp mode with injections of hyperpolarizing and depolarizing current. Input impedances calculated from voltage responses to a hyperpolarizing 1-nA current step were considerably smaller in the lamina than in the axons (Fig. 3). In the lamina, the average impedance was 19.6 ± 2.8 MΩ (n = 11) for L1/2 cells and 29.2 ± 5.6 MΩ (n = 7) for L3 cells. In the axon recordings, the corresponding values were 46.3 ± 9.9 MΩ (n = 5) and 57.8 ± 15.9 MΩ (n = 4) (P = 0.223).

Fig. 3.

Experimental classification of LMCs. L3 cells have more hyperpolarized resting potential (V_rest) and higher input resistance (R_in) than L1/2 cells. High input resistance was used as a sign of an axonal recording.

Recording and Modeling of K_v Conductances in LMCs

Neurons identified as L1/2 were characterized by strikingly dissimilar voltage responses to current steps injected in the dark in the two cellular compartments studied (Fig. 4). In the synaptic region, voltage responses showed generally less voltage dependence than the corresponding responses of L3 cells (see below), with almost purely passive (RC circuit-like) responses observed in some cases. During modeling, the best fits were obtained with higher g_pas and smaller K_d conductance values than in L3 cells. No evidence for K_a current was found.

Fig. 4.

Typical current-clamp recordings and modeled traces for L1/2 cells. A and B: examples of responses to injected current steps recorded either from the synaptic region (A) or from the axon (B). C: fitting of the axonal recording with the model. D: voltage-gated K⁺ (K_v) currents obtained from the model after the fitting of traces in C. Gray trace, total K_v current [A type (K_a) + delayed rectifier (K_d)]; black trace, K_d current. E: steady-state conductance (g) as a function of membrane potential (V_m).

In contrast, axon recordings revealed the presence of a pronounced K_a conductance, especially at voltages positive to −30 mV (Fig. 4B). The voltage responses presented first with a relatively short depolarizing transient, indicative of rapid opening of transient K_a channels, and then, after a brief dip, with a progressive increase in voltage (Fig. 4B, top trace), suggesting inactivation of a conductance accompanied by an increase in membrane resistance. (Note that in these recordings voltage responses to injected current approximate changes in membrane resistance plus membrane charging.) Fitting of the experimental voltage responses to the model (Fig. 4C) revealed the underlying K_v conductances (Fig. 4D). Figure 4E shows the voltage dependence of the total sustained membrane conductance for the axonal recording from Fig. 4B. These results clearly demonstrate the differences in voltage dependencies of activation between the transient and sustained K_v conductances. K_d activated at voltages between −50 and −70 mV (Fig. 4D). A small fraction of these channels were open at resting potential. Stepping to more negative potentials but still above the reversal potential (E_K) for K_d channels resulted in slow relaxation of K_d current (Fig. 4B, 4th trace from top). More hyperpolarizing pulses (Fig. 4B, 5th and 6th traces from top) evoked a residual rapidly deactivating inward K⁺ current.

Fig. 5.

Typical current-clamp recordings and modeled traces for L3 cells. A and B: examples of responses to injected current steps recorded either from the synaptic region (A) or from the axon (B). C: fitting of the axonal recording with the model. D: K_v current obtained from the model after the fitting of traces in C. E: steady-state conductance as a function of membrane potential.

However, the model was not able to fully reproduce the experimental voltage responses. Specifically, K_a and K_d currents used in the model could not fit properly the large fast transients at the onset of responses to depolarizing pulses. One reason for this could be that depolarization activates voltage-gated Na⁺ channels, which might be expressed in the axons of these neurons (Uusitalo et al. 1995b). This is supported by our observations: when the cell membrane was hyperpolarized with steady current and depolarizing current pulses were applied, the changes caused by the activation of K_a conductance often disappeared but the fast depolarizing transient at the onset remained (data not shown). In addition, the contribution of other conductances, such as the inward Cl⁻ conductance found in insect photoreceptors (Salmela et al. 2012; Ugarte et al. 2005), cannot presently be ruled out.

Neurons identified as L3 were characterized by the noninactivating K_v current, as can be inferred from voltage responses to depolarizing current injections in the dark (Fig. 5, A and B) displaying relaxation toward a steady potential during depolarizing current pulses. No sign of the transient K_a conductance was detected. Axonal recordings demonstrated much higher input resistances than recordings from the synaptic zone. Figure 5C shows superposition of the experimental and modeled voltage responses, while Fig. 5D shows the corresponding K_d current derived from the model of the axon. Properties of K_d in L3 cells were very similar to those in L1/2. During modeling of L3 neurons, introduction of a transient K_a current did not result in better fits; in fact, best fits were achieved when K_d channels were noninactivating or very slowly inactivating.

Analysis of voltage responses to current steps with the model revealed the following properties of K_v conductances. The E_r for K⁺ was between −65 and −70 mV in both types of LMCs. The maximal K_d conductance values in L3 cells were on average higher than in L1/2 cells and consistent with the previous report (Hardie and Weckström 1990). In both cell types K_d conductance was much larger in the synaptic zone than in the axon (on average by ∼30 times). Voltage dependencies of activation and inactivation for K_d and K_a conductances are plotted in Fig. 6A. Voltage dependencies of activation time constants are shown in Fig. 6B (the inactivation time constant of K_a conductance was made non-voltage-dependent in the model, equaling 19.9 ms). In both cell types K_d conductance is activated within the operational range, which spans from ∼40 mV below the resting potential to ∼20 mV above it (the half-activation potential was −40 mV in L3 cells and −41 mV in L1/2 cells). K_d channels closed by deactivation only at highly hyperpolarizing responses. Note that the arrows in Fig. 6A depict the physiological operating range determined in light responses such as those shown in Fig. 2, with the arrow to the left indicating its lower limit (the values obtained from the light-on transient), the arrow to the right approximating the upper limit (from the light-off transient), and the transverse tick indicating the resting potential value. It should also be noted that these potentials were reached by using unrealistically bright light stimulation of the dark-adapted eye. Compared with K_d channels, K_a channels in L1/2 cells operate at more depolarized membrane potentials (half-activation potential was −30 mV and half-inactivation potential was −53 mV), from 0 to 20 mV above the resting potential, thus mainly affecting only the depolarizing light-off responses.

Fig. 6.

K_v kinetics parameters. A and B: voltage dependencies of activation and inactivation for K_v currents in L3 (A) and L1/2 (B) cells obtained from the model after data fitting; vertical ticks indicate mean resting potential, and arrows show the operating voltage range as recorded from maximum light-on and -off responses. C: voltage dependencies of K_d activation time constants in both types of neurons. D: voltage dependence of K_a activation time constant (τ_m) in L1/2 cells.

Signal Transmission in LMCs

Input impedance determines the character of signal attenuation as it propagates along the cell. A typical example of the voltage response to white noise-modulated current stimulus is shown in Fig. 7.

Fig. 7.

Typical example of a voltage response to white noise-modulated current stimulus; the trace was recorded from the synaptic zone of a putative L1/2 cell.

Signal filtering and transfer properties of different cell classes were studied with the model. The experimental and modeled membrane impedance functions calculated for different membrane potentials are shown in Fig. 8. The relatively low resistance of the synaptic zone is caused by the sustained activation of postsynaptic histaminergic Cl⁻ channels (Uusitalo and Weckström 2000). Low resistance facilitates transmission of high-frequency signals and is associated with a relatively high membrane cutoff frequency. L1/2 and L3 were characterized by similar high-pass properties in the synaptic zone (Fig. 8A), although in the case of L1/2 neurons high-pass filtering was less prominent. In contrast, higher impedance of axons resulted in lower cutoff frequencies than in the synaptic zones. The 3 dB cutoff frequencies were 169 ± 53 Hz for L1/2 and 110 ± 10 Hz for L3 in the synaptic zone and 85 ± 17 Hz for L1/2 and 46 ± 9 Hz for L3 in the axon. When the L3 cell was hyperpolarized in order to deactivate all K_v conductances and then stimulated by white noise-modulated current stimulus (Fig. 8A, black dashed trace), its impedance function started to show passive (RC circuit-like) low-pass properties.

Fig. 8.

Recorded and modeled impedance functions at different membrane potentials. The same white noise-modulated current input that was used in recordings was also used in simulations; all traces are FFT smoothed. A: experimental and modeled input impedance in the synaptic region of L3 and L1/2 cells at different potentials. Note the band pass-like character of the curve at the resting potential and pure low-pass filtering at hyperpolarized potentials (dashed traces; only L3 results are shown). Experimental curves are averages of 4 L3 and 6 L1/2 cell recordings, while simulated traces are obtained from 1 L1/2 and 1 L3 cell model. B and C: recorded and modeled impedance functions for the L3 and L1/2 axons, respectively; the parameters for computer simulation were obtained from the corresponding recordings.

Since these results revealed that the synaptic zone impedance strongly depends on membrane potential (Fig. 8), it was necessary to determine what happens to graded voltage signals as they propagate along the LMC axon to the next ganglion, the medulla. Two approaches were utilized for this purpose: modeling of voltage transfer ratios and modeling of propagation of the actual voltage waveforms. To determine the contribution of K_v conductances to signal propagation, the functional LMC models containing K_v conductances were contrasted with the passive models, which lack K_v conductances. In the passive models, membrane resistance values (g_{pas axon} and g_{pas syn}) were adjusted so that steady-state impedances (at 0 Hz) at rest were identical to the corresponding values from the functional models.

Figure 9 shows voltage transfer ratios between two compartments, the synaptic zone and the end of the axon, modeled for both LMC types under different conditions including the passive membrane, at resting potential, and at four hyperpolarized or depolarized voltages. The results for functional models are quite similar for L1/2 and L3 neurons and characterized by continuous changes in the properties of voltage transfer function from the lower to higher limit of the operational voltage range. At the most negative potential (V_rest −35 mV), the membrane is completely passive, representing a typical low-pass filter with high gain and small cutoff frequency. At more depolarized voltages, opening of K_d channels reduces the transfer gain but confers band-pass properties and increases cutoff frequency. At still more positive voltages (V_rest +25 mV), opening of K_a channels further accentuates high-pass filtering in L1/2 but not in L3 cells (Fig. 9B). Specifically, in the L3 model cell the maximum transfer ratio at resting potential was 0.62 at 16 Hz. In the L1/2 model, under the same conditions, the maximum transfer ratio was 0.32 at 40 Hz. The relatively low input impedance in the axon of the L1/2 model is caused by the combination of the relatively low resistance in the synaptic zone, high K_d conductance at rest, the presence of K_a channels, and low g_{pas axon} value.

Fig. 9.

Modeled voltage transfer ratios for transmission of impedance from the synaptic zone to the end of the axon. Results are shown for L3 (A) and L1/2 (B) models at different membrane potentials as defined in the key. Top: schematics show impedance value ranges in different parts of the cells. Bottom: voltage transfer ratios.

To test how the actual light responses are transferred along the axon, light responses recorded in the synaptic zones were fed into the models in the simulated ideal voltage-clamp mode. The waveform was introduced at the origin of the axon, and the transmitted signal was computed at its end (Fig. 10). The passive model of L3 shows two effects of high membrane resistance: the signal is transmitted with little decrement, but it is also strongly low-pass filtered, with its fast transients attenuated. In contrast, the functional L3 model facilitates transfer of higher frequencies, albeit with a greater overall attenuation as can be seen from the light-on and -off responses, which are sharper and larger than in the passive model (Fig. 10A).

Fig. 10.

Modeled signal transmission from the synaptic zone to the end of the axon. Results are shown for L3 (A) and L1/2 (B) models. The recorded light response (gray trace) was used in the model as an input at the proximal end of the axon, and the output was calculated under different conditions, including passive and normal models, as well as with K_d or K_a conductances selectively removed (in the L1/2 model).

Likewise, although the relatively low impedance of L1/2 cells attenuates signal amplitude stronger than in the L3 model, the relative amplification of the high-frequency band due to the presence of K_a and K_d conductances allows a more reliable transmission of high-frequency transients along the axon. Interestingly, the depolarizing light-off transient is preserved better than the light-on transient, apparently because of the activation of K_a conductance (compare with the trace elicited in the model with K_a absent). The role of K_d conductance in signal transmission can also be visualized by its removal (Fig. 10B, blue trace). In the absence of K_d channels, membrane resistance increased and resting potential depolarized, and, as a result, the amplitude of the light-on transient increased. However, the light-off transient remained nearly the same because of the intact K_a conductance.

Velocity of signal propagation from the proximal to the distal end of the axon differed for L1/2 and L3 model cells. The delay values were 2.8 and 2.4 ms in the L1/2 cell and 3.8 and 3.7 ms in the L3 cell, as measured from the peaks of light-on and light-off transients, respectively. In this model the length of the axon was 1,000 μm, which is near the maximal axon length for these cells (Nicol and Meinertzhagen 1982; Strausfeld 1976).

DISCUSSION

Our objective was to study how voltage-dependent K⁺ channels affect transmission of graded voltage signals in neurons, using the LMC neuron from the compound eye of the blowfly as an experimental model. In this work, we have examined voltage-dependent properties of two functional classes of the LMCs, using the single-electrode intracellular recording method (Uusitalo et al. 1995b). Two different compartments of LMCs were targeted, the postsynaptic zone in the first visual ganglion, the lamina, the locus of sign-inverting histaminergic input from photoreceptors (Hardie 1989), and the axons. To build computational models of these neurons, we used the previously published characteristics of LMCs (Hardie and Weckström 1990), the anatomical data (see, e.g., van Hateren and Laughlin 1990), and the parameters obtained in this study. Finally, mathematical models were used to evaluate frequency-selective signal transmission and filtering properties of LMCs.

Limitations of the Study

The types of LMCs were identified according to the previously defined electrophysiological properties of these cells, including resting potential and input resistance values, and the shape of light response (Uusitalo et al. 1995b). The differential expression of K_a and K_d was also described previously, in a patch-clamp study of dissociated LMC neurons (Hardie and Weckström 1990): K_d channels were found in both cell types, whereas K_a channels were detected only in the putative L1/2 cells. The maximal conductance values were similar in this and the previous study. However, some inconsistencies were detected as well. The major one was a rather dramatic depolarizing shift for voltage dependencies of K_v channel activation: in this study K_d and K_a activation voltages were shifted by about +20 mV and +48 mV, respectively, compared with the patch-clamp study. While the reasons for this are not known, the recording conditions differ drastically between the two methods, with many factors that might be involved in the discrepancy, from dissimilar ionic balance to differing electrode-membrane interface properties. It should be noted that similarly large discrepancies in the half-activation potentials for K_a and K_d were observed previously in Drosophila (Hardie 1991; Niven et al. 2003). Interestingly, the activation potentials for K_a and K_d conductances reported here were close to those found with the intracellular recording method for K_a and K_d channels in LMCs of the locust (Benkenstein et al. 1999). It also cannot be ruled out that K_a channels are differentially expressed in the distal parts of the axon. In such a scenario, stimulating current signals injected in the middle of axons would become substantially attenuated before reaching K_a expression loci, resulting in erroneous estimation of the activation potential.

There are several shortcomings in our mathematical model. First, the model was built in such a way that the channels are distributed homogeneously along the axon, which might be not the case for real cells. However, this is the most conservative assumption and the best approximation that can be achieved currently. Second, the off-spikes, probably involving Na⁺ channels (Uusitalo et al. 1995b), were ignored in this model during fitting. Third, physiologically the impedance of the synaptic zone may be lower than in the model, but because of the transient nature of LMC signals this is likely to be inconsequential (Laughlin et al. 1987). We believe that these discrepancies did not lead to substantial errors in evaluation of filtering properties and signal transmission.

Properties of LMCs

Many neurons, such as photoreceptors and other neurons in the retina, cochlear hair cells (Eatock 2000; Fettiplace and Fuchs 1999; French 1992), and several types of interneurons in various areas of the nervous system (Roberts and Bush 1981), signal without action potentials. It is established that voltage-gated Na⁺ channels expressed in action potential-generating neurons underlie the frequency dependence of signal generation (Debanne 2004; Hutcheon and Yarom 2000; Mauro et al. 1970). However, K_v channels expressed in the neurons can alone alter membrane filtering to a similar effect, conferring band-pass, resonance-like characteristics. The passive properties of cell membranes form low-pass RC filters, limiting high-frequency transmissions. This is then dynamically modified by K_v channels, causing attenuation of low frequencies. Depending on the values of high- and low-frequency roll-offs, the apparent resonance (that is not a real amplification) can be more or less prominent (Hutcheon and Yarom 2000), as also shown in insect photoreceptors (Weckström et al. 1991; Weckström and Laughlin 1995) and fly HS neurons (Borst et al. 2003).

The second-order visual neurons in the insect compound eye, the LMCs, were long considered to be passive, with a low-resistance synaptic region and a high-resistance axonal membrane. According to the cable theory (Koch 1999), a passive cable forms a low-pass filter, which attenuates high-frequency signals and causes a loss of potentially valuable information. In L1 and L2 it has been shown that the high impedance of the axon allows passive transmission of graded signals, albeit with attenuation of fast transients (van Hateren and Laughlin 1990). This attenuation should be particularly strong in L3 cells characterized by higher input resistance than L1/2 cells (Uusitalo et al. 1995b). Thus a purely passive transmission along a high-resistance cable may be inadequate for the behavioral and ecological demands of the highly visual blowfly.

The finding of K_v channels in LMCs (Hardie and Weckström 1990) raised an important question regarding their possible role in the transmission of visual information in the axons, in a cell type-specific manner, according to the patterns of expression of specific types of K_v channels (the channelome). In insect photoreceptors, K_v channels regulate gain and frequency response of the membrane (Anderson and Hardie 1996; Salmela et al. 2012; Weckström and Laughlin 1995). Similar sets of channels were found in LMCs of other dipteran insects (Skingsley et al. 1995) and in the desert locust (Benkenstein et al. 1999). In addition, similar K_v channels are expressed in many other “nonspiking” interneurons, e.g., in photoreceptors and interneurons in vertebrate retina (Klumpp et al. 1995; Pinto and Klumpp 1998) and in local nonspiking motor interneurons in the locust, which receive information from mechanoreceptors (Barnes 1994; Laurent 1990, 1991).

Here we demonstrated that blowfly L1/2 cells express mainly rapidly inactivating K_a channels in the axons, whereas the L3 cells predominantly express delayed-rectifier K_d channels. Since the kinetics of K_v channels is strongly voltage and time dependent, these channels can plausibly provide a mechanism for differential transmission of different frequency bands of signals under dissimilar stimulation conditions, and the efficacy of these mechanisms will be not the same for different types of LMCs. The hypothesis of frequency-selective transmission is supported by the findings that different types of LMC project to different layers in medulla (Campos-Ortega and Strausfeld 1972) and that in Drosophila a clear functional specialization among LMCs was found, with L1 and L2 mainly providing input for the motion detection subsystems and L3 mediating orientation behavior (Rister et al. 2007). Moreover, L3 in the fruit fly is characterized by greater rectification and a higher gain for contrast decrements. This stands in contrast to the properties of other LMC types characterized by similar responses to contrast increments and decrements. Furthermore, L3 showed a slower impulse response than L1/2 (Silies et al. 2013).

Signal Filtering in L1/2 and L3

In L1/2 cells, the synaptic zones have very low resistance and both K_d and K_a currents are expressed in the axons; hence axon impedance is lower than in L3 cells, allowing transmission of higher frequencies. The K_d channels are partly open over the whole operational range, selectively attenuating lower frequencies of signals, thus ensuring the band-pass character of transmission. In contrast, K_a channels activate only at more depolarized potentials and are responsible for further narrowing of the pass band and shifting it toward still higher frequencies. Since K_a conductance is active only at depolarized potentials and fast A-type K⁺ currents are usually associated with spikes (Gustafsson et al. 1982; Rogawski 1985; Rudy 1988), its function in L1/2 neurons is clearly to modify the depolarizing light-off transients, while simultaneously altering the lamina-medulla transfer characteristics. The lower passive impedance of L1/2 cells is associated with higher cutoff frequency than in L3 cells but also with greater overall signal attenuation due to the relatively low gain.

In contrast, the passive impedance of L3 cells is high, providing large gain and allowing low-frequency signals to be transferred with little decrement. However, the signals are more strongly low-pass filtered than in L1/2 cells. What is then the function of small light-off spikes in L3 cells, if they cannot be transmitted effectively? One possibility is that they can be regenerated along the axon by Na⁺ channels and thereby retain the emphasizing effect on the off-response. This is likely to be true for similar “minispikes” in other systems (e.g., Baden et al. 2013; Hausser et al. 2000; Rien et al. 2011; Vallet et al. 1992; Weckström et al. 1993). The explanation for spikes or spikelike light-off responses in L3 cells remains a mystery, because they seem not to be needed for orientation behavior in fruitflies (Rister et al. 2007), although it could be a kind of feature detection system, with light-off spikes emphasizing light-dark borders of objects, but there is currently no experimental evidence for this.

Activation of K_d channels causes high-pass filtering of signals in both cell types (Hutcheon and Yarom 2000; Weckström and Laughlin 1995). This can reduce the intrinsic noise generated by synaptic transmission, which occurs predominantly within low frequencies. Long axons with high resistance filter the high-frequency noise arising in many stages of neural signal generation (Faisal et al. 2008). However, the presence of K_v conductances in the axons of LMCs, which contribute to the relatively hyperpolarized resting potentials, raises a question on the feasibility of reliable signal transmission by the presynaptic voltage-gated Ca²⁺ (Ca_v) channels, since most Ca_v isoforms are activated by more depolarizing potentials and thus information encoded in light intensity increases of the stimulus, which are transmitted by the decreases in membrane potential, would be partially lost. However, if Ca_v channels expressed in the LMC ribbon synapses in the blowfly resemble the analogous Ca_v channels in the periphery of visual and auditory systems of vertebrates (Ca_v1.3 and Ca_v1.4) characterized by very negative activation thresholds (Simms and Zamponi 2014), such a concern would be irrelevant. On the other hand, if L3 is indeed mainly involved in detection of contrast decrements, then the present configuration of the channelome is quite suitable for that purpose.

In conclusion, L3 cells transmit a low-pass version of the signal with high gain, with K_d channels allowing transmission of high frequencies to keep the transmitted frequency band adequate. On the other hand, L1/2 cells transmit a more high-pass version of the signal, with K_a channels used to increase high-frequency transmission and modify light-off spikes.

GRANTS

This work was supported by a grant from the Academy of Finland (no. 269332).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

Author contributions: J.R. and M.W. conception and design of research; J.R. performed experiments; J.R. analyzed data; J.R. and M.W. interpreted results of experiments; J.R. prepared figures; J.R. and M.W. drafted manuscript; J.R. and M.W. edited and revised manuscript; J.R. and M.W. approved final version of manuscript.