Sensory systems must extract behaviorally relevant information and therefore often exhibit a very high sensitivity. How the nervous system reaches such high sensitivity levels is an outstanding question in neuroscience. Weakly electric fish (Apteronotus leptorhynchus/albifrons) are an excellent model system to address this question because detailed background knowledge is available regarding their behavioral performance and its underlying neuronal substrate. Apteronotus use their electrosense to detect prey objects. Therefore, they must be able to detect electrical signals as low as 1 μV while using a sensory integration time of <200 ms. How these very weak signals are extracted and amplified by the nervous system is not yet understood. We studied the responses of cells in the early sensory processing areas, namely, the electroreceptor afferents (EAs) and pyramidal cells (PCs) of the electrosensory lobe (ELL), the first-order electrosensory processing area. In agreement with previous work we found that EAs cannot encode very weak signals with a spike count code. However, PCs can encode prey mimic signals by their firing rate, revealing a huge signal amplification between EAs and PCs and also suggesting differences in their stimulus encoding properties. Using a simple leaky integrate-and-fire (LIF) model we predict that the target neurons of PCs in the midbrain torus semicircularis (TS) are able to detect very weak signals. In particular, TS neurons could do so by assuming biologically plausible convergence rates as well as very simple decoding strategies such as temporal integration, threshold crossing, and combining the inputs of PCs.
- weak signal detection
- sensory processing
- weakly electric fish
sensory systems are the interface between an animal and its environment. For a species' fitness it is therefore essential that this interface capture all behaviorally relevant information for, e.g., localization of prey and navigation. Depending on their habitat and behavioral repertoire the performance level that different sensory systems have to attain varies a lot. Hence, different animal species are specialized in extracting specific information relevant for their survival, and this sometimes requires extracting very weak signals [visual system: humans (Bouman et al. 1985), flies (Borst and Haag 2001); auditory system: barn owls (Payne 1971); olfaction: fish (Hara 1994)]. In several cases evolutionary pressure has even driven the sensitivity of sensory systems close to the limits imposed by physical constraints (Bialek 1987; Borst and Haag 2001; Sebastien et al. 2000).
Weakly electric fish, for example, sample their environment by sensing distortions of their self-generated electric field, which is generated by their electrical organ discharge (EOD). That weakly electric fish use the electrosensory system for spatial navigation tasks, communication, and prey detection has been known for decades. Nevertheless, it is still astonishing to realize how this sense has evolved to be so exquisitely sensitive. Behavioral studies have shown that the black ghost knifefish (Apteronotus albifrons) is able to detect electrical signals as weak or weaker than 1 μV (Knudsen 1974; Nelson and MacIver 1999) with a sensory integration time of <200 ms (Nelson and MacIver 1999). How such weak signals are decoded by the nervous system is still an unsolved problem.
In this study, we addressed this problem by focusing on the first electrosensory processing steps: the primary electrosensory afferents (EAs) and the pyramidal cells (PCs) of electrosensory lobe (ELL) of the hindbrain. EAs carry information about spatially localized changes in the amplitude of current flow through the skin to the ELL. In the ELL, EAs trifurcate and project topographically to three somatotopic maps of the body surface [lateral segment (LS), centrolateral segment (CLS), centromedial segment (CMS); Carr et al. 1982; Heiligenberg and Dye 1982]. Each map is characterized by a particular receptive field (RF) size. Furthermore, network and cell-intrinsic properties result in map-specific frequency tuning curves. PCs in the LS have large RFs and are tuned temporally to high frequencies, making them suitable to respond to communication signals emitted by other fish, while CMS cells have small RFs and respond to low frequencies, indicating their involvement in prey capture behavior. Cells in the CLS have intermediate RF sizes and can switch their tuning properties depending on stimulus geometry (Chacron et al. 2011; Krahe and Maler 2014). CLS PCs have been suggested to be optimal for early prey detection because they combine the ability to integrate over a large population of EAs with low-pass characteristics in response to local (prey) stimuli (Krahe et al. 2008; Maler 2009a, 2009b). Hence, on the basis of their known properties PCs in the CLS and CMS should be most sensitive to prey objects, and accordingly we investigated their sensitivity to these signals.
Several behavioral and theoretical studies have shown that just-noticeable preylike sensory signals do not modulate the firing rate of afferent spike trains significantly and are difficult to distinguish from the natural rate variability (Babineau et al. 2007; Gussin et al. 2007; Lüdtke and Nelson 2006). This is in agreement with the data we obtained from EAs. However, at the level of the ELL we showed that even very weak stimuli give rise to an increase in PC spike count, suggesting that a spike timing or spike pattern code may be transformed into a rate code at the EA-to-PC connection (Nesse et al. 2010). PCs project to a large midbrain region [torus semicircularis (TS)] that contains neurons responsive to prey motion (Khosravi-Hashemi and Chacron 2012; Vonderschen and Chacron 2011). In the last part of this work we modeled TS neurons that receive the convergent input spike trains of previously recorded PCs. Despite using a very generic model based on minimal assumptions about the underling circuitry, we found that such putative higher-order neurons can extract information close to the limits of the behavioral performance.
MATERIALS AND METHODS
Surgery was performed as previously described (Marsat et al. 2009; Middleton et al. 2006). Apteronotus leptorhyncus (n = 22) and albifrons (n = 2) were used for experiments. These fish are similar in terms of their appearance and EOD rate (Turner et al. 2007). Importantly, no notable differences in the first-order processing centers regarding anatomy have been found, and both species have been used in parallel in anatomical studies that were essential for establishing the circuit diagrams of the ELL (Maler 1979; Maler et al. 1991). Preliminary analyses revealed no difference (not even the slightest trend) in the responses, and the data were therefore pooled across species. Briefly, fish were respirated during surgery with demineralized water containing tricaine methanesulfonate (Finquel MS-222; Argent Chemical Laboratories, Redmond, WA) as general anesthetic. To ensure that the skin and receptors did not dry out during surgery, the skin was kept moist by placing a tissue over the fish that was soaked in water from the experimental tanks. The skin and skull above the ELL were removed after the application of local anesthetic (Anbesol; Wyeth Consumer Healthcare, Mississauga, ON, Canada). After surgery the skull anterior to the surgery hole was glued to a post for stability. General anesthesia was stopped, and the fish was immobilized with an injection of curare (pancuronium bromide). The fish was then transferred to the experimental tank (40 × 45 × 20 cm) containing water with a conductivity around 130–230 μS and a temperature kept between 25 and 27°C.
In vivo, single-unit recordings of PCs were performed with metal-filled extracellular electrodes (Frank and Becker 1964). PCs can easily be located by the anatomy of the ELL and overlying cerebellum as well as by their response properties (Bastian and Courtright 1991; Saunders and Bastian 1984). The electrode placement relative to the three maps of the ELL was determined from surface landmarks and recording depths (Maler et al. 1991). Recordings were limited to the centrolateral and centromedial ELL segments. In analogy to the ON/OFF system of retinal ganglion cells in vertebrates, PCs come in pairs (Bastian et al. 2002; Maler 1979). EAs contact PCs either directly (ON or E cells or basilar PCs) via excitatory synapses or indirectly through GABAergic inhibitory interneurons (OFF or I cells or nonbasilar PCs) (see Fig. 4A). Hence, ON and OFF cells respond with excitation to stimuli of opposite sign. Furthermore, deep, intermediate, and superficial PCs can be distinguished on the basis of firing rate (Bastian and Nguyenkim 2001). PC types, ON vs. OFF as well as deep/intermediate or superficial, were identified on the basis of recording depth and previously established firing characteristics (Bastian and Courtright 1991; Saunders and Bastian 1984). For EA recordings high-resistance glass micropipettes (90–120 MΩ) containing 3 M KCl solution were used. Electrodes were advanced through the hindbrain with a microdrive (Burleigh; triple axes in vivo Scientifica S-IVM-3000) until either the PC or the EA layer was reached. When glass electrodes were used, EA action potentials were recorded and amplified with Axoclamp 900A (Molecular Devices, Sunnyvale, CA). Extracellular recorded action potentials were amplified before digitalization (model 2015F; Intronix Technologies). The signal was digitized at 20 kHz with a Power 1401 analog-to-digital converter [Cambridge Electronic Design (CED), Cambridge, UK] and collected in Spike2, version 7.03 (CED). All experiments and protocols were approved by the University of Ottawa Animal Care Committee.
The electric organ of Apteronotus consists of modified motor neurons; hence their EOD remains intact during the neuromuscular blockade used in these experiments. The unperturbed EOD was recorded between the head and the tail of the fish. Each EOD cycle triggered a sine wave generator (195 Universal waveform generator; Fluke, Everett, WA) to output one cycle of a sinusoidal signal of frequency matching that of the fish's EOD. This sinusoidal output was modulated by multiplication with our amplitude modulation (AM) signal. AM signals were created off-line with a sampling rate of 10 kHz. Stimuli were attenuated (PA4; Tucker-Davis Technologies, Alachua, FL), isolated (model 2200; A-M Systems, Carlsborg, WA), and delivered through a dipole centered on the cell's RF. The cell's RF was determined by the position of a local stimulation dipole that best excites the cell. Recordings of the cells were used for analysis only if the neuron produced a clear response to locally presented (within the neuron's RF center) sinusoidal stimuli and the RF was located at the central trunk (with respect to the ventral-dorsal as well as anterior-posterior axes) of the fish's body. The dipole was placed at a distance 2 cm away from the RF of the recorded cell along an axis perpendicular to the surface of the fish. To mimic preylike signals for a slowly moving fish, we gave repeated ramp-hold-ramp stimuli of different amplitudes (see Fig. 2A). The ramp duration was 20 ms and the hold duration was 300 ms, representing the typical stimulus integration time that an animal has during a prey capture scenario (Nelson and MacIver 1999). The stimulus was designed to partly mimic a prey moving parallel to the fish (Fig. 1) during a prey capture scenario (Nelson and MacIver 1999). Even though the stimulus profile in such a scenario would be reflected better by a Gaussian, the ramp-hold stimulus is still a good approximation for weak stimuli at a distance. Furthermore, this stimulus allows us to more accurately estimate stimulus detection as a function of its constant amplitude and also gives us the possibility of testing for different sensory integration times at constant stimulus amplitude. The stimulus was delivered at a rate of 0.5 Hz, allowing the cell to come back to baseline activity between stimulations. In the following a stimulus that locally increases the AM is referred to as an ON-stimulus, while a stimulus that locally decreases the AM is referred to as an OFF-stimulus.
Stimulus intensity was adjusted to obtain a range of amplitudes of the EOD at the surface of the fish between the bottom and top of an artificially generated sinusoidal beat cycle equal to 0–40 μV/cm AM. The stimulus strength was measured in parallel with the delivery with a recording dipole placed 2 cm away from the stimulus electrode and ∼4 cm away from the fish. The measured amplitude of the stimulus at this location should be the same as at the surface of the fish if the electric field produced by the animal is relatively parallel to the fish body. To verify this assumption, for most cells the stimulus strength was measured again after recording directly at the location of the RF. When restricting the recording of cells to those that have RF at the central trunk region, no differences were found in the measurements.
To calculate the maximum number of cells that can be used for prey detection, the stimulus spread on the skin in a prey capture scenario has to be known at the moment of prey detection, along with the RF size and anatomical connections within the neuronal circuits involved (Fig. 1). For our experiments we assumed a detection distance around 2 cm. At this distance a Daphnia would produce a peak signal strength of ∼1 μV across the skin, which should definitely be detectable by the animal based on modeling and behavioral studies conducted primarily on A. albifrons (Knudsen 1974; Nelson and McIver 1999). The skin resistance (ρskin) is ∼3 kΩ·cm2; this is 10 times higher than in the interior of the fish's body at the trunk (Scheich and Bullock 1974), and hence it acts as a voltage divider. By Ohm's law, the change in current density outside the skin is approximately ΔJ = ΔE/ρwater. The current flow across the skin will generate a change in transdermal potential of ΔV = ΔJ·ρskin = ΔE·ρskin/ρwater. With a water resistivity (ρwater) of 5 kΩ·cm (200 μS/cm), a 1-μV transdermal potential will then correspond to ∼1.67 μV/cm (Rasnow 1996).
To calculate the spread of the image of a Daphnia, the Daphnia is represented as a sphere having an electrical contrast of 0.6 (Chen et al. 2005; Maler 2009b). In previous studies the image that the Daphnia creates on the skin was modeled as a two-dimensional Gaussian with different spreads for the longitudinal (θL) and transverse (θT) directions (Maler 2009b). The difference between θL and θT is important because it takes the nonnegligible curvature of the fish's body in the transverse direction into account. If we represent a Daphnia as a sphere with a 2.5-mm radius at a distance of 2 cm, and assume equal potentials at one standard deviation away from the center of the image, then the spread of the image on the skin has the diameters of θL = 19.2 and θT = 15.2 mm (Fig. 1).
For EAs, RFs are small compared with the stimulus; hence for simplicity we assume them as having no spatial extent. Anatomical studies have shown that, on average, 25 EAs converge onto a CMS cell and 100 onto a CLS cell (Maler 2009a). To approximate the RF of PCs we truncated the estimated RFs based on EA projection patterns to a radius of 2θ. The 2θ RF area is 6 mm2 (radius: 1.5 mm longitudinal, 1.3 mm transverse) for CMS cells and 26 mm2 (radius: 3.1 mm longitudinal, 2.7 mm transverse) for CLS cells. The RF center spacing is approximately equal between longitudinal and transverse directions (CMS 2.1 mm; CLS 2.8 mm) (Maler 2009a). It is important to note that the RF estimations here are based only on feedforward projections. It is known that the responses of PCs to a local stimulus can be influenced by feedback, and even nonclassical RFs have been shown (Chacron et al. 2003). However, the threshold for modulating the feedback is higher than for the feedforward projection, and we hence assume that feedback is not modulated during early prey detection (Bastian et al. 2002).
To calculate from this information the number of cells participating in prey detection, one now has to consider that each map in the ELL has three layers of PCs (deep, intermediate, and superficial). These cell types can be distinguished from each other based on the amount of feedback they receive from higher brain areas (Bastian et al. 2004; Bastian and Courtwright 1991; Berman and Maler 1999). Feedback projections are essential to cancel out slow global noise signals (Bol et al. 2011). Deep PCs receive little feedback from higher brain areas, which furthermore acts via nonplastic synapses, and are therefore unable to cancel global “noise” signals arising, e.g., from tail bending (Bastian et al. 2004). Hence it is likely that local weak signals are not detected within the global “noise” by deep PCs. In the following we are assuming therefore that only superficial PCs are participating in the detection of weak signals. This is a relatively conservative estimate of the number of participating cells because intermediate PCs also receive feedback, but it is substantially less pronounced than that for superficial PCs (Bastian et al. 2004). Based on this assumption, we calculated that approximately 50 superficial CMS cells or 20 superficial CLS cells have their RF field covered by the image of the Daphnia; in both cases, this is the number of either ON or OFF cells.
PCs of the ELL all project to the midbrain TS (Bastian et al. 2004). The connectivity within the TS is less well understood. However, it is known that the spatial topography is still conserved in the TS and that the four electrosensory maps converge to the same area within the TS (Maler et al. 1982). RFs in the TS are rather complex but are often larger than those of ELL cells and can extend to about half the fish's body length (Chacron et al. 2009). Therefore, we assume that all activated ELL cells can project to the same TS neuron.
Stimulus integration time.
Behavioral studies have shown that the relative longitudinal velocity between the fish and prey at the time of detection is ∼92 mm/s (Nelson and McIver 1999). If we assume an image size of 19.2 mm in the longitudinal direction for a prey object at a 2-cm distance, then a single EA will be stimulated by the prey signal for ∼210 ms (19.2/92 s). The time that the image is covering the RF of a PC depends on the RF size of the specific map. The proportion of the RF that is not covered by the image is not contributing to the detection of the stimulus, and EAs in the area will act as a noise source (Chacron and Bastian 2008). For reliable detection, we assume that the RF of a cell has to be covered by the stimulus. Based on the RF sizes estimated by Maler (2009a), we now can calculate the time that the image of the Daphnia is covering the RF of a CMS, CLS, or LS PC. This leads to the conclusion that PCs in the CMS can use 176 ms, PCs in the CLS 141 ms, and PCs in the LS only 20 ms as the stimulus integration time. These values are obtained by assuming as before that a single point is covered for 210 ms by the image and subtracting from this value the time an image needs to pass to cover the distances of the respective RF spread in longitudinal direction.
Receiver operating characteristic analysis.
To determine whether a cell could detect the stimulus, a receiver operating characteristic (ROC) analysis based on spike count was performed (see also Wilcoxon test of ranks; Hanley and McNeil 1982). This analysis relies on comparing the probability P(stim) of the number of spikes elicited during stimulation with the probability P(without stim) of the number of spikes without stimulation (Fig. 2). Thirty stimulus repetitions were used to obtain the probability distributions. For our analysis the probability P(without stim) of the number of spikes without stimulation could be referred to spike count either before stimulation [P(before stim)] or after stimulation [P(after stim)]. ROC curves were generated by varying a threshold T on the spike count. ON cells are expected to produce more spikes during an ON-stimulus than without a stimulus present, whereas OFF cells are expected to fire more during an OFF-stimulus. In these cases, for each threshold value, the probability of detection (PD) was calculated as P(stim) > T and the probability of false alarm/detection (PFD) as P(no stim) > T, where “no stim” refers to either before or after stimulation. Furthermore, PCs were expected to produce more spikes before stimulation than after stimulation because of adaptation affects (Bastian and Courtright 1991; Shumway 1989). Here PD was defined as P(before stim) > T and PFD as P(after stim) > T (Fig. 2B). PD and PFD were plotted versus one another as T covers the range of spike count values. The area under the curve (AUC) was then calculated: values close to 1 indicate a detection of the stimulus, whereas values close to 0.5 suggest detection at the chance level (Fig. 2D). To account for different stimulus integration times we varied the spike count window length L (100, 200, or 300 ms). This window length spans a wider range than that estimated from the time the prey covers the RF of PCs; it also takes into account variability in swimming speed.
Preylike signals are always characterized as ON-stimuli. OFF cells decrease their firing rate when an ON-stimulus is used and increase their firing rate after the stimulus offset. For OFF cells, PD was calculated as P(stim) < T and PFD as P(no stim) < T. OFF cells were expected to produce more spikes after stimulation than before stimulation also because of adaptation effects (Bastian and Courtright 1991; Shumway 1989). For consistency purposes we defined PD as P(before stim) < T and PFD as P(after stim) < T (Fig. 2C). The AUC value was then extracted from the corresponding ROC curve.
To test whether the performances of the three different cell types were above chance level we then used the ROC value averaged over all cells of one type obtained during the stimulus conditions in question and tested whether this value was above 0.5 (90% confidence interval AUC > 0.5; corresponds to α/2 ≤ 0.05).
In the following we define the onset response as the measured response to the onset of the stimulus independent of its polarity; it compares P(stim) to the baseline activity P(before stim) (see Fig. 6A). The offset response is the response to the offset of the stimulus and compares P(stim) with P(after stim). Finally, the off response compares P(after stim) with the baseline P(before stim).
The detection analysis was performed for ON-stimuli only (see Fig. 7). It is derived from the ROC analysis and was done using the same categories such as onset, offset, and off response; however, the major difference is that it does not take the variability of the spike count across multiple trials into account. Furthermore, we pooled the data over multiple cells; hence the data pool reflects some of the variability of the population. The aim of the detection analysis is to estimate the number of cells (N) needed for prey detection. The simplest mechanism by which higher-order neurons can extract information about the presence of a stimulus is to just sum up the incoming spike trains. We therefore assumed that each response trace to a single stimulus repetition represents a different cell and created a data pool containing the response traces of all cells of one cell type to a 1- to 2-μV signal. Then N binarized spike trains (spt) were chosen randomly from the data pool and were added; N corresponds to the number of cells putatively used for signal detection. For each resulting sequence, we compute the maximum/minimum firing rate (max-fr/min-fr) in small windows of length L (20 ms) occurring during the 100-ms time frame before, during, or after the stimulus. Previous ROC analysis has shown that the detection performance for PCs does not improve significantly for longer integration windows when weak stimuli are considered. Added to the fast detection revealed by behavioral studies, integration windows longer than 100 ms will probably not be utilized by PCs, even if EAs can improve their detection performance for longer windows. We further used the 20-ms integration window as a realistic synaptic integration time for higher-order neurons (Berman and Maler 1998a). Whether we used the maximum or minimum firing rate as a threshold criterion depended on our expectation of the cell's behavior. For example, ON cells increase their firing rate to the onset of a stimulus, and hence the maximum firing rate was used; OFF cells decrease their firing rate to the same stimulus. Here the minimum firing rate was used as threshold criterion. We calculated the spike count (spc) by first sliding the 20-ms window over the 100-ms time interval spc(t)= ∑N∑Lspt(t). Then max-fr(x) is defined as max-fr(x) = max[spc/(L × N)] and min-fr(x) is defined as min-fr(x) = min[spc/(L × N)]; x refers to the location of the 100-ms window time, i.e., before, during, or after stimulation. We were also interested in investigating whether the combinatory response of ON and OFF cells improved the detection of weak signals. Therefore we first calculated the spike count for ON and OFF cells separately. The response of one cell type was subtracted from the other cell type, e.g., spcON-OFF(t) = spcON(t) − spcOFF(t), and the detection analysis was performed on the resulting sequence. We used the assignment criteria defined in Table 1 as an indicator [combined response value (CRV)] of whether or not a signal was detected. To actually calculate the curves in Fig. 7, the analysis procedure was repeated 1,000 times for each N, meaning for each calculation N traces were chosen randomly from the data pool. Then the average CRV was plotted.
Model of TS circuitry.
Within the ELL ON and OFF cells are arranged in pairs and have overlapping RFs (Bastian et al. 2002; Chacron and Bastian 2008; Maler 1979; Maler 2009a). Furthermore, EAs trifurcate such that all three ELL maps receive the same EA input; the same region of the body surface is thus represented multiple times. Hence it is reasonable to assume that information about an object perceived by ON and OFF cells in the same as well as different maps can be combined in higher brain areas.
Both ON and OFF cells of all three ELL maps project to the midbrain TS via excitatory synapses. The TS is composed of 12 layers and contains ∼50 neuron types. The topography is preserved within the TS. ELL input terminates mainly in layers 3, 5, and 7. Neurons have been described that were excited by increases in stimulus amplitude (ON type/E type), while others were inhibited (OFF type/I type) (McGillivray et al. 2012). There is little known about the exact connectivity within the TS; however, dendrites distribute across layers (Krahe and Maler 2014).
Our model was designed to simulate a higher-order TS neuron that responds to either the onset or the offset of a weak preylike signal with excitation. The TS neuron was simulated with a leaky integrate-and-fire (LIF) model. Responses from previously recorded ON and OFF cells were taken as input spike trains. In order for ON and OFF cells to coactivate a TS neuron during the stimulation, one of the population responses has to be inverted (see Fig. 8A). To simulate a TS neuron that responds to the onset of a stimulus with excitation (ON-circuitry; see Fig. 8A, left), the ON cell responses are assumed to excite (ex) whereas the OFF cell responses inhibit (inh) the TS neuron. For simulation of a TS neuron that responds to the offset of a stimulus with excitation (OFF-circuitry; see Fig. 8A, right), OFF cells are assumed to form an excitatory synapse onto the TS neuron whereas the ON cell responses are inverted.
Since the direct connections between the ELL and the TS are known to be excitatory, this can only be achieved by local inhibition via interneurons (Wang and Maler 1994). Therefore, the spike train of the cell population responsible for the inhibition is delayed by 5 ms. Varying the delay (0–10 ms) did not change the results qualitatively (data not shown). The membrane potential of the TS neuron is given by the following equation (on the basis of McGillivray et al. 2012):
where V is the membrane voltage, τm is the membrane time constant, Ibias is a bias current, ε(t) is a Gaussian white noise process with zero mean and strength σ, and A is a constant. Θ(t) is the Heaviside function [Θ(t) = 1 if t ≥ 0 and Θ(t) = 0 otherwise], while α(t) is a single-exponential alpha function and β(t) is a function containing two exponentials with different time constants. The time course of the alpha functions are given by the following equations:
where τinh is the time constant for an inhibitory synapse (i.e., GABAA) and τex(r) and τex(d) set the rising and decaying time constant of an excitatory synapse (AMPA and NMDA). B1 and B2 are constants that were adjusted to normalize the areas under the alpha function to 1. A very similar model was used in previous studies and calibrated for TS neurons (McGillivray et al. 2012); we based most of our chosen parameters on this model but adapted Ibias to compensate for our changes in the connectivity pattern and synaptic time constants.
For the simulation of TS neurons responding with excitation to the onset of a preylike stimulus, tex,k are the spike times of the recorded ON-type and tinh,k are the spike times of the recorded OFF-type ELL pyramidal neurons. For the simulation of TS neurons responding with excitation to the offset of a preylike stimulus, the roles of ON and OFF cells are reversed.
When V(t) exceeds the threshold θ, it is immediately reset to θreset and maintained there for the duration of the absolute refractory period TR, and a spike is said to have occurred at time t.
The model was numerically integrated with MATLAB using the Euler-Maruyama method with integration time step of 0.000025 s. Parameter values used for simulations are shown in Table 2. These parameter values were chosen on the basis of available experimental data [membrane and excitatory postsynaptic potential (EPSP) time constants, absolute refractory periods, baseline firing rate] (Berman et al. 1997; McGillivray et al. 2012; Toporikova and Chacron 2009; Vonderschen and Chacron 2011). The high Ibias as well as the high noise level compared with the McGillivray model are a consequence of using seconds instead of milliseconds as the unit of the simulation time step.
The baseline firing rate of TS neurons is very low (5 Hz; Chacron and Fortune 2010; Vonderschen and Charon 2011) compared with PCs (∼5–60 Hz; Bastian and Courtright 1991), in particular when considering the high anatomical convergence rate (see above; Chacron et al. 2009; Maler et al. 1982). We assumed that at least 20 PCs of ON type innervate each TS cell. The firing rates of superficial and intermediate PCs range from ∼5 to 30 spikes/s; the TS cell might therefore be expected to receive an excitatory drive between 100 and 600 spikes/s as a minimum. There are various mechanisms that might account for this reduction in firing, e.g., a high threshold in the TS neurons and/or stimulus-independent bias currents evoked for example by network activity or feedback from higher brain areas. In our analysis we adjusted Ibias by first running the TS neuron simulation with the baseline activity of ON and OFF cells as an input. We used the same convergence rate and synaptic strength as in the simulations of the response to the stimulus. Ibias was adjusted so that for each condition the baseline firing rate of the TS neuron was ∼5 Hz (McGillivray et al. 2012; Vonderschen and Chacron 2011). For the response to the stimulus, we then investigated the role of feedforward inhibition/excitation as well as the balance of both. To estimate the contribution that different populations of PC types make to the signal detection in the TS, we turned off one of the cell types by setting its synaptic strength to 0.
The aim of our study was to investigate how first-order sensory processing brain regions are able to extract very weak signals in real time, in particular, how the electrosense of gymnotiform fish can rapidly detect prey signals (Nelson and McIver 1999). We restricted our measurements to two of the electrosensory maps of the ELL, the CMS and the CLS, that are expected to be involved in prey detection (Maler 2009a, 2009b). We only recorded from cells having a firing rate below 30 Hz, and for our modeling approach we used low-firing-rate PCs (below 20 Hz) as an input to the TS neuron. Thus we only took intermediate and superficial PCs into account, or likewise cells with large feedback projections that are known to be able to cancel out common input (e.g., from tail bending) that might act as a noise source (Bastian et al. 2004; Bastian and Courtright 1991).
In total 11 EAs, 13 ON cells (6 CMS, 7 CLS), and 16 OFF cells (10 CMS, 6 CLS) were recorded extracellularly using their preferred stimulus sign (increase in AM for EAs and ON cells; decrease in AM for OFF cells). The average firing rate for EAs during baseline activity was 241.9 ± 129.4 Hz (mean ± SD) (range: 99–507 Hz), for ON cells 16.4 ± 7.9 Hz (range: 6.6–28.5 Hz), and for OFF cells 11.4 ± 6.4 Hz (range: 4.3–29.0 Hz). Additionally, the responses of eight OFF cells with an average baseline firing rate of 13.3 ± 5.3 Hz (range: 6.4–23.4 Hz) were recorded to an increase in AM. The EA baseline activity is in the same range as previously reported (Gussin et al. 2007). The firing rate of the recorded PCs lies on average far below the baseline activity of deep PCs but corresponds well with firing rates of superficial and intermediate PCs recorded in other studies (Bastian et al. 2002, 2004; Bastian and Nguyenkim 2001). The stimulus was delivered at a rate of 0.5 Hz, allowing the cell to come back to baseline activity between stimulations.
Response of EAs and PCs to strong, intermediate, and weak signals.
As shown by Gussin et al. (2007), EAs did not significantly change their firing rate to low stimulus amplitudes (<2 μV/cm); hence the peristimulus time histogram (PSTH) did not show any change in the firing rate during stimulation (Fig. 3). About 60% of the cells showed some increase in firing rate for stimulation amplitudes around 3 μV/cm, and responses were reliable for stimulus amplitudes around 10 μV/cm. This is in agreement with previous work in which it has been calculated that, when using a rate code, only relatively strong low-frequency signals (>5 μV/cm) could be encoded by a moderate number of EAs (Gussin et al. 2007).
ON and OFF cells have very different innervation patterns regarding the input they receive from sensory neurons. ON cells increase their firing rate to their preferred stimulus via direct excitation, whereas OFF cells increase their firing to the opposite sign stimulus via indirect disinhibition (Bastian 1981; Berman and Maler 1999; Maler et al. 1981). Figure 4A schematically illustrates the circuitry that we assume to contain the key elements for weak signal detection. Considering the differences in innervation patterns, it is interesting to study whether both ON and OFF cells have the same level of sensitivity and response characteristics to local stimulation. The increase in firing rate for PCs of both types to very weak stimuli for their preferred sign is hardly noticeable at a single-cell level (Fig. 4, B and C). However, for intermediate stimulus strength an increase in firing rate becomes visible and a decrease in firing rate at the stimulus offset becomes detectable. Increasing the stimulus strength magnifies both effects. In particular, a strong inhibition after stimulus offset becomes pronounced for both ON and OFF cells.
ROC analysis of EAs and PCs to AM stimulus.
Next we analyzed the detection threshold for EAs, ON cells, and OFF cells using ROC curves. We used the area under the ROC curve (AUC) as a measurement of detection performance (Fig. 2D). By performing the ROC analysis on distributions gained from repeated measurements to the same stimulus, the AUC value reflects not only the differences between the means of spike count between both conditions being compared but also the trial-to-trial variability in the response and baseline activities of the neurons.
In the following analysis the counting windows were 100, 200, or 300 ms during stimulation and before stimulation. EAs and ON cells were stimulated with an ON-stimulus; OFF cells were stimulated with an OFF-stimulus (Fig. 5, insets). In Fig. 5, A–C, each line represents the tuning curve of an individual cell using a 300-ms counting window. Each data point was collected with 30 subsequent repetitions of the same stimulus strength. Since the stimulus strength was calibrated for each cell individually, the exact value given differed from cell to cell. We therefore grouped the stimulus strength in different categories for further analysis (0–1 μV/cm, 1–2 μV/cm, 2–4 μV/cm, 4–7 μV/cm, 7–10 μV/cm, 10–15 μV/cm, 15–20 μV/cm, 20–40 μV/cm). The bold black lines in Fig. 5, A–C, then show the average AUC value of all EAs and ON and OFF cells, respectively. The first deviation from chance level occurred around a stimulus strength of 2–4 μV/cm in EAs (AUC > 0.5, 90% confidence interval, α/2 = 0.05; 200- and 300-ms windows).
Remarkably, both ON and OFF cells showed on average responses to the stimuli around 1–2 μV/cm (ON cell: AUC > 0.5, 90% confidence interval, α/2 = 0.05; 100-ms window; OFF cell: AUC > 0.5, 90% confidence interval, α/2 = 0.05; 200- and 300-ms windows); therefore, despite the very different sources of excitatory input, the cells are matched in their sensitivity to weak signals. In addition, EAs are clearly less sensitive. We did not have the same number of cells stimulated by each stimulus amplitude. To ensure that the different significance values were not due to different sample sizes, we repeated the significance tests using the same number of recorded cells (first 10 cells recorded) of each cell type for the stimulus intensities 1–2 μV/cm and 2–4 μV/cm. The significance level did not change, except that the AUC > 0.5 for the 100-ms window for OFF cells (stimulus strength: 1–2 μV/cm) now also became significant (α/2 = 0.05).
Both the CLS and CMS maps of the ELL are known to respond to local signals; however, cells in the different maps have very different characteristics with respect to RF size and frequency tuning. Therefore we checked whether there was also a difference in sensitivity between the CLS and CMS maps. A preliminary analysis revealed no significant difference between the CLS and the CMS for both ON and OFF cells in the level of sensitivity (not shown), and therefore the data from these maps were pooled for all subsequent analyses.
EA and PC responses to preylike signals.
Prey signals are characterized by an increase in AM. Since only positive deflections occur during prey capture, the responses of EAs and ON and OFF cells to an ON-stimulus were analyzed more closely (Fig. 6). Furthermore, during a prey capture scenario the duration of the signal depends on the relative speed between the fish and the prey. Therefore, we next investigated how the stimulus integration time influenced the performance level of individual EAs and ON and OFF cells. The ROC analysis was performed for different counting windows (100, 200, and 300 ms), representing different relative speeds between fish and prey as well as different relations between speed and time required to saturate the RFs of CMS and CLS. The analysis of the response also included a transient ramp, which represents the stimulus dynamics when a prey moves into the RF of the cells. Importantly, it has been shown that EAs have high-pass characteristics and hence should be sensitive to these signals (Benda et al. 2005; Nelson et al. 1997).
Three different measures of response to the preylike stimuli were compared: the onset response, the off response, and the offset response (Fig. 6A). Therefore, the AUC value for each cell and stimulus condition was first calculated; then we tested whether the average AUC value across cell type was above chance level.
The onset response average over the whole population of EAs did not show any significant response to stimulus strength in the 1–2 μV/cm range for all different integration windows (Fig. 6B, left). Using a spike count code, the first significant detection occurred around 2–4 μV/cm but only when longer (200 and 300 ms) time windows were considered. For higher stimuli all other average AUC values were above 0.5, though some of the values were not significant. This was at least partly due to the fact that not all stimulus strengths were presented to all cells; for example, only five EAs received a 7- to 10-μV stimulation; merging the 4–7 μV/cm and 7–10 μV/cm stimulations into one category and therefore increasing the sample size leads to significant values, at least for long integration times (300 ms). EAs did not show an off response, meaning that their firing rates before and after stimulation were very similar (Fig. 6B, center). The offset response did seem to depend a lot on the stimulus integration time (Fig. 6B, right). Since the off response was insignificant, differences in the onset and offset response are based on the location of the counting window during stimulation. For a 300-ms counting window, the analysis window is only shifted by 20 ms, which corresponds to the time of the ramp of the stimulus, and the results for onset and offset response are almost identical. By looking at smaller counting windows (100 ms) one compares more the transient versus the steady-state response. For strong stimulation (>10 μV/cm) there is a trend where the transient response increases the AUC value compared with the steady-state response. The onset response for a 100-ms time window (transient component) is higher than the offset response for a 100-ms time window (steady-state component) (compare Fig. 6B left with right). This is in agreement with previous studies where it has been shown that for strong stimuli EAs show a firing frequency adaptation to the onset of the stimulus (Benda et al. 2005). First significant deviations from the 0.5 chance level for both onset and offset responses were reached at stimulus strengths around 2–7 μV/cm.
By averaging over all AUC values of one stimulus strength, the ON cells responded significantly to the stimulus onset around 1–2 μV/cm, for a stimulus integration time of 100 ms (Fig. 6C, left); the lack of further increase in response strength to the longer integration times is presumably due to their rapid adaptation (Fig. 4; Bastian 1986). The stimulus integration time did not seem to have a strong effect on the corresponding AUC value, in particular when compared with the EA response. This suggests stronger adaptation in ON cells than in EAs. ON cells showed an off response to stimuli stronger then 2–4 μV/cm (Fig. 6C, center), meaning their firing rate was reduced after stimulus offset compared with baseline activity. This is different from the EA response and implies signal amplification. Similar to the EA response, the offset response of ON cells showed a strong dependence on stimulus integration time (Fig. 6C, right).
OFF cells respond to the onset of a preylike stimulus with a decrease in their firing rate; hence, when creating the ROC curve we were looking at whether the stimulus can be detected by a decrease in firing rate. Also, OFF cells seemed to respond to very low stimulus intensities (Fig. 6D, left). However, despite increasing the stimulus strength the AUC value stayed at a relatively low level compared with the ON cell response. This is not surprising because the decrease in firing rate is quite restricted because of the relatively low firing rate of PCs. For low stimulus strength, the stimulus integration time did not have an effect on the AUC value, likely because the inhibition of OFF cells was restricted to a small window after stimulus onset. Higher stimulus strength leads to a longer inhibition time, making the effect of longer stimulus integration time more valuable. The off response of OFF cells is just significant at the 1–2 μV/cm stimulus level and increases with increasing stimulus strength (Fig. 6D, center). The AUC values are on average higher than for the onset response; this can be partly explained by the fact that the dynamic range for an increase in firing rate is bigger than for a decrease. The offset response of OFF cells showed the highest AUC values found for all cell types studied and all response analyses (Fig. 6D, right).
In summary, EAs had lower AUC values than PCs throughout the different stimulus conditions (strength and response type; Fig. 6). Longer stimulus integration times improved the onset and offset responses (except onset response of ON cells). The degree of improvement is probably dependent on the level of adaptation. Both EA and PCs show spike frequency adaption to a step stimulus of their preferred stimulus sign (see also Fig. 4); however, whereas adaptation rates for EA only depend on intrinsic properties, because they lack any kind of feedback, the adaption rate for PCs is strongly influenced by network properties, such as surround inhibition and descending feedback (Bastian 1986; Benda et al. 2006). Hence strong adaptation might prevent an increase in AUC values with stimulus duration for ON cells. Interestingly, for weak stimuli cells could profit less from longer integration windows. The off response did not depend on stimulus integration time. This is not surprising since, upon turning off the stimulus, there is no more incoming information and the firing rate should quickly return to baseline activity. The increase in sensitivity between EAs and PCs was most pronounced for the off response. Differences in intracellular or network adaptation mechanisms are likely to also play a critical role here. PCs showed in general a response to stimulus strength around 1–2 μV/cm except for the off response in ON cells. The stimulus response encoded by an increase in firing rate (ON cells: onset response; OFF cells: off response) showed a trend of being better represented by the AUC value than the stimulus response encoded by a decrease in firing rate, i.e., AUC values for the onset response are higher for ON cells than for OFF cells whereas AUC values for the off response are higher for OFF cells than for ON cells. This can be in partly explained by the rectification due to low baseline firing rates of PCs.
Detection of weak signal using multiple cells.
We addressed whether increasing the number of PCs can in principle improve detection performance, as well as how higher-order neurons in receipt of PC input can implement the detection.
For downstream decoding, the simplest mechanism consists of a postsynaptic neuron summing the incoming spike trains. To reproduce such a mechanism, we used the detection analysis that is based on simple trial-by-trial threshold detection.
The values for the maximum/minimum spike count with and without stimulus were compared, and a value of 1, 0.5, or 0 was assigned following the criteria of Table 1 (Fig. 7A). The choice of using either the maximum or minimum firing rate depended on whether we expect the cell type to decrease or increase its firing rate for the given stimulus condition. Figure 7 is the average of 1,000 calculated CRVs. One conceptual difference between this type of analysis and the AUC in the previous section is that here the trial-to-trial variability plays a less significant role since no probability distributions of the responses were calculated.
In agreement with the ROC analysis, EAs showed the lowest values for the detection analysis (Fig. 7). In particular, adding cells only improved the response to the onset of the stimulus. Interestingly, there was little increase in the CRV between adding 30 EAs and 100 EAs (30 EAs: 0.54 CRV; 100 EAs: 0.56 CRV), values that reflect the convergence ratios of EAs onto PCs in the CMS and CLS, respectively. This result might in part explain our observation that there are no significant differences in sensitivity between CMS and CLS cells (data not shown). Also in agreement with the ROC analysis, the CRV of EAs stayed at chance level for the off/offset response.
As expected, increasing the number of PCs led to a monotonic increase of the CRV for the three different response types. For the onset response, when low numbers of cells are considered (<10), the CRV for OFF cells stayed below the value for ON cells. This can be explained as previously, i.e., that cells with low baseline firing rates can poorly encode information by reducing this rate. When calculating the CRV for higher cell numbers, OFF cells became more sensitive. Our previous estimate of the number of cells in the different ELL maps that are stimulated at one time point by the prey signals was 20 PCs in the CLS and 50 PCs in the CMS for each ON and OFF cell. Here, the specific CRVs were 0.59 and 0.66 for ON cells and 0.6 and 0.7 for OFF cells, respectively. Combining the responses from both maps, and hence considering 70 cells, only slightly increased the CRV to 0.66 for ON and 0.72 for OFF cells.
In a last test of the onset response, we focused on the discrepancy between ON- and OFF-cell responses by subtracting the summed OFF-cell response from the summed ON-cell response and calculated again the maximum firing rate over short 20-ms windows across the resulting response traces. Using both ON and OFF cells in this way increased the CRV over the whole set of population sizes (2 × 20 cells: 0.66; 2 × 50 cells 0.73; 2 × 70 cells: 0.75). Importantly, the CRV was clearly above the OFF-cell-only CRV for low N and clearly above the ON-cell-only CRV for high N (Fig. 7B).
The analysis of the off response suggests that this signal can be encoded by both ON and OFF cells (Fig. 7C). However, the CRV value for OFF cells was always higher than for ON cells; furthermore, there was no difference between using the OFF-cell response alone to calculate the CRV and using the combined ON-/OFF-cell response (20 cells: ON 0.55, OFF 0.66, ON and OFF 0.67; 50 cells: ON 0.61, OFF 0.74, ON and OFF 0.73; 70 cells: ON 0.58, OFF 0.78, ON and OFF 0.77). The results for OFF cells were similar for the offset response analysis (Fig. 7D); however, ON cells improved their detection performance compared with the off response substantially. In addition, using the combined ON-/OFF-cell response slightly increased the CRV compared with using the OFF cell response only (20 cells: ON 0.58, OFF 0.64, ON and OFF 0.66; 50 cells: ON 0.69, OFF 0.76, ON and OFF 0.76; 70 cells: ON 0.66, OFF 0.78, ON and OFF 0.84).
In summary, EAs had lower CRVs for the same number of cells than PCs. However, in contrast to the results of the ROC analysis, EAs showed an onset response to the stimulus for weak signals. PCs showed a response to the onset of the stimulus as well as to the offset of the stimulus; which cell type showed a better performance level depended on the number of cells used and on the response type analyzed. Combining the ON- and OFF-cell responses by simply calculating the difference between both spike trains improved the onset response as well as the offset response, whereas the off response was equally well detected by the OFF cells or the combination of ON and OFF cells.
Model of a higher-order electrosensory region.
The previous results have already shown that there is a substantial increase in sensitivity in going from EAs to PCs when one considers a spike count code and that this increase in sensitivity depends on various factors such as the response type, the integration window, and whether or not the trial-to-trial variability is considered. We next investigated whether target neurons of PCs in the TS can use the information provided by PCs, especially when considering the restricted number of PC cells available during a prey capture scenario (20 CLS, 50 CMS; ON and OFF cells).
Therefore 20, 50, or 70 randomly chosen recorded traces from ON, OFF, or ON and OFF cells are used as the input for the LIF model representing a postsynaptic TS neuron. Since ON and OFF cells come in pairs, and since therefore each cell in a pair shares a huge proportion of its RF with the other, their information can be pooled in higher brain areas without losing precision in time or space. This is important for the detection of a stationary object. For a moving object, information from cells with different RFs is integrated. However, for this integration the relative speed between object and fish is important, whereas the integration of information for a population of cells sharing a RF is relatively independent of speed.
Figure 8Bii shows the overlaid response of 5 TS neurons receiving input from 70 different ON and OFF cells (140 cells in total) either via the ON pathway (Fig. 8Bii, left) or via the OFF pathway (Fig. 8Bii, right). In both cases a clear response pattern can be observed. As detailed in materials and methods, each pathway assumes an inverting subpathway. The raster plot (Fig. 8Biii) and PSTH (Fig. 8Biv) of 30 simulated TS neurons are plotted below in order to make the simulations visually comparable to the PC responses of Fig. 4. Just by visual inspection it is evident that the response to weak stimuli is greatly increased in the TS compared with the ELL. The performance level of the model was quantified both by measuring the difference in spike count in a 300-ms window with or without stimulation and by measuring the gain (defined below). The onset, off, and offset response types were as defined above for the ROC analysis (Fig. 6A). The model was run 500 times with different PC spike trains as input data as well as different internal noise realizations to calculate the spike count difference with and without stimulus, and significance was assessed with a two-sided t-test (P < 0.05). We defined the gain as the quotient between the number of spikes counted in the window in which we expected most spikes (during stimulation for the ON pathway/without stimulation for OFF pathway) divided by the number of spikes in the other window. The gain value was calculated using the averaged spike count over 500 realizations to avoid dividing by zero (since some realizations had zero counts); hence, no significance test was performed.
We analyzed the response of TS neurons using the hypothesized circuitry (Fig. 8A) that received 20, 50, or 70 PC traces as an input to mimic the integration of CMS, CLS, or CMS and CLS cells. TS cells increased their firing rate to the stimulus onset by using either ON or OFF cells or both as an input (Fig. 8C). Despite the high CRVs OFF cells displayed, the responses of TS neurons were higher for the pathway that utilized ON cells. Combining the input of ON and OFF cells increased the onset response (Fig. 8C, center and right). The off response was encoded only by OFF cells or by the combination of ON and OFF cells; ON cells alone did not increase the firing rate of the TS neuron. Interestingly, combining ON and OFF cell responses significantly increased the response to the stimulus offset compared with ON and OFF alone based on the increase in firing rate. Using the gain instead revealed very similar results as using the difference in spike count (Table 3). Using either ON or OFF cells as a model input to TS led to similar strong onset responses. The response gain was further increased when the combination of both was used. Using OFF cells as an input increased the gain to the off response. For the offset response, both ON- and OFF-cell input led to a strong increase in gain; however, the combination of both cell types seems to even further increase the gain.
In summary, increasing the number of cells that are used as an input to the TS model amounts to going from integrating over the CLS map and the CMS map to using the combined input of both maps. This increase was paralleled by an improved signal detectability in a model TS neuron, for both the difference in spike count and the response gain measures for the onset, off, and offset responses. Interestingly, when using the differences in spike count as a measurement the stimulus onset was slightly better encoded by ON cells, whereas the stimulus offset was better encoded by OFF cells. When using the response gain as a measurement ON and OFF cells encode both stimulus conditions well. In general, using a combined input from ON and OFF cells increased the difference in spike count and the response gain for the onset as well as the offset response but not for the off response.
In this report, we focus on whether a simple sensory encoding strategy—spike counts and threshold detection—is sufficient to explain the high level of behavioral sensitivity exhibited by the gymnotiform electrosensory system. To address the question of whether a certain code is good enough to explain an animal's behavior, a lot of background knowledge about the neuronal circuitry involved has to be available, such as the number of available cells participating in the task as well as the stimulus integration time that is available for the neuron. We use the electrosensory system of wave-type gymnotiform fish because of their behavioral sensitivity to very weak electric signals emanating from prey (Chen et al. 2005; Nelson and MacIver 1999) and the extensive knowledge of their low-level electrosensory circuitry (Maler 2009a), but we expect that our conclusions will generalize to other sensory systems.
As a first step we recorded the responses of EAs and PCs in the CMS and CLS maps of the ELL to local AMs and investigated their sensitivity to these signals. Neurons in both maps are known to have small RFs and respond well to localized weak signals (Chacron et al. 2011; Krahe and Maler 2014). The ROC analysis based on spike count showed a clear increase in sensitivity between EAs and PCs. PCs in the CLS and CMS showed similar sensitivity. Furthermore, ON and OFF cells showed equal sensitivity to their preferred stimulus (ON-/OFF-stimulus), which is remarkable considering their differences in presynaptic circuitry (Bastian et al. 2002; Maler 1979; Maler et al. 1981).
Since we were mainly interested in the encoding of prey signals in the ELL, we analyzed the response to the onset and offset of a preylike stimulus using both ROC analysis and CRV analysis, which is based on simple trial-by-trial threshold detection. EAs only modulated their firing rate to the onset of a weak to medium-strong stimulus based on both—ROC and the threshold detection analysis—but the sensitivity increased substantially with the latter method. With application of these methods, PCs, on the contrary, responded with a modulation in their spike count to both onset and offset of the stimulus.
We then used the recorded spike trains from PCs as input to an LIF model of a TS neuron. The output model neuron responded well to weak stimuli using the ON pathway for the onset response and the OFF pathway for the off/offset response. The response of the model increased both with the number of cells used as well as by combining ON- and OFF-cell responses.
Population coding and the role of correlations.
All data presented came from individually recorded cells. Hence there are potential limitations on what we can say about the role of correlated responses on the population code. Correlated discharge can be due to neurons receiving the same signal. These are referred to as “signal correlations” and are important for encoding input; we implement such correlations in our model via the ON/OFF cell convergence on TS cells. Neurons can also show firing rate correlations due to common input but not related to any signal; these are referred to as “noise correlations.” The functional role of noise correlations is currently under debate because they might on one hand introduce redundancy and therefore reduce the information that could be encoded by a population. On the other hand, it has been shown recently that this view may be too simple (Schneidman et al. 2006; Zohary et al. 1994). Mechanisms and scenarios have been proposed that could demonstrate that the role of correlations is highly dependent on specific parameters such as the network architectures (Averbeck et al. 2006; Hong et al. 2012). Noise correlations have been found in the ELL and appear to be positively correlated with the amount of RF overlap (Chacron and Bastian 2008). Chacron and Bastian (2008) recorded from CLS and LS but did not assign specific recordings to a specific map; however, anatomical data suggest that CLS has moderate RF overlap (30–36%; Maler 2009a) while overlap in LS is strong (50–65%; Maler 2009a). RF overlap in the CMS appears to be minimal (<15%; Maler 2009a), and Krahe et al. (2002) reported no significant noise correlations in this map. We therefore conclude that, while noise correlations of CLS cells might diminish the sensitivity of TS cells, the effect for CMS cells is likely to be minimal. Furthermore, for weak signals, spiking in the CLS and also in the CMS is driven by a summating NMDA current in addition to a cell-specific noise source (Marcoux et al. 2015). This suggests minimal short-timescale, non-stimulus-induced correlated activity at the synaptic level. This conclusion is reinforced by our model: single-unit recordings, when used as an input to a putative TS neuron, lead to responses that suggest a signal detection performance that is comparable to the behavioral performance (Nelson and MacIver 1999). The time constants we used for the synaptic transmission to TS neuron determine over which time window spikes from PCs can be integrated; hence they set the time frame over which signal correlations will be effective.
Prey detection by EAs.
Anatomical studies have shown that at least ∼25 EAs innervate 1 PC in the CMS and ∼100 EAs innervate 1 PC in the CLS (Maler 2009a). Hence, the 30 stimulus repetitions can be used to give a good estimate of the EA population response that contributes to the response of CMS PCs. The ROC analysis did not show any increase in the EA firing rate for very weak stimuli around 1–2 μV/cm; all information about the stimulus was lost in the trial-to-trial variability. This is in agreement with previous studies that showed that the behavioral sensitivity cannot be explained by a linear rate code of EAs (Gussin et al. 2007). Also, that study emphasized that the variability of the EA baseline and response discharge is responsible for their apparent inability to detect weak signals. Another interesting aspect was that the P value (baseline firing rate/EOD frequency) was positively correlated with the absolute gain defined as increase in number of spikes per 1 μV/cm. There is to our knowledge no anatomical evidence that EAs of different baseline rates innervate different PCs. However, it has been suggested that differences in baseline activity are important for encoding specific aspects of the stimulus (Metzen and Chacron 2015). We therefore checked whether the ROC value (based on 300-ms intervals) is linearly correlated with the firing rate (Fig. 9). We did find weak linear correlations for high stimulus amplitudes (20–40 μV/cm, R2 = 0.37) but not for low stimulus amplitudes (1–2 μV/cm, R2 = 0.02). Hence we do not expect to get different results regarding the detection threshold when dividing the EA population into different groups. EAs did show a response to the onset of the stimulus even for very small stimulus amplitudes when one considers the CRV analysis; however, it was well below the response of PCs when the same numbers of cells were considered. Nevertheless, it is possible that detection in downstream neurons could benefit if they could adapt to the temporal fluctuations of the baseline firing rate (Fairhall et al. 2001).
Prey detection by PCs.
Both ON and OFF cells showed a very similar sensitivity to their preferred stimulus polarity. It is clear that ON cells are involved in prey detection since they respond to an increase in AM. However, the strong response of OFF cells to the end of an OFF-stimulus (and hence a temporary increase in AM) motivated us to further investigate their role in prey detection. With the ROC analysis ON cells slightly increased their firing rate on average to very weak (1–2 μV/cm) stimuli; OFF cells on the other hand decreased their firing rate slightly but significantly; EAs showed no response. This means that, in contrast to EAs, PCs can detect weak stimuli despite the trial-to-trial variability. Even though the AUC value was not very high, this indicates that higher-order neurons might be able to improve the signal further by simple integration/convergent mechanisms.
PCs clearly outperformed EAs also with the CRV analysis. In particular, because the curve for EAs saturated relatively quickly with increasing number of cells considered, the increase in sensitivity might be relevant beyond simple convergence rates and suggest some form of nonlinear signal amplification. Previous studies have suggested that EAs encode very weak stimuli with a spike pattern code, and PCs are able to utilize this code using synaptic dynamics that work on very short timescales (Khanbabaie et al. 2010; Lüdtke and Nelson 2006; Nesse et al. 2010). Furthermore, it has been shown that voltage-dependent channels are present in PCs (Berman and Maler 1999). The EA-to-ON cell synapse contains, for example, NMDA receptors (Berman and Maler 1998a). Also, persistent sodium channels have been found in ON cells (Turner et al. 1994). The most striking observation, however, was the improved encoding to the offset of the stimulus. With the current stage of knowledge, it is not clear how this improved encoding is achieved; however, intracellular adaption mechanisms or network effects might play an important role here in addition to the decoding of a spike-pattern code from EAs (Berman and Maler 1999; Marcoux et al. 2016; Nesse et al. 2010).
Another important aspect to reevaluate at this point is the question of which individual map contributes the most to the detection of weak stimuli. Even though we did not find any significant differences on a single-cell level between PCs in the CMS and CLS, and therefore pooled these data, higher-order neurons, e.g., in the TS, might gain more from the input of CMS cells because more cells are activated by the stimulus at the same time (CMS: 50 cells vs. CLS: 20 cells) and noise correlations in the CMS are lower than in the CLS (Chacron and Bastian 2008; Krahe et al. 2002). It will take more detailed studies to determine how the ELL maps converge in TS and the resulting net effect of noise correlations across ELL PCs on the sensitivity of TS cells.
Prey detection by TS neurons.
The integration of sensory input in the TS is less well understood than that at the level of the ELL and EAs. Therefore, we used a relatively simple LIF model to study how such a higher-order neuron could possibly extract information from the ELL, relying on minimal assumptions. It is evident from the model response that using a simple algorithm such as integration and threshold detection is sufficient for extraction of weak signals in a TS neuron. In particular, just using feedforward excitation as an input for our TS model cell led to a strong response. Including the inhibitory pathway to the same model cell further increased the response of the TS model neuron to transient signals (onset/offset). The offset response was particularly well encoded.
So one might wonder why it may be important for the fish to detect the exiting of an object from the RF. First of all, we have the standard reasoning that knowing both the onset and the offset of a stimulus will give information about the size of an object and its relative speed, even though this information may still be ambiguous. However, when considering prey capture by the fish one has to consider its movement sequence. Apteronotus is known to strike prey by first passing the object and then swimming backward without changing orientation (Nelson and McIver 1999). Knowledge of the offset response may help determine how far to swim back, thereby fine-tuning prey capture.
Balanced inhibitory and excitatory circuitries.
In addition to the striking sensitivity of the electrosensory pathways of weakly electric fish, another interesting observation of our work is the degree of balance between the inhibitory and excitatory pathways in the early sensory processing centers. Balance of excitation and inhibition could be observed on two levels. Inhibition evoked by granular interneurons has to be well balanced with the direct excitatory input from EAs to explain both the high sensitivity of ON cells and the similar sensitivity of OFF cells. Furthermore, modeling TS neurons reveals benefits of balance of the ON and OFF circuitry in higher brain areas. TS neurons responded the strongest to the preylike stimulus if both the inhibitory and the excitatory circuitry were involved. Therefore we propose that balanced excitation and inhibition is crucial for the detection of weak signals associated with prey in weakly electric fish. Balanced excitation and inhibition is a recurring theme in systems neuroscience and has been suggested to play an important role in gain control for increased sensitivity (Anderson et al. 2000; Haider et al. 2006; Rubenstein and Merzenich 2003; Shu et al. 2003). Also, the role of balance in sensory processing has been studied. In the visual system, it is important for the formation of the RF and properties of simple cells in V1, as well as for barrel cortex, which shows a similar organization (Miller et al. 2001). Our results provide further support of its strong involvement in early sensory processing, especially in the context of detection of extremely weak signals at the threshold of perception.
This work was supported by Canadian Institutes for Health Research Grants 6027 and 49510 as well as a CREATE Training grant from the Natural Sciences and Engineering Research Council of Canada. S. N. Jung received a postdoctoral fellowship from the German Science Foundation (DFG; JU-2931/1-1).
No conflicts of interest, financial or otherwise, are declared by the author(s).
Author contributions: S.N.J., A.L., and L.M. conception and design of research; S.N.J. performed experiments; S.N.J., A.L., and L.M. analyzed data; S.N.J., A.L., and L.M. interpreted results of experiments; S.N.J., A.L., and L.M. prepared figures; S.N.J., A.L., and L.M. drafted manuscript; S.N.J., A.L., and L.M. edited and revised manuscript; S.N.J., A.L., and L.M. approved final version of manuscript.
The authors thank W. Ellis for technical support.
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