Chem. Senses 28: 671-679,
2003
© Oxford University Press 2003
Estimation of the Individual Firing Frequencies of Two Neurons Recorded with a Single Electrode
1 Unité de Phytopharmacie et Médiateurs chimiques, INRA, F-78026 Versailles Cedex, France 2 Institute of Physiology, Academy of Sciences, CZ-142 20 Prague 4, Czech Republic 3 Unité BIA, INRA, F-78352 Jouy-en-Josas, France
Correspondence to be sent to: Nicolas Meunier, Station de Phytopharmacie et Médiateurs Chimiques, INRA Centre de Versailles, F-78026 Versailles Cedex, France
 |
Abstract |
|---|
 Top Abstract IntroductionMaterials and methodsResultsDiscussionAppendix: general proof of...References |
|---|
When monitoring neurons with a single extracellular electrode, it is common to record action potentials from different neurons. A recurring problem with such recordings is to identify which neuron is active. Sorting spikes into separate classes is possible if each neuron discharge spikes differing by their shapes and sizes. However, this approach is not applicable when the spikes are indistinguishable. In this paper, we develop a method for estimating the respective firing frequencies of two neurons, producing indistinguishable spikes. It is based on the fact that, when a neuron fires a spike, there is an interval of time during which the probability of generating a second spike is very low. If a spike occurs during this ‘silent period’, it is likely to be generated from another neuron and the number of occurrences of such ‘doublets’ can be used to estimate the respective frequencies of two spike trains. We demonstrate here that a simple relation holds between the frequency of doublets d, the respective frequencies of the two neurons A and B, fA and fB, and a chosen value
shorter than the silent period, d = 2fAfB. This relation holds for a wide class of firing processes. We used this method to analyze responses from Drosophila taste sensilla. We first checked if the method was consistent with results obtained with stimuli that elicit responses of two taste neurons firing distinguishable spikes. We then applied this method to the study of a pair of taste neurons involved in the coding for salt taste in Drosophila melanogaster.
Key words: Drosophila, interspike intervals, mathematical model, spikes sorting
|
Introduction |
|---|
|
TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix: general proof of...References |
|---|
Extracellular recordings are a common practice in neurophysiology and often represent the only way to measure the electrical activity of neurons. Arthropod sensilla represent such a situation because neurons are tightly packed and intimately embedded within a layer of epithelial cells just below the cuticula. Most insect chemosensory sensilla house two to four neurons whose dendrites extrude in an hair-like structure covered with cuticle (Stocker, 1994
; Steinbrecht, 1996). Given the layout of the neurons within the layer of epithelial cells, when a single electrode is brought into contact with the sensillum liquor, it will record electrical activities originating from this small group of neurons (Hodgson et al., 1955). In order to fully exploit these recordings, each spike should be assigned to its neuron of origin. This is sometimes possible when each neuron fires spikes with a distinct amplitude and/or shape (Stitt et al., 1998). However, when neurons discharge indistinguishable spikes, no method has yet been proposed to estimate the firing frequencies of each neuron. A similar problem is faced when recording from several channels present under the same patch-clamp electrode. Methods have been developed to analyze such multi-channel recordings to get single-channel information (Jackson, 1985; Colquhoun and Hawkes, 1995), but they are of limited value here because they are based on the study of tens of thousands events. More recently, methods has been developed based on multi recording sites (Pouzat et al., 2002; Takahashi et al., 2003) but they are also based on the study of a number of events much higher than data usually obtained when stimulating chemoreceptor neurons.
In order to circumvent these limitations, we propose to take advantage of the firing properties of the neurons. Firing of a neuron under given stimulation conditions can be characterized by the histogram of its interspike intervals (ISIs). The smallest ISIs on the left-hand side of the histogram can be used to define the silent period of the neuron, i.e. the longest interval during which the probability of having a ‘natural’ spike (i.e. in the absence of artificial electrical stimulation) is negligible. This silent period is usually much longer than the refractory period, especially under moderate stimulation. By this definition, ISIs shorter than the silent period are very rare in single-neuron recordings. Conversely, in recordings from two neurons, such ISIs can be frequent, with the leading spike coming from one neuron and the following spike from the other neuron. Here we call ‘doublets’ two spikes separated by a chosen time interval shorter than the silent period. The presence of doublets in recordings has been used to show that a stimulus triggers the response of more than one neuron when their spikes are indistinguishable (Perkel et al., 1967). In the following we show that the frequency of doublets can be used to estimate the individual neuron frequencies in a two-neuron recording containing indistinguishable spikes.
We used this method of doublets to analyze experimental data obtained from insect taste sensilla which house four taste neurons. Previous studies showed that stimulation with sugars elicited the activity of two neurons in taste sensilla of Drosophila, one, S, sensitive to sugars and the other, W, to water (Fujishiro et al., 1984). The spikes from these two neurons are very different in amplitude, and easy to sort manually. Using three sugars eliciting different ratio of firing frequencies in S and W neurons, we first verified that the firing activities predicted with our theoretical method were consistent with the experimental data. Then, we recorded on the same preparation, the responses to salts. Previous studies have shown that salts (NaCl, KCl) stimulate two taste neurons (L1 and L2) firing indistinguishable spikes (Meunier et al., 2000) and the respective sensitivities of these two neurons remained unknown. The use of our new method allows to discriminate the activities of these two neurons across a range of salt concentrations and to obtain for the first time dose–response plots for these tarsal taste neurons.
|
Materials and methods |
|---|
|
TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix: general proof of...References |
|---|
Chemicals
Glucose, fructose, sucrose, NaCl and KCl were obtained from Sigma Chemical Co. (France). Solutions were prepared in advance and stored at –15°C. Glucose, fructose and sucrose solutions were prepared as dilutions in 1 mM KCl and kept at 4°C for <1 week.
Flies
Stocks (Drosophila melanogaster, Canton-S) were maintained at 25°C on a standard corn-meal agar medium. Flies were kept for 1 day on fresh medium after emergence prior to electrophysiological experiments.
Electrophysiology
Taste cell recording technique
A decapitated fly was secured to a flat support with insect pins and tape, and electrically grounded via a glass capillary filled with Ringer’s solution inserted into the abdomen. All stimulations were performed on tarsal sensilla 5b and 4s (Meunier et al., 2003). Consecutive stimuli were applied at least 1 min apart to avoid adaptation. Each stimulation was performed by covering the tip of a sensillum for <2 s with a recording electrode containing both an electrolyte (1 mM KCl) and the stimulus (Hodgson et al., 1955). The recording electrode (a glass capillary with a tip diameter of 20 µm) was connected to a TastePROBE amplifier (Marion-Poll and Van der Pers, 1996). The electric signals were amplified and filtered (CyberAmp 320, Axon Instrument, USA; gain: 1000; eighth-order Bessel pass-band filter: 1–2800 Hz). Contacting a taste hair with the stimulus electrode triggered the data acquisition and storage (sampling rate 10 kHz, 12 bits; Data Translation DT2821), under the control of a custom-made software Awave (Marion-Poll, 1996). Sensilla used in this study are located symmetrically and present on both legs. Thus, we could record from four homologous sensilla per preparation. This sampling procedure introduced pseudo-replicates as noted below. However, only two sensilla 5b and one sensillum 4s were recorded on average on a single fly and care was taken to sample data from at least four different flies.
Stimulation with sugars and salts
A first set of data was obtained by stimulating sensilla 5b or 4s (Meunier et al., 2003) with 100 mM glucose, fructose and sucrose, or with increasing concentrations of sucrose (10, 20, 30, 50 and 100 mM). In these recordings (n 
16 observations per data point), the spikes clearly fell into two amplitude classes, which allowed to sort them manually and to estimate their respective firing frequencies. A second set of data was recorded from sensilla 5b and 4s to a series of dilutions (100, 200, 400, 700, 1000 mM) of either NaCl or KCl (four different flies for each compound; n 15 recordings per data point). In these recordings, spike amplitudes could not be separated into different classes, although earlier observations on the proboscis suggested that two cells are concurrently active (Siddiqi and Rodrigues, 1980).
Data analysis and spikes sorting
Action potentials frequency was determined by counting spikes during the 0.2–1 s interval after stimulation. We excluded from the analysis the first 200 ms, in order to keep only the tonic part of the response (Meunier et al., 2000) and to meet one of the conditions imposed by the method (see Discussion). No more than two taste neurons were concurrently active in our recordings. When spikes could be differentiated by their amplitude and shape (i.e. responses to sugars), spikes were sorted manually (see Figure 1). For all recordings, we calculated two parameters, the total frequency f and the frequency of doublets d. Both those operations and the manual sorting were done using interactive procedures of custom-made software dbWave (available at http://quasimodo.versailles.inra.fr/fred/awave/awave1.htm).
|
|
Results |
|---|
|
TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix: general proof of...References |
|---|
Mathematical method
Presentation of the problem
We consider two neurons, A and B, recorded simultaneously, so that only the pooled process resulting from the superposition of the two spike trains can be observed and we wish to estimate their respective frequencies fA and fB . Even if the action potentials fired by neurons A and B are indistinguishable by their shape and size, fA and fB can be estimated, provided the overall frequency f and the frequency of the doublets d, are known. Two spikes are considered as a doublet if they are separated by a chosen time interval shorter than a period we call the silent period. By silent period, we mean a time interval following a spike during which the probability of occurrence of a second spike from the same neuron is small. In case the silent periods of the neurons are different, the smallest must be taken. This interval does not need to be chosen equal to the absolute or relative refractory period; although it can be taken shorter, it is usually more useful to take it longer (see Discussion). The only condition is that remains less than the shortest ISIs of the most active neuron in the experimental conditions considered. Then one of the spikes in the doublet comes from neuron A and the other from neuron B.
The basic relationship between these quantities is
For a given recording the frequency of doublets increases with higher values of . The second equation necessary for identification of individual frequencies is based on the fact that the frequency f of the pooled process is the sum of the component frequencies, so
A general proof of equation (1) is given in Appendix. In practice, frequency f can be estimated from the total number of spikes N during the observation period T,
Similarly, from the number Nd of doublets in the observation period T, their frequency is
Heuristic proof
A simple proof can be given in the special case of a couple of Poissonian neurons, i.e. neurons for which the probability of emitting a spike within any time interval dt has probability fidt (i = A or B), where dt is sufficiently short. Then, during the observation period, T the number of spikes fired by neuron A is statistically equal to fAT. Each of these spikes can be followed by a spike from neuron B within time with probability fB. Thus the number of doublets in which the leading spike is from neuron A and the second from neuron B is fAT fB. In the same way, the number of spikes fired by neuron B is fBT and each of them can be followed by a coincident spike emitted by neuron A with probability fA. Thus the number of doublets in which the leading spike is from neuron B and the second from neuron A is fBT fA. The total number of doublets Nd is the sum of the two types of doublets, so
from which equation (1) is obtained from equation (4), dividing both sides by T.
Method for estimating frequencies
Utilizing equation (2), equation (1) can be written as
The graph of function d(fA) is a parabola starting from d = 0 at fA = 0 (only neuron B is firing), rising to a maximum for fA = f/2 (both neurons are equally active),
and returning to d = 0 at fA = f (only neuron A is active) (Figure 2). Equations (1) and (2) have two solutions, one on the rising branch and the other on the decreasing branch of the parabola,
|
in which we chose to call A the most active neuron and B the least active one.
Experimental validation of the method
We stimulated terminal tarsal sensilla of Drosophila with sucrose, fructose and glucose at 100 mM. As it is the case of most sensilla on the proboscis (Fujishiro et al., 1984), sugars elicit the responses of two neurons with different spike amplitudes on tarsal taste sensilla (Meunier et al., 2000). Small spikes originate from the S cell, which is sensitive to sugar while large spikes originate from the W cell (Figure 1A). The sugars stimulated the S neuron at different frequencies while the W cell was less affected. This situation allows a comparison between experimental data and predicted values for different ratios of the firing discharges from both neurons and for different values of the overall frequency f (Table 1). We also compared the experimental and estimated value of fA according to (8) for varying between 1 and 15 ms (Figure 3A). For some values of , equation (6) had no solution. This happened when experimental values of d were higher than dmax. In this case, if d did not exceed dmax by more than 10%, we chose a value of fA equal to f/2 (corresponding to dmax). Because in the plot fA vs. , the differences for the small values of are difficult to interpret, we also compared the theoretical and experimental values of d for varying between 1 and 15 ms (Figure 3B). There was a good fit between experimental and theoretical values of fA for between 5 and 9 ms. For < 5 ms, theoretical values were higher than experimental one and this was the reverse for > 9 ms. The best fit was obtained for = 6 ms and we chose this value in the analysis of the second set of experimental data (Table 1).
|
|
By using a
value of 6 ms, we extended the previous experiment to determine the response of the S cell over a series of concentrations of sucrose (Figure 4). Both estimated and experimental values were found to be in good agreement. We obtained a value of d slightly greater than dmax for the recordings corresponding to the concentration 20 mM (d = 7.73; dmax = 7.43 doublets/s), thus we estimated frequencies of the W and S cell to be half the total frequency (24.6 spikes/s).
|
Application to responses to salts on Drosophila tarsal sensilla
The sensitivity to salts in Drosophila involves two taste neurons named L1 and L2 that are present in all sensilla responding to salts. These two neurons fire indistinguishable spikes on tarsal sensilla (Figure 1B) and thus no data exists yet on their relative frequencies (Meunier et al., 2000). On the proboscis they can be sorted manually (Siddiqi and Rodrigues, 1980) and L1 neuron is known to be activated at low concentration of salts whereas L2 is activated at higher concentration (Singh, 1997). We used the method presented above to estimate the respective firing of L1 and L2 neurons in response to increasing concentration of NaCl and KCl in terminal tarsal sensilla (Figure 5). Both neurons were activated by the two kinds of salts without reaching saturation of their activity below 1 molar of salt. We found that L1 neuron activity was always much higher than that of L2, and that L1 was more sensitive to KCl.
|
|
Discussion |
|---|
|
TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix: general proof of...References |
|---|
In this paper, we develop an approach for estimating the respective frequencies of two neurons firing indistinguishable spikes based on the occurrence of ‘doublets’. A doublet corresponds to an interspike interval shorter than a chosen value
that must be less than the smallest silence period of the two neurons considered. We showed that a simple relationship exists between the discharge rate of the two neurons firing independently, the number of doublets and the total number of spikes observed. We tested the validity of this method on spike trains originating from neurons firing spikes of different amplitudes. Then, we used this method to discriminate the firing activities from two neurons delivering spikes of similar amplitudes in the presence of salts. This method was designed to analyze time series where only two neurons are active. It is not applicable in other situations, except if the other neurons exhibit different spike shapes, so that they can be removed from the time series prior to analysis. Conditions of application of the method
The proof of relation (1) given in the Appendix is based on two assumptions. The first assumption is that spike generation in each of the component processes follows a renewal process, i.e. a process in which the intervals (ISIs) between events are stationary, independent (not serially correlated) and identically distributed random variables. The second assumption is that the individual processes are mutually independent, i.e. that firing in one of the neurons does not modify the probability of firing in the other. These conditions must be met by the pair of neurons under study otherwise formula (1) may lead to wrong results. They may be difficult to prove although gross deviations from them will be easily observable, e.g. from abnormal regularities in the recording (thus recordings including erratic bursting activities should be avoided).
Sources of errors and limitation of the method
If the conditions of the method are fulfilled, errors in estimation of the component frequencies fA and fB can arise from three possible causes, as apparent from equations (1) and (2). The first source concerning the choice of higher than the silent period is discussed in the next section. The two other sources concern the reliability of the estimates of the firing frequency f and of the frequency of doublets d. They depend on the observation period T which must be as long as possible within the limits of experimental constraints and the requirement of stationarity. For this reason we chose to analyze data coming from taste neurons during the tonic part of the response, i.e. the interval 0.2–1 s after the stimulation (Meunier et al., 2000).
Errors on the estimation of the frequency of doublets d had two different effects. The first effect, illustrated in Figure 2, is that the error on fA depends on the magnitude of d. The same small relative error on d yields a larger relative error on fA if d is near its maximum value dmax [corresponding to an equal frequency of discharge from both neurons, equation (7)] than if d is relatively small and far from dmax. If d is close to dmax, it is thus advisable to use different recording conditions (e.g. changing the concentration of stimulus). The second effect arises when the two neurons fire at approximately the same rate. Then the measured value of d may happen to be slightly greater or smaller than dmax. If it is smaller, a unique solution fA is found, but if it is greater no solution exists. This means that two random fluctuations of equal magnitude around d lead to different situations depending on the direction of the fluctuation. In practice if d is close to dmax (e.g. do not differ by more than 10%, see Figure 3), d can be safely replaced by dmax. If the difference is greater some caution must be exerted because either the conditions of application of the method are not fulfilled or the value of has not be well chosen (see below).
It should be stressed that this method does not allow to assign an estimated frequency either to neuron A or to B. If one is concerned by the identity of the neurons, other sources of information must be used. For example, when stimulating the same neurons with a series of closely related stimuli, we expect to find a graduated effect on the firing activities. If the two neurons have different dose–response curves, it is then possible to resolve the activity of cell A and cell B without ambiguity. We used that approach to identify the cell responding to bitter compounds in Drosophila (Meunier et al., 2003).
Choice of the interval of time
We have investigated quantitatively the validity of the method by estimating fA and d for a range of s from recordings where the spikes from the two neurons could be distinguished. We then compared the predicted values of fA and d to their experimentally observed counterparts. Figure 3 shows that predicted values depart from the experimental ones when is too small or too large, and that the range of acceptable values depends on the firing rate. This is a positive feature of the method proposed that, in general, the result obtained does not depend on a strict choice of . How can we restrict the range of potentially good values?
For small values of , on the left-hand side of plots in Figure 3, the difference between experimental and estimated values can be explained by our inability to differentiate two superimposed spikes. In the case of responses to sugars, spikes from the W neuron last 3 ms and are much bigger than those of the S neuron (Figure 1A). Therefore it is easy to miss a spike coming from the S neuron if they are occurring close to each other and mistakes on counting doublets are more frequent when is small (only a few ms). To avoid this difficulty, should be greater than 3 ms. This type of error is critical when spikes are dissimilar, because it is easy to miss superposition of a small spike over a large spike. This source of errors may be of less concern when neurons discharge indistinguishable spikes. However, values of less than the duration of the spikes studied should be avoided.
For large values of , the difference on the right side comes from the fact that the selected is greater than the silent period. Therefore some doublets come from the same neuron, which violates one of the assumptions of the model. The values of must be smaller than the minimum ISI of the fastest firing neuron and thus significantly smaller than the mean ISI (inverse of the firing rate, which is not known) to take into account statistical fluctuations. We observed this difference only for the stimulation with sucrose which elicits a strong response of the taste neurons, f = 86 spikes/s, which is the upper limit of fA (the other neuron being silent, fB = 0). In this case, experimental and estimated values start to diverge at = 9 ms, i.e. at 75% of the mean ISI of the pooled process. We can generalize this observation to set a maximum value of , max for a mean frequency f at
On Figure 3A this limit is indicated on the right-hand side of the sucrose line. For glucose and fructose, it does not appear on the graph because f is too small. Those left and right limits are only ‘rules of thumb’ to investigate a range of potentially good values of . When frequency increases, this range narrows down and reaches a limit of 4 ms for spike duration of 3 ms. According to equation (10), this limit corresponds to an overall frequency f of 190 spikes/s. Thus the method should not be applied to estimate the firing rate of neurons with an overall frequency higher than that.
In summary, the choice of is a compromise between the number of doublets counted, which must be as large as possible (and this calls for as long as possible), and the number of doublets coming from the same neuron, which must be negligible. Doublets obtained with a long minimize the inherent error coming from superposition of spikes and the corresponding failure to detect some doublets. The optimal value of will thus be close to the shortest silent period of the two neurons considered. For neurons firing at a much lower rate than the maximum, this value will be longer than the refractory period. It will be close to the relative refractory period (the time interval following a spike that require an electrical stimulation to evoke another spike from the same neuron) only for neurons firing at very high rate. But in that case it would be better not to use our method, since would be probably to small to minimize the error coming from superposition of spikes.
Estimation of the respective frequency of L1 and L2 cells on response to salts
Whereas sensilla on the proboscis respond to NaCl at a threshold of 1 mM (Fujishiro et al., 1984), we found that tarsal sensilla are not activated below 100 mM. On the proboscis, the L1 neuron was defined on the proboscis as responding to low concentrations of salts (Singh, 1997); it reaches a maximal response at around 100 mM with a frequency of 70 Hz. At this concentration, the L2 neuron starts being activated and reaches 30 Hz for 1 M NaCl (Siddiqi and Rodrigues, 1980). Our estimations of the respective frequencies of the two neurons activated by salts on tarsae are consistent with those values. Even if the range of salts concentration activating both types of sensilla are different, we can assign the most active neuron on tarsae to L1 (Figure 5). The least active neuron can be assigned to L2. This result is coherent with previous data because, the level of activation of L2 neuron by salts on tarsae is (i) very similar to the level elicited on L2 neurons of the proboscis in response to salts (Siddiqi and Rodrigues, 1980), and (ii) consistent with the level of activation of L2 neuron by bitter compounds on tarsae (Meunier et al., 2003).
|
Appendix: general proof of equation (1) |
|---|
|
TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix: general proof of...References |
|---|
The aim of this section is to prove that relation (1) holds true for any renewal firing process, not only for Poissonian processes as shown in the Result section. First we determine the cumulative distribution function (cdf) of the intervals in the pooled process. Then from the value of this function at D we deduce the probability to have an interval shorter than
, which is the probability of a doublet. Finally from the relation between the individual and pooled firing frequencies we obtain equation (1). 1. Frequency of spikes in the pooled process
For a given value of , which is assumed to be less or equal to the shortest silent period of both neurons, we can write for individual frequencies
where mi + is the mean ISI of neuron i and i = A, B. Using equation (2) it can be shown that the frequency of spikes in the pooled process is
2. Distribution of interspike intervals in the pooled process
In this section, we determine the cdf, denoted F(t), of the ISIs in the pooled process, i.e. the probability of an interval of length smaller than t.
Let us denote u(t) the probability density function (pdf) of the time interval, 
, to the next action potential from a randomly selected instant of time (forward recurrence time) in the pooled process. The corresponding cdf is denoted by U(t). The relationship between the forward recurrence time and the length of intervals between events, i.e. spikes in the pooled process, is given by the (standard) formula (Cox and Lewis, 1966)
where µ is the mean ISI in the pooled process. So, F(t) is given by
therefore for evaluation of F we need to know u.
The same definitions and relationships hold for each of the two superimposed processes. We denote Fi(t) the cdf of the ISIs in the ith process and ui(t) the pdf of the forward recurrence time i, i = A, B. Relation (A3) now reads
It follows from these definitions that the probability of forward recurrence time longer than t is
and by using (A5) in (A6) it gives
This quantity is used now for evaluating U(t).
The forward recurrence time for the pooled process is the minimum of the recurrence times of the components, = min(A,B) and thus Prob( t) = Prob(A t and B t). The cdf of is U(t) =1 – Prob( t), therefore
where multiplication follows from the independence of the components. Using (A7), we obtain
The pdf u(t) is the derivative of U(t),
Finally, utilizing u(t) given by equation (A12), equation (A6) becomes
3. Probability of doublets
Now, we derive the probability F() of having an interval shorter than in the pooled process. Because of the silent period properties, the probability of an interval shorter than in the component process i is zero, Fi() = 0. So, using t = in (A11) gives
which changes by using equation (A3) to
From the standard formula for the mean, m, of a positive random variable
and from the fact that Fi() = 0, we have
Thus, using (A14) in (A13) gives
Now, replacing the denominator of (A15) by its expression derived from (A2), we find
and using relationship (A1) we obtain
Taking into account that,
we obtain equation (1).
|
Acknowledgements |
|---|
This work was supported by the French Ministry of Education and Research and by the French Ministry of Foreign Affairs through a Lavoisier program grant delivered by EGIDE, by joint cooperation project Barrande No. 972SL between France and the Czech Republic, by NATO linkage grant LST CLG 976786 and by Grant Agency of the Czech Republic (309/02/0168).
|
References |
|---|
|
TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendix: general proof of...References |
|---|
Colquhoun, D. and Hawkes, A.G. (1995) Single-channel Recording. Plenum Press, New York.
Cox, D.R. and Lewis, P.A.W. (1966) Statistical Analysis of Series of Events. Methuen, London.
Fujishiro, N., Kijima, H. and Morita, H. (1984) Impulse frequency and action potential amplitude in the labellar chemosensory neurones of Drosophila melanogaster. J. Insect Physiol., 30, 317–325.[CrossRef]
Hodgson, E.S., Lettvin, J.Y. and Roeder, K.D. (1955) Physiology of a primary chemoreceptor unit. Science, 22, 417–418.
Jackson, M.B. (1985) Stochastic behavior of a many-channel membrane system. Biophys. J., 47, 129–137.[Medline]
Marion-Poll, F. (1996) Display and analysis of electrophysiological data under MS-Windows. Entomol. Exp. Appl., 80, 113–115.
Marion-Poll, F. and Van der Pers, J. (1996) Un-filtered recordings from insect taste sensilla. Entomol. Exp. Appl., 80, 116–119.
Meunier, N., Ferveur, J.F. and Marion-Poll, F. (2000) Sex-specific non-pheromonal taste receptors in Drosophila. Curr. Biol., 10, 1583–1586.[CrossRef][Medline]
Meunier, N., Marion-Poll, F., Rospars, J.P. and Tanimura, T. (2003) Peripheral coding of bitter taste in Drosophila. J. Neurobiol., 56, 139–152.[CrossRef][ISI][Medline]
Perkel, D.H., Gerstein, G.L. and Moore, G.P. (1967) Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys. J., 7, 419–440.
Pouzat, C., Mazor, O. and Laurent, G. (2002) Using noise signature to optimize spike-sorting and to assess neuronal classification quality. J. Neurosci. Methods, 122, 43–57.[CrossRef][ISI][Medline]
Siddiqi, O. and Rodrigues, V. (1980) Genetic analysis of a complex chemoreceptor. Basic Life Sci., 16, 347–359.[Medline]
Singh, R.N. (1997) Neurobiology of the gustatory systems of Drosophila and some terrestrial insects. Microsc. Res. Tech., 39, 547–563.[CrossRef][ISI][Medline]
Steinbrecht, R.A. (1996) Structure and function of insect olfactory sensilla. Ciba Found. Symp., 200, 158–174; discussion 174–157.
Stitt, J.P., Gaumond, R.P., Frazier, J.L. and Hanson, F.E. (1998) Action potential classifiers: a functional comparison of template matching, principal components analysis and an artificial neural network. Chem Senses, 23, 531–539.
Stocker, R.F. (1994) The organization of the chemosensory system in Drosophila melanogaster: a review. Cell Tissue Res., 275, 3–26.[CrossRef][ISI][Medline]
Takahashi, S., Anzai, Y. and Sakurai, Y. (2003) A new approach to spike sorting for multi-neuronal activities recorded with a tetrode—how ICA can be practical. Neurosci. Res., 46, 265–272.[CrossRef][ISI][Medline]
Accepted August 4, 2003
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  N. Meunier, Y. H. Belgacem, and J.-R. Martin Regulation of feeding behaviour and locomotor activity by takeout in Drosophila J. Exp. Biol., April 15, 2007; 210(8): 1424 - 1434. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 Y. T. Qiu, J. J.A. van Loon, W. Takken, J. Meijerink, and H. M. Smid Olfactory Coding in Antennal Neurons of the Malaria Mosquito, Anopheles gambiae Chem Senses, November 1, 2006; 31(9): 845 - 863. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||