Slice electrophysiology.

The brain was covered in 2% agarose and submerged in a Slicing Medium after which it was sliced in 300 μM thickness using a VF-300 compresstome (Precisionary Instruments LLC) and then incubated for 30 min in 37°C artificial cerebrospinal fluid (ACSF, composition in mM: 1200NaCL, 35KCL, 13MgSO_4.7H₂O, 25CaCl_2.2H₂O, 100 Glucose.H₂O, 12.5NaH₂PO₄.H₂O, 250NaHCO₃), oxygenated (95%O₂/5%CO₂). The bath was then transferred to room temperature. Slices were allowed to accomodate to room temperature for 30 min and were kept in this bath until use. Slices were placed into the recording chamber under the microscope (Eclipse FN1, Nikon) and perfused continuously at a rate of 1 ml/min with the oxygenated ACSF at room temperature. Patch pipettes for whole-cell recordings were pulled from borosilicate glass capillaries, 1.0 mm outer diameter, 0.5mm inner diameter, on a pipette-puller (Sutter Instrument Co. Model P-2000), until an impedance of 8±2 MΩ for the tip was obtained. Pipettes were filled with a solution containing (in mM) 115CsMeSO₃, 20CsCl, 10HEPES, 2.5MgCl₂, 4Na₂ATP, 0.4NaGTP, 10Na − phosphocreatine, 0.6EGTA, 5QX − 314 (Sigma). The whole cell access was obtained after reaching the gigaohm seal and breaking the membrane. Upon entering the cell and the whole-cell mode, the membrane potential was kept fixed at -70mV, outside stimulation.

Input current generation.

Data acquisition was performed with HEKA EPC9 amplifier controlled via HEKA’s PatchMaster software (version 2.90x.2), and subsequent analysis with MatLab (Mathworks, v.2016b). Three types of experiments were performed: current clamp (CC) step-and-hold, current clamp (CC) frozen noise, and voltage clamp (VC).

The current clamp (CC) step-and-hold protocol was performed in every cell and used to distinguish between cell types, according to the firing rate and spike shape (Fig 1). The protocol consisted of clamping the neuron at a baseline current I_baseline, corresponding to the one required to keep its membrane at -70mV, and providing a 500ms long stimulus of fixed current value I = I_baseline + (40pA * step number), for a total of 10 steps, reaching a maximum current injected of I_baseline + 400pA. Between each current injection step, a 5.5s recovery window was allowed.

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Fig 1. Cell Classification with the CC step-and-hold protocol.

A, B: We selected neurons to record from the mouse somatosensory cortex (barrel cortex), in L2/3. Visually, the shape and size of soma were a good indicator of the cell type: smaller and roundish shapes would point towards fast-spiking neurons, while slightly larger and triangular shapes would point to regular spiking (putative excitatory) neurons. C: Example responses of an excitatory cell to a constant injected current. D: Example responses of an inhibitory cell to a constant injected current. E: Cell classification using agglomerative clustering based on the maximum firing frequency and spike width. Cell classification using agglomerative clustering based on the maximum firing frequency and spike width. This method was used to verify that cells were correctly classified as inhibitory (blue) or excitatory (red) during the experiment: in pink the cell(s) where the agglomerative clustering and the initial classification disagreed, and were excluded from the analysis (see Materials & methods). F: Maximum firing frequency distribution for incremental current injection amplitudes for inhibitory (blue) and excitatory (red) neurons. G: Same as F, but for the latency of the first spike. H: After-hyperpolarization distribution. I: Spike half-width distribution. For threshold behaviour in the current-clamp step-and-hold protocol, see S1 Fig.

https://doi.org/10.1371/journal.pcbi.1012043.g001

Information transfer was measured using the ‘frozen noise’ method introduced by Zeldenrust et al. [15]. To measure information transfer from input to spike train in short periods of time, instead of the long measurements needed for the traditional methods (see Introduction), the noisy input current injected into a neuron in the current clamp setting was generated as the output of a simulated Poisson neural network (SPNN) that responded to a randomly appearing and disappearing preferred stimulus or ‘hidden state’ (Markov process) x: a binary variable that can take the values of 1 (preferred stimulus present, ‘on-state’) and 0 (preferred stimulus absent, ‘off-state’, see Fig 2A). This hidden state is switched on and off according to a Markov process with rates r_on and r_off. The advantage of using such a binary hidden state stimulus is that there is no need to reconstruct the full input current (which is high-dimensional and therefore requires long recordings), but it is sufficient to reconstruct the binary stimulus, for which less data is needed. The N = 1000 neurons of the SPNN fired Poisson spike trains, whose firing rates were modulated by the hidden state stimulus, so that each neuron fired with rate when x = 1, and when x = 0. These rates were drawn from a Gaussian distribution with mean μ_q (see Table 1) and standard deviation . Each spike was convolved with an exponential kernel with a unitary surface and a decay time of 5ms. The spike trains from different presynaptic neurons contribute to the output with weight . In order to choose the parameters of this input current two considerations needed to be made:

1. The Markov process had rates r_on and r_off, which correspond to a switching time constant : since excitatory neurons do not fire at rates higher than a few Hz, but the inhibitory neurons show a much broader working range, up to 100 Hz (Fig 1), the information transfer could not be measured in the two types of neurons with the same switching speed of the hidden state τ_input, but the switching speed of the hidden state needed to be adapted to the working range of the neuron type. Fortunately, the method allows for keeping the information about the hidden state in the input constant while changing τ_input, by adjusting the mean firing rate of the SPNN μ_q (see Fig 2B). So the information transfer in the two neuron types could still be compared by choosing a time constant τ_input of 50 or 250 ms for inhibitory/fast spiking or excitatory/regular spiking neurons respectively, with matching values of μ_q of 0.5 Hz or 0.1 Hz respectively (see Table 1, so that the mutual information between the input current and the hidden state (MI_I) was about 0.3 bit (Fig 2E). This target mutual information between the input current and the hidden state was chosen so that the input current was informative about the hidden state, but not too informative.
2. The input generated by the SPNN responding to the Markov Process (I_Markov(t)) is dimensionless. Therefore, this dimensionless theoretical “input current” needed to be scaled to Ampère so that it could be injected into the neuron in a current clamp setup. Therefore, the injected current was defined as I_injected = I_hold + I_scaleI_Markov(t). Here, the neuron was clamped a baseline current I_baseline, corresponding to the current required to keep its membrane at -70mV, and I_scale was set at 2100 pA for excitatory and 700 pA for inhibitory cells (see Table 1). This way, the input was scaled to be at roughly the same point on each neuron’s I-V curve.

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Fig 2. Input for the CC frozen noise protocol.

A: Overview of the frozen noise method for input generation and measurement of mutual information (copied with permission from [15]) B: Mutual information between the input current and the hidden state, for different values of the switching speed of the hidden state (τ_input) and the average firing rate of neurons in the SPNN (average over 10 trials). The white squares denote the used values for the input for the inhibitory (top left) and excitatory (bottom right) neurons. C: Average (over the trial) input current (i.e. I_baseline and D: membrane potential for all trials. Green data points/lines denote the control experiments where the inhibitory neurons received the input current that was otherwise given to the excitatory neurons. E: Mutual information between the hidden state and the input current, for all trials. Note that because frozen noise was used, every frozen noise trial was actually the same. Therefore, there are not many different realizations and hence not many different MI values. F: Example injected frozen noise current for an excitatory neuron. The grey shaded area corresponds to times when the hidden state was 1. G: Example injected frozen noise current for an inhibitory neuron. H: Example resulting membrane potential of an excitatory neuron. I: Example resulting membrane potential of an inhibitory neuron.

https://doi.org/10.1371/journal.pcbi.1012043.g002

The scripts for generating this current can be found in this GitHub repository: https://github.com/DepartmentofNeurophysiology/Analysis-tools-for-electrophysiological-somatosensory-cortex-databank.

In the experimental paradigm, we used a ‘frozen’ current injection: the exact same current (except for the overall baseline and amplitude) for all excitatory neurons and the exact same one for all inhibitory neurons. This had of 2 reasons: the first was an experimental setup constraint: the current had to be generated offline and loaded onto the setup, which would have made the experiments take a lot longer to perform if we did not use the same current each time. The second was that the experiments were in many neurons also repeated with different neuromodulators [14]. For proper comparisons between aCSF and neuromodulator trials (ie omitted or added spikes for the same input), the input current needed to be frozen. These neuromodulator trials were not included into this manuscript; only the aCSF condition was used.

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Table 1. Input parameters for the ex-vivo experiments.

https://doi.org/10.1371/journal.pcbi.1012043.t001

Cell classification.

Cells were classified using the following procedure: each cell was first stimulated with a current-clamp step-and-hold (CC-step) protocol, which was used to classify the cells on-site, during the experiment, before generating the frozen noise stimulus with parameters matching that cell group. Cells were assigned to the fast spiking (putatively inhibitory) or regular spiking (putatively excitatory) groups, on the basis of the maximum firing rate recorded during the CC-step protocol (in particular, if this was lower than ≈ 50Hz), and the action potential shape (Fig 1). Based on this initial classification the cell received the frozen noise input current with either τ_input = 250 ms (excitatory neurons) or τ_input = 50 ms (inhibitory neurons). From these recordings, the maximum firing rate, the average spike-halfwidth, the latency to the generation of the first action potential, and the average after-hyperpolarization (AHP) amplitude were extracted (Fig 1). Offline, after data collection, the initial classification was verified using an agglomerative clustering protocol (MATLAB ‘clusterdata’) to cluster the data into 2 groups (separated following Ward’s linkage method), according to the maximum firing rate and the average spike-half width (normalized to zero mean and unit standard deviation) reached during the CC-Step protocol (Fig 1E). There was a single cell where the initial classification and the post-hoc classification were in disagreement (Fig 1E, pink star). We decided to keep this cell in the original (inhibitory) group due to its position between the two clusters.

Calculation of mutual information.

The mutual information between the hidden state and the input (MI_I) or a spike train (MI_{spike train}) was estimated with the help of the hidden state x (see Input current generation and Fig 1A). The method was explained in detail in Zeldenrust et al. (2017) [15] and followed derivations from Denève (2008) [21] and Lochmann and Denève (2011) [27]). Code for how to calculate the mutual information can be found in the following repository: https://github.com/DepartmentofNeurophysiology/Analysis-tools-for-electrophysiological-somatosensory-cortex-databank as well as with the data.

In short, the mutual information was calculated using the log odds ratio that the hidden state is 1, given the history of the input until now I(t) (1) (2) The estimated log-odds ratio that the hidden state is 1, given the history of the input until now I(t) can be calculated by integrating the following differential equation (see [15, 21] for the derivation): (3) where is the constant offset of the input, which is chosen to equal to 0 by generating the input as explained before (drawing and from a Gaussian distribution). We can use the definition of the log-odds ratio to estimate the probability that the hidden state is 1, given the history of the input until now: Using this estimate of the probability that the hidden state is 1 over time, we can now estimate the conditional entropy by averaging over time, where we used an ergodic argument to approximate an average over samples by an average over time. (4) Because the hidden state follows a memory-less Markov process, its entropy at every moment in time equals (5) Here, is the prior probability that the hidden state equals 1. Note that in our case, because P₁ is smaller than 0.5, the entropy of the hidden state is smaller than 1 (H_xx = 0.92 bits). With the canonical MI = H_xx − H_xy, the mutual information between the input and the hidden state can now be estimated. Similarly, the mutual information between a spike train and the hidden state can be estimated by integrating Eq 3 where the input I(t) is now replaced by the spike train input given by (6) where ρ(t) is the spike train of the neuron and its weight w is given by (7) Parameter is calculated similarly based on the observed q_on and q_off in the spike train.

Note that even though theoretically MI ≤ 0, due to our approximation it can happen that our estimate of H_xy > H_xx, due to the integration method, and hence that we find a small negative value of the MI between a spike train and the hidden state. These are often cells that fire either at very low rates or have firing patterns that for other reasons deviate from a Poisson-like response (i.e. cells that stop firing during the experiment). However, to maintain a complete overview of the data, we decided not to discard those that have a low firing rate. However, we did exclude files with negative values in the input current (where the wrong input current was saved) and files with a vanishing firing rate.

In this manuscript, we mostly report on the unitless ‘Fraction of Information’ (FI) in the output spike train: (8) The FI quantifies how much information about the hidden state is transferred from the input current to the spike train, and thus quantifies which fraction of the information is kept during the spike-generating process.

Alternative calculation of mutual information.

For comparison, we used the following alternative method of calculating the mutual information between the hidden state and the input current, membrane potential or spike train. The results are shown in S2 Fig. When the methods are compared, the method of the previous paragraph is referred to as the ‘Bayesian MI’ and the method explained here as the ‘binned MI’.

To calculate the mutual information between the hidden state and any given state parameter y (i.e. the input current, membrane potential or instantaneous firing rate), we first divide the time series in periods between state switches (i.e. periods for which the hidden state is constant, which we will call ‘states’), and average the state parameter y over this ‘state’. This way, we obtain an average value for y for the duration of an ‘up-state’ and ‘down-state’: 〈y〉. Next, we make a distribution of all those average values of y (see S2B–S2E and S2H–S2K Fig). We can then calculate the Kullback-Leibler divergence D_KL between the distribution of average values when the hidden state is 1 and the distribution when the hidden state is 0 (see S2F, S2L, S2N and S2O Fig). In particular, we calculated the Jensen-Shannon divergence (using the code of [28]), or half the ‘Jeffrey divergence’ [29]. Next, we calculate the mutual information directly, by binning the two histograms (we will call the bins b_〈y〉 and the value of 〈y〉 in bin b 〈y〉_b) of and calculating (9) (10) (11) Based on S2F and S2L Fig, we used 500 bins in our calculations.

To calculate the mutual information between the hidden state and the instantaneous firing rate of the neuron, we have to make an estimate of the instantaneous firing rate based on the spike train. This is typically done by convolving the spike train with a a kernel (see [30] for a thorough discussion). We need a causal kernel, because it would not make sense to see the firing rate increase before a state switch. Therefore, we use an exponential kernel with a unit surface. Also, to make the calculation comparable to the ‘Bayesian MI’, we make the decay time constant of the exponential kernel equal to the time constant of the input τ_input, so 50 ms for inhibitory neurons and 250 ms for excitatory neurons.

The two methods result in very comparable values for the mutual information between the hidden state and the spike train (see S2M Fig). Moreover, we can calculate the slope of the IV curve (S2D and S2J Fig) and determine the correlation with the mutual information (S2P Fig). This leads to the same conclusion as with the ‘Bayesian MI’ and the dynamic IV curve (i.e. a greater resistance R_in/ lower conductance g is associated with a larger information transfer). Because the two methods result in similar conclusions, this method is not used throughout the paper and its results are only shown in the Supplementary Material for reference. However, here we will shortly discuss the advantages and disadvantages of both methods. In terms of computational resources, the ‘binned MI’ computational costs come from the convolution of the spike train with the kernel to obtain the instantaneous rate, and for the ‘Bayesian MI’ most computational costs come from the integration of the log-likelihood (Eq 3). Which one requires more computational resources depends on the parameters of the methods and properties of the spike trains. In terms of intuition, the ‘binned MI’ might be more intuitive to understand (a measure of how easy it is to distinguish the two values of the hidden state depending on observing average state parameter 〈y〉). However, for this method one also needs to make a few non-trivial choices (number of bins, kernel size and shape for the calculation of the instantaneous firing rate). Finally, a more fundamental difference between the two methods, is that the ‘binned MI’ is post-hoc, and can only be calculated after observing a large amount of states, whereas the ‘Bayesian MI’ is essentially an online method, that keeps an estimate of the current most likely value of the hidden state online. Which method is more appropriate will depend on the experimental/simulation setup. A final observation is that the Kullback-Leibler divergence between the histograms for the two states is larger for the membrane for the input, but smaller again for the firing rate, something we have observed before [1].

Threshold detection.

The membrane potential threshold of each recorded spike in the Current Clamp (CC) experiments was determined from the experimentally recorded membrane potential using the method explained in [24]: in a window from 1 to 0.25 ms before each spike maximum, the earliest time in the window at which either the first derivative exceeded 18 mV/ms or the second derivative exceeded 140 mV/ms2 was designated as the threshold-time, and the threshold value was determined as the corresponding membrane potential of that time point.

ROC curves.

A Receiver Operator Characteristic (ROC) curve shows how well a system can be classified into two binary classes by comparing the number of correctly detected positives or ‘hits’ to the number of false positives or ‘false alarms’ depending on a threshold parameter. Here, we assumed every trial had its own threshold, and we defined a ‘hit’ as a period during which the hidden state was 1, in which at least 1 action potential was fired, and a ‘miss’ as a period during which the hidden state was 1, in which no action potentials were fired. Similarly, we defined a ‘false alarm’ as a period during which the hidden state was 0, in which at least 1 action potential was fired, and a ‘correct reject’ as a period during which the hidden state was 0, in which no action potentials were fired. So each period in which the hidden state was 1, was either defined as a ‘hit’ or a ‘miss’, and each period in which the hidden state was 0, was either defined as a ‘false alarm’ or a ‘correct reject’. The total number of hits was divided by the total number of periods during which the hidden state was 1, which resulted in the fraction of hits 0 ≤ f_h ≤ 1. Similarly, the fraction of ‘misses’, ‘false alarms’, and ‘correct rejects’ were defined as the fraction of periods during which the hidden state was 1 but no spike was fired, the fraction of periods during which the hidden state was 0, but a spike was fired and the fraction of periods during which the hidden state was 0, and no spike was fired, respectively. We calculated the fractions of hits, misses, false alarms, and correct rejects for each spike train, as well as for a corresponding Poisson spike train of the same length and with the same number of spikes. Note that for these Poisson spike trains, the hit fraction is actually below the hit fraction = false alarm fraction line, due to the nature of the hidden state: because the hidden state is more often 0 than 1 (P₁ < 0.5), a random spike will have a higher chance of occurring during a period where the hidden state equals 0. Therefore, the false alarm fraction will be higher than the hit fraction for Poisson spike trains.

Fitting of exponential functions.

In the results, we fit saturating functions to how FI (Eq (8)) depends on different input variables x ∈ {I_scale, r, r_n}: (12) where r is the firing rate of an output spike train, and r_n = r ⋅ τ_input is the unitless firing rate normalized by the switching speed of the hidden state τ_input. We fit parameters FI_max and λ, and in the case of x = I_scale also I_scale,offset (in the case of x ∈ {r, r_n} the offset value is set equal to 0). To fit these curves, we use Matlab’s ‘fit’ function, which automatically calculates 95% confidence intervals. When the data does not only saturate, but decreases again after the maximum, we include only data up to the maximum.

Calculation of membrane capacitance and conductance using dynamic IV curves.

We used the derivation of Badel et al. (2008) [31] to calculate the membrane capacitance (C_m) and conductance (g_m) for each analysis window. In short, we calculated from the recorded traces, and calculated the variance of between the values of −76 ≤ V_m ≤ −74 mV for different values of . The membrane capacitance C_m was determined as the value of for which the variance was minimized: Next, we defined the membrane current as and binned the I_m − V_m curve in bins of 5 mV and calculated the average for each bin. A linear fit was made for subthreshold voltage values (−200 ≤ V_m ≤ −60 mV), and the slope was defined as the membrane conductance g_m. We excluded files where this fit did not succeed (the value of g_m was found to be negative).

Spike-triggered average.

The whitened and regularized spike-triggered average (STA) was calculated as (13) where X is a stimulus-lag matrix, where each row is the stimulus vector with a different lag (see [32–35]), X^TX is the correlation matrix and I is the identity matrix. Operator ‘\’ denotes multiplication with the inverse, and T denotes a transpose. Parameter λ is a regularization (i.e. smoothing) parameter which was set to 10 and μ₍X^TX) is the mean of the diagonal of the correlation matrix. Finally, ρ denotes the spike train. The resulting STA was normalized with the L₂ norm.

Following the derivation of Slee et al. (2005) [36], the inner product of all spike-triggering stimuli with the STA was calculated for each trial (P(stimulus—spike), the posterior distribution), as well as the inner product of the same number of random-triggered stimuli (P(stimulus), the prior distribution. With the random-triggered stimuli, the prior distribution of the input was calculated, and compared to the distribution of spike-triggering stimuli (the posterior distribution). With Bayes’ law, the shape of the threshold function could be calculated: (14) However, if the distributions are not smooth due to limited sampling, the threshold function cannot be calculated. Therefore, the difference in mean between the prior and posterior was calculated for each neuron, and the distribution of means over all neurons was shown.

To assess the variability between the STAs calculated for each cell, we calculated the inner product between all pairs of STAs of inhibitory cells and between all pairs of STAs of excitatory cells. Because excitatory cells fire less, the STAs are based on a lower number of spikes for excitatory cells than for inhibitory cells. This in itself could introduce a higher variability of the STAs. To control for this, we also calculated the STAs for the inhibitory cells based on a comparable number of spikes as for the excitatory cells: we matched each inhibitory trial to an excitatory trial and reduced the number of spikes by only including the first spikes until they had the same amount of spike, and discarding the rest. Subsequently, we calculated the STA based on this reduced number of spikes, normalized them, calculated the posterior and prior for these, and calculated the inner product between all pairs of these STAs.

Optimal observer: Bayesian Neuron.

Next to the possibility of information estimation in short time windows, the in vitro information transfer method [15] has another advantage: the availability of an optimal observer model. This ‘Bayesian neuron’ [21] is a spiking neuron model that optimally integrates evidence about the hidden state from the SPNN described above. It is optimal given an efficient coding or redundancy reduction assumption: it only generates new spikes if those spikes transfer new information about the hidden state, that cannot be inferred from the past spikes in its spike train. In practice, the neuron performs a leaky integration of the input, in order to calculate the log-odds ratio L for the hidden state being 1 (NB Note the similarity with Eq 3): (15) where r_on and r_off are the switching speeds of the hidden state, and is the constant offset of the input generated by the SPNN as before, which is chosen to be equal to 0 in this paper. The neuron compares this log-odds ratio from the input, L, with the log-odds ratio of the hidden state being 1 inferred from its own spike train, G: (16) Each time the log-odds ratio based on the input (L) exceeds the log-odds ratio based on the output spike train (G) by an amount , a spike is fired: (17) For the optimal observer, the parameters of the Bayesian neuron (r_on, r_off, θ) are the same as the ones chosen for the hidden state and the SPNN for generating the input. As the model is made as an optimal observer for this input, the input does not have to be scaled (I_baseline = 0; I_scale = 1), making η the only free parameter of the Bayesian neuron model. This precision parameter η describes the distance between the threshold and the reset of the Bayesian neuron, or in other words, the precision with which G tracks L. This parameter is varied in order to obtain the different firing rates in the Results section (from 0.25 to 6 in steps of 0.25). Note that this neuron model has a form of threshold adaptation: if it did not spike for a long time, G decays to its prior value . With each spike, G is increased by η, and more input (larger L) is needed to fire a spike, thereby reducing its firing rate.

The simulated neurons received the same frozen noise input as used in the experiments (see Input current generation), but unscaled (I_baseline = 0; I_scale = 1). The simulations were performed in Matlab, using a standard forward Euler with a time step of 0.05 ms.

ExpIF neuron with (sub)threshold adaptation and non-linear I-V curve.

In order to obtain more biologically interpretable results, and to disentangle the subthreshold and threshold effects of adaptation, we used the expIF neuron with subthreshold [22, 23] and/or threshold [24] adaptation. The equations are given by (18) (19) (20) where w describes the subthreshold adaptation and the threshold θ decays to a steady state (21) A spike is defined when V_m passes a cutoff value V_cutoff and is reset to a reset potential V_r = V_t + 5Δ_T: (22) Moreover, we added the following instantaneous currents to the right-hand side of the membrane potential Eq (18) in order to simulate non-linearities in the I-V curve: (23) (24) and (25) (26)

To assess the effect of adaptation, we simulated 4 parameter regimes: 1) no adaptation, 2) subthreshold adaptation only, 3) threshold adaptation only, and 4) combined adaptation (both subthreshold and threshold adaptation), with the parameters given in Table 2. To assess the effect of a non-linear I-V curve, we simulated 3 parameter regimes: 1) we added an instantaneous hyperpolarization-activated depolarizing current, similar to an h-type current: ‘vary g_h’, 2) we added an instantaneous depolarization-activated hyperpolarizing current, similar to a subthreshold potassium current: ‘vary g_K’, 3) and we varied the leak-conductance: ‘vary g_L’, with the following parameters given in Table 3. Note that for large values of I_scale the simulations diverge: the membrane potential diverges and no further spikes are fired. These simulations are not included in the analyses.

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Table 2. Parameters for the adaptive expIF model with (sub)threshold adaptation.

https://doi.org/10.1371/journal.pcbi.1012043.t002

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Table 3. Parameters for the expIF model with non-linear I-V curve.

https://doi.org/10.1371/journal.pcbi.1012043.t003

The simulated neurons received the same frozen noise input as used in the experiments (see Input current generation), but with a different scaling (see Tables 2 and 3). Simulations were performed in Brian 2 [37], using a standard forward Euler with a time step of 0.025 ms.

Excitatory neurons fire at low rates.

Whole-cell recordings were made from pyramidal cells and interneurons in layer 2/3 (L2/3) of mouse barrel cortical slices [13]. Cells were classified as either ‘excitatory’ or ‘inhibitory’ based on their electrophysiological responses to a standard current-step protocol (Fig 1, see Materials & methods). In response to depolarizing steps, excitatory neurons show strong spike-frequency adaptation, limiting their maximum firing rate (Fig 1 and S1 Table, see also [13]), whereas inhibitory neurons fire at much higher rates.

To measure the information transfer from input current to output spike train, traditionally long (∼1 hour) experiments were needed to obtain a single mutual information estimate [16–20]. To estimate the information transfer in a shorter time period we used a recently developed method [15] that uses the output of an simulated Poisson neural network (SPNN) to generate the frozen noise current input used in our ex-vivo experiments (Fig 2A, see Materials & methods). Such a frozen noise input constitutes an optimum between giving naturalistic stimuli (as far as possible in an ex-vivo setup, given that we do not have access to the spatiotemporal input distribution a cell would normally receive), being able to assess information transfer, and being able to assess membrane properties (which are typically only stably accessible in slice experiments). The SPNN responds to a randomly appearing and disappearing preferred stimulus or ‘hidden state’ x (Markov process). This hidden binary state can either be ‘on’ (i.e. x = 1) or ‘off’ (i.e. x = 0), and switches randomly between these states with time constant τ_input. The neurons in the SPNN respond to this hidden state with Poisson-generated spike trains, of which the firing rate depends on the hidden state (i.e. each neuron i responds with a rate of when x = 1, and a rate of when x = 0). The mutual information between the input current and the hidden state depends on three properties of the SPNN: the number of neurons (N), the average firing rate of the neurons (μ_q), and the time constant of the hidden state (τ_input). We can now compare the mutual information between the input current and the hidden state with the mutual information between the output spike train and the hidden state. This has the advantage that because the hidden state is low-dimensional (it has only two states), the mutual information can be estimated in a short time-window.

Because of the differences in maximum firing rate between the excitatory and inhibitory cells, it was not possible to use the exact same frozen noise input current for the two cell types: τ_input had to be large for the excitatory neurons (neurons firing at a low rate cannot transfer information about a fast-switching stimulus, so the hidden state had to switch slowly), but this is not the case for the inhibitory neurons (which fire at high rates, so the hidden state can switch fast, i.e. a small value for τ_input should be used). However, the information in the input could be kept constant by adapting the firing rates of the neurons in the SPNN μ_q (Fig 2, see also Materials & methods). This resulted in the parameters in Table 1 for the frozen noise experiments to generate the input currents shown in Fig 2.

Inhibitory neurons show broadband information transfer; Excitatory neurons transfer less information and at low frequencies.

By using the ‘frozen noise protocol’ as described before (see Materials & methods and [15]), the information transfer from the hidden state to the output spike train of a single neuron can be estimated in a short time window. In order to obtain the information transfer from the input current to the output spike train, we define the unitless fraction of transferred information (FI) as the mutual information between the spike train and the hidden state (MI_{spike train} divided by the mutual information between the input current and the hidden state (MI_input, see Eq (8). The FI quantifies how much information about the hidden state is transferred from the input current to the output spike train, and thus quantifies which fraction of the information is kept during the spike-generating process. In Fig 3, we show the FI as a function of the firing rate r, for inhibitory (blue) and excitatory (red) neurons, and compare it to the FI obtained from the ‘Bayesian Neuron’ (BN) model [21] for which parameters (see Materials & methods) were optimized for the input generated for the excitatory neurons (pink) or inhibitory neurons (turquoise). Excitatory neurons transfer more information at low firing rates (<∼8 Hz) compared to inhibitory neurons. This is due to our choice of slower switching speed (i.e. large τ_input) of the hidden state for excitatory neurons: a fast-switching hidden state cannot be properly tracked by neurons firing at a low firing rate (see also [15]). To compare inhibitory and excitatory neurons, we normalized the firing rate of each neuron relative to the switching speed of the hidden state: r_n = r ⋅ τ_input (unitless). The FI was plotted as a function of this normalized firing rate in Fig 3B. The FI increases up to a maximal value at about r_n = 1.5, after which the FI appears to decrease again. Apparently, at very high firing rates, the transferred information goes down due to too many spikes during x = 0. We fitted a saturating function (see Materials & methods) to the measured values, where FI_max is the saturation value and is the rate with which this saturation value is reached (both unitless). We fitted the data up to r_n = 1.5, because we do not have a mathematical description for the type of curve that saturates and then dips again (but note that all panels and figures contain all data points, including those for r_n > 1.5). In Fig 3E and 3F, the fit values and their 95% confidence intervals are shown. Inhibitory experimental and BN values saturate around similar values (FI_max = 0.65 (0.64–0.66) and FI_max = 0.64 (0.63–0.65) respectively), with experiments having a slightly lower rate ( (5.6–6.0) and 7.7 (7.3–8.0) respectively). Excitatory neurons saturate at lower experimental values (FI_max = 0.51 (0.48–0.54)) and slightly lower BN values (FI_max = 0.58 (0.54–0.63), and the saturation rates are also lower ( (4.0–4.9) and (5.0–7.2) respectively). This shows that in the case of the excitatory neurons, the experimentally recorded spike trains transmit less information than the spike trains of the BN, whereas in the inhibitory case, the model and experimental spike trains perform similarly. This means that inhibitory neurons perform close to optimal for representing the hidden state, whereas excitatory neurons do not. As a control, we presented the input for the excitatory neurons also to inhibitory neurons (Fig 3, green, FI_max = 0.63 (0.52–0.75), (1.6–3.7)); these inhibitory neurons fired at a higher normalized rate (Fig 3C) and performed better than the excitatory neurons. In conclusion, putative interneurons transfer more information than putative excitatory neurons.

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Fig 3. Inhibitory neurons transfer more information.

A: Fraction of information kept during the spike generating process (FI, see Eq (8) as a function of the firing rate, for inhibitory neurons (blue) and excitatory neurons (red). In green, the control experiments where the inhibitory neurons received the input current that was normally given to the excitatory neurons (τ_input = 250 ms). In turquoise and pink, the simulations with the Bayesian Neuron (Materials & Methods, see Table 1 for parameter values). B: Fraction of information kept during the spike generating process, as a function of the normalized firing rate (normalized by the switching speed of the hidden state: r_n = r ⋅ τ_input, see Table 1). The solid lines denote fits of the data up to a normalized firing frequency of r_n = 1.5 (Eq (7), Materials and methods). Colors/markers the same as in A. C: and D: Normalized firing frequency and FI distribution of the spike trains in all conditions. E: Zoom of B. F: and G: Fit values and their 95% confidence intervals (error bars) for parameters FI_max (F) and (G), see Eq (12). Data from 144 excitatory neurons (220 trials), 72 inhibitory neurons (78 trials) and 9 control inhibitory neurons (11 trials). NB Note that even though theoretically MI ≥ 0, due to our approximation, our estimate of MI can take small negative values (see Materials & methods).

https://doi.org/10.1371/journal.pcbi.1012043.g003

Inhibitory neurons perform well as classifiers.

The setup with the hidden state makes it possible to show ‘receiver-operator curves’ (ROCs): we define a ‘hit’ as a period during which the hidden state was 1 (up-state), in which at least 1 action potential was fired, and a ‘miss’ as an up-state in which no action potentials were fired. Similarly, we define a ‘false alarm’ as a period during which the hidden state was 0 (down-state), in which at least 1 action potential was fired, and a ‘correct reject’ as a down state in which no action potentials were fired. We then define the ‘hit fraction’ as the number of hits divided by the total number of up-states, and similarly the false alarm fraction for the number of false alarms divided by the total number of down-states. In Fig 4A the results are shown, for the same five conditions as discussed above. For each experiment, a control experiment was simulated by generating a Poisson spike train with the same number of spikes as the original experiment. Note that this ‘control’ is below the line hit fraction = false alarm fraction because the hidden state is more often 0 than 1 (). Since the hidden state is longer in the ‘0’ state, the probability that a random spike occurs when the hidden state equals 0 is higher, hence the probability of a false alarm is higher than the probability of a hit.

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Fig 4. Binary classification.

A) Receiver Operator Curve (ROC), where the hit rate was defined as the fraction of up-states, in which at least 1 action potential was fired. Similarly, the false alarm rate was defined as the fraction of down-states, in which at least 1 action potential was fired. In black the results for Poisson spike trains with firing rates matched to those of the experimental/simulation conditions are shown. B) Distribution of the number of spikes per period where the hidden state was 1 (up state), for inhibitory neurons (blue) and excitatory neurons (red). C) Same as B), but for periods where the hidden state was 0 (down state). D) Firing rate r distribution in the up-state. E) Firing rate r distribution in the down-state. F) Normalized firing rate r_n distribution in the up-state G) Normalized firing rate r_n distribution in the down-state. H) Delay (in ms) of each correct spike since the state switches from down to up. I) Delay (in ms) of each incorrect spike since the state switches from up to down. J) Normalized delay (delay/τ, unitless) of each correct spike since the state switches from down to up. K) Normalized delay of each incorrect spike since the state switch from up to down. The results of hypotheses test for A-F are in S2 and S3 Tables. Data from 144 excitatory neurons (220 trials), 72 inhibitory neurons (78 trials), and 9 control inhibitory neurons (11 trials).

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Inhibitory neurons perform comparably to the BN, as shown in Fig 4, whereas the excitatory neurons perform less optimally than their model counterparts. We performed control experiments where input currents generated for excitatory neurons were injected into inhibitory neurons, (green triangles in Figs 3 and 4). The results suggest that interneurons perform comparably to (on the same curve as) excitatory neurons, but with a lower discrimination threshold (i.e. with a higher firing rate), which is in agreement with our previous observation that inhibitory neurons responded with a higher firing rate than excitatory neurons. Note that inhibitory neurons fire slightly less spikes during the up-states (Fig 4B) and the normalized firing rate in the up-state is somewhat lower for the inhibitory neurons (Fig 4F). Since the excitatory neurons fire more spikes during the down states (Fig 4C and 4G), this corresponds to a lower efficiency for excitatory neurons and a worse performance on the binary classification task (Fig 4A). Indeed, the number of spikes per down state (Fig 4C) and normalized firing rate in the down state (Fig 4G) differs between inhibitory and excitatory neurons (S2 and S3 Tables). Note that most ‘incorrect’ spikes are actually fired shortly after a down switch (Fig 4H–4K), so they might be ‘correct’ spikes that were a few milliseconds too late. In conclusion, putative interneurons are better binary classifiers than putative excitatory neurons.

Dynamic threshold of both neuron types.

To assess how intrinsic properties of the putative interneurons and pyramidal cells correlate with their information transfer capabilities in this setup, we next assess the threshold adaptation of these neuron types. In Fig 5, we show the threshold behaviour of the inhibitory and excitatory neurons. The membrane potential threshold of each spike was determined based on the method of [24] (see Materials & methods). We show the distribution of the membrane potential as a function of the inter-spike interval (ISI, Fig 5A and 5E). For both inhibitory and excitatory neurons, the membrane potential threshold goes up with short ISIs, as expected, and for long ISIs the threshold is low. This effect has a long time scale (at least several tens of milliseconds), longer than expected based on the relative refractory period alone (typically less than ten milliseconds). The thresholds of excitatory neurons are almost 10 mV higher than those of inhibitory neurons (Fig 5A and 5E and S1A–S1C Fig). Next to the ISI, the threshold also depends on the history of the membrane potential (Fig 5C and 5F): we calculated the regression between the action potential threshold and the average membrane potential in different windows preceding the spike. There is a strong correlation between the threshold and the membrane potential immediately preceding the spike for both neuron types, which reduces gradually with time before the spike. However, for both neuron types, some relation between the membrane potential several tens of milliseconds before the spike and the threshold is still visible. The current clamp step protocol (S1 Fig) confirms the overall higher thresholds (S1A and S1B Fig) and strong spike-frequency adaptation (S1D Fig) for excitatory neurons. The threshold adaptation rate however, shows significant differences between fast spiking and regular spiking neurons at current injection intensities ranging from +240 to +320pA, while they do not show significant changes at lower or higher intensities, possibly due to low firing rates or reaching a steady state firing rate. (S1C Fig, S1 Table).

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Fig 5. Dynamic threshold.

A-C) Inhibitory neurons. D-F) Excitatory Neurons. A) Distribution of membrane potential threshold values (see Materials & methods) for each inter-spike interval (ISI); normalized per ISI. B) Average spike shape (shaded region denotes standard deviation). Vertical lines denote the windows in C. C) Heatmap and regression for the relation between the threshold and the average membrane potential in the given window. D-F) Same as in A-C, but for excitatory neurons. This is all in the Frozen Noise protocol, for threshold behaviour in the current-clamp step-and-hold protocol, see S1 Fig.

https://doi.org/10.1371/journal.pcbi.1012043.g005

So in conclusion, both inhibitory and excitatory neurons show a dynamic threshold behaviour, with inhibitory neurons having much lower thresholds, so they can fire at high rates, whereas the dynamic threshold of excitatory neurons promotes low-frequency firing and shows stronger adaptation.

Information transfer in neuron models with (sub)threshold adaptation.

In the previous section, we saw that both inhibitory and excitatory neurons show a dynamic threshold behaviour, suggesting that both cell types have in theory the adaptation mechanisms that can influence information transfer, as is also present in the Bayesian Neuron. In biophysical models, spike-frequency adaptation can be implemented in different ways [11]. Particularly, in the expIF model, it has been implemented as either a subthreshold process [22, 23] or as an adaptation of the spike threshold [24]. We research the effects of these two types of adaptation on the information transfer in the aforementioned mutual information protocol.

In Fig 6C, we first note that the ‘slow’ input to the excitatory neurons is apparently more difficult to transfer than the ‘fast’ one: the exact same expIF model transfers less of the ‘slow’ input information (red) than of the ‘fast’ one (blue). Next, in Fig 6D–6G, we show that adding threshold adaptation does not increase the amount of information that is transferred by the neuron. However, it does shift its working range towards higher values of the input amplitude I_scale, effectively increasing its working range. Contrasting, in Fig 6H–6K, we show that adding subthreshold adaptation does increase the maximum information transfer when it is properly tuned, i.e. when the time constant of adaptation fits the input properties. However, too slow adaptation suppresses the firing rate too much (Fig 6J and 6K), resulting in a reduction of information transfer.

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Fig 6. Effects of the dynamics of adaptation on information transfer.

A-C) No adaptation. D-G) Threshold adaptation. H-K) Subthreshold adaptation. L-N) Combined adaptation. Left column: ‘slow’ input (time constant hidden state τ_input = 250 ms). Middle column: ‘fast’ input (time constant hidden state τ_input = 50 ms). Right column: ‘slow’ and ‘fast’ input together. The time constant of the adaptation, τ_textrmadap, corresponds to τ_w for subthreshold adaptation or τ_θ for threshold adaptation (Eq (18)) A) Fraction of information (FI, black) and normalized firing rate r_n (pink) as a function of the input amplitude I_scale for the expIF model without adaptation. B) same as A but for the ‘fast’ input. C) Fraction of information as a function of the normalized firing rate for the ‘slow’ (red) and ‘fast’ (blue) input for the expIF model without adaptation. D) Fraction of information (colorbar) as a function of the input amplitude I_scale for the expIF model with threshold adaptation with different adaptation time constants τ_adap (vertical axis) receiving the ‘slow’ input. E) Same as D, but for the ‘fast’ input. F) Fraction of information as a function of the normalized firing rate for the ‘slow’ input or the expIF model with threshold adaptation with different adaptation time constants τ_adap (colours). G) Same as F, but for the ‘fast’ input. H-K) Same as D-G, but for the expIF model with subthreshold adaptation. L-N) Same as A-C, but for the model with both threshold (τ_adap = 1 ms) and subthreshold (τ_adap = 10 ms) adaptation.

https://doi.org/10.1371/journal.pcbi.1012043.g006

We ask whether the effects on information transfer are a result of a higher firing rate, or of a better detection. Therefore, we turn to the ROC curves discussed before. In Fig 7 we show that both forms of adaptation do not change the shape of the ROC curve. However, we do note that for the ‘slow’ input, the expIF neuron performs much worse than both the Bayesian neuron and the experimentally recorded neurons.

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Fig 7. Effects of the dynamics of adaptation on binary classification.

A) Receiver Operator Curve (ROC) (see also Fig 4) for the expIF neuron with threshold adaptation (colors denote time constant) receiving ‘slow’ input. Note that the adaptation does not change the shape of the ROC curve, and that the neuron performs much worse than the Bayesian neuron (pink). B) Same as A, but for subthreshold adaptation. C) Same as A, but for the neuron receiving ‘fast’ input and the response of the Bayesian neuron in turquoise. D) Same as C, but for the neuron with subthreshold adaptation.

https://doi.org/10.1371/journal.pcbi.1012043.g007

In conclusion, we see that subthreshold, but not threshold, adaptation can increase the maximum information transfer. Threshold adaptation, on the other hand, can increase the working range of the neuron. Moreover, an expIF neuron performs worse than both the Bayesian neuron and the experimentally recorded neurons. Since the Bayesian neuron differs from the expIF model in its IV curve, we next determine how information transfer is influenced by the shape of the IV curve.

The shape of the IV curve.

We assess the effects of changing the shape of the I-V curve (the right-hand side of the membrane voltage equation). The Bayesian neuron, tailor-made to transfer information efficiently for this type of input, has two features that distinguish it from a classical integrate-and-fire model: an adaptation mechanism, discussed in the previous paragraph, and a non-linear IV-curve, as can be seen in Fig 8A: the amplitude of the IV-curve increases exponentially when moving away from the steady-state value (dotted vertical line). We add such non-linearities in the expIF neuron in a biologically realistic way, to see how they would influence the classification (ROC curve) and the information transfer. Firstly we model the effects of the suppression of hyperpolarization (i.e. increasing slope of the IV curve when hyperpolarizing the cell) by adding an instantaneous ‘h-current’ to the expIF neuron (see Materials & methods), as shown in Fig 8B. Next, we model the effects of the suppression of depolarization (i.e. increasing slope of the IV curve when depolarizing the cell) by adding an instantaneous subthreshold potassium current, as shown in Fig 8C. Finally, we also change the overall slope, but not the shape of the IV curve, by changing the leak conductance of the neuron, as shown in Fig 8D. In Fig 8F and 8J, we show that adding the ‘h-current’ (with conductance g_h) does not change the shape of the ROC curve. However, its effect is similar to lowering the detection threshold (i.e. the values shift over the curve towards higher hit and false alarm fractions). On the contrary, the addition of the potassium current (with conductance g_K) does not change the shape of the ROC curve, but its effect is similar to an increase in the detection threshold (i.e. the values shift over the curve towards lower hit and false alarm fractions, Fig 8G and 8K). Changing the overall slope of the IV curve (i.e. the ‘leak conductance’ g_L) does change the shape of the ROC curve (Fig 8H and 8L): for the slow input current (τ_input = 250 ms) it needs to be tuned to a lower value (g_L ≈ 1 nS) than for the faster input current (τ_input = 50 ms) for optimal information transfer and classification.

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Fig 8. Effects of the IV-curve shape on binary classification.

A-D) IV-curves (i.e. right-hand side of the membrane voltage equation) for the Bayesian Neuron (A) and for the expIF neuron (without adaptation) with added ‘h-current’ (B), ‘subthreshold potassium current’ (C) and while varying the membrane conductance (D), colours denote conductances (see legends below). E-H) Receiver Operator Curve (ROC) (see also Fig 4) for the expIF neuron with different IV curve shapes (colors denote time constant) receiving ‘slow’ input. Note that only g_L changes the shape of the ROC curve. I-L) Same as E-H, but for the neuron receiving ‘fast’ input.

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The effects seen in the ROC curves are confirmed by the information transfer measurements: in Fig 9A, 9D, 9G and 9J we show that adding an ‘h-current’ can strongly increase the information transfer of the expIF neuron, by increasing its firing rate. Adding a subthreshold instantaneous potassium current shows the opposite effect: it decreases both firing rates and information transfer (Fig 9B, 9E, 9H and 9K). Finally, the slope of the IV curve needs to be matched to the input statistics: the slow input needs a flatter IV-curve (lower g_L) than the fast input for information transfer (Fig 9C, 9F, 9I and 9L).

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Fig 9. Effects of the IV-curve shape on information transfer.

A) Fraction of transferred information FI as a function of the input amplitude I_scale for the expIF model with added instantaneous ‘h-current’ with different values of conductance g_h (vertical axis) receiving the ‘slow’ input. B) Same as A but for the subthreshold instantaneous ‘potassium current’ (g_K). C) Same as A but for the leak conductance g_L. D-F) Fraction of information as a function of the normalized firing rate for the ‘slow’ input or the expIF model with different IV shapes (colours). G-L) Same as A-F but for the ‘fast’ input.

https://doi.org/10.1371/journal.pcbi.1012043.g009

In conclusion, we saw that the recorded excitatory neurons perform better for slow input than the expIF model with or without adaptation; in fact, these neurons perform similarly to the optimal simulated model (the Bayesian Neuron). Recorded inhibitory neurons perform close to optimal for fast input, a result well captured with an expIF model that includes an adaptation mechanism. Threshold adaptation increases the working range of the expIF model, but does not increase, or even slightly reduces, the amount of transferred information. Subthreshold adaptation, on the other hand, does not increase the working range but does increase the maximum transferred information if correctly tuned. Neither form of adaptation changes the shape of the ROC curve. The slope of the IV curve does play an important role in the information transfer and needs to be tuned to the statistics of the input. To check this conclusion, we will next assess this statement in our experimental recordings.

Back to the recordings: Dynamic IV curve unravels the relationship between membrane conductance and information transfer.

We assess the relation between the slope of the IV-curve and the information transfer, by determining the dynamic IV-curve [31] for each of our recordings (see Materials and methods). In Fig 10, we show the fraction of transferred information (FI) as a function of the membrane conductance g_m and membrane capacitance C_m (Fig 10A and reffigdynIVB) and as a function of the membrane time constant τ_m (Fig 10C and 10D). As in the expIF model simulations, we can conclude that the fraction of transferred information depends on the slope of the IV-curve: we see a clear inverse relation between membrane conductance and transferred information. However, the recorded neurons show quite a large variability of intrinsic properties, in particular the regular spiking excitatory neurons. To assess how this large heterogeneity of excitatory neurons influences their response properties, we calculate their spike-triggered averages.

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Fig 10. Effects of the dynamic IV-curve shape on information transfer of recorded neurons.

A) Fraction of transferred information FI as a function of the membrane conductance g_m and capacitance C_m for inhibitory neurons. B) Same as A), but for excitatory neurons. C) Fraction of transferred information FI as a function of the inverse of the membrane time constant τ_m for inhibitory neurons. D) Same as C), but for excitatory neurons.

https://doi.org/10.1371/journal.pcbi.1012043.g010

Back to the recordings: Response heterogeneity of the Spike-Triggered Average.

In Fig 11, we show the normalized spike-triggered averages (STAs) for spikes of inhibitory (A and E) and excitatory neurons (C). The filter was whitened and regularized (see Materials & methods). Note that the filters contain an acausal part, because of the autoroccelations in the input current: the spikes of the SPNN were convolved with an exponential kernel of 5 ms, and this is reflected in the STAs. Next, the projection values of spike-triggering and random currents were calculated (see Fig 11B for an example for 1 cell), and the distance between the means of the distributions for random and spike-triggering currents was calculated for each cell (Fig 11D). The average STAs for all inhibitory (Fig 11A, blue) and excitatory (Fig 11C, red) neurons were quite similar, but the traces for individual neurons (grey lines) were much more variable for excitatory neurons than inhibitory neurons. This indicates that the excitatory neurons have a higher variability in their feature selectivity of incoming current stimuli than inhibitory neurons, as was expected from the higher intrinsic variability discussed in the previous section. However, it is also possible that this is an effect of the lower number of spikes available for excitatory neurons. To control for this possibility, we calculated the STAs for spike trains of inhibitory neurons, where the number of spikes was reduced to match an 186 excitatory trial (Fig 11E, brown). For all three groups (inhibitory, excitatory, and inhibitory control spike trains) we calculated the inner product between all calculated STAs. Fig 11F shows the distributions of these inner products, and it is clear that both inhibitory full and control spike trains are much less variable (inner product closer to 1) than the excitatory spike trains (two-sample Kolmogorov-Smirnov test E-I p = 0, E-C p < 1e − 223, I-C p < 1e − 228). The distribution of all distances between the means is shown in Fig 11D. The distances between the distributions, measured in standard deviations of the prior (random triggered currents) distribution, are much higher for excitatory neurons than for inhibitory neurons, indicating that excitatory neurons are more selective (p-values two-sample t-test: E-I p < 1e − 28, E-C p < 1e − 24, I-C p = 0.14). In conclusion, excitatory cells fire less than inhibitory cells and are therefore more selective, but at the same time, there is more variability between excitatory neurons in what input features they respond to than between inhibitory cells.

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Fig 11. Linear filtering properties of recorded neurons.

A) Whitened and regularized (see Materials and methods) Spike-Triggered average (STA) for inhibitory neurons. The STAs for individual neurons are shown as thin grey lines, and the average over neurons is shown as a thick coloured line. B) Example of a prior (random triggered, black line) and posterior (spike-triggered, red line) distribution of stimulus projection values for a single inhibitory neuron. C) Same as A), but for excitatory neurons. D) Distribution of the differences between the means (see arrow in B) between the prior and posterior distribution over all neurons.-E) Same as A), but for the reduced (i.e. fewer spikes) spike trains of the inhibitory neurons. F) Distribution of the inner products between the STAs for the three groups (note that because the STAs are normalized by the L2-norm, the maximal value of the inner product is limited to 1). Data from 144 excitatory neurons (220 trials) and 72 inhibitory neurons (78 trials).

https://doi.org/10.1371/journal.pcbi.1012043.g011