1 Introduction

In spite of intensive studies of the anatomy and physiology of the cortex in recent decades, the question about how exactly sensory information is encoded in the laminar cortical architecture remains unanswered. Therefore, the purely computational approaches to the large-scale simulations of cortical structures have received much attention in the recent years due to the increasing availability of powerful parallel supercomputers (Hill and Tononi 2004; Traub et al. 2005; Markram 2006; Haeusler and Maass 2007; Grossberg and Versace 2008; Izhikevich and Edelman 2008; Rasch et al. 2011).

The fact that the cortex is organized into the six-layered structure raises the possibility that information could be processed differently in different cortical layers. In order to gain insight into the information-processing properties of laminar cortical microcircuits, we applied a recently developed information theory approach (Montemurro et al. 2007a, 2008; Kayser et al. 2009) to the analysis of cortical responses in a large-scale computational model of cat primary visual cortex (Basalyga and Wennekers 2009). In this approach, the information is defined as the Shannon mutual information about the input stimulus transmitted by the neuronal responses (Shannon 1948; Cover and Thomas 1991). This allows the quantification of the information in a very general and model-independent way, without ad hoc assumptions about precisely which stimulus features (orientation, direction, etc.) drive the neuronal response.

The traditional hypothesis regarding neural coding states that the main carrier of information is the time dependent firing rate (Adrian 1928; Shadlen and Newsome 1998). More recently, however, different alternatives in which the timing of spikes contributed relevant information to the neural code, have been found in a number of neural systems (Bialek et al. 1991; Salinas and Sejnowski 2001; Tiesinga et al. 2008). While for some of these systems the extra information gain was achieved when measuring spike timing with respect to an external clock, cells in the hippocampus, visual and auditory cortices have to encode significant amounts of information in the timing of spikes relative to a measure of an ongoing population activity (O’Keefe and Recce 1993; Montemurro et al. 2008; Kayser et al. 2009). In particular, in the case of visual and auditory cortices it was shown that when spikes were tagged, or labelled, with the current angular phase of the Local Field Potentials (LFP), there was substantially more information about an external stimulus compared with that conveyed by the firing rate alone. Moreover, the analysis of the information encoded about natural sounds in the auditory cortex of alert animals indicated that information was preferentially carried by a nested code, which considers both precise spike patterns and their relative timing with respect to the LFP phase. This code was not only highly informative, but also highly robust when the stimulus was corrupted by sensory noise (Kayser et al. 2009).

Unfortunately, the laminar microcircuit mechanisms responsible for generating and transferring such information remain unknown. This is due to lack of experimental data on the laminar-specific cortical responses to rich natural stimuli. While the information carried by LFP and current source densities has recently been addressed at the specific laminar level (Szymanski et al. 2011), there are no studies yet on the computational role of spikes at specific layers, or more complex codes involving the phase of the LFP and spikes from local populations. Therefore, we developed a computational model of the laminar thalamo-cortical system (Basalyga and Wennekers 2009) which represents a simplified version of the X visual pathway for one eye to the primary visual area of the cat cortex. All parameters in the model were constructed according to recent anatomical and biophysical data (Gilbert 1977; Thomson and Lamy 2007). When physiological data were unavailable, cell and synapse parameters were chosen in order to obtain the desired functional properties such as orientation preference in response to full-field drifting gratings. As a rough approximation of a rich natural image input stimulus, we used a stochastic moving grating—a full-field drifting grating that changes the orientation, direction, temporal and spatial frequencies every 10 to 40 ms during 10 s of stimulation. The neural responses to a 100 presentations of this input stimulus were recorded and then analyzed using information theory methods.

The paper is organized as follows. A brief description of the model and short introduction to the information theory methods are given in Section 2. Section 3 contains the results of our information theory analysis of neural responses in different layers of the model. A general discussion is given in Section 4.

2 Methods

2.1 Model

The model consists of three connected subsystems: Retina, Thalamus and V1 model (see Fig. 1(a)). The model details are provided in Table 1, following the model description standards suggested by Nordlie et al. (2009).

Fig. 1
figure 1

(a) Model Schematic. The model consists of the three major subsystems: retina, thalamus and V1 cortical model. Retina is represented via two layers (ON and OFF) retinal ganglion X-cells. Thalamus model consists of two layers (ON and OFF) of thalamic relay cells, two layers of thalamic interneurons and one layer of thalamic reticular nucleus (RTN) neurons. The V1 module contains four layers of primary visual cortex (layers 4, 2/3, 5 and 6) which is modeled after a restricted portion of cat striate cortex (area 17). Arrows denote the major excitation flow across the model. (b) Thalamocortical connections are set to produce the realistic orientation preference map in layer 4 via a two-dimensional Gabor connectivity kernel given by Eq. (1). (c) Histogram of relative modulation F1/F0 across the entire population of excitatory cells in the model. Cells with F1/F0 > 0.5 are considered to be simple cells. Cells with F1/F0 < 0.5 are classified as complex cells. (d) Laminar distribution of relative modulation in the model compared to the experimental values estimated from Gilbert (1977)

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Table 1 Model summary
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The retina model is taken identically from Wohrer and Kornprobst (2009). All parameters are the same as in that work. The model reflects the layered structure of the retina and implements some contrast adaptation mechanisms. Output is provided by two layers of ON and OFF ganglion cells. Spikes are generated from the graded outputs of ganglion cells in the original model using rate-modulated Poisson processes. The retina model represents a 3° ×3° monocular patch of in the central (parafoveal) visual field.

The thalamic system consists of two layers (ON and OFF) of lateral geniculate nucleus (LGN) neurons and two layers of corresponding local inhibitory interneurons (Sillito and Jones 2002). We assume a one-to-one correspondence between retinal ganglion cells and LGN cells, so that the LGN cells can be described as thalamic relay cells (Destexhe et al. 1998). Additional inhibition to LGN is provided by a layer of thalamic reticular nucleus (RTN) neurons (Destexhe et al. 1996).

The simulated cortex is divided into four layers: granular layer 4, supragranular layer 2/3 and two infragranular layers 5 and 6. The V1 model is scaled to span approximately 1.3 ×1.3 mm2 of striate cortical surface. Each cortical layer is represented by a two-dimensional 20 by 20 grid of excitatory pyramidal cells. Inhibitory cortical cells are organized in 10 by 10 grid. All cells here are modeled according to a conductance-based single-compartment Hodgkin-Huxley neuron model (Hodgkin and Huxley 1952; Traub and Miles 1991) with a minimal set of channels (Pospischil et al. 2008). All thalamic and thalamo-cortical synapses are modeled as fixed conductance-based synapses (Brette et al. 2007). Cortical synapses are chosen to have a short-term plasticity which is a mixture of depression and facilitation. We modeled the short-term synaptic dynamics according to the model proposed in (Tsodyks et al. 1998, 2000). See Table 1 for the set of typical neuron/synapse model parameters.

Local cortical connections are considered to be isotropic and non-specific (Hellwig 2000; Holmgren et al. 2003). The connection weights are modeled by a Gaussian function, \( g (x, \sigma, a_0 ) = a_0 \exp(-x^2/2 \sigma^2)\), with a peak of a 0 and a width of σ. Here x is intercellular distance in the model. A single pyramidal neuron usually receives connections from a patch with a typical radius of 500 \(\upmu\)m. For local (intralaminar) excitatory connections, we set a 0 = 1 and σ = 250 \(\upmu\)m. For vertical (extralaminar) excitatory connections between layers, we set a 0 = 1 and σ = 125 \(\upmu\)m. For local inhibitory connections, we used = a 0 = 0.6 and σ = 150 \(\upmu\)m. The connections weights are chosen to support the propagation of the excitation across the layers. The model is also set up so that all layers have roughly the same mean firing rates in response to the input stimulus.

The connectivity pattern from a patch in the LGN layer to a cortical cell in layer 4 is modeled by a two-dimensional Gabor function (see Fig. 1(b)),

$$ G (x, y, \theta) = e^{-\frac{x_1^2}{2 \sigma_x^2}- \frac{y_1^2}{2\sigma_y^2}} \cos(k x_1 - \phi), \label{gaborf} $$
(1)

with clockwise rotation,

$$ x_1 (x, y, \theta) = x \cos(\theta) - y \sin(\theta) , $$
(2)
$$ y_1 (x, y, \theta) = x \sin(\theta) + y \cos(\theta) . $$
(3)

Here, θ is the preferred orientation of a cortical cell, k/(2 π) is the preferred spatial frequency and φ is the preferred spatial phase. Coordinates (x, y) define the position inside the patch in the LGN layer. The size of the LGN patch is proportional to the size of the cortical receptive field (1.7° of visual field of a cat). Parameters of the Gabor function are chosen so that ON and OFF subregions are elongated in the preferred orientation of the cell under consideration. The preferred orientation of each cell in layer 4 is chosen according to the 1.3 ×1.3 mm2 realistic orientation map of an adult macaque monkey (adopted from Miikkulainen et al. 2005, Fig 2.4), measured by optical imaging techniques. The obtained orientation map is further used to infer the lateral connectivity inside layer 2/3 in accordance with known principles governing horizontal local and long-range connections in V1 (Hellwig 2000; Holmgren et al. 2003; Buzas et al. 2006). The spatial phase preference of the cells is considered to be uniformly distributed in the range from 0 to 180 degrees (DeAngelis et al. 1999).

It is known that the majority of cortical layers of cat primary visual cortex are dominated by complex cells with complex nonlinear response properties (Gilbert 1977). Only layer 4 is populated by simple cells with simple linear responses. In our model, the complex receptive fields in layer 2/3 are achieved by convergence of many simple cells with different preferred phases from layer 4. We use a wide Gaussian profile with a 0 = 1 and σ = 500 \(\upmu\)m for setting connection weights from layer 4–2/3. In similar fashion, complex cells in layer 5 and 6 are achieved by convergence of simple cells from layer 6, which also receives the thalamic input via the Gabor connectively filter defined in Eq. (1). Linearity of cell responses is measured by the modulation ratio F1/F0, where F0 is the mean firing rate of the response and F1 is the magnitude of the fundamental (first) harmonic of the response corresponding to the temporal frequency of the input grating (Skottun et al. 1991). We collected the spike activity of excitatory cells in our model in response to the one second presentation of full-field sinusoidal drifting gratings and we binned the responses into a spike histogram at 10 ms intervals. Then we applied the discrete Fourier transform and computed the ratio F1/F0. Cells with F1/F0 > 0.5 are considered to be simple cells. Cells with F1/F0 < 0.5 are classified as complex cells. A histogram representing relative modulation F1/F0 across the entire population of excitatory cells in the model is shown in Fig. 1(c). Laminar distribution of complex and simple cells in the model is illustrated in Fig. 1(d). One can see that the model values are in good agreement with the experimental values (estimated from Gilbert 1977, Fig. 7).

In the simple case of single-compartment neurons, one can consider the average membrane potentials of neurons in the network as an approximate estimation of the Local Field Potentials (LFP) (Ursino and Cara 2006; Mazzoni et al. 2008). As it was demonstrated in Mazzoni et al. (2008), Figure S4, this simplified approach fails to reproduce the spectrum of the measured LFP, but it succeeds to capture the information content of the recorded LFP.

We assume that the extracellular medium is ohmic in nature and it has a isotropic conductivity. This view is supported by experimental measurements of cortical impedance spectrum in monkeys (Logothetis et al. 2007). In our simplified two-dimensional model layout, we decided to neglect the inter-laminar influence on the LFP. Proper account of inter-layer distance requires building a three dimensional model of cortical layers which is the subject of future modeling.

We calculated LFP at some point (x 0,y 0) inside a two-dimensional layer in our model by averaging the membrane potentials V m (x i ,y i ) of cells in the local patch of radius 600 \(\upmu\)m, weighted with distance to that point:

$$ LFP(x_0,y_0) \sim \sum\limits_i g (x_0 - x_i, y_0 - y_i, \sigma, a_0 ) V_m(x_i,y_i) ,\nonumber\\ $$
(4)

where \( g (x, y, \sigma, a_0 ) = a_0 \exp((-x^2-y^2)/2 \sigma^2)\) is a Gaussian function with a peak of a 0 = 1 and a width of σ = 200 \(\upmu\)m. A number of studies had reported the spatial spread of LFP signals to range from about 400 \(\upmu\)m to 600 \(\upmu\)m (Engel et al. 1990; Kruse and Eckhorn 1996; Berens et al. 2008). More recent studies (Katzner et al. 2009; Lindén et al. 2011) report that the average LFP spread is even more local, about 200 \(\upmu\)m, and its laminar variation lies in the range from 120–250 \(\upmu\)m for monkey V1 (Xing et al. 2009). Therefore, we have chosen sigma of 200 \(\upmu\)m everywhere in this paper.

Another common method of calculating the LFPs is the spacial summation of synaptic currents to a single neuron (Protopapas et al. 1999; Holt and Koch 1999; Pettersen and Einevoll 2008). We do not model here the three dimensional organization of cortical neurons and, therefore, one can simply estimate LFPs as the sum of the absolute values of excitatory and inhibitory currents to a pyramidal cell, following Mazzoni et al. (2008), who has demonstrated that this approach was able to reproduce correctly both the power spectrum of recorded LFPs and its information content. To test the validity of our approach, we also computed the LFP from the currents and found qualitatively similar results regarding the laminar information analysis (see Fig. 5 in Section 3). Therefore, we will use averaging membrane potentials as primary method for estimation of LFPs in this paper.

The main type of input stimulus is a full-field sinusoidal drifting grating. The statistical structure of natural scenes is obviously different from this simple artificial stimulus. See report by (Onat et al. 2011) where cortical responses to moving gratings are compared to responses to natural stimuli. In order to make our stimulus closer to a natural image, we decided to change randomly the orientation, direction, temporal and spatial frequencies of the sinusoidal drifting grating every 10–40 ms during 10 s of simulation. The direction of motion of each drifting grating was always orthogonal to its orientation (we have 24 orientations with a step of 15°).

Simulations of the model were performed using the parallel kernel of the NEURON v6.0 simulation software (Carnevale and Hines 2006; Migliore et al. 2006; Hines and Carnevale 2008) on a Beowulf Linux computer cluster. Information theory analysis was performed using custom Matlab software.

2.2 Information theory analysis

The information theoretic methods follow closely those used in Kayser et al. (2009). We assessed the performance of each candidate code by means of Shannon mutual information (Shannon 1948). In general, the responses r to different stimuli s from a stimulus set S, can be characterized by the conditional probability P(r|s). Then, Shannon mutual information is defined as

$$\label{info2} I (R; S) = \sum\limits_{s \in S} P(s) \sum\limits_{r \in R} P(r|s) \log_2 \frac{P(r|s)}{P(r)} \, , $$
(5)

where P(s) is the probability of stimulus presentation and P(r) is the average of the conditional probability P(r|s) taken over the whole stimulus set. The mutual information is a model-independent quantification of the reduction in uncertainty about which stimulus was presented, obtained from the observation of the neural response. When the base of the logarithm is 2, then the information is expressed in units of bits. The 10 s stimulus presentation was divided into non-overlapping windows of length T, and each individual window was considered as a different stimulus s (Belitski et al. 2008; de Ruyter van Steveninck et al. 1997; Montemurro et al. 2008; Strong et al. 1998). We used values of T between 10 and 50 ms.

While the stimuli are completely specified throughout the experiment, the response R is a particular representation of the neural output. In this way, by computing the information in different choices of the neural response representation, it is possible to compare quantitatively the performance of different candidate neural codes. The specific choices of the neural representation depend on the individual hypotheses about the nature of the neural codes that are going to be studied. More specifically, we compared the information carried by the following representation of the neural response: (1) the firing rate of single neurons, I_rate; (2) the spike patterns within a time window of duration T, I_pattern; (3) the firing rate of single neurons labelled by the angular phase of the LFP, I_rate & phase; (4) the spike patterns within a time window T labelled with the angular phase of the LFP, I_pattern & phase.

For the code that involved spike patterns, the window T was divided into L bins of duration ∆ t each and L varied between 1 and 5. The bias in the information quantities was corrected using tested methods (Montemurro et al. 2007a, b; Panzeri et al. 2007; Montemurro et al. 2008; Kayser et al. 2009).

In the case of phase coding, the angular phase of the LFP was obtained by means of the Hilbert transform (Montemurro et al. 2008). The resulting continuous phase signal was then discretised by subdividing the range [ − π, π) into four discrete bins of size π/2. The choice of four levels for the discretisation of the phase proved optimal in the previous analyses (Montemurro et al. 2008; Kayser et al. 2009): it was sufficient to capture the information related to phase fluctuations and, at the same time, allowed a tight control of the bias in the numerical estimation.

3 Results

We recorded the spike activity and membrane potentials of all neurons in four layers of the model in response to 100 repeated presentations of the stochastically changing drifting grating. We selected in each cortical layer a population of 156 local neurons for our analysis. These neurons represent a local patch with the radius of 500 \(\upmu\)m near cell with index 288 in the middle of the layer. We calculated LFPs for each selected cell by averaging the membrane potentials of cells in the local patch, weighted with distance according to Eq. (4). The obtained spikes and LFP data for each selected cell were binned into 10 ms bins and four types of information were computed: the firing rate information I_rate, the spike pattern information I_pattern, the rate-and-phase information I_rate & phase and the pattern-and-phase information I_pattern & phase.

The results are shown in Fig. 2, where the information from different coding strategies is demonstrated as a function of stimulus time window T (number of bins L times bin size ∆ t). Information in the different codes for a single cell with index 288 in layer 4 is shown in Fig. 2(a). Figure 2(b) illustrates information values for individual cell 288 in layer 2/3. Averaging over 156 neurons around cell 288 leads to the results presented in Fig. 2(c) for layer 4 and in Fig. 2(d) for layer 2/3. Consistent with previous reports from other modalities (Kayser et al. 2009), the rate information I_rate and the pattern information I_pattern increase steadily with the size of the observation window T. However, I_pattern grows faster than I_rate. This demonstrates that a temporal spike pattern code is a more informative code than a firing rate code for time windows longer then 30 ms. The rate-and-phase information I_rate & phase also increases with stimulus window size but more slowly than I_pattern & phase. In spite of the fact that I_pattern increases faster than I_rate & phase with increasing window length, for windows shorter than 30 ms, I_pattern provided less information than I_rate & phase and I_pattern & phase, suggesting that, at the biologically relevant timescales of membrane time constants, phase coding may be more informative than the temporal code. Moreover, for all considered lengths T of stimulus time windows, the pattern-and-phase information I_pattern&phase shows superior performance compared to the other codes.

Fig. 2
figure 2

Information in different codes as a function of time window length T for layers 4 and 2/3. Here, ∆ t = 10 ms, and the phase information is calculated in the 4–16 Hz frequency band

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The information as a function of the considered LFP frequency in response to the stochastically changing drifting grating stimulus is shown in Fig. 3 for the case with bin size ∆ t = 10 ms and time window T = 40 ms. All data points are averaged over a patch of 156 neurons in the middle of layer 4 (figures on the left) and layer 2/3 (figures on the right). Information gain by the phase-of-firing codes versus the rate and pattern codes is shown in Fig. 5(c) for layer 4 and in Fig. 5(d) for layer 2/3. Information gain (in percent) of the rate-and-phase code relative to the rate code is calculated using the formula (I_rate & phase-I_rate)*100 / I_rate for each data point. As can be seen for both layers, for high LFP frequencies (> 80 Hz), the rate-and-phase information asymptotically converges to the rate information. However, for low LFP frequencies (< 30 Hz), there is substantially more information in the rate-and-phase code compared with the rate alone. Calculations for different time windows indicate that the maximum of information gain for phase codes always happened at the 4–16 Hz frequency range. Similar results have been reported by (Mazzoni et al. 2011) for a non-laminar model of macaque V1. In the case of the pattern-and-phase information compared to the spike pattern information, the information gain, which is given by (I_pattern & phase-I_pattern)*100 / I_pattern, is also high for low LFP frequencies. However, it is less significant compared to the information gain by the rate-and-phase code.

Fig. 3
figure 3

Information as function of the considered LFP frequency for layers 4 and 2/3. Here, bin size ∆ t = 10 ms and time window T = 40 ms. Data points are averaged over a patch of 156 neurons in layer 4 (a) and in Layer 2/3 (b) (mean ± standard error). The rate information is denoted by black line. The blue line denotes the pattern information or spike timing information. The green circles denote the rate-and-phase information. The red triangles denote the pattern-and-phase information. Information gain by the phase-of-firing codes in layer 4 (c) and in layer 2/3 (d). The green circles denote the information gain by the rate-and-phase code compared to the rate code alone. The red triangles denote the information gain by the pattern-and-phase code versus the spike pattern code

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We also have a similar situation with the rest of the cortical layers. Figure 4 shows the information analysis for layers 5 and 6. Note that the information gain for the rate-and-phase code in Layer 4 may reach 90 % (see Fig. 5(c)), while in other layers it reaches only 60 %, compared to the rate information. An even stronger information gain by phase coding (up to 100 %) can be found when considering responses of individual cells in layer 4.

Fig. 4
figure 4

Information in different codes for layers 5 and 6. Here, ∆ t = 10 ms, and the phase information is calculated in the 4–16 Hz frequency band. Data points are averaged over a patch of 156 neurons around cell 288

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Fig. 5
figure 5

Information analysis for a single cell with index 288 in layer 4 and 2/3 for the case when LFPs were defined as a sum of synaptic currents. Here, ∆ t = 10 ms, and the phase information is calculated in the 4–16 Hz frequency band

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Qualitatively similar results regarding the laminar differences in the information gain were found for the case when LFPs were defined as a sum of synaptic currents. Figure 5 shows the information analysis for cell with index 288 in layer 4 and 2/3 for the case where LFPs were calculated as the sum of the absolute values of excitatory and inhibitory currents to a single cell, following Mazzoni et al. (2008).

4 Discussion

In this article, we studied the laminar distribution of information in a large-scale computational model of cat primary visual cortex. We computed and compared the four types of information about a stimulus carried by the different representations of the neural response: (1) the rate information carried by the firing rate of single neurons; (2) the spike pattern information carried by spike patterns within a particular time window; (3) the rate-and-phase information carried by the firing rate of individual neurons labelled by the phase of the LFP; (4) the pattern-and-phase information carried by the spike patterns labelled with the LFP phase.

We found that for longer stimulus time window durations (T > 40 ms), temporal spike patterns typically convey several times more information than firing rates alone (see Fig. 2). The pattern-and-phase coding or so called “nested” code, which combines the spiking activity with the phase of slow LFP oscillations, was found to be the most informative coding strategy in the considered time windows. Also, there is substantially more information in the phase code compared with the rate and pattern codes for low LFP frequencies (see Fig. 3). These findings are consistent with previous information theory analyses of experimental data of the neural responses in visual and other modalities (Montemurro et al. 2007a, 2008; Kayser et al. 2009).

A novel finding in our model is the possibility of a nonuniform distribution of information processing across cortical layers in the cat primary visual cortex. The averaged information gain for the rate-and-phase code in layer 4 may reach up to 90 % (see Fig. 5(c)), while in other layers it reaches only 50–60 %, compared to the rate information alone. This can be explained by the fact that layer 4 is a thalamo-cortical layer populated by simple cells with simple linear responses. Its activity is overwritten by direct sensory input from thalamus. Other layers in cat visual cortex are populated by complex cells with nonlinear response properties. Layer 2/3, for example, not only has stronger recurrent connectivity but also specific long-range connectivity compared to layer 4. All these properties contribute to the reduction of information gain about the input stimulus in the phase-of-firing codes.

Based on these findings, we put forward the following hypothesis about the laminar specificity of the information coding properties of cat primary visual cortex: the thalamo-cortical layers populated by simple cells should convey more information about the input stimulus than cortico-cortical layers or layers populated by cells with nonlinear response properties. This hypothesis should receive further studies in experimental settings.