Thalamic neuron models encode stimulus information by burst-size modulation

Abstract

Thalamic neurons have been long assumed to fire in tonic mode during perceptive states, and in burst mode during sleep and unconsciousness. However, recent evidence suggests that bursts may also be relevant in the encoding of sensory information. Here, we explore the neural code of such thalamic bursts. In order to assess whether the burst code is generic or whether it depends on the detailed properties of each bursting neuron, we analyzed two neuron models incorporating different levels of biological detail. One of the models contained no information of the biophysical processes entailed in spike generation, and described neuron activity at a phenomenological level. The second model represented the evolution of the individual ionic conductances involved in spiking and bursting, and required a large number of parameters. We analyzed the models' input selectivity using reverse correlation methods and information theory. We found that n-spike bursts from both models transmit information by modulating their spike count in response to changes to instantaneous input features, such as slope, phase, amplitude, etc. The stimulus feature that is most efficiently encoded by bursts, however, need not coincide with one of such classical features. We therefore searched for the optimal feature among all those that could be expressed as a linear transformation of the time-dependent input current. We found that bursting neurons transmitted 6 times more information about such more general features. The relevant events in the stimulus were located in a time window spanning ~100 ms before and ~20 ms after burst onset. Most importantly, the neural code employed by the simple and the biologically realistic models was largely the same, implying that the simple thalamic neuron model contains the essential ingredients that account for the computational properties of the thalamic burst code. Thus, our results suggest the n-spike burst code is a general property of thalamic neurons.

Keywords: burst; information theory; multivariate analysis; neural code; reverse correlation; single neuron model; spike-triggered average; thalamus.

Figure 1

Diagrams of the MC (A) and IFB (B) thalamic models. The net synaptic input is represented by an Ornstein-Uhlenbeck (OU) process (bottom), here termed the stimulus. The models have no spatial structure. The conductances governing the evolution of the membrane potential (top traces) are marked.

Figure 2

Analysis of spike-train correlations. Mean and variance of the spike count in a 20 ms window from 100 trials, for the full responses (A1, B1), tonic model responses (A2, B2), and full responses with bursts removed (A3, B3). The fraction of information contained in stimulus-modulated correlations (ΔI∕I) is shown for MC (A4) and IFB (B4) models, for the full response (F), tonic response (T), and the full response with bursts removed (BR). Response window size L = 40 ms.

Figure 3

Stimulus features associated with bursts containing n spikes. Event-triggered averages for the MC (A1) and IFB (B1) models, for different n-values (see color key at top center). Time = 0 ms marks the first spike in the burst. The values of several stimulus features are averaged and plotted as a function of n (A2–A7, B2–B7), including pre-onset hyperpolarizing stimulus charge (N.int) (2), post-onset depolarizing stimulus charge (P.int) (3), stimulus minimum prior to onset (4), stimulus amplitude (5), slope (6), and stimulus phase (7). Amplitude, slope and phase are all calculated at burst onset. Error bars represent ±1SE of the mean. Mean phase and the corresponding error bars are calculated with circular statistics.

Figure 4

Most relevant vectors obtained by covariance analysis, for the MC (A) and the IFB (B) models and different n-values (see color code in Figure 3). Vectors with smallest variance [V₄₈₀ for the MC (A1) and V₃₈₀ for the IFB (B1)] and second smallest variance [V₄₇₉ for the MC (A2) and V₃₇₉ for the IFB model (B2)].

Figure 5

Probability density functions of stimulus features triggering bursts of n spikes and associated information, for MC (A) and IFB (B) models. Instantaneous stimulus features (A1–A6, B1–B6), with the same color code as in Figure 3 (see key). For better visualization, distributions are plotted with a resolution of M = 256 bins. Information values (displayed in A7, B7) were calculated with a coarser binning M = 32 to reduce estimation bias.

Figure 6

Information encoded by several instantaneous stimulus features, registered at varying time with respect to burst onset, for the MC (A) and IFB (B) models. Information transmitted by the discrimination of stimulus amplitude (blue), phase (red) and slope (green) at varying times, for different n-values. Digitization M = 32, information estimates are shuffle-corrected (see Section Materials and Methods).

Figure 7

Optimal stimulus dimensions obtained with multi-discriminant analysis in MC (A) and IFB (B) models. (A1,B1) Optimal discriminant vector V₁ (A1,B1) for each model. (A2,B2) Distribution of projections of the stimuli triggering n-spike bursts onto V₁. Inset: Mutual information between n and projected stimuli. Information was estimated with distributions discretized into M = 32 equally populated bins. (A3,B3,A4,B4) Same as A1,B1,A2,B2 but for the second discriminant vector V₂.

Figure 8

Dependence of the encoded information on the location of the window used to define the stimulus. (A) Explanatory diagrams illustrating the definition of the windows (A1), and the subdivision of maps (A2) into regions: Stimuli may be taken entirely before (A2 a), after (A2 b), or astride (A2 c) burst onset (T = 0). Vertical dashed black lines mark T_start = 0 ms and horizontal lines represent T_end = 0 ms. (B, C) Information between n and V₁-projected stimuli is color-plotted as a function of the location of the times T_start and T_end of the window, for the MC (B) and the IFB models (C). Models were driven with stimuli with σ_OU = 1μA, τ_OU = 5 ms, μ_OU = 0μA. Information is calculated with digitization of M = 32 bins and shuffle-corrected to account for bias.