Thalamocortical transformations of periodic stimuli: the effect of stimulus velocity and synaptic short-term depression in the vibrissa–barrel system

Abstract

Recent works on the response of barrel neurons to periodic deflections of the rat vibrissae have shown that the stimulus velocity is encoded in the corti cal spike rate (Pinto et al., Journal of Neurophysiology, 83(3), 1158–1166, 2000; Arabzadeh et al., Journal of Neuroscience, 23(27), 9146–9154, 2003). Other studies have reported that repetitive pulse stimulation produces band-pass filtering of the barrel response rate centered around 7–10 Hz (Garabedian et al., Journal of Neurophysiology, 90, 1379–1391, 2003) whereas sinusoidal stimulation gives an increasing rate up to 350 Hz (Arabzadeh et al., Journal of Neuroscience, 23(27), 9146–9154, 2003). To explore the mechanisms underlying these results we propose a simple computational model consisting in an ensemble of cells in the ventro-posterior medial thalamic nucleus (VPm) encoding the stimulus velocity in the temporal profile of their response, connected to a single barrel cell through synapses showing short-term depression. With sinusoidal stimulation, encoding the velocity in VPm facilitates the response as the stimulus frequency increases and it causes the velocity to be encoded in the cortical rate in the frequency range 20–100 Hz. Synaptic depression does not suppress the response with sinusoidal stimulation but it produces a band-pass behavior using repetitive pulses. We also found that the passive properties of the cell membrane eventually suppress the response to sinusoidal stimulation at high frequencies, something not observed experimentally. We argue that network effects not included here must be important in sustaining the response at those frequencies.

Appendices

Appendix 1

1.1 Values of the parameters

We take the synaptic parameters from in vitro and in vivo studies. In agreement with in vitro data obtained by Gil et al. (1999) we take as mean quantal EPSP size is J/C _m  ≃ 0.35 mV with a coefficient of variation Δ ≃ 0.25; mean number of release sites M = 7; release probability U = 0.8. In the absence of any spontaneous activity in the thalamus these values produce a mean EPSP amplitude < PSP > = M U J/C _m  = 1.96 mV. Experiments in anesthetized and sedated rats have recently reported smaller mean amplitudes which depend on the animal state: for anesthetized animals mean = 1.94 mV (median 1.3 mV) whereas for sedated animals the mean = 0.49 mV (median 0.24 mV; Bruno and Sakmann 2006). These variation was accompanied with a difference in the spontaneous thalamic rate (ν ₀ = 1.0 Hz for anesthetized and 5.4 Hz for sedated (Bruno and Sakmann 2006)) suggesting that TC synapses are continuously depressed in vivo (Castro-Alamancos 2002; Bruno and Sakmann 2006). This continuous depression is expected to be larger in awake animals were spontaneous thalamic firing is even higher (~10 Hz; Fanselow and Nicolelis 1999; Swadlow and Gusev 2001). Finally, a different study in anesthetized rats has shown that the depressed TC EPSP amplitude recovers to rest values exponentially with a time constant τ _v ~5 s (Chung et al. 2002). Had we used this value, which is almost two orders of magnitude larger than that measured in in vitro recordings of TC synapses in the visual system (Stratford et al. 1996), and spontaneous thalamic rates like those found in vivo (~5–10 Hz), we would have obtained an average TC EPSP lower than 0.05 mV. We therefore set τ _v  = 300 ms to reproduce average TC EPSP like those found in (Bruno and Sakmann 2006) when the spontaneous thalamic rate was 5 Hz.

We consider N = 85 thalamic neurons impinging onto the single target barrel cell based on an estimate of 200 cells per barreloid (Land et al. 1995; Varga et al. 2002) and a TC convergence ratio of 0.43 (Bruno and Sakmann 2006). Other parameters of the cortical cell model are: τ _m  = 1 − 10 ms, θ = 10–17 mV, H = 6–10 mV, τ _ref = 2 ms, C _m  = 100 pF and E _L  = 0. Background parameters: M _E  = 3, M _I  = 6, J _E /C _m  = 0.2 mV, J _I /C _m  = − 0.4 mV, U _E  = U _I  = 0.4, $\nu_E=5\;\textrm{ms}^{-1}$, $\nu_I=1\;\textrm{ms}^{-1}$. The excitatory background rate being five times larger than the inhibitory background rate, reflects the approximate ratio of one inhibitory cell every five excitatory cells found in the cortex.

Appendix 2

1.1 The temporal contrast

The temporal contrast is defined as (Pinto et al. 2000):

$$\textrm{Temporal Contrast} \!=\! \frac{40\% \textrm{of spikes per deflection}}{\textrm{time to produce 40\%}}$$

(14)

It measures in spiking rate units the mean firing rate of the early part of the response. Parameterizing the thalamic CPSTH with a Gamma function given by:

$$G(t) = \frac{C}{\Sigma} \, t \, e^{-t / \Sigma + 1}$$

(15)

the temporal contrast can be evaluated easily: The numerator equals 0.4 e C Σ, while the denominator is obtained by solving the equation:

$$\int_0^t G(z) {\rm d} z = 0.4 \, e \, C \, \Sigma$$

(16)

which performing the integral becomes

$$\frac{t}{\Sigma}+\ln(1-0.4) = \ln\left(\frac{t}{\Sigma}+1\right) \;\;,$$

(17)

which yields to t = 1.37 Σ, giving finally:

$$\textrm{Temporal Contrast} = \frac{0.4 \, e \, C \,\Sigma}{1.37\,\Sigma}\simeq 0.8\,C$$

(18)

that is, it is simply proportional to the Gamma amplitude. Now, modeling the temporal contrast dependence on the velocity obtained by Pinto et al. (2000) using this Gamma parameterization implies that as the stimulus velocity increases the VPm response has to vary (1) increasing its amplitude C and (2) decreasing Σ so that the product CΣ remains fixed. Doing so, the temporal contrast depends on the velocity while the spike count is independent of it.