Transition between Functional Regimes in an Integrate-And-Fire Network Model of the Thalamus

Abstract

The thalamus is a key brain element in the processing of sensory information. During the sleep and awake states, this brain area is characterized by the presence of two distinct dynamical regimes: in the sleep state activity is dominated by spindle oscillations (7 - 15 Hz) weakly affected by external stimuli, while in the awake state the activity is primarily driven by external stimuli. Here we develop a simple and computationally efficient model of the thalamus that exhibits two dynamical regimes with different information-processing capabilities, and study the transition between them. The network model includes glutamatergic thalamocortical (TC) relay neurons and GABAergic reticular (RE) neurons described by adaptive integrate-and-fire models in which spikes are induced by either depolarization or hyperpolarization rebound. We found a range of connectivity conditions under which the thalamic network composed by these neurons displays the two aforementioned dynamical regimes. Our results show that TC-RE loops generate spindle-like oscillations and that a minimum level of clustering (i.e. local connectivity density) in the RE-RE connections is necessary for the coexistence of the two regimes. We also observe that the transition between the two regimes occurs when the external excitatory input on TC neurons (mimicking sensory stimulation) is large enough to cause a significant fraction of them to switch from hyperpolarization-rebound-driven firing to depolarization-driven firing. Overall, our model gives a novel and clear description of the role that the two types of neurons and their connectivity play in the dynamical regimes observed in the thalamus, and in the transition between them. These results pave the way for the development of efficient models of the transmission of sensory information from periphery to cortex.

Fig 1. Dynamical properties of single RE and TC neurons as a function of input current.

(A) Depolarization induced activity of a RE neuron. Membrane voltage (top) and adaptation variable (middle) of a RE neuron in response to a depolarizing current (bottom). (B) Corresponding post-stimulus time histograms for increasing depolarizing currents. (C) Hyperpolarization-rebound activity of a RE neuron and (D) corresponding post-stimulus time histograms for increasing hyperpolarizing currents. Parameters a and b, representing respectively the dynamics and the strength of adaptation (see Eq (2)) of RE neurons are defined in this way: a = 0.4 μS and b = 0.02 nA. (E) Depolarization induced activity of a TC neuron and (F) corresponding post-stimulus time histograms for increasing depolarizing currents. (G) Hyperpolarization-rebound activity of a TC neuron and (H) corresponding post-stimulus time histograms for increasing hyperpolarizing currents. The values a and b are 0.2 μS and 0 nA. The current intensity in (A,C,E,G) is 1000 nA, while it varies between 1000 nA and 5000 nA in panels (B,D,F,H). V_T = −50 mV is the threshold potential for both types of neurons. Other parameters are defined in the Materials and Methods section.

Fig 2. Dynamical properties of two-neuron loops.

(A) Scheme of a two-neuron TC-RE loop. (B) Membrane voltage traces of the TC and RE neurons generated by this minimal TC-RE loop. (C) Interspike interval (ISI) distribution of the TC-RE loop as a function of the synaptic strength g_{TC → RE}. The value of g_{RE → TC} is appropriately set to 550 μS in order to support self-sustained activity, while g_{TC → RE} varies between 10 μS and 60 μS. RE and TC ISI distributions are shown in the top and bottom plots, respectively. (D) ISI distribution of a TC-RE loop as a function of the synaptic strength g_{RE → TC}. The value of g_{TC → RE} is chosen equal to 32 μS to reproduce the two-spike bursting dynamical regime of panel B while g_{RE → TC} varies between 200 μS and 800 μS. RE and TC ISI distributions are shown in the top and bottom plots, respectively. (E) Scheme of a minimal purely reticular RE-RE loop. (F) ISI distribution of this loop as a function of the synaptic strength g_{RE → RE}. g_{RE → RE} varies between 200 μS and 800 μS. (G) Scheme of an input-driven two-neuron TC-RE loop. (H) ISI distribution of this loop as a function of external sensory input strength. RE and TC ISI distributions are shown in the top and bottom plots, respectively. The synaptic strengths are respectively: g_{RE → TC} = 550 μS, g_{TC → RE} = 32 μS and g_{EXT → TC} = 1 μS.

Fig 3. Four-neuron motifs in the form of coupled pairs of TC-RE loops.

The two TC-RE oscillators are bidirectionally coupled through (A) TC-RE connections, (B) RE-TC connections, (C) RE-RE connections, and (D) all three connections. (E) Frequency of the power spectral peak and (F) phase coherence at that frequency for the four different motifs. The power spectral density and phase coherence during self-sustained activity were averaged across 50 trials for random values of the GABA decay time (see text). GABA rise time and AMPA rise and decay times are set constant (see Materials and Methods section). When the corresponding connections exist in the motifs, the synaptic strengths are respectively: g_{RE → TC} = 550 μS, g_{TC → RE} = 32 μS, and g_{RE → RE} = 20 μS.

Fig 4. Spindle self-sustained activity generated by a full network of TC-RE neurons depending on RE-RE clustering.

(A) Connectivity matrix of a random TC-RE network. The presynaptic neurons are represented in the x axis and the postsynaptic neurons in the y axis. The network is made of 500 neurons, of which the first 250 are RE neurons and the remaining ones are TC neurons. (B) Connectivity matrix in the presence of RE-RE clustering (rewiring probability RP = 0.25) (C) Membrane voltage dynamics of a couple of arbitrarily chosen TC and RE neurons in the case of random network. (D) Membrane voltage dynamics of a couple of arbitrarily chosen TC and RE neurons in the presence of clustering: evidence of typical spindle oscillations. (E,F) Distribution of inter-spike intervals (along the horizontal axis, color-coded and normalized to unit area) as a function of the rewiring probability (along the vertical axis) for RE (panel E) and TC (panel F) neurons. The synaptic strengths are respectively: g_{RE → TC} = 300 μS, g_{TC → RE} = 200 μS and g_{RE → RE} = 300 μS.

Fig 5. Bursting and tonic modes displayed by a TC-RE network with RE-RE clustering as a function of external input on TC neurons.

(A) Firing rate of TC (red) and RE (blue) neurons as a function of external driving input impinging on TC neurons. (B,C) ISI distribution as a function of external driving input on TC neurons of RE (B) and TC (C) neurons. (D) Mutual information between the set of increasing external stimulus (0-150 spikes/s) and the neural response given by the firing rate of TC and RE neurons. Different external sensory inputs are considered for the two regimes, following panel A: 0-50 spikes/s for the bursting mode and 60-150 spikes/s for the tonic mode. The white dashed line in the bar plots refers to significance threshold (p < 0.05, bootstrap test). The measures are averaged over 100 trials for each external stimulus. (E,F) Adaptation variable w of RE (E) and TC (F) neurons (color coded) as a function of the external input on TC neurons, averaged across 100 trials for each external stimulus. (G) Number of positive w values (depolarizing events, green) and negative w values (rebound events, black) of TC neurons. (H) Coefficient of variation of the ISI for both TC and RE cells as the input rate on TC neurons increases. The synaptic strengths are respectively: g_{RE → TC} = 300 μS, g_{TC → RE} = 200 μS and g_{RE → RE} = 300 μS.

Fig 6. Bursting and tonic modes displayed by the TC-RE network with RE-RE clustering as a function of external input on TC neurons for different corticothalamic inputs.

(A) Firing rate of TC (red) and RE (blue) neurons as a function of the external driving input impinging on TC neurons for different corticothalamic input amplitudes. (B) Number of positive (depolarizing, red) and negative (rebound, blue) w values of TC spikes for different corticothalamic inputs. The w values are averaged across 100 trials for each external stimulus. (C,D) Mutual information carried by the firing rate of TC (red) and RE (blue) neurons with a cortico-thalamic input of (C) 1000 spikes/s and (D) 2000 spikes/s, calculated between the set of increasing sensory stimuli (10 − 150 spikes/s) and the neural response given by the firing rate. The white dashed lines in the bars refer to the significance threshold (p < 0.05, bootstrap test). Measures are averaged over 100 trials for each external stimulus. The synaptic strengths are respectively: g_{RE → TC} = 300 μS, g_{TC → RE} = 200 μS and g_{RE → RE} = 300 μS.