Source-linked AI summary
Self-sustained asynchronous irregular states and Up/Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons
Alain Destexhe
TL;DR
The paper examines whether asynchronous irregular states occur in networks of nonlinear integrate-and-fire neurons with realistic intrinsic properties, including thalamic, cortical, and thalamocortical networks. Using adaptive exponential integrate-and-fire models, it finds AI states across these systems, with LTS cells favoring AI activity in small networks and adaptation shaping transitions between sustained AI and Up/Down dynamics.
Problem
It is unclear whether asynchronous irregular states extend from simple integrate-and-fire networks to networks of neurons with complex intrinsic properties, particularly in the thalamocortical system.
Method
The study uses adaptive exponential integrate-and-fire neurons to analyze oscillatory and asynchronous-irregular dynamics in cortical, thalamic, and thalamocortical network models without external input after initialization.
Results
AI states occur in thalamic, cortical, and thalamocortical networks; LTS cells favor AI states in small networks, while cortical adaptation determines sustained AI versus Up/Down dynamics.
Takeaways & Limitations
Intrinsic properties such as LTS and spike-frequency adaptation are crucial determinants of AI and Up/Down states in thalamocortical network models.
Takeaways & Limitations
The model does not attempt to reproduce the correct cellular conductance patterns of the different network states.
Abstract
from arXiv · showhide
Randomly-connected networks of integrate-and-fire (IF) neurons are known to display asynchronous irregular (AI) activity states, which resemble the discharge activity recorded in the cerebral cortex of awake animals. However, it is not clear whether such activity states are specific to simple IF models, or if they also exist in networks where neurons are endowed with complex intrinsic properties similar to electrophysiological measurements. Here, we investigate the occurrence of AI states in networks of nonlinear IF neurons, such as the adaptive exponential IF (Brette-Gerstner-Izhikevich) model. This model can display intrinsic properties such as low-threshold spike (LTS), regular spiking (RS) or fast-spiking (FS). We successively investigate the oscillatory and AI dynamics of thalamic, cortical and thalamocortical networks using such models. AI states can be found in each case, sometimes with surprisingly small network size of the order of a few tens of neurons. We show that the presence of LTS neurons in cortex or in thalamus, explains the robust emergence of AI states for relatively small network sizes. Finally, we investigate the role of spike-frequency adaptation (SFA). In cortical networks with strong SFA in RS cells, the AI state is transient, but when SFA is reduced, AI states can be self-sustained for long times. In thalamocortical networks, AI states are found when the cortex is itself in an AI state, but with strong SFA, the thalamocortical network displays Up and Down state transitions, similar to intracellular recordings during slow-wave sleep or anesthesia. Self-sustained Up and Down states could also be generated by two-layer cortical networks with LTS cells. These models suggest that intrinsic properties such as LTS are crucial for AI states in thalamocortical networks.
1 Introduction
The paper asks whether asynchronous irregular activity states extend beyond simple leaky integrate-and-fire networks to neurons with complex intrinsic properties, including within thalamocortical systems.
- Awake cortical neurons show noisy, highly irregular discharges at 1-20 Hz with substantial membrane-potential fluctuations.
- Leaky integrate-and-fire networks can reproduce asynchronous irregular activity resembling irregular spike discharge in awake cortex.
- The study investigates whether such states occur in cortical, thalamic, and thalamocortical networks whose neurons express complex intrinsic properties.
2 Methods
The methods section describes the equations, connectivity, and procedures used to model neurons, synapses, and network activity.
- The study specifies equations for modeling neurons and synapses before describing connectivity in the different network models.
- It also defines methods for quantifying activity across the network models.
2.1 Single-cell models
The adaptive exponential integrate-and-fire model combines an exponential spike-threshold nonlinearity with adaptation dynamics to represent intrinsic properties of central neurons.
- The adaptive exponential integrate-and-fire model combines Izhikevich’s two-variable integrate-and-fire model with an exponential nonlinearity around spike threshold.
- The model uses membrane capacitance, leak conductance, resting potential, threshold, membrane area, reset, and refractory-period parameters.The cited parameter values include Cm = 1 µF/cm2, gL = 0.05 mS/cm2, EL = -60 mV, VT = -50 mV, and a 2.5 ms refractory period.
- An adaptation variable w evolves with time constant τw = 600 ms and is incremented by b after each spike to regulate adaptation strength.
2.2 Single-cell intrinsic properties
The model represents several thalamocortical cell types by varying intrinsic parameters, especially adaptation and bursting-related dynamics.
- Cortical regular-spiking cells use a = 0.001 µS and b = 0.04 nA for strong adaptation, or b = 0.005 nA for weak adaptation.
- Fast-spiking cortical inhibitory interneurons are represented as cells with negligible adaptation.
- Moderate a produces cortical low-threshold-spike-like rebound bursting alongside spike-frequency adaptation, even when b = 0.
- Larger a values produce stronger bursting and weaker adaptation, modeling thalamocortical neurons with rebound bursts.
- The study considers only selected intrinsic-property parameter combinations, although other combinations can generate additional behaviors.
2.3 Network models
The networks were built from adaptive exponential integrate-and-fire neurons with conductance-based synapses and random initial stimulation. After 50 ms, activity evolved without external input or added noise.
- Network equations used adaptive exponential integrate-and-fire neurons with indexed parameters to represent different cell types.Synaptic interactions entered through conductance terms with excitatory and inhibitory reversal potentials.
- Synaptic conductances increased after presynaptic spikes and decayed exponentially, with 5 ms excitation and 10 ms inhibition time constants.Excitatory and inhibitory strengths varied by network type, and synaptic delays were omitted.
- Small networks required relatively large synaptic strengths, with typical values of ge = 6 nS and gi = 67 nS.These values produced resting postsynaptic potentials of 11 mV for excitation and 8.5 mV for inhibition at -70 mV.
- 2% to 10% of randomly chosen neurons received random excitatory stimulation during the first 50 ms to initiate activity.The stimulation was then removed, leaving random connectivity as the only noise source.
- The equations were solved using the NEURON simulation environment.
2.4 Connectivity
Connectivity was random while incorporating anatomical constraints across thalamic, cortical, thalamocortical, and corticothalamic networks. Connection probabilities were scaled with network size to preserve incoming synapse counts.
- Connectivity: Random connectivity was constrained by anatomical and morphological connection probabilities among thalamic, cortical, and thalamocortical cell types.
- Thalamus: Thalamic networks contained thalamocortical relay and reticular layers, with N=100 in the standard configuration.
- Cortex: Cortical networks used approximately 2% connection probabilities and a standard size of N=2000 neurons.Connection probabilities were rescaled inversely with network size to preserve connections per neuron.
- Thalamocortical relations: Thalamocortical and corticothalamic projections formed a reciprocal excitatory feedback loop involving cortical Layer VI and the corresponding thalamic area.
- Thalamocortical relations: Table 1 reports outgoing connection probabilities and example average incoming synapse counts for PY, IN, TC, and RE populations.The example network contains 1600 PY, 400 IN, 100 TC, and 100 RE neurons.
- Cortex: Cortical interlayer connectivity was excitatory-only at 1%, half the 2% intra-layer probability.
2.5 Quantification of network states
Network states were quantified by temporal regularity and synchrony. Regularity used the mean interspike-interval coefficient of variation, while synchrony used averaged pairwise spike-count cross-correlation.
- Regularity: Temporal regularity was measured with the coefficient of variation of interspike intervals, averaged across neurons.
- Regularity: CVISI values at least 1 defined irregular activity, with 1 corresponding to a Poisson process.
- Synchrony: Synchrony was quantified using averaged pairwise cross-correlation between neurons’ spike counts.The correlation averaged across many disjoint neuron pairs and used 5 ms bins, with results also checked using 2 ms bins.
- Synchrony: CC ranged from -1 to 1, and states were considered asynchronous when CC was typically below 0.1.
3 Results
Networks of nonlinear integrate-and-fire neurons produced self-sustained irregular activity across thalamic, cortical, and thalamocortical models. Network size, low-threshold spike cells, and cortical spike-frequency adaptation shaped whether activity was asynchronous irregular, transient, or organized into Up/Down states.
- Thalamic networks: Thalamic networks generated self-sustained aperiodic activity at small sizes, becoming more asynchronous and irregular as network size increased.A 20-neuron network had CVISI = 1.36 and CC = 0.025; at N=100, CVISI = 1.47 and CC = 0.016.
- Thalamic networks: Thalamic irregular oscillations persisted across a broad conductance domain, approximately ge > 4 nS and gi > 40 nS.Transient oscillations that failed to survive 10 seconds were excluded from the indicated domain.
- Cortical networks: Strong adaptation made cortical AI activity transient, whereas reducing adaptation allowed self-sustained AI states in the same N=2000 network.The weak-adaptation state had CVISI = 2.47 and CC = 0.005.
- Cortical networks: Adding a small proportion of LTS cells enabled self-sustained AI states in relatively small cortical networks of N=400 or N=500.The N=400 network showed intermittent switching between SR and AI states, while the larger network remained in AI activity.
- Thalamocortical networks: In thalamocortical networks, strong cortical adaptation produced alternating Up and Down states, while weak adaptation produced continuous self-sustained AI activity.The continuous AI state had CVISI = 2.45 and CC = 0.004; the model averaged around 40 Hz, higher than experimental data.
- Thalamocortical networks: A two-layer cortical network combining transient and AI dynamics generated self-sustained Up and Down states while retaining a stable resting state.The authors relate these behaviors to the intrinsic properties of the neurons included in the system.
4 Discussion
Networks with complex intrinsic neuronal properties can generate diverse AI, Up/Down, and activated states across thalamic, cortical, and thalamocortical configurations. LTS cells favor AI states, while adaptation modulates whether activity is self-sustained or transitions between states.
- Networks with complex intrinsic properties display diverse AI states across thalamic, cortical, and thalamocortical configurations.
- Thalamic networks with rebound bursting can display AI states at remarkably small sizes, around N∼100.
- Two-layer cortical networks can generate self-sustained Up/Down dynamics from internal activity, combining an AI-generating subnetwork with an adapting network.
- The models omit neuromodulatory effects on leak conductances and do not reproduce experimentally measured cellular conductance patterns.
- LTS cells greatly favor AI states by making networks less vulnerable to firing gaps caused by occasional synchronized inhibition.
- Reducing cortical adaptation can shift thalamocortical networks from Up/Down dynamics to sustained AI states, paralleling neuromodulatory activation.