Self-sustained activity in neural networks: influence of network topology and cell types

The cerebral cortex exhibits neural activity even in the absence of external stimuli. This self-sustained activity is characterized by irregular firing of individual neurons and population oscillations with a broad frequency range. Questions that arise in this context, are: What are the mechanisms responsible for the existence of neuronal spiking activity in the cortex without external input? Do these mechanisms depend on the structural organization of the cortical connections? Do they depend on intrinsic characteristics of the cortical neurons? To approach the answers to these questions, we have used computer simulations of cortical network models. Our networks have hierarchical modular architecture and are composed of combinations of neuron models that reproduce the firing behavior of the five main cortical electrophysiological cell classes: regular spiking (RS), chattering (CH), intrinsically bursting (IB), low threshold spiking (LTS), and fast spiking (FS). The population of excitatory neurons is built of RS cells (always present) and either CH or IB cells. Inhibitory neurons belong to the same class, either LTS or FS. Long-lived self-sustained activity states in our network simulations display irregular single neuron firing and oscillatory activity similar to experimentally measured ones. The duration of self-sustained activity strongly depends on the initial conditions, suggesting a transient chaotic regime. Extensive analysis of the self-sustained activity states showed that their lifetime expectancy increases with the number of network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class. These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.

Gamma (gamma) oscillation, a hallmark of cortical activity during sensory processing and cognition, occurs during persistent, self-sustained activity or "UP" states, which are thought to be maintained by recurrent synaptic inputs to pyramidal cells. During neocortical "UP" states, excitatory regular spiking (RS) (pyramidal) cells and inhibitory fast spiking (FS) (basket) cells fire with distinct phase distributions relative to the gamma oscillation in the local field potential. Evidence suggests that gamma-modulated RS --> FS input serves to synchronize the interneurons and hence to generate gamma-modulated FS --> RS drive. How RS --> RS recurrent input shapes both self-sustained activity and gamma-modulated phasic firing, although, is unclear. Here, we investigate this by reconstructing gamma-modulated synaptic input to RS cells using the conductance injection (dynamic clamp) technique in cortical slices. We find that, to show lifelike gamma-modulated firing, RS cells require strongly gamma-modulated, low-latency inhibitory inputs from FS cells but little or no gamma-modulation from recurrent RS --> RS connections. We suggest that this demodulation of recurrent excitation, compared with inhibition, reflects several possible effects, including distributed propagation delays and integration of excitation over wider areas of cortex, and maximizes the capacity for representing information by the timing of recurrent excitation.

Simulation of neuron spiking activity models has been carried out using the Euler method. This study aims to simulate spiking activity in a neuron model. The neuron model used is the Hodgkin-Huxley neuron model, Integrate and Fire neuron model, Wilson neuron model, and Izhikevich neuron model. The research was conducted by implementing the mathematical equations of each neuron model used and then recording the membrane potential changes from time to time using the Euler method in MATLAB. The different forms of spiking activity were done by varying the variable’s value in each mathematical equation of a neuron model that describes the processing of action potentials (spikes) influenced by ion channel activity. The results showed that the Integrate and Fire neuron models produce regular spiking (RS), Hodgkin-Huxley neuron models have regular spiking (RS) forms, Wilson neuron models produce regular spiking (RS), fast-spiking (FS), and intrinsic bursting (IB), Izhikevich neuron model produces regular spiking (RS), fast-spiking (FS), intrinsic bursting (IB), chattering neurons (CH), and low threshold spiking (LTS). The complexity of the variables used and the spiking activity generated by each neuron model can provide an overview of computational efficiency and proximity to actual biological neurons.

Self-sustained activity of low firing rate in balanced networks

Somatostatin-expressing, low threshold-spiking (LTS) cells and fast-spiking (FS) cells are two common subtypes of inhibitory neocortical interneuron. Excitatory synapses from regular-spiking (RS) pyramidal neurons to LTS cells strongly facilitate when activated repetitively, whereas RS-to-FS synapses depress. This suggests that LTS neurons may be especially relevant at high rate regimes and protect cortical circuits against over-excitation and seizures. However, the inhibitory synapses from LTS cells usually depress, which may reduce their effectiveness at high rates. We ask: by which mechanisms and at what firing rates do LTS neurons control the activity of cortical circuits responding to thalamic input, and how is control by LTS neurons different from that of FS neurons? We study rate models of circuits that include RS cells and LTS and FS inhibitory cells with short-term synaptic plasticity. LTS neurons shift the RS firing-rate vs. current curve to the right at high rates and reduce its slope at low rates; the LTS effect is delayed and prolonged. FS neurons always shift the curve to the right and affect RS firing transiently. In an RS-LTS-FS network, FS neurons reach a quiescent state if they receive weak input, LTS neurons are quiescent if RS neurons receive weak input, and both FS and RS populations are active if they both receive large inputs. In general, FS neurons tend to follow the spiking of RS neurons much more closely than LTS neurons. A novel type of facilitation-induced slow oscillations is observed above the LTS firing threshold with a frequency determined by the time scale of recovery from facilitation. To conclude, contrary to earlier proposals, LTS neurons affect the transient and steady state responses of cortical circuits over a range of firing rates, not only during the high rate regime; LTS neurons protect against over-activation about as well as FS neurons.

The cerebral cortex displays a rich repertoire of internally-generated dynamic states even in the absence of external stimuli [1]. Most theoretical studies of cortical activity are based on networks of randomly connected units [2] or with architectures artificially built from random networks [3]. In spite of the usefulness of these models, it is also important to have computational models that try to accurately represent cortical network architecture. Recently, Potjans and Diesmann [4] presented a network model of the local cortical microcircuit based on extensive experimental data on the intrinsic circuitry of striate cortex. The model is a full-scale representation of the cortical network under a surface area of 1 mm2 of striate cortex (~80,000 neurons) and contains two cell types (excitatory and inhibitory) distributed over four layers: L2/3, L4, L5, and L6. The cells are modeled as current-based leaky integrate-and-fire neurons with exponential synaptic currents. In this work, we used the connectivity map of the Potjans and Diesmann model [4] to construct a cortical model with 4,000 neurons (i.e. with the number of cells reduced by a factor of 20 in comparison with the Potjans and Diesmann model). Cells were described by the Izhikevich model [5] with parameters adjusted so that excitatory neurons were of the regular spiking (RS) type, 50% of the inhibitory neurons were of the fast spiking (FS) type and the other 50% of the inhibitory neurons were of the low-threshold spiking (LTS) type. Synapses were modeled as conductance-based with exponentially decaying conductances (we used the same synaptic parameters as in [3]). Instantaneous excitatory/inhibitory synaptic increments were denoted by gex/gin. Brief (10 ms) but strong direct current pulses were applied to 15% of L4 excitatory cells to stimulate the network and, after stimulus removal, we kept the simulation running until Tsim = 3000 ms. We performed this experiment for 10 different initial conditions to randomize the construction of the network as well as for at least 100 different combinations of gex/gin in the range gex = [0, 0.1], gin = 0[1]. The measurements taken were the lifetime of network activity, the activity of the network and the coefficients of variation of the interspike intervals of network neurons. In addition, we performed the same experiments with L4 isolated and in all possible combinations (in pairs or triplets) with the other layers, and with 100% of inhibitory cells of the FS type. The major results of our simulations are: (1) For networks made of RS and FS cell types, long-lived network activity was observed for combinations of gex/gin in the region of highest values of both of them. These states displayed irregular neuronal firing. For other combinations of gex/gin the network activity decayed rapidly after a short transient; (ii) Introduction of LTS neurons increased the region of gex/gin combinations that generated long-lived activity and reduced the average network firing rate; (iii) Different combinations of layers favored more or less the occurrence of long-lived activity. L4 alone, L4-L5 and L4-L5-L6 could not sustain long-lived activity while L4-L6 and L23-L4-L6 displayed long-lived activity for larger regions of gex/gin combinations.

Spiking Irregularity and Frequency Modulate the Behavioral Report of Single-Neuron Stimulation

Neocortex plays key role in diverse brain functions. Understanding this role involves the study of collective neural activity patterns under different situations, and how these patterns relate to the structural and functional organization of neocortex. Here we study the effect of synaptic plasticity on neural spiking activity patterns in a neocortical network model. We measure changes in neural spiking patterns due to changes in the strengths of the synapses connecting neurons and relate them to changes in the functional connectivity of the network as disclosed by graph-theoretic measures. Our neocortical network model was composed of excitatory and inhibitory neurons in the proportion of four excitatory cells for each inhibitory cell. Neurons were described by the Izhikevich model [1]. The parameters of the model were adjusted so that excitatory neurons were of the regular spiking (RS) type and inhibitory neurons were all of either the fast spiking (FS) or the low-threshold spiking (LTS) type. Synapses were modeled as event-based, and two types of synaptic dynamics were considered: one without synaptic plasticity in which the synaptic weight received a fixed increment after the pre-synaptic event and decayed exponentially after that, and one with synaptic plasticity in which the synapse obeyed an asymmetric spike-timing dependent plasticity (STDP) rule described by [2]. Neurons were organized into four layers (2/3, 4, 5 and 6) with layer- and cell-specific statistical connectivity rules based on [3]. The total number of neurons in the model was about 4,000. Two experiments were done: one with all synapses described by the model without synaptic plasticity, and the other with synapses between excitatory neurons described by the STDP rule while the remaining synapses were described by the model without synaptic plasticity. In both cases, the model was stimulated by a current injection of random amplitude applied to neurons of layer 4 (L4), which is the main input layer of the cortex. The spiking activity of the network was evaluated by measures extracted from the raster plot of the spikes produced by the neurons, e.g. layer-specific and network mean and time-dependent firing rates. The structural and functional connectivities of the network were represented by the respective structural and functional adjacency matrices. The functional adjacency matrix was constructed by taking in consideration neuron pairs with strength of their synaptic coupling above a specific threshold. The topology of the adjacency matrices was characterized by graph-theoretic measures, e.g. clustering coefficient. We determined a set of parameters for which the spiking activity generated in L4 by the external input propagated to the entire network. This network-wide activity was oscillatory, and we found that its mean frequency was higher for the network version with synaptic plasticity than for the version without synaptic plasticity. We also found that the formation of clusters of synchronous neural activity was facilitated in the case with LTS cells as inhibitory neurons. Our results suggest that synaptic plasticity may induce changes in the functional connectivity of the neocortical network with impact on its global activity.

Author response: Ultrafast (400 Hz) network oscillations induced in mouse barrel cortex by optogenetic activation of thalamocortical axons

Editor's evaluation: Ultrafast (400 Hz) network oscillations induced in mouse barrel cortex by optogenetic activation of thalamocortical axons

A digital-controlled silicon neuron is presented, which can achieve a multi-mode biologically plausible spike shape. The proposed circuit can mimics the behaviors of known kinds of excitatory and inhibitory cortical neurons, including regular spiking (RS), chattering (CH), intrinsic bursting (IB), fast spiking (FS), and low-threshold spiking (LTS). The circuit is capable of generating different spiking patterns through simple digital control, which makes the circuit configurable for a large-scale spiking neural network (SNN). Implemented in a 65-nm CMOS technology, the proposed circuit maintains a good robustness over process, voltage and temperature (PVT) variations.

Experimental studies have shown that neuronal excitation is balanced with inhibition and spikes are triggered only when that fine balance is perturbed. It is also known that inhibition is critical for receptive field tuning, yet it is not clear what role is played by different types of inhibitory interneurons and how the corresponding balanced circuitry could emerge via spike timing dependent plasticity (STDP). To study these questions we have constructed a large-scale detailed spiking model of V1 involving a variety of simulated neurons: fast-spiking (FS) interneurons, low threshold spiking (LTS) interneurons and regular spiking (RS) neurons. We modeled layer 4 and layer 2/3 of the primary visual cortex and a number of projections between cell types in agreement with anatomical data. Synaptic dynamics is governed by a set of STDP and activity dependent plasticity mechanisms for both inhibitory and excitatory synapses. The plasticity rules have been chosen to be in quantitative agreement with experiment where the data is available. For many of connections however, the data is either unavailable or noisy. In these cases plasticity rules were chosen based on a guided guess constrained by the requirement of structural stability of the system and expected response properties of cells to probing stimuli. Together, the plasticity rules lead to stable neuronal response and formation of orientation-selective receptive fields. The network learns simple and complex cells of a broad range of orientations and spatial frequencies. The model converges to a balanced neurodynamics and biologically reasonable firing rates. Our study shows that in the presence of strong thalamic drive, plastic inhibition is necessary for feature selectivity. The FS cells remove DC component of the input while firing of the LTS cells imposes sparse response and balances out feedback excitation.

We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities p of directed random connections, a localized transient stimulus results either in self-sustained persistent activity or in a brief transient followed by failure. Averages over the quenched ensemble reveal that the probability of failure changes from 0 to 1 over a narrow range in p; this failure transition can be described analytically through an extension of an existing mean-field result. Exceedingly long transients emerge at higher densities p; their activity patterns are disordered, in contrast to the mostly periodic persistent patterns observed at low p. The times at which such patterns die out follow a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation.

V3 Spinal Neurons Establish a Robust and Balanced Locomotor Rhythm during Walking

Decision letter: Interacting rhythms enhance sensitivity of target detection in a fronto-parietal computational model of visual attention