Link to Paper

Action potential is the principal mode of neural communication. It’s a way to represent and process information through the temporal and spatial pattern of spikes. These spiking patterns are very variable, even across similar trials. Normally, these variabilities are treated as arising from stochastic (Poisson) generation of spikes on the basis of a firing rate. In network simulations, it is a common practise to assume random homogeneous connectivity between neurons i.e. a uniform network. However, anatomical studies indicate that is not a good approximation. To combat this, models are often designed to allow firing rates to themselves be variable across trials. Thus, the observed data is often ‘doubly stochastic’: a variable firing rate gives rise to variable spiking. Although this allows for a good description of the data, there is no known biophysics of neurons to account for this.

This paper shows how a simulated network of spiking neurons can exhibit both spontaneous firing rate fluctuations and spontaneous spiking variability as a network property with deterministic neurons, without endowing a firing rate directly. To do this, the principle of balanced excitation and inhibition is employed. To induce firing rate fluctuations, clustered connections are introduced in a balanced network of spiking neurons - the connection probability for two neurons in the same cluster is higher than for two neurons belonging to different clusters. These clusters cause a group of spiking neurons to act like a firing rate unit, yielding the desired behaviour in firing-rate fluctuations. It is interesting to note that these fluctuations can emerge when less than 4% of the connections of a network are rearranged to form clusters. Such a small modification is sufficient to increase the cluster excitation by five times!

The paper further investigates the effects of introducing clustered excitatory connections in balanced networks. A small network of uniform networks is stimulated. Clustering is then introduced in this network. To study how specific clusters increase/decrease their firing rates over long time periods, several statistical analysis methods are employed. Network models were simulated for 4000 excitatory neurons and 1000 inhibitory LIF neurons, without noise. For the clustered network, 50 clusters of 80 neurons each were introduced in the uniform network with a connection probability outside the cluster to be 2.5. The voltage trace and spike raster plot of excitatory neurons for uniform and clustered network show the irregular firing of the neurons. Neurons asynchronously fire as expected. As clustering is introduced, neurons in the same cluster act as a firing unit. Neurons now have synchronous irregular firing. Entire clusters either fire together or don’t fire at all. This bi-stability introduces slow dynamics during which clusters transiently increase/decrease their firing rate along with randomness in the spike times of individual neurons, yielding dynamics substantially different from those of the uniform network despite the small change in architecture.

Fluctuations in firing rate exist due to the competition between clusters. Each cluster tries to excite itself and get in the upstate while inhibiting the others. When one cluster becomes active, it tends to stay active while continually suppressing the others. Hence, the active cluster has an elevated overall firing rate. Later, a different cluster may win the competition and become active. This ongoing competition between the clusters produces extended fluctuations in firing rate.

In conclusion we can now reproduce experimental data in simulations without the need of external factors but instead just from the behaviour of the clustered networks itself. It successfully shows that a small alteration of the connectivity in a uniform network leads to the introduction of dynamical phenomena, namely the slow firing rate fluctuations in spontaneous conditions while spike time variability remains intact.