Fluctuation scaling in neural spike trains

Fluctuation Scaling of Neuronal Firing and Bursting in Spontaneously Active Brain Circuits

We employed high-density microelectrode arrays to investigate spontaneous firing patterns of neurons in brain circuits of the primary somatosensory cortex (S1) in mice. We recorded from over 150 neurons for 10min in each of eight different experiments, identified their location in S1, sorted their action potentials (spikes), and computed their power spectra and inter-spike interval (ISI) statistics. Of all persistently active neurons, 92% fired with a single dominant frequency - regularly firing neurons (RNs) - from 1 to 8Hz while 8% fired in burst with two dominant frequencies - bursting neurons (BNs) - corresponding to the inter-burst (2-6Hz) and intra-burst intervals (20-160Hz). RNs were predominantly located in layers 2/3 and 5/6 while BNs localized to layers 4 and 5. Across neurons, the standard deviation of ISI was a power law of its mean, a property known as fluctuation scaling, with a power law exponent of 1 for RNs and 1.25 for BNs. The power law implies that firing and bursting patterns are scale invariant: the firing pattern of a given RN or BN resembles that of another RN or BN, respectively, after a time contraction or dilation. An explanation for this scale invariance is discussed in the context of previous computational studies as well as its potential role in information processing.

The Jacobi diffusion process as a neuronal model

The Jacobi process is a stochastic diffusion characterized by a linear drift and a special form of multiplicative noise which keeps the process confined between two boundaries. One example of such a process can be obtained as the diffusion limit of the Stein's model of membrane depolarization which includes both excitatory and inhibitory reversal potentials. The reversal potentials create the two boundaries between which the process is confined. Solving the first-passage-time problem for the Jacobi process, we found closed-form expressions for mean, variance, and third moment that are easy to implement numerically. The first two moments are used here to determine the role played by the parameters of the neuronal model; namely, the effect of multiplicative noise on the output of the Jacobi neuronal model with input-dependent parameters is examined in detail and compared with the properties of the generic Jacobi diffusion. It appears that the dependence of the model parameters on the rate of inhibition turns out to be of primary importance to observe a change in the slope of the response curves. This dependence also affects the variability of the output as reflected by the coefficient of variation. It often takes values larger than one, and it is not always a monotonic function in dependency on the rate of excitation.

Anti-correlated cortical networks arise from spontaneous neuronal dynamics at slow timescales

In the highly interconnected architectures of the cerebral cortex, recurrent intracortical loops disproportionately outnumber thalamo-cortical inputs. These networks are also capable of generating neuronal activity without feedforward sensory drive. It is unknown, however, what spatiotemporal patterns may be solely attributed to intrinsic connections of the local cortical network. Using high-density microelectrode arrays, here we show that in the isolated, primary somatosensory cortex of mice, neuronal firing fluctuates on timescales from milliseconds to tens of seconds. Slower firing fluctuations reveal two spatially distinct neuronal ensembles, which correspond to superficial and deeper layers. These ensembles are anti-correlated: when one fires more, the other fires less and vice versa. This interplay is clearest at timescales of several seconds and is therefore consistent with shifts between active sensing and anticipatory behavioral states in mice.