Fractal spike dynamics and neuronal coupling in the primate visual system

Abstract

Key points r We measured fractal (self-similar) fluctuations in ongoing spiking activity in subcortical (lateral geniculate nucleus, LGN) and cortical (area MT) visual areas in anaesthetised marmosets. r Cells in the evolutionary ancient koniocellular LGN pathway and in area MT show high-amplitude fractal fluctuations, whereas evolutionarily newer parvocellular and magnocellular LGN cells do not. r Spiking activity in koniocellular cells and MT cells shows substantial correlation to the local population activity, whereas activity in parvocellular and magnocellular cells is less correlated with local activity.r We develop a model consisting of a fractal process and a global rate modulation which can reproduce and explain the fundamental relationship between fractal fluctuations and population coupling in LGN and MT.r The model provides a unified account of apparently disparate aspects of neural spiking activity and can improve our understanding of information processing in evolutionary ancient and modern visual pathways.Abstract The brain represents and processes information through patterns of spiking activity, which is influenced by local and widescale brain circuits as well as intrinsic neural dynamics. Whether these influences have independent or linked effects on spiking activity is, however, not known. Here we measured spiking activity in two visual centres, the lateral geniculate nucleus Brandon Munn received his PhD in Physics from the University of Sydney in 2019, and he is currently employed as a postdoctoral researcher at the University of Sydney, Brain and Mind Centre. His PhD research investigated mesoscale dynamics, within the early visual system. His interests are in utilising Physics methodology with a particular interest in criticality and how the brain has evolved to decode the statistics of natural scenes optimally. 1552B. Munn and others J Physiol 598.8 (LGN) and cortical area MT, in marmoset monkeys. By combining the Fano-factor time curve, power spectral analysis and rescaled range analysis, we reveal inherent fractal fluctuations of spiking activity in LGN and MT. We found that the evolutionary ancient koniocellular (K) pathway in LGN and area MT exhibits strong fractal fluctuations at short (<1 s) time scales. Parvocellular (P) and magnocellular (M) LGN cells show weaker fractal fluctuations at longer (multi-second) time scales. In both LGN and MT, the amplitude and time scale of fractal fluctuations can explain short and long time scale spiking dynamics. We further show differential neuronal coupling of LGN and MT cells to local population spiking activity. The population coupling is intrinsically linked to fractal fluctuations: neurons showing stronger fluctuations are more strongly correlated to the local population activity. To understand this relationship, we modelled spiking activity using a fractal inhomogeneous Poisson process with dynamic rate, which is the product of an intrinsic stochastic fractal rate and a global modulatory gain. Our model explains the intrinsic links betwee...

Fractional diffusion theory of balanced heterogeneous neural networks

“…The power-law index of the Fano factor around the optimal parameter α = 1.2 is approximately 0.5 (Fig. 6, black dashed line), consistent with experimental findings on the firing activity of cortical neurons [26]. As noted in previous studies [55], the Fano factors in the classical asynchronous state α = 2 have the Poisson-like value of unity only when there is no refractory period, with sub-Poisson behavior in the presence of refractory effects; however, the fractional state is able to exhibit a power-law increase in the Fano factor regard-less of the existence of refractory effects.…”

“…In this state, membrane potential resides far from the threshold, exhibiting heavy-tailed, skewed distributions, quantitatively consistent with neurophysiological recordings in the visual cortex of awake monkeys [27]. Neural firing activity exhibits great variability with firing rate fluctuations, as observed in [7,24,26]. The collective firing rate fluctuations of neural networks happen at multiple scales in a scale-free manner, as widely observed in experimental studies [25,39].…”

“…The fractional regime shows that for T > 10 ms, the Fano factor increases in a fractal manner as T increases, indicating the presence of great firing rate fluctuations. Such fluctuations can actually be fitted as power-law functions as found in [24,26]. The power-law index of the Fano factor around the optimal parameter α = 1.2 is approximately 0.5 (Fig.…”

“…For instance, it has been found that synaptic connection strengths [21,22] and the number of synaptic connections [23] exhibit heavy-tailed distributions with non-Gaussian features. Furthermore, it has been empirically found that neural firing activity has super-Poisson dynamics [7], with great heterogeneity and fluctuations occurring at multiple scales [24][25][26], and that membrane potentials fluctuate far from the firing threshold [27]. Some of these properties are not necessarily incompatible with Gaussian input statistics: non-Gaussian, lognormal distributions of synaptic strengths lead to the classical, normal diffusion theory in the large network limit.…”

Core and Matrix Thalamic Sub-Populations Relate to Spatio-Temporal Cortical Connectivity Gradients

“…Finally, we calculated the RMS fluctuation for varying window sizes and calculated the slope of ( ) vs plotted on a logarithmic scale, again using a Levenberg-Marquardt nonlinear least-squares fitting algorithm. The slope of log-log plot corresponds to the Hurst exponent, H, where H = 0.5 corresponds to Brownian motion (Beran, 1992;Munn et al, 2020). As H increases, the level of positive long-range temporal correlation in the signal increases.…”