How neuronal morphology impacts the synchronisation state of neuronal networks.

The biophysical properties of neurons not only affect how information is processed within cells, they can also impact the dynamical states of the network. Specifically, the cellular dynamics of action-potential generation have shown relevance for setting the (de)synchronisation state of the network. The dynamics of tonically spiking neurons typically fall into one of three qualitatively distinct types that arise from distinct mathematical bifurcations of voltage dynamics at the onset of spiking. Accordingly, changes in ion channel composition or even external factors, like temperature, have been demonstrated to switch network behaviour via changes in the spike onset bifurcation and hence its associated dynamical type. A thus far less addressed modulator of neuronal dynamics is cellular morphology. Based on simplified and anatomically realistic mathematical neuron models, we show here that the extent of dendritic arborisation has an influence on the neuronal dynamical spiking type and therefore on the (de)synchronisation state of the network. Specifically, larger dendritic trees prime neuronal dynamics for in-phase-synchronised or splayed-out activity in weakly coupled networks, in contrast to cells with otherwise identical properties yet smaller dendrites. Our biophysical insights hold for generic multicompartmental classes of spiking neuron models (from ball-and-stick-type to anatomically reconstructed models) and establish a connection between neuronal morphology and the susceptibility of neural tissue to synchronisation in health and disease.

Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses.

Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a non-monotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper.