Systems and Network Neuroscience Meeting

Stephen Coombes
Professor of Applied Mathematics in the School of Mathematical Sciences at Nottingham and member of the Brain and Body Centre.

Understanding the effect of white matter delays on large scale brain dynamics
The presence of myelin is a powerful structural factor that controls the conduction speed of mammalian axons. Here, we present perspectives from neural mass and network modelling and develop a new set of mathematical tools able to unravel the contributions of axonal delays to large-scale spatiotemporal patterning of brain activity.  Firstly, we show that the method of harmonic balance is ideally suited to describing delay-induced and delay-modulated periodic oscillations and their linear stability, at both the node and network level.  When combined with numerical continuation techniques this allows us to build the skeleton of a network bifurcation diagram and highlight the role of distance-dependent delays in contributing to novel spatiotemporal patterns arising from the instability of a synchronous state, including travelling periodic waves, alternating anti-phase solutions, cluster states, and more exotic behaviours.  Secondly, we consider reductions to delay differential equation (DDE) systems for the evolution of phases. We highlight that relative equilibria in the form of phase-locked network states (and not just synchrony) can be analysed with many of the standard tools previously developed for the analysis of steady states in more general DDE settings.  Finally, we discuss outstanding challenges for when the delays are plastic and state dependent, and present preliminary results for a new form of biologically motivated white matter plasticity rule. 

Mark van den Brink

Amélie Fréal
Assistant Professor, Center for Neurogenomics and Cognitive Research, Vrije Universiteit Amsterdam.

Controlling neuronal excitability: molecular mechanisms of axon initial segment plasticity 
Activity-dependent plasticity of the axon initial segment (AIS) allows neurons to adapt action potential output to changes in network activity and is emerging as a crucial regulator of network activity homeostasis. The initiation of action potentials at the AIS highly depends on the local density and distribution of voltage-gated ion channels, but the molecular mechanisms regulating their plasticity remain largely unknown. Here, we developed genetic tools to label endogenous sodium channels and their scaffolding protein Ankyrin-G, to reveal their nanoscale organization and longitudinally image AIS plasticity in hippocampal neurons both in slices and primary cultures.  
During short-term plasticity, we found that NMDA receptor activation causes long-term synaptic depression as well as rapid shortening of the AIS. During this shortening, Nav1.2 channels are endocytosed from the distal AIS, and this correlates with an increase in the threshold for action potential generation. During long-term silencing of neuronal network, we found that while excitatory neurons strongly upregulate Nav1.6 channels at their AIS, the expression of this channel is downregulated in inhibitory neurons. We are now investigating the transcriptional regulation and the membrane trafficking of the Nav1.6 channel to get insight into the molecular mechanisms allowing neurons to adjust their intrinsic excitability and balance excitation/inhibition homeostasis in neuronal networks.