Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. Stationary and travelling bumps have similar meso- and macroscopic profiles, but different microscopic structure, hence we propose lifting operators which use microscopic motifs to disambiguate them. We provide numerical evidence that waves are supported by a combination of high synaptic gain and long refractory times, while meandering bumps are elicited by short refractory times

Septin6 and Septin7 GTP binding proteins regulate AP-3- and ESCRT-dependent multivesicular body biogenesis

Septins (SEPTs) form a family of GTP-binding proteins implicated in cytoskeleton and membrane organization, cell division and host/pathogen interactions. The precise function of many family members remains elusive. We show that SEPT6 and SEPT7 complexes bound to F-actin regulate protein sorting during multivesicular body (MVB) biogenesis. These complexes bind AP-3, an adapter complex sorting cargos destined to remain in outer membranes of maturing endosomes, modulate AP-3 membrane interactions and the motility of AP-3-positive endosomes. These SEPT-AP interactions also influence the membrane interaction of ESCRT (endosomal-sorting complex required for transport)-I, which selects ubiquitinated cargos for degradation inside MVBs. Whereas our findings demonstrate that SEPT6 and SEPT7 function in the spatial, temporal organization of AP-3- and ESCRT-coated membrane domains, they uncover an unsuspected coordination of these sorting machineries during MVB biogenesis. This requires the E3 ubiquitin ligase LRSAM1, an AP-3 interactor regulating ESCRT-I sorting activity and whose mutations are linked with Charcot-Marie-Tooth neuropathies