Neuronal networks are controlled by a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a minimal model of the preBotzinger complex, a small neuronal network that controls the bre
athing rhythm of mammals through periodic firing bursts. We show that the properties of a such a randomly connected network of identical excitatory neurons are fundamentally different from those of uniformly connected neuronal networks as described by mean-field theory. We show that (i) the connectivity properties of the networks determines the location of emergent pacemakers that trigger the firing bursts and (ii) that the collective desensitization that terminates the firing bursts is determined again by the network connectivity, through k-core clusters of neurons.
Motivated by recent experiments showing the buckling of microtubules in cells, we study theoretically the mechanical response of, and force propagation along elastic filaments embedded in a non-linear elastic medium. We find that, although embedded m
icrotubules still buckle when their compressive load exceeds the critical value $f_c$ found earlier, the resulting deformation is restricted to a penetration depth that depends on both the non-linear material properties of the surrounding cytoskeleton, as well as the direct coupling of the microtubule to the cytoskeleton. The deformation amplitude depends on the applied load $f$ as $(f- f_c)^{1/2}$. This work shows how the range of compressive force transmission by microtubules can be as large as tens of microns and is governed by the mechanical coupling to the surrounding cytoskeleton.
