Topic: Bistability

Leonid Berlyand discusses mathematical models for the onset of cell motion driven by myosin contraction. A two-dimensional free-boundary PDE model links cell-shape evolution to diffusion and Keller–Segel-type transport. The talk examines linear stability, a stability-determining eigenvalue and the way nonlinear diffusion changes the bifurcation from supercritical to subcritical. It also considers the curvature of the bifurcation curve, connections to bistability, and the role of non-self-adjoint operators. An example illustrates why a spectral gap alone need not guarantee stability. This is an

Neural oscillations are ubiquitously observed in many brain areas. One proposed functional role of these oscillations is that they serve as an internal clock, or ‘frame of reference’ relative to which information can be encoded. In line with this hypothesis, there have been many empirical observations of this phase code in the brain. What are the latent dynamics and circuits that support phase coding with neural oscillations? Here, we propose a new computational hypothesis which is derived from analyzing trained recurrent neural networks (RNNs). We train RNNs on a working memory task, while al

Neuronal dendritic trees display a wide range of nonlinear input integrations due to their voltage-dependent active calcium channels. We reveal that in vivo-like fluctuating input enhances nonlinearity substantially in a single dendritic compartment and shifts the input-output relation to exhibiting nonmonotonous or bistable dynamics. In particular, with the slow activation of calcium dynamics, we analyze noise-induced bistability and its timescales. We show bistability induces long-timescale fluctuation that can account for observed dendritic plateau potentials in vivo conditions. In a multic

For more than 20 years, a growing body of evidence indicates that the brain functions near a critical point, where neural activity is balanced between damping and amplification. One of the appealing benefits of criticality is its optimal information processing [1, 2]. In addition, deviations from criticality are associated with age and disease [3] but also physiological state [4]. Yet the neural mechanisms involved in maintaining and/or altering this criticality remain unclear. To investigate how cellular mechanisms can influence criticality, we analyze a model of neuronal network [5] and quan

Sharp wave-ripples (SPW-Rs) are widely studied oscillatory patterns observed during sleep and awake immobility in the hippocampal formation of most mammals [Buzsáki, 2015]. During SPW-Rs behavioral sequences are replayed compressed in time [Wilson & McNaughton, 1994; Diba & Buzsáki, 2007], which led to the hypothesis that they are mediating memory transfer from the hippocampus to the neocortex [Buzsáki, 1989]. SPW-Rs can be internally generated in the highly recurrent CA3 network [Maier et al., 2003], but their incidence during sleep is affected by slow oscillations in the cortex [Sirota et al

Interneurons, ubiquitous in the central nervous system, form networks connected through both inhibitory chemical synapses and gap junctions. These networks are essential for regulating neuronal activity notably by regulating temporally patterned dynamic states. We aim to understand the mechanisms that allow for synchronization to arise in networks of interneurons with both chemical synapses and electrical gap junctions (Panel 1). To this end, we use the exact mean-field reduction, often referred to as the “neural mass model” in the literature (Montbrio et al, PRX, 2015). We first analyse a sin