Turing pattern formation on the sphere is robust to the removal of a hole.

The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit diffusion-driven pattern formation, thus providing a mechanism for bud formation. However, it is not known how the accumulation of bud scars on the cell membrane affect the ability of the Schnakenberg system to form patterns. We have approached this problem by modelling a bud scar on the cell membrane with a hole on the sphere. We have studied how the spectrum of the Laplace-Beltrami operator, which determines the resulting pattern, is affected by the size of the hole, and by numerically solving the Schnakenberg system on a sphere with a hole using the finite element method. Both theoretical predictions and numerical solutions show that pattern formation is robust to the introduction of a bud scar of considerable size, which lends credence to the hypothesis that bud formation is driven by diffusion-driven instability.

Using Micro-Electrode-Array Recordings and Retinal Disease Models to Elucidate Visual Functions: Simultaneous Recording of Local Electroretinograms and Ganglion Cell Action Potentials Reveals the Origin of Retinal Oscillatory Potentials.

BACKGROUND: The electroretinogram (ERG) is an essential diagnostic tool for visual function, both in clinical and research settings. Here, we establish an advanced in vitro approach to assess cell-type-specific ERG signal components. METHODS: Retinal explant cultures, maintained under entirely controlled conditions, were derived from wild-type mice and rd10 rod- and cpfl1 cone-degeneration mouse models. Local micro-ERG (µERG) and simultaneous ganglion cell (GC) recordings were obtained from the retinal explants using multi-electrode arrays. Band-pass filtering was employed to distinguish photoreceptor, bipolar cell, amacrine cell (AC), and GC responses. RESULTS: Scotopic and photopic stimulation discriminated between rod and cone responses in wild-type and mutant retina. The 25 kHz sampling rate allowed the visualization of oscillatory potentials (OPs) in extraordinary detail, revealing temporal correlations between OPs and GC responses. Pharmacological isolation of different retinal circuits found that OPs are generated by inner retinal AC electrical synapses. Importantly, this AC activity helped synchronise GC activity. CONCLUSION: Our µERG protocol simultaneously records the light-dependent activities of the first-, second-, and third-order neurons within the native neuronal circuitry, providing unprecedented insights into retinal physiology and pathophysiology. This method now also enables complete in vitro retinal function testing of therapeutic interventions, providing critical guidance for later in vivo investigations.