Sequentially activated discrete modules appear as traveling waves in neuronal measurements with limited spatiotemporal sampling.

Numerous studies have identified traveling waves in the cortex and suggested they play important roles in brain processing. These waves are most often measured using macroscopic methods that are unable to assess the local spiking activity underlying wave dynamics. Here, we investigated the possibility that waves may not be traveling at the single neuron scale. We first show that sequentially activating two discrete brain areas can appear as traveling waves in EEG simulations. We next reproduce these results using an analytical model of two sequentially activated regions. Using this model, we were able to generate wave-like activity with variable directions, velocities, and spatial patterns, and to map the discriminability limits between traveling waves and modular sequential activations. Finally, we investigated the link between field potentials and single neuron excitability using large-scale measurements from turtle cortex ex vivo. We found that while field potentials exhibit wave-like dynamics, the underlying spiking activity was better described by consecutively activated spatially adjacent groups of neurons. Taken together, this study suggests caution when interpreting phase delay measurements as continuously propagating wavefronts in two different spatial scales. A careful distinction between modular and wave excitability profiles across scales will be critical for understanding the nature of cortical computations.

Quantitative Analysis of Delta-like 1 Membrane Dynamics Elucidates the Role of Contact Geometry on Notch Signaling.

Notch signaling is ubiquitously used to coordinate differentiation between adjacent cells across metazoans. Whereas Notch pathway components have been studied extensively, the effect of membrane distribution and dynamics of Notch receptors and ligands remains poorly understood. It is also unclear how cellular morphology affects these distributions and, ultimately, the signaling between cells. Here, we combine live-cell imaging and mathematical modeling to address these questions. We use a FRAP-TIRF assay to measure the diffusion and endocytosis rates of Delta-like 1 (Dll1) in mammalian cells. We find large cell-to-cell variability in the diffusion coefficients of Dll1 measured in single cells within the same population. Using a simple reaction-diffusion model, we show how membrane dynamics and cell morphology affect cell-cell signaling. We find that differences in the diffusion coefficients, as observed experimentally, can dramatically affect signaling between cells. Together, these results elucidate how membrane dynamics and cellular geometry can affect cell-cell signaling.