Anisotropic invasion and its consequences in two-strategy evolutionary games on a square lattice.

We have studied invasion processes in two-strategy evolutionary games on a square lattice for imitation rule when the players interact with their nearest neighbors. Monte Carlo simulations are performed for systems where the pair interactions are composed of a unit strength coordination game when varying the strengths of the self-dependent and cross-dependent components at a fixed noise level. The visualization of strategy distributions has clearly indicated that circular homogeneous domains evolve into squares with an orientation dependent on the composition. This phenomenon is related to the anisotropy of invasion velocities along the interfaces separating the two homogeneous regions. The quantified invasion velocities indicate the existence of a parameter region in which the invasions are opposite for the horizontal (or vertical) and the tilted interfaces. In this parameter region faceted islands of both strategies shrink and the system evolves from a random initial state into the homogeneous state that first percolated.

Dendritic spikes induce ripples in parvalbumin interneurons during hippocampal sharp waves.

Sharp-wave ripples are transient oscillatory events in the hippocampus that are associated with the reactivation of neuronal ensembles within specific circuits during memory formation. Fast-spiking, parvalbumin-expressing interneurons (FS-PV INs) are thought to provide fast integration in these oscillatory circuits by suppressing regenerative activity in their dendrites. Here, using fast 3D two-photon imaging and a caged glutamate, we challenge this classical view by demonstrating that FS-PV IN dendrites can generate propagating Ca(2+) spikes during sharp-wave ripples. The spikes originate from dendritic hot spots and are mediated dominantly by L-type Ca(2+) channels. Notably, Ca(2+) spikes were associated with intrinsically generated membrane potential oscillations. These oscillations required the activation of voltage-gated Na(+) channels, had the same frequency as the field potential oscillations associated with sharp-wave ripples, and controlled the phase of action potentials. Furthermore, our results demonstrate that the smallest functional unit that can generate ripple-frequency oscillations is a segment of a dendrite.