Flexible rerouting of hippocampal replay sequences around changing barriers in the absence of global place field remapping.

Flexibility is a hallmark of memories that depend on the hippocampus. For navigating animals, flexibility is necessitated by environmental changes such as blocked paths and extinguished food sources. To better understand the neural basis of this flexibility, we recorded hippocampal replays in a spatial memory task where barriers as well as goals were moved between sessions to see whether replays could adapt to new spatial and reward contingencies. Strikingly, replays consistently depicted new goal-directed trajectories around each new barrier configuration and largely avoided barrier violations. Barrier-respecting replays were learned rapidly and did not rely on place cell remapping. These data distinguish sharply between place field responses, which were largely stable and remained tied to sensory cues, and replays, which changed flexibly to reflect the learned contingencies in the environment and suggest sequenced activations such as replay to be an important link between the hippocampus and flexible memory.

Inferring circuit mechanisms from sparse neural recording and global perturbation in grid cells.

A goal of systems neuroscience is to discover the circuit mechanisms underlying brain function. Despite experimental advances that enable circuit-wide neural recording, the problem remains open in part because solving the 'inverse problem' of inferring circuity and mechanism by merely observing activity is hard. In the grid cell system, we show through modeling that a technique based on global circuit perturbation and examination of a novel theoretical object called the distribution of relative phase shifts (DRPS) could reveal the mechanisms of a cortical circuit at unprecedented detail using extremely sparse neural recordings. We establish feasibility, showing that the method can discriminate between recurrent versus feedforward mechanisms and amongst various recurrent mechanisms using recordings from a handful of cells. The proposed strategy demonstrates that sparse recording coupled with simple perturbation can reveal more about circuit mechanism than can full knowledge of network activity or the synaptic connectivity matrix.

A model of grid cell development through spatial exploration and spike time-dependent plasticity.

Grid cell responses develop gradually after eye opening, but little is known about the rules that govern this process. We present a biologically plausible model for the formation of a grid cell network. An asymmetric spike time-dependent plasticity rule acts upon an initially unstructured network of spiking neurons that receive inputs encoding animal velocity and location. Neurons develop an organized recurrent architecture based on the similarity of their inputs, interacting through inhibitory interneurons. The mature network can convert velocity inputs into estimates of animal location, showing that spatially periodic responses and the capacity of path integration can arise through synaptic plasticity, acting on inputs that display neither. The model provides numerous predictions about the necessity of spatial exploration for grid cell development, network topography, the maturation of velocity tuning and neural correlations, the abrupt transition to stable patterned responses, and possible mechanisms to set grid period across grid modules.

Resonant mixing in perturbed action-action-angle flow.

This paper presents a quantitative theory of mixing via chaotic advection in near-integrable time-dependent volume-preserving flows for the case when the base (unperturbed) flow possesses two invariants (or actions). Using a model cellular flow introduced by Solomon and Mezic as an example, we construct a quantitative theory of mixing caused by the resonance-induced diffusion of an adiabatic invariant of the flow. We compute the fraction of the mixed volume as a function of the frequency of the perturbation and show that this function is strikingly nonmonotonic, with multiple peaks. In particular, essentially complete mixing inside a flow cell is achieved on experimentally accessible time scales for certain special frequencies.

Resonant chaotic mixing in a cellular flow.

This Letter presents a quantitative theory of resonant mixing in time-dependent volume-preserving 3D flows using a model cellular flow introduced in T. Solomon and I. Mezic, Nature (London) 425, 376 (2003), as an example. Specifically, we show that chaotic advection is dramatically enhanced by a time-dependent perturbation for certain resonant frequencies. We compute the fraction of the mixed volume as a function of the frequency of the perturbation and show that essentially complete mixing in 3D is achieved at every resonant frequency.