Clique topology reveals intrinsic geometric structure in neural correlations

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a two-dimensional environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during non-spatial behaviors such as wheel running and REM sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits, and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.Comment: 29 pages, 4 figures, 13 supplementary figures (last two authors contributed equally

Understanding short-timescale neuronal firing sequences via bias matrices

The brain generates persistent neuronal firing sequences across varying timescales. The short-timescale (~100ms) sequences are believed to be crucial in the formation and transfer of memories. Large-amplitude local field potentials known as sharp-wave ripples (SWRs) occur irregularly in hippocampus when an animal has minimal interaction with its environment, such as during resting, immobility, or slow-wave sleep. SWRs have been long hypothesized to play a critical role in transferring memories from the hippocampus to the neocortex [1]. While sequential firing during SWRs is known to be biased by the previous experiences of the animal, the exact relationship of the short-timescale sequences during SWRs and longer-timescale sequences during spatial and nonspatial behaviors is still poorly understood. One hypothesis is that the sequences during SWRs are “replays” or “preplays” of “master sequences”, which are sequences that closely mimic the order of place fields on a linear track [2,3]. Rather than particular hard-coded “master” sequences, an alternative explanation of the observed correlations is that similar sequences arise naturally from the intrinsic biases of firing between pairs of cells. To distinguish these and other possibilities, one needs mathematical tools beyond the center-of-mass sequences and Spearman’s rank-correlation coefficient that are currently used

Memory:Forget me not

An enzyme called PKM zeta may have a role in long-term memory after all

Theta-mediated dynamics of spatial information in hippocampus.

In rodent hippocampus, neuronal activity is organized by a 6-10 Hz theta oscillation. The spike timing of hippocampal pyramidal cells with respect to the theta rhythm correlates with an animal's position in space. This correlation has been suggested to indicate an explicit temporal code for position. Alternatively, it may be interpreted as a byproduct of theta-dependent dynamics of spatial information flow in hippocampus. Here we show that place cell activity on different phases of theta reflects positions shifted into the future or past along the animal's trajectory in a two-dimensional environment. The phases encoding future and past positions are consistent across recorded CA1 place cells, indicating a coherent representation at the network level. Consistent theta-dependent time offsets are not simply a consequence of phase-position correlation (phase precession), because they are no longer seen after data randomization that preserves the phase-position relationship. The scale of these time offsets, 100-300 ms, is similar to the latencies of hippocampal activity after sensory input and before motor output, suggesting that offset activity may maintain coherent brain activity in the face of information processing delays

Place fields and the cognitive map

The discovery of place cells by John O'Keefe in the early 1970s was a breakthrough not just for systems neuroscience, but also for psychology: place fields provided a clear neural substrate for the notion of a cognitive map, a construct devised to explain rat learning and spatial cognition. However, is the robust location-related firing of place cells still best conceptualised as a cognitive map? In this commentary, we reassess this view of hippocampus function in light of subsequent findings on place cells. We argue that as place fields encode local space, and as they are modulated by ongoing behavior, the representation they provide may be more cognitive than map-like

Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control

It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent dynamics for two main reasons: nonlinear recurrent networks often exhibit chaotic behavior and most known learning rules do not work in robust fashion in recurrent networks. Here we address both these problems by demonstrating how random recurrent networks (RRN) that initially exhibit chaotic dynamics can be tuned through a supervised learning rule to generate locally stable neural patterns of activity that are both complex and robust to noise. The outcome is a novel neural network regime that exhibits both transiently stable and chaotic trajectories. We further show that the recurrent learning rule dramatically increases the ability of RRNs to generate complex spatiotemporal motor patterns, and accounts for recent experimental data showing a decrease in neural variability in response to stimulus onset

Coordinated grid and place cell replay during rest

Hippocampal replay has been hypothesized to underlie memory consolidation and navigational planning, yet the involvement of grid cells in replay is unknown. During replay we found grid cells to be spatially coherent with place cells, encoding locations 11 ms delayed relative to the hippocampus, with directionally modulated grid cells and forward replay exhibiting the greatest coherence with the CA1 area of the hippocampus. This suggests grid cells are engaged during the consolidation of spatial memories to the neocortex

Zeta Inhibitory Peptide attenuates learning and memory by inducing NO-mediated downregulation of AMPA receptors

Zeta inhibitory peptide (ZIP), a PKMζ inhibitor, is widely used to interfere with the main- tenance of acquired memories. ZIP is able to erase memory even in the absence of PKMζ, via an unknown mechanism. We found that ZIP induces redistribution of the AMPARGluA1 in HEK293 cells and primary cortical neurons, and decreases AMPAR-mediated currents in the nucleus accumbens (NAc). These effects were mimicked by free arginine or by a modified ZIP in which all but the arginine residues were replaced by alanine. Redistribution was blocked by a peptidase-resistant version of ZIP and by treatment with the nitric oxide (NO)- synthase inhibitor L-NAME. ZIP increased GluA1-S831 phosphorylation and ZIP-induced redistribution was blocked by nitrosyl-mutant GluA1-C875S or serine-mutant GluA1-S831A. Introducing the cleavable arginine-alanine peptide into the NAc attenuated expression of cocaine-conditioned reward. Together, these results suggest that ZIP may act as an arginine donor, facilitating NO-dependent downregulation of AMPARs, thereby attenuating learning and memory

Erasing Sensorimotor Memories via PKMζ Inhibition

Sensorimotor cortex has a role in procedural learning. Previous studies suggested that this learning is subserved by long-term potentiation (LTP), which is in turn maintained by the persistently active kinase, protein kinase Mzeta (PKMζ). Whereas the role of PKMζ in animal models of declarative knowledge is established, its effect on procedural knowledge is not well understood. Here we show that PKMζ inhibition, via injection of zeta inhibitory peptide (ZIP) into the rat sensorimotor cortex, disrupts sensorimotor memories for a skilled reaching task even after several weeks of training. The rate of relearning the task after the memory disruption by ZIP was indistinguishable from the rate of initial learning, suggesting no significant savings after the memory loss. These results indicate a shared molecular mechanism of storage for declarative and procedural forms of memory