A longstanding conjecture in neuroscience is that aspects of cognition depend on the brain's ability to self-generate sequential neuronal activity. We found that reliably and continually-changing cell assemblies in the rat hippocampus appeared not only during spatial navigation but also in the absence of changing environmental or body-derived inputs. During the delay period of a memory task each moment in time was characterized by the activity of a unique assembly of neurons. Identical initial conditions triggered a similar assembly sequence, whereas different conditions gave rise, uniquely, to different sequences, thereby predicting behavioral choices, including errors. Such sequences were not formed in control, non-memory, tasks. We hypothesize that neuronal representations, evolved for encoding distance in spatial navigation, also support episodic recall and the planning of action sequences.A prominent theory states that the hippocampal system primarily serves spatial navigation (1,2), a component of which is that the place-dependent activity of neurons ("place cells"; 1, 2) in the hippocampus arises from external, serially ordered environmental stimuli (3-7). Place cells are thought to embody the representation of a 'cognitive map', enabling flexible navigation. However, neural theories of other cognitive processes that may depend on the hippocampus, such as episodic memory and action planning, draw upon the activity of hypothetical, internally organized "cell assemblies" (8-13).Several observations refine the navigation theory. Hippocampal neurons can predict where the animal is coming from, or its destination (14-17); the sequential activity of place cells during locomotion is replicated within single cycles of the theta oscillation (8)(9)(10)(11)(12)(18)(19)(20); furthermore, the temporal recruitment of active neurons in the population bursts of rest and sleep also reflects, again on a faster time scale, their sequential activity as place cells, during locomotion (21-23). Thus, the sequential activation of hippocampal neurons can be disengaged from external landmarks (24-25). However, internally-generated assembly sequences operating at the time scale of behavior have not yet been reported.The frameworks of environment-controlled versus internally-generated assembly sequences give rise to distinct predictions. Imagine that a rat is 'frozen' in position during its travel (and yet, importantly, the theta oscillation is maintained). According to the navigation theory, a subset of landmark-controlled place cells should then display sustained activity, and other neurons would remain suppressed (2-6). In contrast, if assembly sequences were generated by internal mechanisms, neurons might rather display continually-changing activity. We tested these predictions by examining the activity of hippocampal neurons while the rat was required to run in a wheel at a relatively constant speed (26)(27), during the delay of a hippocampusdependent alternation memory task. Internally generated cell assembly sequences...

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 2D 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 nonspatial behaviors such as wheel running and rapid eye movement (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.structure of neural correlation | neural coding | Betti curves | clique topology | topological data analysis N eural activity and connectivity data are often presented in the form of a matrix whose entries, C ij , indicate the strength of correlation or connectivity between pairs of neurons, cell types, or imaging voxels. Detecting structure in such a matrix is a critical step toward understanding the organization and function of the underlying neural circuits. In this work, we focus on neural activity, whose structure may reflect the coding properties of neurons, rather than their physical locations within the brain. For example, place cells in rodent hippocampus act as position sensors, exhibiting a high firing rate when the animal's position lies inside the neuron's "place field," its preferred region of the spatial environment (1). Without knowledge of the coding properties, however, it is unclear whether such a geometric organization could be detected purely from the pattern of neural correlations. Alternatively, a correlation or connectivity matrix could be truly unstructured, such as the connectivity pattern observed in the fly olfactory system (2), indicating random network organization.Can we distinguish these possibilities, using only the intrinsic features of the matrix C ij ? The most common approach is to use standard tools from matrix analysis that rely on quantities, such as eigenvalues, that are invariant under linear change of basis. This strategy is natural in physics, where meaningful quantities should be preserved by linear coordinate transformations. In contrast, measurements in biological settings are often obtained as nonlinear transformations of the underlying "real" variables, whereas the choice of basis is meaningful and fixed. For example, basis elements might represent particul...

The responses of neocortical cells to sensory stimuli are variable and state dependent. It has been hypothesized that intrinsic cortical dynamics play an important role in trial-to-trial variability; the precise nature of this dependence, however, is poorly understood. We show here that in auditory cortex of urethane-anesthetized rats, population responses to click stimuli can be quantitatively predicted on a trial-by-trial basis by a simple dynamical system model estimated from spontaneous activity immediately preceding stimulus presentation. Changes in cortical state correspond consistently to changes in model dynamics, reflecting a nonlinear, self-exciting system in synchronized states and an approximately linear system in desynchronized states. We propose that the complex and state-dependent pattern of trial-to-trial variability can be explained by a simple principle: sensory responses are shaped by the same intrinsic dynamics that govern ongoing spontaneous activity.

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can--in principle--be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode the full combinatorial data of a neural code. Our main finding is that these objects can be expressed in a "canonical form" that directly translates to a minimal description of the receptive field structure intrinsic to the code. We also find connections to Stanley-Reisner rings, and use ideas similar to those in the theory of monomial ideals to obtain an algorithm for computing the primary decomposition of pseudo-monomial ideals. This allows us to algorithmically extract the canonical form associated to any neural code, providing the groundwork for inferring stimulus space features from neural activity alone.