Topological Schemas of Memory Spaces.

Hippocampal cognitive map-a neuronal representation of the spatial environment-is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework-the memory space-that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as "networks of interconnections among the representations of events," have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature-a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.

A Topological Model of the Hippocampal Cell Assembly Network.

It is widely accepted that the hippocampal place cells' spiking activity produces a cognitive map of space. However, many details of this representation's physiological mechanism remain unknown. For example, it is believed that the place cells exhibiting frequent coactivity form functionally interconnected groups-place cell assemblies-that drive readout neurons in the downstream networks. However, the sheer number of coactive combinations is extremely large, which implies that only a small fraction of them actually gives rise to cell assemblies. The physiological processes responsible for selecting the winning combinations are highly complex and are usually modeled via detailed synaptic and structural plasticity mechanisms. Here we propose an alternative approach that allows modeling the cell assembly network directly, based on a small number of phenomenological selection rules. We then demonstrate that the selected population of place cell assemblies correctly encodes the topology of the environment in biologically plausible time, and may serve as a schematic model of the hippocampal network.

Topological Schemas of Cognitive Maps and Spatial Learning.

Spatial navigation in mammals is based on building a mental representation of their environment-a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains vague. A key difficulty is that these maps are collective, emergent phenomena that cannot be reduced to a simple combination of inputs provided by individual neurons. In this paper we suggest computational frameworks for integrating the spiking signals of individual cells into a spatial map, which we call schemas. We provide examples of four schemas defined by different types of topological relations that may be neurophysiologically encoded in the brain and demonstrate that each schema provides its own large-scale characteristics of the environment-the schema integrals. Moreover, we find that, in all cases, these integrals are learned at a rate which is faster than the rate of complete training of neural networks. Thus, the proposed schema framework differentiates between the cognitive aspect of spatial learning and the physiological aspect at the neural network level.

Genetic suppression of transgenic APP rescues Hypersynchronous network activity in a mouse model of Alzeimer's disease.

Alzheimer's disease (AD) is associated with an elevated risk for seizures that may be fundamentally connected to cognitive dysfunction. Supporting this link, many mouse models for AD exhibit abnormal electroencephalogram (EEG) activity in addition to the expected neuropathology and cognitive deficits. Here, we used a controllable transgenic system to investigate how network changes develop and are maintained in a model characterized by amyloid ß (Aß) overproduction and progressive amyloid pathology. EEG recordings in tet-off mice overexpressing amyloid precursor protein (APP) from birth display frequent sharp wave discharges (SWDs). Unexpectedly, we found that withholding APP overexpression until adulthood substantially delayed the appearance of epileptiform activity. Together, these findings suggest that juvenile APP overexpression altered cortical development to favor synchronized firing. Regardless of the age at which EEG abnormalities appeared, the phenotype was dependent on continued APP overexpression and abated over several weeks once transgene expression was suppressed. Abnormal EEG discharges were independent of plaque load and could be extinguished without altering deposited amyloid. Selective reduction of Aß with a γ-secretase inhibitor has no effect on the frequency of SWDs, indicating that another APP fragment or the full-length protein was likely responsible for maintaining EEG abnormalities. Moreover, transgene suppression normalized the ratio of excitatory to inhibitory innervation in the cortex, whereas secretase inhibition did not. Our results suggest that APP overexpression, and not Aß overproduction, is responsible for EEG abnormalities in our transgenic mice and can be rescued independently of pathology.