Topological stability of the hippocampal spatial map and synaptic transience

Spatial awareness in mammals is based on internalized representations of the environment—cognitive maps—encoded by networks of spiking neurons. Although behavioral studies suggest that these maps can remain stable for long periods, it is also well-known that the underlying networks of synaptic connections constantly change their architecture due to various forms of neuronal plasticity. This raises a principal question: how can a dynamic network encode a stable map of space? In the following, we discuss some recent results obtained in this direction using an algebro-topological modeling approach, which demonstrate that emergence of stable cognitive maps produced by networks with transient architectures is not only possible, but may be a generic phenomenon.