Conversions between space and time in network dynamics by neural assemblies

The connectivity structure of many biological systems, including neural circuits, is highly non-uniform. Recent technologies allow detailed mapping of these irregularities, but our understanding of their effect on the overall circuit dynamics is still lacking. By developing complex system analytical tools that perform reduction of the network, I determine the impact of connectivity features on network dynamics. I will demonstrate the use of these tools on neural assemblies (clusters), a ubiquitous non-uniform structure in our brains. I will show how neural assemblies of different sizes naturally generate multiple timescales of activity spanning several orders of magnitude. I will demonstrate how the analytical theory we develop for rate networks, supported by spiking network simulations, reveals the dependency between neural timescales and assembly sizes and how new recordings of spontaneous activity from a million neurons support this analysis. I will also show how our model can naturally explain the particular long-tailed timescale distribution observed in the awake primate cortex. In olfactory cortex, neural assemblies represent odor stimuli.  Previously, I showed how the diffuse recurrent excitation among these assemblies allows the conversion of time-encoded inputs from the bulb to spacial neural assembly representations in olfactory cortex. Here, I will show how changes in the dynamical properties of these assemblies alter both their timing response and properties of the time-encoded inputs via feedback. This demonstrates the role of neural assemblies in time-sensitive modulation needed for cognitive tasks, such as attention. Our results offer a biologically plausible mechanism of assemblies in network connectivity for explaining multiple puzzling dynamical phenomena: The ability of neural circuits to transform external simultaneous temporal fluctuations into spatial representations and alter them; and the ability of neuronal circuits to generate simultaneous temporal fluctuations across a large range of timescales;