Beyond the standard balanced network: Multiple timescales in cortical dynamics
Final Report Abstract
The balanced hypothesis has been proposed to account for temporal spiking irregularity observed in neocortical neurons. This theory is a simplified description of cortical circuits that posits excitatory and inhibitory input to cancel each other dynamically, and resulting fluctuations drive the system chaotically. The standard form of the theory is based on assumptions that connectivity is uniformly random and neuronal heterogeneity averages out. The standard model does not also include active dendritic integration. In this project, I develop theoretical tools and computational models to address the implication of biophysical substrates that deviates from simplifying assumptions in the standard balanced theory. First, we develop a unified theory encompassing the macroscopic dynamics of recurrent balanced interactions of binary neurons within arbitrary network architectures using the mean-field approach. Our analysis based on the system’s martingale structure provides a complete description of nonequilibrium fluctuations in networks with a finite size and finite degree of interactions. Our theory also allows the investigation of conditions for which a deterministic mean-field approach breaks down. Second, we investigate the effect of input fluctuation timescales on the first-passage time of neurons. Using Fredholm's theorem, we derive an exact integral equation for the mean event rate of a leaky integrate-and-fire neuron that receives constant input and temporally correlated noise. This theory paves the way to tackle the challenge of input-output self-consistency for higher-order statistics in balanced networks. Finally, we reveal that in vivo-like cortical fluctuating input enhances nonlinearity in a single dendritic compartment and shifts the input-output relation to exhibiting nonmonotonous or bistable dynamics. In particular, with the slow activation of calcium dynamics, we analyze noise-induced bistability and its emerged timescales. We further show that noise-induced bistability persists in a multicompartmental model neuron with realistic synaptic input. These noise-induced orders could provide far-reaching implications for the dendritic function in the processing of in vivo–like fluctuating cortical input. Our analytical analysis allows us to study the mutual impact of dendritic nonlinearity and irregular spiking in cortical networks. The project's theoretical tools and methods can be employed to tackle multi-timescale dynamics and fluctuations in cortical microcircuits and foster a better understanding of macroscopic phenomena in neuronal circuits.
Publications
- Complete Mean-Field Theory for Dynamics of Binary Recurrent Networks. Phys. Rev. Lett. 119, 208301 (2017)
Farkhooi, F. & Stannat, W.
(See online at https://doi.org/10.1103/physrevlett.119.208301) - Fredholm theory for the mean first-passage time of integrate-and-fire oscillators with colored noise input. Phys. Rev. E 5, (2019)
van Vreeswijk, C. & Farkhooi, F.
(See online at https://doi.org/10.1103/physreve.100.060402) - Noise-induced properties of active dendrites. PNAS 118, (2021)
van Vreeswijk, C. & Farkhooi, F.
(See online at https://doi.org/10.1073/pnas.2023381118)
