Dynamical and geometrical mechanism shaping response precision in neuron models

Abstract: Experimental studies of neuronal dynamics involve recording of both spontaneous activity patterns and the responses to sustained and short-term inputs. In the first part of the talk, I will describe underlying dynamical structures governing phenomena such as post inhibitory facilitation (PIF) and slope detection in a response to transient inputs in a class of nonlinear adaptive hybrid neuron models. In PIF an otherwise subthreshold excitatory input can induce a spike if it is applied with proper timing after an inhibitory pulse, while neurons displaying slope-detection property spike to a transient input only when the input’s rate of change is in a specific, bounded range. A key concept in this analysis is a firing threshold curve which allows us to explain these phenomena in the non-autonomous systems, building upon our understanding of corresponding systems with constant stimulus. On the other hand, studying phenomena such as phase locking requires the time depending sustained stimulus and the use of our knowledge on the underlying autonomous system is very limited in this case. Nevertheless, phase-locking of ongoing oscillations to a periodic signal can be explored with a variety of analytical approaches. However, much less is known about what factors determine the response precision of excitable cells that are intrinsically at rest but are activated by periodic forcing and noise. We shed light on this coding precision by introducing a new tool, the dynamic threshold curve (DTC), which we apply to the study of well-established auditory neuron model. The talk is based on joint works with Jonathan Rubin (University of Pittsburgh) and Jonathan Touboul (Brandeis University).

Mathematics

Audience: general audience

Basic Notions and Applied Topology Seminar