Neuronal behaviors: A control perspective

Abstract

Abstract-The purpose of this tutorial is to introduce and analyze models of neurons from a control perspective and to show how recently developed analytical tools help to address important biological questions. A first objective is to review the basic modeling principles of neurophysiology in which neurons are modeled as equivalent nonlinear electrical circuits that capture their excitable properties. The specific architecture of the models is key to the tractability of their analysis: in spite of their high-dimensional and nonlinear nature, the model properties can be understood in terms of few canonical positive and negative feedback motifs localized in distinct timescales. We use this insight to shed light on a key problem in experimental neurophysiology, the challenge of understanding the sensitivity of neuronal behaviors to underlying parameters in empiricallyderived models. Finally, we show how sensitivity analysis of neuronal excitability relates to robustness and regulation of neuronal behaviors.

Robust Modulation of Integrate-and-Fire Models

“…The novel Type II* excitability discussed in [38] occurs in the situation V 0 s > V 0 , which is shown in Figure 12C. Starting on the lower branch of the V -nullcline, the fixed point loses stability in a saddle-node bifurcation as I increases.…”

Brain and cognitive reserve: Translation via network control theory

“…While early evidence suggests promise in the analysis of simplifying assumptions about network controllability at the macro scale of organization in the human brain, substantial progress will be necessary across many levels (Kopell, 2014) to understand and resolve the clinical challenges that confront us. We suggest that in tandem with important developments in subcortical systems (Schiff, 2012), and rapidly emerging theoretical developments in microscale neural control (Drion et al, 2015), it is equally important to consider much higher scales of neural network organization in the study of cognitive resilience and repair. Indeed, the modular organization across these spatial scales or hierarchies could provide important constraints on observed brain dynamics (Betzel & Bassett, 2016).…”

Introducing neuromodulation in deep neural networks to learn adaptive behaviours

“…The NMN architecture revolves around the neuromodulatory interaction between the neuromodulatory and main networks. We mimic biological cellular neuromodulation [10] in a DNN by assigning the neuromodulatory network the task to tune the slope and bias of the main network activation functions.…”

“…Note that h t grows as the agent interacts with M, motivating the usage of a RNN as neuromodulatory network. A graphical comparison between both architectures is shown on Fig 2. To be as similar as possible to the neuronal model proposed by [10], the main network is a fully-connected neural network built using saturated rectified linear unit (sReLU) activation functions σ(x) = min(1, max(−1, x)), except for the final layer (also neuromodulated), for which σ(x) = x. In Section 4, we also report results obtained with sigmoidal activation functions which are often appreciably inferior to those obtained with sReLUs, further encouraging their use.…”