After-hyperpolarization currents and acetylcholine control sigmoid transfer functions in a spiking cortical model

Abstract

Recurrent networks are ubiquitous in the brain, where they enable a diverse set of transformations during perception, cognition, emotion, and action. It has been known since the 1970's how, in rate-based recurrent on-center off-surround networks, the choice of feedback signal function can control the transformation of input patterns into activity patterns that are stored in short term memory. A sigmoid signal function may, in particular, control a quenching threshold below which inputs are suppressed as noise and above which they may be contrast enhanced before the resulting activity pattern is stored. The threshold and slope of the sigmoid signal function determine the degree of noise suppression and of contrast enhancement. This article analyses how sigmoid signal functions and their shape may be determined in biophysically realistic spiking neurons. Combinations of fast, medium, and slow after-hyperpolarization (AHP) currents, and their modulation by acetylcholine (ACh), can control sigmoid signal threshold and slope. Instead of a simple gain in excitability that was previously attributed to ACh, cholinergic modulation may cause translation of the sigmoid threshold. This property clarifies how activation of ACh by basal forebrain circuits, notably the nucleus basalis of Meynert, may alter the vigilance of category learning circuits, and thus their sensitivity to predictive mismatches, thereby controlling whether learned categories code concrete or abstract information, as predicted by Adaptive Resonance Theory.

Spiking Neurons in a Hierarchical Self-Organizing Map Model Can Learn to Develop Spatial and Temporal Properties of Entorhinal Grid Cells and Hippocampal Place Cells

“…For instance, the membrane potential recovery from afterhyperpolarization in MEC layer II stellate cells is known to be quickened in proportion to the action of I h [83]. Also, the fast and slow-medium currents that determine AHP in stellate cells [84] may have potentially different effects [85]. Moreover, the role of the persistent sodium (NaP) current, whose interplay with I h is known to generate subthreshold MPOs [86], is not fully clear.…”

How reduction of theta rhythm by medial septum inactivation may covary with disruption of entorhinal grid cell responses due to reduced cholinergic transmission

“…In this regard, in vivo observations that cholinergic neurons in MS, compared to GABAergic neurons, have low firing rates that vary on slow time scales of several tens of seconds (Zhang et al, 2010) are not inconsistent with this conclusion, because grid cell recordings ensued 5 min after the start of lidocaine infusions into MS for the Koenig et al (2011) study, and 2 min after the start of muscimol infusions into MS for the Brandon et al (2011) study. Ongoing modeling is starting to characterize how ACh-dependent modulations of various ion channels, notably slow, medium, and fast AHP currents, can influence biophysical properties of individual spiking neurons (Palma et al, 2012b) and networks of such neurons (Palma et al, 2012a). Such studies may in the future be applied to a spiking network model of grid cells (Pilly and Grossberg, 2013) to more completely analyze the disruptive effects on grid cells of silencing the MS.…”

Persistence and storage of activity patterns in spiking recurrent cortical networks: modulation of sigmoid signals by after-hyperpolarization currents and acetylcholine

“…However, as demonstrated in Palma et al (2011), a more realistic approximation uses a mass action law, similar to other kinetic models (Destexhe et al, 1994a,b), to introduce an intermediate variable. This is expressed by two differential equations: $\frac{dR}{dt}=\left(1-R\right)I-\frac{R}{{\tau }_r},$ and $\frac{d{g}_{\text{SD}}}{dt}=\left(\frac{{\tau }_f+{\tau }_r}{{\tau }_f}\right)\left[\frac{2}{{\tau }_r}\left(1-g_{\text{SD}}\right)R-\frac{g_{\text{SD}}}{{\tau }_f}\right]$…”

“…The Palma et al (2011) analysis revealed simple rules that govern conductance changes in the three AHP currents as they combine to generate desired changes in signaling. It was shown that, for spiking neurons, a leftward threshold shift occurs when the sAHP and mAHP currents decrease, while the fAHP current increases.…”