Acetylcholine Mediates Dynamic Switching Between Information Coding Schemes in Neuronal Networks

Abstract

Rate coding and phase coding are the two major coding modes seen in the brain. For these two modes, network dynamics must either have a wide distribution of frequencies for rate coding, or a narrow one to achieve stability in phase dynamics for phase coding. Acetylcholine (ACh) is a potent regulator of neural excitability. Acting through the muscarinic receptor, ACh reduces the magnitude of the potassium M-current, a hyperpolarizing current that builds up as neurons fire. The M-current contributes to several excitability features of neurons, becoming a major player in facilitating the transition between Type 1 (integrator) and Type 2 (resonator) excitability. In this paper we argue that this transition enables a dynamic switch between rate coding and phase coding as levels of ACh release change. When a network is in a high ACh state variations in synaptic inputs will lead to a wider distribution of firing rates across the network and this distribution will reflect the network structure or pattern of external input to the network. When ACh is low, network frequencies become narrowly distributed and the structure of a network or pattern of external inputs will be represented through phase relationships between firing neurons. This work provides insights into how modulation of neuronal features influences network dynamics and information processing across brain states.

Keywords: acetylcholine; information coding; networks; neuromodulation; neuronal excitability.

Figure 1

Modulation of neuronal properties in a model of cholinergic modulation. (A) The f/I curve increases its slope as ACh increases (${\overline{g}}_{Ks}$ decreases). Blue colors represent the high ACh case. The onset of spike frequency adaptation in the Ks model occurs at a high ${\overline{g}}_{Ks}$. SFA is quantified here by the SFA index, which compares the inter-spike interval between the first two and the last two spikes in an induced burst. (B, top) When ${\overline{g}}_{Ks}$ is low SFA is minimal and ISIs are equivalent throughout the burst. (B, bottom) When ${\overline{g}}_{Ks}$ is high ISIs gradually increase though out the burst. (C) Measured SFA indices for various ${\overline{g}}_{Ks}$ and injected current values show that SFA is only significantly reducing frequency during the burst above ${\overline{g}}_{Ks}$ = 0.25 mS/cm², below this the effects are negligible. Stars indicate the parameters of the voltage traces shown in (B). Dark blue squares indicate parameters that do not elicit spikes and bright yellow squares parameters that yield <3 spikes. (D) The PRC is measured by comparing perturbed vs. unperturbed periods when neurons fire at a fixed frequency. When the next spike is earlier the phase response is positive (blue), when it is delayed it is negative (red). (E) Type 1 neurons have a strictly positive PRC (blue) while Type 2 neurons have a biphasic PRC. (F) Transitions in biophysical properties in the Ks model occur over different ranges of ${\overline{g}}_{Ks}$. Modulation of the f/I slope occurs continuously over the range of ${\overline{g}}_{Ks}$. The slope is steep for low ${\overline{g}}_{Ks}$ and gradual for high ${\overline{g}}_{Ks}$. The transition between a Type 1 and a Type 2 PRC occurs for high ${\overline{g}}_{Ks}$, though the PRC shape does change in a continuous manner as ${\overline{g}}_{Ks}$ changes. SFA has little effect for low ${\overline{g}}_{Ks}$ and only significantly effects the frequency of neurons for high ${\overline{g}}_{Ks}$.

Figure 2

Example dynamics show rate specificity during high ACh dynamics and high phase specificity during low ACh dynamics. (A) Raster plots show that high ACh networks have high similarity in firing rates, but low temporal organization. Changes in network structure (Net 1 vs. Net 2) alter which neurons are high frequency vs. low frequency, but this is stable between simulations on the same network. Low ACh networks have a more uniform firing rate but more temporal organization and synchrony. The phase relationships between neurons is stable across stimulations, but not across networks. Black rasters indicate the spike time of excitatory neurons and red rasters indicate inhibitory spikes. (B) During High ACh conditions the firing rate of neurons is highly correlated during simulations run on the same networks and uncorrelated between runs on different networks (left). The order of neuron firing during bursts is higher between runs on the same network compared with runs on different networks during low ACh conditions (right). Error bars indicate s.e.m.

Figure 3

The transition from high frequency variance to high phase locking shows how cholinergic modulation can change coding principles. (A) High ACh networks have highly varied firing rates as measured by the coefficient of variation. Firing rates quickly become more uniform as ${\overline{g}}_{Ks}$ increases. Conversely, MPC (phase locking) is high for low ACh networks. (B) Frequency CDFs for single simulations, each on the same network structure, show that the same network display large differences in the variance of firing rates across the network. High ACh networks have high variance, which deceases dramatically as ACh is reduced. Error bars indicate s.e.m.

Figure 4

Variations in current input between neuron subsets leads to changes in average frequency and phase. (A) The difference in average frequency of the two neuron populations shows a positive relationship with the difference in current input, labeled as I_offset, when ${\overline{g}}_{Ks}$ is 0.0. (B) Raster plot shows phase leading in spike times of neuron subset. The raster plot shows spike times for neuron population where 20 neurons receive an additional current input of 1.95 μA/cm². Blue rasters indicate subpopulation with additional current while black rasters indicate sub population with baseline current input. Red trace shows convolution of spike times with Gaussian function which is used to define the phase reference. The above simulation is conducted with a ${\overline{g}}_{Ks}$ value of 1.5. (C) Phase difference between subpopulation with additional current input and subpopulation with baseline current input shows a negative relationship with the current input. (D) Comparison of the phase difference and frequency difference for a given current input. Plot shows comparison of phase difference for ${\overline{g}}_{Ks}$ = 1.5 and frequency difference for ${\overline{g}}_{Ks}$ = 0.0 for a given current offset.

Figure 5

High ACh networks show increased rate coding which is diminished in low ACh networks. Rate coding, measured by the specificity of neuronal firing rates across simulations with the same pattern of inputs across the network vs. different patterns of input, occurs for high ACh networks. This effect is decreased in low ACh networks, largely because firing rates become more similar between different networks. (A) NS_Freq is the network score based on comparing frequency correlations on simulations with the same input pattern against simulations with different patterns. (B) ${\widetilde{NS}}_{Freq}$ scales NS_Freq by the coefficient of variation for frequency. (C) Color plots show the correlation of firing rates between simulations for ${\overline{g}}_{Ks}=0.0$ and ${\overline{g}}_{Ks}=1.4$ mS/cm² (top and bottom, respectively). Each simulation is sorted along the x and y axis by network structure. A similar effect occurs when information is represented through network structure. (D–F) NS_Freq, ${\widetilde{NS}}_{Freq}$, and correlation plots for simulations with varying network structure. Gray points show the NS_Freq for each input pattern or network structure. Gray crosses show NS_Freq for scrambled data. Error bars indicate s.e.m.

Figure 6

Low ACh networks show increased phase coding. Phase coding, measured by the network specificity of mean phase coherence across simulations with the same input pattern vs. different patterns, occurs for low ACh networks on all topologies. This effect is decreased in high ACh networks, due to the increased frequency variation and decreased phase locking. (A) NS_Phase is the network score based on phase correlations. (B) ${\widetilde{NS}}_{Phase}$ scales NS_Phase by the mean MPC of the simulations. Scaling average MPC accounts for low MPC reflecting essentially random firing. (C) Color plots show the correlation of phase values between simulations for ${\overline{g}}_{Ks}=0.0$ and ${\overline{g}}_{Ks}=1.4$ mS/cm² (top and bottom, respectively). Each simulation is sorted along the x and y axis by network structure. (D–F) NS_Phase, ${\widetilde{NS}}_{Phase}$, correlation plots for simulations with varying network structure. Gray points show the NS_Phase for each input pattern or network structure. Gray crosses show NS_Phase for scrambled data. Error bars indicate s.e.m.