Cellularly-Driven Differences in Network Synchronization Propensity Are Differentially Modulated by Firing Frequency

Abstract

Spatiotemporal pattern formation in neuronal networks depends on the interplay between cellular and network synchronization properties. The neuronal phase response curve (PRC) is an experimentally obtainable measure that characterizes the cellular response to small perturbations, and can serve as an indicator of cellular propensity for synchronization. Two broad classes of PRCs have been identified for neurons: Type I, in which small excitatory perturbations induce only advances in firing, and Type II, in which small excitatory perturbations can induce both advances and delays in firing. Interestingly, neuronal PRCs are usually attenuated with increased spiking frequency, and Type II PRCs typically exhibit a greater attenuation of the phase delay region than of the phase advance region. We found that this phenomenon arises from an interplay between the time constants of active ionic currents and the interspike interval. As a result, excitatory networks consisting of neurons with Type I PRCs responded very differently to frequency modulation compared to excitatory networks composed of neurons with Type II PRCs. Specifically, increased frequency induced a sharp decrease in synchrony of networks of Type II neurons, while frequency increases only minimally affected synchrony in networks of Type I neurons. These results are demonstrated in networks in which both types of neurons were modeled generically with the Morris-Lecar model, as well as in networks consisting of Hodgkin-Huxley-based model cortical pyramidal cells in which simulated effects of acetylcholine changed PRC type. These results are robust to different network structures, synaptic strengths and modes of driving neuronal activity, and they indicate that Type I and Type II excitatory networks may display two distinct modes of processing information.

Dynamic control of modeled tonic-clonic seizure states with closed-loop stimulation

“…Our findings can be explained with PRC theory, which we previously used to explain the effects of the stimulus at different frequency amplitudes and its effect on population synchrony (Beverlin et al, 2011). The effect of firing rate shifting the peak of the PRC to the left in response to excitatory inputs is generally true and should therefore not be heavily model dependent (Gutkin et al, 2005; Fink et al, 2011). We chose the M–L model because it is one of the simplest conductances based neuronal models that can demonstrate this effect.…”

Synaptic Impairment and Robustness of Excitatory Neuronal Networks with Different Topologies

“…The model features a fast Na + current, a delayed rectifier K + current and a leakage current (Amitai, 1994; Stiefel et al, 2009; Rich et al, 2016). The current balance equation for cell i is: $\begin{array}{c}eqnarrayright\; center\; leftC\frac{d{V}_i}{dt}=-g_{Na}{m}_{\infty }^{3}hfalse(V_i-E_{Na}false)-g_{Kdr}{n}^{4}false(V_i-E_{K}false)\\ -g_{L}false(V_i-E_{L}false)+I_{ext}-I_i^{syn},\end{array}$ where C = 1.0 μF/cm 2 , g Na = 24.0 mS/cm 2 , $g_{Kdr}=3.0text\text{ mS}/text\text{c}{text\text{m}}^2$, $g_L=0.02text\text{ mS}/text\text{c}{text\text{m}}^2$, E Na = 55.0 mV , E K = −90.0 mV, E L = −60.0 mV (Amitai, 1994; Stiefel et al, 2009; Fink et al, 2011). I ext is the external current (measured in μA/cm 2 ) that controls the firing frequency of the neuron.…”

Effects of Neuromodulation on Excitatory–Inhibitory Neural Network Dynamics Depend on Network Connectivity Structure

“…The E-I networks studied here are comprised of neurons modeled, in the HodgkinHuxley formalism, on the cortical pyramidal neuron (Fink et al 2011;Stiefel et al 2009). This neuron is modulated by ACh such that it can display either Type I or Type II properties, and thus allows us to analyze the role of neuromodulation in these networks.…”