Fig 1.
Characteristics of network model.
A) The network contained one excitatory (PC) and two inhibitory (FS and NFS) populations stimulated by external (Eext and Iext) input. Neuron models possessed intrinsic electrophysiological properties typical for each population and, under the baseline conditions, both the FS and NFS populations had mean firing rates of ~2Hz. B) Raster plot of network activity under baseline conditions. C) Distributions of synaptic latencies and post-synaptic potentials for all synaptic connections onto the PC population. FS to PC connections had shorter latencies and elicited greater post-synaptic potential amplitudes compared with NFS to PC connections.
Fig 2.
Network spike characteristics and excitation-inhibition balance.
A) Distributions of spike characteristics for PC neurons under baseline conditions. PC spiking is irregular with a long-tailed ISI distribution and mean ISICV of 1.1. B) Breakdown of excitation-inhibition balance and synaptic input current sources onto the PC population during the baseline condition. Points within each cloud represent mean input current from different sources onto individual PC neurons. Mean current from external stimulation (Eext, shown in orange) represented the majority (97%) of mean total excitatory current (E, shown in yellow). A similar proportion of inhibitory current was derived from both external (Iext) and network sources (FS & NFS). Net current (E+I) was of similar magnitude to total excitatory and inhibitory currents (denoted E & I, respectively). Net conductance onto the PC population (S1 Fig) was dominated by inhibitory inputs. C) Mean cross-correlation between synaptic conductance’s received from the PC and FS (PC-FS), NFS (PC-NFS) or both inhibitory populations (PC-I) onto the PC population. There is stronger and more rapid cross-correlation between the PC and FS, compared to PC and NFS, populations (peak cross-correlation at 6 and 12ms, respectively). The temporal lag and co-fluctuation of PC and FS synaptic conductance’s can be appreciated from a trace of mean synaptic conductance onto the PC population (C, lower).
Fig 3.
Changes in network properties with modulation of interneuron excitability.
A) FS interneuron input-frequency relationship following modulation of interneuron excitability in response to random excitatory synaptic input. Interneuron excitability was quantified as the percentage increase in rheobase relative to baseline in response to a constant current stimulus (shown here for baseline, 25% and 50% increase in rheobase). B) Increased NFS rheobase produced stepwise reductions of NFS firing rates and increases of FS & PC firing rates. Increased NFS rheobase did not produce a significant change in PC spike correlations (C) or population oscillations (D). In contrast, an increase in FS firing rates beyond a 25% increase in FS rheobase was observed (B, right), together with large increases in both PC spike correlations and population synchrony (normalised relative to baseline, C & D). E) Changes in characteristics of excitatory and inhibitory input current onto the PC population with modulation of interneuron excitability. As FS rheobase was increased, the proportion of excitatory current onto the PC population derived from within the network (i.e., from other PC neurons, denoted Int) increased from ~3 to 9% (E, upper left). Since external stimulation remained fixed, this change in network-derived excitatory current must drive increased firing rates observed in B. Furthermore, increased FS rheobase also produced greater network-derived inhibition (E, top right). Despite increased population firing rates, a paradoxical reduction of EI balance was observed (E, bottom).
Fig 4.
Reduced FS excitability promotes a paradoxical response to inhibitory stimulation.
A) The presence of an ISN was explored by applying an external current stimulus to the FS (y axis) and NFS (x axis) population and recording the mean change in inhibitory (hyperpolarising) current received by the PC population (increased inhibitory current in green, decreased inhibitory current in red). This process was repeated after increasing FS (B & C) and NFS (S2 Fig) rheobase. During the baseline condition and increased NFS rheobase, external stimulation of the inhibitory population increased inhibitory current received by the PC population. In contrast, increased FS rheobase (C) was associated with a paradoxical reduction of inhibitory current received by the PC population despite lower PC firing rates, consistent with an ISN regime. This effect was more pronounced with greater increases of FS rheobase (panel 3).
Fig 5.
FS interneurons enhance PC gain and promote transition to an ISN regime in a rate model.
A) A rate model was optimised with synaptic weights (W) based on features of the spiking network. During baseline conditions the gain of each population was set to 1.0. B) Under the assumption that synaptic weights remain fixed, changes of PC population gain (BE) in the rate model were required to reproduce firing rates from the spiking network associated with increased FS/NFS rheobase. Increased FS rheobase increased BE such that the effective recurrent excitatory synaptic strength (BE x WEE) exceeded 1.0. C) Two rate models were developed based on changes in PC gain shown in B: one approximating increased NFS rheobase (‘NFS model’) and one FS rheobase (‘FS model’, firing rates during baseline conditions in lower left caption). C) The FS model loses stability via a Hopf bifurcation as BE x WEE exceeds 1.0 (asterix) and exhibits sustained oscillations, whereas a qualitative change in network behaviour does not occur in the NFS model. D) Phase portraits and firing rate trajectories of the NFS and FS models for inputs shown in C under the condition of fixed NFS firing rate. The PC nullcline of the FS model has a rightward inflection, and stimulation of the FS population moves the fixed point to lower PC and FS firing rates, suggestive of an ISN regime. In contrast, stimulation of the FS population in the NFS model increases the steady-state FS firing rate, suggestive of a non-ISN regime. These findings are confirmed by changes of inhibitory current onto the PC population in response to stimulation of the FS and NFS population (S5 Fig).
Fig 6.
PC gain modulation in the spiking network.
A) Raster plot of PC spiking (spikes denoted in red) and average population response (top trace, grey) in response to a brief stimulus applied to 20% of the PC population (black arrow). The stimulus elicited a bi-modal population response: the first peak (P1) in response to the stimulus and the second peak (P2) from PC-to-PC interactions. The effective synaptic weight was estimated by calculating the ratio of the area under the curves of P2 (yellow) to P1 (blue). B) Estimated effective synaptic weight (BEWEE) under conditions of increased FS and NFS rheobase. FS rheobase increased BEWEE above 1, consistent with excitatory subnetwork instability, and produced a significant increase in BEWEE compared to NFS rheobase (P < 0.001). C) Examples of normalised average population response to the perturbation (arrow) following increased FS rheobase.
Fig 7.
Interneuron properties and PC gain modulation.
A) A network with a homogeneous FS interneuron population was developed to explore the role of interneuron synaptic properties upon PC gain. B) Histogram of FS-to-PC synaptic latencies before (purple, ‘FS’) and after (green, ‘NFS’) modification to resemble NFS latencies. Connectivity and synaptic distribution were modified in a similar manner. C) Example of normalised average population response to the perturbation (arrow) following modification of interneuron latency. C) Estimated effective PC synaptic weight (BEWEE) within the FS network after modifying interneuron properties to resemble the NFS population (100% represents NFS values). An increase in estimated BEWEE was observed across all parameters, and at 100% latency and connectivity generated a significant change compared to baseline (P < 0.01, Welch’s t test).
Fig 8.
Intrinsic interneuron electrophysiological properties.
A) To explore the influence of interneuron electrophysiological properties, a network of just FS or NFS interneurons was developed and stimulated with excitatory synaptic input of increasing mean frequency (‘Stim’). B) Normalised average interneuron population responses to synaptic input demonstrating differences in mean response latency between the FS and NFS populations. C) Mean latency to peak response as a function of excitatory input frequency. Excitatory inputs generated a more rapid-onset response within the FS compared to NFS population (P < 0.001 for input rates above 15 Hz). D) Efficacy of modifying intrinsic electrophysiological and synaptic NFS interneuron properties upon rescuing the original three-population network from an ISN regime. The spiking network was first initialised into an ISN by increasing FS rheobase by 50% (‘Baseline’). Specific properties of the NFS population were then modified to resemble the FS population, and a paradoxical response assessed by perturbing the FS and NFS populations, calculating the change of inhibitory current onto the PC population and then averaging these responses (paradoxical response denoted by negative values in red, e.g., Fig 4). Synaptic connectivity, distribution and latency were adjusted incrementally to resemble the FS population (25, 50, 75 & 100%).