Increasing or decreasing ACh leads to a localized traveling wave of activation a bump that traverses the entire network space Fig 2C bottom. Local dynamics are characterized by high frequency, asynchronous spiking. Spike dynamics in the global state are also asynchronous, but oscillate between a high frequency upstate and a low frequency down state. In each, black markers represent spikes from excitatory cells and red markers represent those from inhibitory cells. Cells are sorted by spatial coordinate, a measure described in the methods section.
The SFA level i. For any given level of inhibition, the transition between stationary and traveling frequency dynamics occurs over a narrow range of. The effect of inhibition becomes clearer in the traveling wave regime, where the speed of the wave propagation is slowed by increased inhibitory strength. For strong values of inhibition waves are arrested. The empty squares of Fig 2A indicate parameter values that yield networks where excitatory cells are completely quiescent or involved in network-wide synchronous bursting.
From the single cell perspective, the level of SFA has the largest effect on the length of an upstate. Scanning between 0. This reduction of spike number corresponds to an increase of both the length and variability of inter-spike intervals ISIs within an upstate Fig 3A.
Increasing inhibitory strength has a less dramatic effect on the length of an upstate. For a given value of increasing inhibition reduces the average number of spikes per upstate in a linear fashion, independent of Fig 3B. For very low levels of individual upstates of neurons last for a longer and more variable number of spikes black data series.
Specific basal forebrain–cortical cholinergic circuits coordinate cognitive operations
The adaptive effect of the slow potassium conductance is shown by the large variation in ISI for values above 0. Increasing reduced the number of spikes per upstate to about 3. An increase in spike synchrony within upstates corresponds to the shift from a type 1 to type 2 PRC which occurs at high levels of as indicated by the distribution of inter-spike intervals. Time is shown as normalized phase based on the average period of firing during an upstate and the colors of the bar graphs corresponds to the PRCs shown in Fig 1. Each cell is represented by a different color.
It is known from other studies that in a stationary bump regime, dynamics can be pinned to a specific region by enhanced recurrent excitation [ 20 , 21 ].
We used this effect to map the transition between local and global dynamics Fig 5A. Network preference manifests as longer upstates within the heterogeneous zone than outside it. An important function of neural networks is the ability to recognize and respond to structural features such as information encoded in synaptic weights. To explore this idea, we compared how changes in the SFA level affect preferential activation of a region with enhanced recurrent excitation. This effect has been previously shown to localize stationary bump dynamics in spiking networks [ 20 , 21 ].
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Sensitivity to heterogeneity decreases as SFA increases as networks allow wave dynamics, but persists for strong heterogeneities well into the wave regime. For low levels of SFA this effect is driven by upstates lasting significantly longer within the heterogeneous area than outside Fig 5C. These states arise from an interaction between neural excitability and the network-wide strength of lateral inhibition. The magnitude of SFA is a determining factor in whether or not network activity can be pinned by structural heterogeneities such as recurrent excitation.
Our results indicate that large scale spatio-temporal dynamics can be induced by ACh mediated SFA and that neural networks composed of highly excitable cells will be more responsive to synaptic heterogeneities. In the model we used the changes induced by ACh resemble the dynamical cycles seen in the cortex during sleep. Experiments have shown that in vivo stimulation of cholinergic neurons can induce the transition from SWS to REM like sleep activity [ 22 , 23 ]. The low ACh state in this model creates traveling waves of high frequency upstates and quiescent down states, reminiscent of what occurs during SWS.
Analysis of EEG data in sleeping humans has identified the slow wave in SWS as a traveling wave originating in the frontal cortex and propagating to the posterior [ 24 ]. An interesting and relevant feature of the traveling slow wave is that the origins are stable within individuals. Traveling waves in the conductance based model are sensitive to strong heterogeneities for intermediate values of. Experiments have shown that inducing local synaptic potential via transcranial magnetic stimulation can define the orgin of traveling slow waves [ 6 , 7 ].
These results dovetail nicely with our mechanism of recurrent excitation and SFA modulation highlighting regions with strengthened synaptic connectivity. This model replicates two cellular effects of cholinergic modulation; a reduction of SFA and the shift from a type 1 to a type 2 PRC.
The network level consequences of these cellular effect occur over distinct ranges of. Previous modeling studies have shown that networks composed of type 1 neural oscillators are generally asynchronous while type 2 networks are highly synchronous [ 12 ]. Here we show that neurons with a type 2 PRC are able to synchronize over the short time scale of a single upstate Fig 4.
It is remarkable that type 2 neurons show much higher synchrony than type 1 cells which have much longer to entrain. Type 2 neural oscillators transfer information, measured through spike train correlation, on a much shorter time scale than type 1 oscillators which could explain the difference upstate synchrony [ 25 ]. It has been shown previously that network models that learn via spike timing dependent plasticity SDTP will strengthen synapses when composed of type 1 neurons, while weakening occurs when component neurons are of type 2 [ 26 ].
Fast Cholinergic Synaptic Transmission in the Mammalian Central Nervous System
SWS is critical for memory consolidation, particularly during early stages [ 27 — 29 ]. The changes in both SFA level and in the PRC shape are both likely to play a role in the changes in synaptic strength during SWS, but whether they interact synergistically is unclear and will be the topic of further study. Another important implication of these results is to show how stationary versus traveling dynamics fit into the frameworks proposed by the synaptic homeostasis hypothesis SHY [ 30 ], which proposes synaptic renormalization during sleep, and the synaptic embossing hypothesis SEH [ 31 ], in which select circuits are strengthened by synchronous firing during REM in addition to renormalization during SWS.
It may be that localized asynchronous activity during REM sleep can further strengthen regions specified by enhanced synaptic strength during waking, while traveling, but synchronous, activity within a globally traveling wave can cause global depotentiation of synapses. This would lead to a large increase in synaptic signal to noise ratio as proposed by SHY [ 30 ] while employing a REM dependent dynamical mechanism proposed by SEH [ 31 ]. Recent in vitro and in silico studies have demonstrated the importance of REM sleep on experience dependent plasticity [ 32 , 33 ].
The differing ranges for SFA induced local to global and the PRC induced asynchronous to synchronous transitions may account for the importance of SWS to REM transitions in synaptic restructuring recently reported [ 33 ]. The interaction between ACh level and inhibitory strength in our model could be functionally significant. This may be due to the interaction of the two aforementioned mechanisms, but also to the increased GABA levels changing features of the traveling waves during SWS.
During SWS, increased activity of GABAergic projections from the basal forebrain increase both phasic and tonic inhibition within the cortex [ 35 ]. Increasing inhibition caused a decrease in the average number of spikes per upstate and narrowed the spatial extent of an upstate, both of which would lead to a decrease in LFP power. On the other hand, increasing tonic inhibition leads to an increase of delta power [ 36 ]. This model does not include a representation of tonic inhibition and adding this feature would be a valuable extension of these results.
During high ACh conditions a more complicated inhibition conditions exist. While state dependent GABA input from the basal forebrain is reduced, muscarinic agonists increase the amplitude and frequencies of spontaneous inhibitory postsynaptic currents [ 37 ]. This enhanced inhibition on its own would increase localization and sensitivity of stationary dynamics. Cholinergic drugs decrease the magnitude of evoked inhibitory input, however [ 38 ].
When the network is in the stationary state when is low and SFA is minimal; the high ACh state the excited region generates large levels of distal inhibition that reduces the likelihood that neurons outside this region will fire. Reducing the strength of inhibition causes a corresponding increase in the likelihood that far away cells will fire, eventually leading to a global high frequency state Fig 1C.
As excited cells enter a period of quiescence, neighboring neurons are able to enter an upstate due to a relaxation of distal inhibition. This relaxation increases the spatial extent of cells that are in an upstate at the same time.
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The strength of inhibition sets dx , with lower levels increasing its magnitude and thus total wave speed as well. A large amount of SFA shortens dt which drives large increases in wave speed. This notion also explains how synaptic heterogeneity i.
When the excited region passes over areas with increased excitatory coupling the recurrent excitation is able to reduce the effects of SFA on neurons causing an increase in dt when activity is within this area decreasing the propagation of excitation. The strength of inhibition determines the spatial scope of an active zone, or the space a traveling bump will traverse in a given time the dx shown in blue above. The length of an upstate at any given point in space is governed by the strength of the slow potassium conductance illustrated by the red dt above.
As in Fig 2. Stationary bump dynamics have long been used as a model of working memory [ 39 — 41 ]. In this model, the location of excitation preserves the location of a transient input and synaptic heterogeneities stabilize bump location [ 20 , 21 ]. Recent experimental results have demonstrated both the importance of stationary bumps in attention tasks [ 5 ] and the importance of the muscarinic system in this state [ 3 ].
In neural field models, the conditions that lead to the formation of stationary bumps and traveling waves have been well documented [ 43 , 44 ]. Lateral inhibition is necessary for the formation of stationary bumps and traveling waves [ 17 , 45 ], and is critical for our results. While our results hold when the range of inhibition is reduced from global, we do need the radius of inhibitory connections to be larger than that of excitation. In fact, we do not believe that traveling waves can form unless the inhibitory range is larger than that of excitatory connections.
While our scheme is supported by some experimental evidence [ 14 , 15 ], other results have failed to find lateral inhibition as a model for cortical connectivity [ 46 , 47 ]. Trends Neurosci. Rasmusson, D. Long-term enhancement of evoked potentials in cat somatosensory cortex produced by co-activation of the basal forebrain and cutaneous receptors. Brain Res. Jones, B.