Phase response theory explains cluster formation in sparsely but strongly connected inhibitory neural networks and effects of jitter due to sparse connectivity

Tikidji-Hamburyan, Ruben A.; Leonik, Conrad A.; Canavier, Carmen C.

doi:10.1152/jn.00728.2018

Cited by 12 publications

(22 citation statements)

References 76 publications

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“…One important manifestation of the simplifications inherent in this choice is in the lack of any synaptic delay. Recent work by Tikidji-Hamburyan et al (2019) has illustrated that synaptic conductance delays may serve an important role in the synchronous dynamics, particularly the clustered dynamics, of purely inhibitory networks. However, we note that the neurons studied here have distinct PRC properties from those of primary focus by Tikidji-Hamburyan et al (2019) (Type I vs.…”

Section: Limitations and Future Workmentioning

confidence: 99%

“…Additional studies have explored the effect of connection probabilities and cell characteristics manifested by classifications of cell excitability on inhibitory network synchrony (Tikidji-Hamburyan et al, 2015;Rich et al, 2016), and have noted that bistability between asynchronous and synchronous firing was possible (Rich et al, 2016). More recently, Tikidji-Hamburyan et al (2019) have examined in great detail the stability of "clustered" solutions in these types of networks, noting a specific link to the biology in both the mechanism underlying the dynamic of interest (the phase response curve, or PRC) and the application of the transitions between these states (which may relate to changes in cognitive states). Further examples of how the study of this synchrony has direct application to the brain are found in the study of the onset of sharp wave ripples in the hippocampus (Schlingloff et al, 2014;Gulyás and Freund, 2015).…”

Section: Introductionmentioning

confidence: 99%

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Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Rich

Chameh

Rafiee

et al. 2020

Front. Neural Circuits

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Recent experimental literature has revealed that GABAergic interneurons exhibit increased activity prior to seizure onset, alongside additional evidence that such activity is synchronous and may arise abruptly. These findings have led some to hypothesize that this interneuronal activity may serve a causal role in driving the sudden change in brain activity that heralds seizure onset. However, the mechanisms predisposing an inhibitory network toward increased activity, specifically prior to ictogenesis, without a permanent change to inputs to the system remain unknown. We address this question by comparing simulated inhibitory networks containing control interneurons and networks containing hyperexcitable interneurons modeled to mimic treatment with 4-Aminopyridine (4-AP), an agent commonly used to model seizures in vivo and in vitro. Our in silico study demonstrates that model inhibitory networks with 4-AP interneurons are more prone than their control counterparts to exist in a bistable state in which asynchronously firing networks can abruptly transition into synchrony driven by a brief perturbation. This transition into synchrony brings about a corresponding increase in overall firing rate. We further show that perturbations driving this transition could arise in vivo from background excitatory synaptic activity in the cortex. Thus, we propose that bistability explains the increase in interneuron activity observed experimentally prior to seizure via a transition from incoherent to coherent dynamics. Moreover, bistability explains why inhibitory networks containing hyperexcitable interneurons are more vulnerable to this change in dynamics, and how such networks can undergo a transition without a permanent change in the drive. We note that while our comparisons are between networks of control and ictogenic neurons, the conclusions drawn specifically relate to the unusual dynamics that arise prior to seizure, and not seizure onset itself. However, providing a mechanistic explanation for this phenomenon specifically in a pro-ictogenic setting generates experimentally testable hypotheses regarding the role of inhibitory neurons in pre-ictal neural dynamics, and motivates further computational research into mechanisms underlying a newly hypothesized multi-step pathway to seizure initiated by inhibition.

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Section: Limitations and Future Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Rich

Chameh

Rafiee

et al. 2020

Front. Neural Circuits

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“…The conduction delays between neurons were also uniformly distributed between 0.7 and 3.5 ms. In a homogeneous network with strong but fast inhibitory synapses, delays on the short end of this range favor a solution with two subclusters in antiphase, whereas delays at the longer end of the range favor global synchrony of a single cluster (Tikidji-Hamburyan et al, 2019). Using a mixture of delays results in solutions that are not obviously one or two clusters, but are transitional between these two extremes.…”

Section: Steady State Synchrony In Oscillatory Networkmentioning

confidence: 99%

Shunting Inhibition Improves Synchronization in Heterogeneous Inhibitory Interneuronal Networks with Type 1 Excitability Whereas Hyperpolarizing Inhibition Is Better for Type 2 Excitability

Tikidji-Hamburyan

Canavier

2020

eNeuro

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All-to-all homogeneous networks of inhibitory neurons synchronize completely under the right conditions; however, many modeling studies have shown that biological levels of heterogeneity disrupt synchrony. Our fundamental scientific question is "how can neurons maintain partial synchrony in the presence of heterogeneity and noise?" A particular subset of strongly interconnected interneurons, the PV+ fast spiking basket neurons, are strongly implicated in gamma oscillations and in phase locking of nested gamma oscillations to theta. Their excitability type apparently varies between brain regions: in CA1 and the dentate gyrus they have type 1 excitability, meaning that they can fire arbitrarily slowly, whereas in the striatum and cortex they have type 2 excitability, meaning that there is a frequency threshold below which they cannot sustain repetitive firing. We constrained the models to study the effect of excitability type (more precisely bifurcation type) in isolation from all other factors. We use sparsely connected, heterogeneous, noisy networks with synaptic delays to show that synchronization properties, namely the resistance to suppression and the strength of theta phase to gamma amplitude coupling, are strongly dependent on the pairing of excitability type with the type of inhibition. Shunting inhibition performs better for type 1 and hyperpolarizing inhibition for type 2. Gamma oscillations and their nesting within theta oscillations are thought to subserve cognitive functions like memory encoding and recall; therefore, it is important to understand the contribution of intrinsic properties to these rhythms. Significance Statement The collective, synchronized activity of neurons produces brain rhythms. These rhythms are thought to subserve cognitive functions such as attention and memory encoding and retrieval. We focus on fast spiking basket cells, a subset of inhibitory interneurons. These neurons play an important role in brain rhythms. In some brain regions these neurons can fire arbitrarily slowly (type 1 dynamics) whereas in others they cannot fire below a minimum cutoff frequency (type 2 dynamics). We show that excitability type determines whether shunting or hyperpolarizing inhibition more effectively synchronizes the fast oscillatory activity of networks of these neurons in the presence of heterogeneity and noise, and more effectively drives modulation of fast activity by slower oscillations.

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“…The conduction delays between neurons were also uniformly distributed between 0.7 and 3.5 ms. In our previous work [35] in a homogeneous network, delays on the short end of this range favor a solution with two subclusters in antiphase, whereas delays at the longer end of the range favor global synchrony of a single cluster. Using a mixture of delays results in solutions that are not obviously one or two clusters, but are transitional between these two extremes.…”

Section: Steady State Synchrony In Oscillatory Networkmentioning

confidence: 89%

“…However, they did not show raster plots or report on suppression in the type 2 networks. We also used a distribution of delays (from 0.7 to 3.5) to prevent the formation of two cluster solutions [35] and stabilize global synchrony by moving the operating point away from the destabilizing discontinuity in the phase resetting curve at 0 and 1.…”

Section: Previous Studies On Suppressionmentioning

confidence: 99%

Mechanisms of Synchrony in Heterogeneous Inhibitory Interneuronal Networks for Type 1 versus Type 2 Excitability

Tikidji-Hamburyan

Canavier

2019

Preprint

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PV+ fast spiking basket interneurons are often implicated in gamma rhythms. Here we focus on mechanisms present in purely inhibitory networks. Neurons with type 1 excitability can fire arbitrarily slowly, whereas those with type 2 excitability cannot fire below a minimum frequency. We systematically examine how excitability type affects synchronization of individual spikes to a population rhythm in the presence of heterogeneity and noise, using model neurons of each type with matched F/I curve, input resistance, time constant and action potential shape. Population synchrony in noisy heterogeneous networks is maintained because neurons either fire within a tight time window or skip that cycle. Type 2 neurons with hyperpolarizing inhibition skip cycles due to their intrinsic dynamics; we show here the cycle skipping mechanism for type 1 neurons or type 2 neurons with shunting inhibition is synaptic and not intrinsic. Type 2 neurons are more resistant than type 1 to partial and complete suppression in networks with hyperpolarizing inhibition that exhibit network gamma. Moreover, type 2 neurons are recruited more rapidly and more completely into theta-nested gamma. In contrast, type 1 networks perform better with shunting inhibition on both counts, because the nonlinear dynamics in that case favor suppression of type 2 compared to type 1 neurons. Conductances that control excitability type may provide a therapeutic target to improve spatial and working memory and other tasks that rely on gamma synchrony or phase amplitude coupling. Author SummaryThe collective, synchronized activity of neurons produces brain rhythms. These rhythms are thought to subserve cognitive functions such as attention and memory encoding and retrieval. Faster rhythms are nested in slower rhythms as a putative way of chunking information. A subset of neurons called fast spiking basket cells tend to inhibit other neurons from firing. These neurons play an important role in oscillations, and in the coupling of faster oscillations to slower ones. In some brain regions these neurons can fire arbitrarily slowly (type 1 dynamics) whereas in others they cannot fire below a minimum cutoff frequency (type 2 dynamics). Mathematically, these distinct origins of rhythmic firing are signatures of very different dynamics. Here, we show that these distinct excitability types affect the ability of networks of these neurons to synchronize their fast oscillatory activity, as well as the ability of slower oscillations to modulate these fast oscillations. The exact nature of the inhibitory coupling, which may vary between brain regions, determines which type synchronizes better and is modulated better.

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Phase response theory explains cluster formation in sparsely but strongly connected inhibitory neural networks and effects of jitter due to sparse connectivity

Cited by 12 publications

References 76 publications

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Shunting Inhibition Improves Synchronization in Heterogeneous Inhibitory Interneuronal Networks with Type 1 Excitability Whereas Hyperpolarizing Inhibition Is Better for Type 2 Excitability

Mechanisms of Synchrony in Heterogeneous Inhibitory Interneuronal Networks for Type 1 versus Type 2 Excitability

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