Kinetics and Connectivity Properties of Parvalbumin- and Somatostatin-Positive Inhibition in Layer 2/3 Medial Entorhinal Cortex

Existence and Stability Criteria for Global Synchrony and for Synchrony in two Alternating Clusters of Pulse-Coupled Oscillators Updated to Include Conduction Delays

Phase Response Curves (PRCs) have been useful in determining and analyzing various phase-locking modes in networks of oscillators under pulse-coupling assumptions, as reviewed in Mathematical Biosciences, 226:77-96, 2010. Here, we update that review to include progress since 2010 on pulse coupled oscillators with conduction delays. We then present original results that extend the derivation of the criteria for stability of global synchrony in networks of pulse-coupled oscillators to include conduction delays. We also incorporate conduction delays to extend previous studies that showed how an alternating firing pattern between two synchronized clusters could enforce within cluster synchrony, even for clusters unable to synchronize themselves in isolation. To obtain these results, we used self-connected neurons to represent clusters. These results greatly extend the applicability of the stability analyses to networks of pulse-coupled oscillators since conduction delays are ubiquitous and strongly impact the stability of synchrony. Although these analyses only strictly apply to identical oscillators with identical connections to other oscillators, the principles are general and suggest how to promote or impede synchrony in physiological networks of neurons, for example. Heterogeneity can be interpreted as a form of frozen noise, and approximate synchrony can be sustained despite heterogeneity. The pulse-coupled oscillator model can not only be used to describe biological neuronal networks but also cardiac pacemakers, lasers, fireflies, artificial neural networks, social self-organization, and wireless sensor networks.

AMS Subject Classification

37N25, 39A06, 39A30, 92B25, 92C20.

Resistance to age-related hearing loss in the echolocating big brown bat ( Eptesicus fuscus )

Hearing mediates many behaviors critical for survival in echolocating bats, including foraging and navigation. Most mammals are susceptible to progressive age-related hearing loss; however, the evolution of biosonar, which requires the ability to hear low-intensity echoes from outgoing sonar signals, may have selected against the development of hearing deficits in echolocating bats. Although many echolocating bats exhibit exceptional longevity and rely on acoustic behaviors for survival to old age, relatively little is known about the aging bat auditory system. In this study, we used DNA methylation to estimate the ages of wild-caught big brown bats ( Eptesicus fuscus ) and measured hearing sensitivity in young and aging bats using auditory brainstem responses (ABRs) and distortion product otoacoustic emissions (DPOAEs). We found no evidence for hearing deficits in aging bats, demonstrated by comparable thresholds and similar ABR wave and DPOAE amplitudes across age groups. We additionally found no significant histological evidence for cochlear aging, with similar hair cell counts, afferent, and efferent innervation patterns in young and aging bats. Here we demonstrate that big brown bats show minimal evidence for age-related loss of peripheral hearing sensitivity and therefore represent informative models for investigating mechanisms that may preserve hearing function over a long lifetime.

A Continuous Attractor Model with Realistic Neural and Synaptic Properties Quantitatively Reproduces Grid Cell Physiology

Computational simulations with data-driven physiological detail can foster a deeper understanding of the neural mechanisms involved in cognition. Here, we utilize the wealth of cellular properties from Hippocampome.org to study neural mechanisms of spatial coding with a spiking continuous attractor network model of medial entorhinal cortex circuit activity. The primary goal is to investigate if adding such realistic constraints could produce firing patterns similar to those measured in real neurons. Biological characteristics included in the work are excitability, connectivity, and synaptic signaling of neuron types defined primarily by their axonal and dendritic morphologies. We investigate the spiking dynamics in specific neuron types and the synaptic activities between groups of neurons. Modeling the rodent hippocampal formation keeps the simulations to a computationally reasonable scale while also anchoring the parameters and results to experimental measurements. Our model generates grid cell activity that well matches the spacing, size, and firing rates of grid fields recorded in live behaving animals from both published datasets and new experiments performed for this study. Our simulations also recreate different scales of those properties, e.g., small and large, as found along the dorsoventral axis of the medial entorhinal cortex. Computational exploration of neuronal and synaptic model parameters reveals that a broad range of neural properties produce grid fields in the simulation. These results demonstrate that the continuous attractor network model of grid cells is compatible with a spiking neural network implementation sourcing data-driven biophysical and anatomical parameters from Hippocampome.org. The software (version 1.0) is released as open source to enable broad community reuse and encourage novel applications.

A Continuous Attractor Model with Realistic Neural and Synaptic Properties Quantitatively Reproduces Grid Cell Physiology

Computational simulations with data-driven physiological detail can foster a deeper understanding of the neural mechanisms involved in cognition. Here, we utilize the wealth of cellular properties from Hippocampome.org to study neural mechanisms of spatial coding with a spiking continuous attractor network model of medial entorhinal cortex circuit activity. The primary goal was to investigate if adding such realistic constraints could produce firing patterns similar to those measured in real neurons. Biological characteristics included in the work are excitability, connectivity, and synaptic signaling of neuron types defined primarily by their axonal and dendritic morphologies. We investigate the spiking dynamics in specific neuron types and the synaptic activities between groups of neurons. Modeling the rodent hippocampal formation keeps the simulations to a computationally reasonable scale while also anchoring the parameters and results to experimental measurements. Our model generates grid cell activity that well matches the spacing, size, and firing rates of grid fields recorded in live behaving animals from both published datasets and new experiments performed for this study. Our simulations also recreate different scales of those properties, e.g., small and large, as found along the dorsoventral axis of the medial entorhinal cortex. Computational exploration of neuronal and synaptic model parameters reveals that a broad range of neural properties produce grid fields in the simulation. These results demonstrate that the continuous attractor network model of grid cells is compatible with a spiking neural network implementation sourcing data-driven biophysical and anatomical parameters from Hippocampome.org. The software is released as open source to enable broad community reuse and encourage novel applications.

Synchrony in Networks of Type 2 Interneurons Is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes

Synchronization in the gamma band (25-150 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's Type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple Type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator (SPO), as previously shown for Type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and SPO regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Glial expression of Drosophila UBE3A causes spontaneous seizures modulated by 5-HT signaling

Misexpression of the E3 ubiquitin ligase UBE3A is thought to contribute to a range of neurological disorders. In the context of Dup15q syndrome, excess genomic copies of UBE3A is thought to contribute to the autism, muscle tone and spontaneous seizures characteristic of the disorder. In a Drosophila model of Dup 15q syndrome, it was recently shown glial-driven expression of the UBE3A ortholog dube3a led to a "bang-sensitive" phenotype, where mechanical shock triggers convulsions, suggesting glial dube3a expression contributes to hyperexcitability in flies. Here we directly compare the consequences of glial- and neuronal-driven dube3a expression on motor coordination and neuronal excitability in Drosophila. We utilized IowaFLI tracker and developed a hidden Markov Model to classify seizure-related immobilization. Both glial and neuronal driven dube3a expression led to clear motor phenotypes. However, only glial-driven dube3a expression displayed spontaneous immobilization events, that were exacerbated at high-temperature (38 °C). Using a tethered fly preparation we monitored flight muscle activity, we found glial-driven dube3a flies display spontaneous spike discharges which were bilaterally synchronized indicative of seizure activity. Neither control flies, nor neuronal- dube3a overexpressing flies display such firing patterns. Prior drug screen indicated bang-sensitivity in glial-driven dube3a expressing flies could be suppressed by certain 5-HT modulators. Consistent with this report, we found glial-driven dube3a flies fed the serotonin reuptake inhibitor vortioxetine and the 5HT 2A antagonist ketanserin displayed reduced immobilization and spike bursting. Together these findings highlight the potential for glial pathophysiology to drive Dup15q syndrome-related seizure activity.

Identifying distinct neural features between the initial and corrective phases of precise reaching using AutoLFADS

Many initial movements require subsequent corrective movements, but how motor cortex transitions to make corrections and how similar the encoding is to initial movements is unclear. In our study, we explored how the brain's motor cortex signals both initial and corrective movements during a precision reaching task. We recorded a large population of neurons from two male rhesus macaques across multiple sessions to examine the neural firing rates during not only initial movements but also subsequent corrective movements. AutoLFADS, an auto-encoder-based deep-learning model, was applied to provide a clearer picture of neurons' activity on individual corrective movements across sessions. Decoding of reach velocity generalized poorly from initial to corrective submovements. Unlike initial movements, it was challenging to predict the velocity of corrective movements using traditional linear methods in a single, global neural space. We identified several locations in the neural space where corrective submovements originated after the initial reaches, signifying firing rates different than the baseline before initial movements. To improve corrective movement decoding, we demonstrate that a state-dependent decoder incorporating the population firing rates at the initiation of correction improved performance, highlighting the diverse neural features of corrective movements. In summary, we show neural differences between initial and corrective submovements and how the neural activity encodes specific combinations of velocity and position. These findings are inconsistent with assumptions that neural correlations with kinematic features are global and independent, emphasizing that traditional methods often fall short in describing these diverse neural processes for online corrective movements.

Significance Statement

We analyzed submovement neural population dynamics during precision reaching. Using an auto- encoder-based deep-learning model, AutoLFADS, we examined neural activity on a single-trial basis. Our study shows distinct neural dynamics between initial and corrective submovements. We demonstrate the existence of unique neural features within each submovement class that encode complex combinations of position and reach direction. Our study also highlights the benefit of state-specific decoding strategies, which consider the neural firing rates at the onset of any given submovement, when decoding complex motor tasks such as corrective submovements.

Functionally Distinct Circuits Are Linked by Heterocellular Electrical Synapses in the Thalamic Reticular Nucleus

The thalamic reticular nucleus (TRN) inhibits sensory thalamocortical relay neurons and is a key regulator of sensory attention as well as sleep and wake states. Recent developments have identified two distinct genetic subtypes of TRN neurons, calbindin-expressing (CB) and somatostatin-expressing (SOM) neurons. These subtypes differ in localization within the TRN, electrophysiological properties, and importantly, targeting of thalamocortical relay channels. CB neurons send inhibition to and receive excitation from first-order thalamic relay nuclei, while SOM neurons send inhibition to and receive excitation from higher-order thalamic areas. These differences create distinct channels of information flow. It is unknown whether TRN neurons form electrical synapses between SOM and CB neurons and consequently bridge first-order and higher-order thalamic channels. Here, we use GFP reporter mice to label and record from CB-expressing and SOM-expressing TRN neurons. We confirm that GFP expression properly differentiates TRN subtypes based on electrophysiological differences, and we identified electrical synapses between pairs of neurons with and without common GFP expression for both CB and SOM types. That is, electrical synapses link both within and across subtypes of neurons in the TRN, forming either homocellular or heterocellular synapses. Therefore, we conclude that electrical synapses within the TRN provide a substrate for functionally linking thalamocortical first-order and higher-order channels within the TRN.

Physiological features of parvalbumin-expressing GABAergic interneurons contributing to high-frequency oscillations in the cerebral cortex

Parvalbumin-expressing (PV+) inhibitory interneurons drive gamma oscillations (30-80 Hz), which underlie higher cognitive functions. In this review, we discuss two groups/aspects of fundamental properties of PV+ interneurons. In the first group (dubbed Before Axon), we list properties representing optimal synaptic integration in PV+ interneurons designed to support fast oscillations. For example: [i] Information can neither enter nor leave the neocortex without the engagement of fast PV+ -mediated inhibition; [ii] Voltage responses in PV+ interneuron dendrites integrate linearly to reduce impact of the fluctuations in the afferent drive; and [iii] Reversed somatodendritic Rm gradient accelerates the time courses of synaptic potentials arriving at the soma. In the second group (dubbed After Axon), we list morphological and biophysical properties responsible for (a) short synaptic delays, and (b) efficient postsynaptic outcomes. For example: [i] Fast-spiking ability that allows PV+ interneurons to outpace other cortical neurons (pyramidal neurons). [ii] Myelinated axon (which is only found in the PV+ subclass of interneurons) to secure fast-spiking at the initial axon segment; and [iii] Inhibitory autapses - autoinhibition, which assures brief biphasic voltage transients and supports postinhibitory rebounds. Recent advent of scientific tools, such as viral strategies to target PV cells and the ability to monitor PV cells via in vivo imaging during behavior, will aid in defining the role of PV cells in the CNS. Given the link between PV+ interneurons and cognition, in the future, it would be useful to carry out physiological recordings in the PV+ cell type selectively and characterize if and how psychiatric and neurological diseases affect initiation and propagation of electrical signals in this cortical sub-circuit. Voltage imaging may allow fast recordings of electrical signals from many PV+ interneurons simultaneously.

Antiepileptogenic and neuroprotective effect of mefloquine after experimental status epilepticus

Acquired temporal lobe epilepsy (TLE) characterized by spontaneous recurrent seizures (SRS) and hippocampal inhibitory neuron dysfunction is often refractory to current therapies. Gap junctional or electrical coupling between inhibitory neurons has been proposed to facilitate network synchrony and intercellular molecular exchange suggesting a role in both seizures and neurodegeneration. While gap junction blockers can limit acute seizures, whether blocking neuronal gap junctions can modify development of chronic epilepsy has not been examined. This study examined whether mefloquine, a selective blocker of Connexin 36 gap junctions which are well characterized in inhibitory neurons, can limit epileptogenesis and related cellular and behavioral pathology in a model of acquired TLE. A single, systemic dose of mefloquine administered early after pilocarpine-induced status epilepticus (SE) in rat reduced both development of SRS and behavioral co-morbidities. Immunostaining for interneuron subtypes identified that mefloquine treatment likely reduced delayed inhibitory neuronal loss after SE. Uniquely, parvalbumin expressing neurons in the hippocampal dentate gyrus appeared relatively resistant to early cell loss after SE. Functionally, whole cell patch clamp recordings revealed that mefloquine treatment preserved inhibitory synaptic drive to projection neurons one week and one month after SE. These results demonstrate that mefloquine, a drug already approved for malaria prophylaxis, is potentially antiepileptogenic and can protect against progressive interneuron loss and behavioral co-morbidities of epilepsy.

Progressive Excitability Changes in the Medial Entorhinal Cortex in the 3xTg Mouse Model of Alzheimer's Disease Pathology

Alzheimer's disease (AD) is a chronic neurodegenerative disorder characterized by memory loss and progressive cognitive impairments. In mouse models of AD pathology, studies have found neuronal and synaptic deficits in hippocampus, but less is known about changes in medial entorhinal cortex (MEC), which is the primary spatial input to the hippocampus and an early site of AD pathology. Here, we measured neuronal intrinsic excitability and synaptic activity in MEC layer II (MECII) stellate cells, MECII pyramidal cells, and MEC layer III (MECIII) excitatory neurons at 3 and 10 months of age in the 3xTg mouse model of AD pathology, using male and female mice. At 3 months of age, before the onset of memory impairments, we found early hyperexcitability in intrinsic properties of MECII stellate and pyramidal cells, but this was balanced by a relative reduction in synaptic excitation (E) compared with inhibition (I; E/I ratio), suggesting intact homeostatic mechanisms regulating MECII activity. Conversely, MECIII neurons had reduced intrinsic excitability at this early time point with no change in synaptic E/I ratio. By 10 months of age, after the onset of memory deficits, neuronal excitability of MECII pyramidal cells and MECIII excitatory neurons was largely normalized in 3xTg mice. However, MECII stellate cells remained hyperexcitable, and this was further exacerbated by an increased synaptic E/I ratio. This observed combination of increased intrinsic and synaptic hyperexcitability suggests a breakdown in homeostatic mechanisms specifically in MECII stellate cells at this postsymptomatic time point, which may contribute to the emergence of memory deficits in AD.SIGNIFICANCE STATEMENT AD causes cognitive deficits, but the specific neural circuits that are damaged to drive changes in memory remain unknown. Using a mouse model of AD pathology that expresses both amyloid and tau transgenes, we found that neurons in the MEC have altered excitability. Before the onset of memory impairments, neurons in layer 2 of MEC had increased intrinsic excitability, but this was balanced by reduced inputs onto the cell. However, after the onset of memory impairments, stellate cells in MEC became further hyperexcitable, with increased excitability exacerbated by increased synaptic inputs. Thus, it appears that MEC stellate cells are uniquely disrupted during the progression of memory deficits and may contribute to cognitive deficits in AD.

Synchrony in Networks of Type 2 Interneurons is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes

Synchronization in the gamma band (30-80 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator, as previously shown for type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and stochastic population oscillator regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Significance Statement

Brain rhythms in the gamma frequency band (30-80 Hz) depend on the activity of inhibitory interneurons and evidence for a causal role for gamma oscillations in cognitive functions is accumulating. Here we extend previous studies on synchronization mechanisms to interneurons that have an abrupt threshold frequency below which they cannot sustain firing. In addition to current based synapses, we examined inhibitory networks with conductance based synapses. We found that if the reversal potential for inhibition was below the average membrane potential (hyperpolarizing), synchrony was more robust to noise than if the reversal potential was very close to the average potential (shunting). These results have implications for therapies to ameliorate cognitive deficits.

Progressive excitability changes in the medial entorhinal cortex in the 3xTg mouse model of Alzheimer's disease pathology

Alzheimer's disease (AD) is a chronic neurodegenerative disorder that is characterized by memory loss and progressive cognitive impairments. In mouse models of AD pathology, studies have found neuronal and synaptic deficits in the hippocampus, but less is known about what happens in the medial entorhinal cortex (MEC), which is the primary spatial input to the hippocampus and an early site of AD pathology. Here, we measured the neuronal intrinsic excitability and synaptic activity in MEC layer II (MECII) stellate cells, MECII pyramidal cells, and MEC layer III (MECIII) excitatory neurons at early (3 months) and late (10 months) time points in the 3xTg mouse model of AD pathology. At 3 months of age, prior to the onset of memory impairments, we found early hyperexcitability in MECII stellate and pyramidal cells' intrinsic properties, but this was balanced by a relative reduction in synaptic excitation (E) compared to inhibition (I), suggesting intact homeostatic mechanisms regulating activity in MECII. Conversely, MECIII neurons had reduced intrinsic excitability at this early time point with no change in the synaptic E/I ratio. By 10 months of age, after the onset of memory deficits, neuronal excitability of MECII pyramidal cells and MECIII excitatory neurons was largely normalized in 3xTg mice. However, MECII stellate cells remained hyperexcitable and this was further exacerbated by an increased synaptic E/I ratio. This observed combination of increased intrinsically and synaptically generated excitability suggests a breakdown in homeostatic mechanisms specifically in MECII stellate cells at this post-symptomatic time point. Together, these data suggest that the breakdown in homeostatic excitability mechanisms in MECII stellate cells may contribute to the emergence of memory deficits in AD.

Involvement of GABAergic Interneuron Subtypes in 4-Aminopyridine-Induced Seizure-Like Events in Mouse Entorhinal Cortex in Vitro

Single-unit recordings performed in temporal lobe epilepsy patients and in models of temporal lobe seizures have shown that interneurons are active at focal seizure onset. We performed simultaneous patch-clamp and field potential recordings in entorhinal cortex slices of GAD65 and GAD67 C57BL/6J male mice that express green fluorescent protein in GABAergic neurons to analyze the activity of specific interneuron (IN) subpopulations during acute seizure-like events (SLEs) induced by 4-aminopyridine (4-AP; 100 μm). IN subtypes were identified as parvalbuminergic (INPV, n = 17), cholecystokinergic (INCCK), n = 13], and somatostatinergic (INSOM, n = 15), according to neurophysiological features and single-cell digital PCR. INPV and INCCK discharged at the start of 4-AP-induced SLEs characterized by either low-voltage fast or hyper-synchronous onset pattern. In both SLE onset types, INSOM fired earliest before SLEs, followed by INPV and INCCK discharges. Pyramidal neurons became active with variable delays after SLE onset. Depolarizing block was observed in ∼50% of cells in each INs subgroup, and it was longer in IN (∼4 s) than in pyramidal neurons (<1 s). As SLE evolved, all IN subtypes generated action potential bursts synchronous with the field potential events leading to SLE termination. High-frequency firing throughout the SLE occurred in one-third of INPV and INSOM We conclude that entorhinal cortex INs are very active at the onset and during the progression of SLEs induced by 4-AP. These results support earlier in vivo and in vivo evidence and suggest that INs have a preferential role in focal seizure initiation and development.SIGNIFICANCE STATEMENT Focal seizures are believed to result from enhanced excitation. Nevertheless, we and others demonstrated that cortical GABAergic networks may initiate focal seizures. Here, we analyzed for the first time the role of different IN subtypes in seizures generated by 4-aminopyridine in the mouse entorhinal cortex slices. We found that in this in vitro focal seizure model, all IN types contribute to seizure initiation and that INs precede firing of principal cells. This evidence is in agreement with the active role of GABAergic networks in seizure generation.

Interneuronal network model of theta-nested fast oscillations predicts differential effects of heterogeneity, gap junctions and short term depression for hyperpolarizing versus shunting inhibition

Theta and gamma oscillations in the hippocampus have been hypothesized to play a role in the encoding and retrieval of memories. Recently, it was shown that an intrinsic fast gamma mechanism in medial entorhinal cortex can be recruited by optogenetic stimulation at theta frequencies, which can persist with fast excitatory synaptic transmission blocked, suggesting a contribution of interneuronal network gamma (ING). We calibrated the passive and active properties of a 100-neuron model network to capture the range of passive properties and frequency/current relationships of experimentally recorded PV+ neurons in the medial entorhinal cortex (mEC). The strength and probabilities of chemical and electrical synapses were also calibrated using paired recordings, as were the kinetics and short-term depression (STD) of the chemical synapses. Gap junctions that contribute a noticeable fraction of the input resistance were required for synchrony with hyperpolarizing inhibition; these networks exhibited theta-nested high frequency oscillations similar to the putative ING observed experimentally in the optogenetically-driven PV-ChR2 mice. With STD included in the model, the network desynchronized at frequencies above ~200 Hz, so for sufficiently strong drive, fast oscillations were only observed before the peak of the theta. Because hyperpolarizing synapses provide a synchronizing drive that contributes to robustness in the presence of heterogeneity, synchronization decreases as the hyperpolarizing inhibition becomes weaker. In contrast, networks with shunting inhibition required non-physiological levels of gap junctions to synchronize using conduction delays within the measured range.