The frequency preference of neurons and synapses in a recurrent oscillatory network

Empirical Frequency Bound Derivation Reveals Prominent Mid-Frontal Alpha Associated with Neurosensory Dysfunction in Fragile X Syndrome

The FMR1 gene is inactive in Fragile X syndrome (FXS), resulting in low levels of FMRP and consequent neurochemical, synaptic, and local circuit neurophysiological alterations in the fmr1 KO mouse. In FXS patients, electrophysiological studies have demonstrated a marked reduction in global alpha activity and regional increases in gamma oscillations associated with intellectual disability and sensory hypersensitivity. Since alpha activity is associated with a thalamocortical function with widely distributed modulatory effects on neocortical excitability, insight into alpha physiology may provide insight into systems-level disease mechanisms. Herein, we took a data-driven approach to clarify the temporal and spatial properties of alpha and theta activity in participants with FXS. High-resolution resting-state EEG data were collected from participants affected by FXS (n = 65) and matched controls (n = 70). We used a multivariate technique to empirically classify neural oscillatory bands based on their coherent spatiotemporal patterns. Participants with FXS demonstrated: 1) redistribution of lower-frequency boundaries indicating a "slower" dominant alpha rhythm, 2) an anteriorization of alpha frequency activity, and 3) a correlation of increased individualized alpha power measurements with auditory neurosensory dysfunction. These findings suggest an important role for alterations in thalamocortical physiology for the well-established neocortical hyper-excitability in FXS and, thus, a role for neural systems level disruption to cortical hyperexcitability that has been studied primarily at the local circuit level in animal models.

Distinct Mechanisms Underlie Electrical Coupling Resonance and Its Interaction with Membrane Potential Resonance

Neurons in oscillatory networks often exhibit membrane potential resonance, a peak impedance at a non-zero input frequency. In electrically coupled oscillatory networks, the coupling coefficient (the ratio of post- and prejunctional voltage responses) could also show resonance. Such coupling resonance may emerge from the interaction between the coupling current and resonance properties of the coupled neurons, but this relationship has not been clearly described. Additionally, it is unknown if the gap-junction mediated electrical coupling conductance may have frequency dependence. We examined these questions by recording a pair of electrically coupled neurons in the oscillatory pyloric network of the crab Cancer borealis. We performed dual current- and voltage-clamp recordings and quantified the frequency preference of the coupled neurons, the coupling coefficient, the electrical conductance, and the postjunctional neuronal response. We found that all components exhibit frequency selectivity, but with distinct preferred frequencies. Mathematical and computational analysis showed that membrane potential resonance of the postjunctional neuron was sufficient to give rise to resonance properties of the coupling coefficient, but not the coupling conductance. A distinct coupling conductance resonance frequency therefore emerges either from other circuit components or from the gating properties of the gap junctions. Finally, to explore the functional effect of the resonance of the coupling conductance, we examined its role in synchronizing neuronal the activities of electrically coupled bursting model neurons. Together, our findings elucidate factors that produce electrical coupling resonance and the function of this resonance in oscillatory networks.

Neocortical localization and thalamocortical modulation of neuronal hyperexcitability contribute to Fragile X Syndrome

Fragile X Syndrome (FXS) is a monogenetic form of intellectual disability and autism in which well-established knockout (KO) animal models point to neuronal hyperexcitability and abnormal gamma-frequency physiology as a basis for key disorder features. Translating these findings into patients may identify tractable treatment targets. Using source modeling of resting-state electroencephalography data, we report findings in FXS, including 1) increases in localized gamma activity, 2) pervasive changes of theta/alpha activity, indicative of disrupted thalamocortical modulation coupled with elevated gamma power, 3) stepwise moderation of low and high-frequency abnormalities based on female sex, and 4) relationship of this physiology to intellectual disability and neuropsychiatric symptoms. Our observations extend findings in Fmr1-/- KO mice to patients with FXS and raise a key role for disrupted thalamocortical modulation in local hyperexcitability. This systems-level mechanism has received limited preclinical attention but has implications for understanding fundamental disease mechanisms.

Synaptic Dynamics Convey Differential Sensitivity to Input Pattern Changes in Two Muscles Innervated by the Same Motor Neurons

Postsynaptic responses depend on input patterns as well as short-term synaptic plasticity, summation, and postsynaptic membrane properties, but the interactions of those dynamics with realistic input patterns are not well understood. We recorded the responses of the two pyloric dilator (PD) muscles, cpv2a and cpv2b, that are innervated by and receive identical periodic bursting input from the same two motor neurons in the lobster Homarus americanus. Cpv2a and cpv2b showed quantitative differences in membrane nonlinearities and synaptic summation. At a short timescale, responses in both muscles were dominated by facilitation, albeit with different frequency and time dependence. Realistic burst stimulations revealed more substantial differences. Across bursts, cpv2a showed transient depression, whereas cpv2b showed transient facilitation. Steady-state responses to bursting input also differed substantially. Neither muscle had a monotonic dependence on frequency, but cpv2b showed particularly pronounced bandpass filtering. Cpv2a was sensitive to changes in both burst frequency and intra-burst spike frequency, whereas, despite its much slower responses, cpv2b was largely insensitive to changes in burst frequency. Cpv2a was sensitive to both burst duration and number of spikes per burst, whereas cpv2b was sensitive only to the former parameter. Neither muscle showed consistent sensitivity to changes in the overall spike interval structure, but cpv2b was surprisingly sensitive to changes in the first intervals in each burst, a parameter known to be regulated by dopamine (DA) modulation of spike propagation of the presynaptic axon. These findings highlight how seemingly minor circuit output changes mediated by neuromodulation could be read out differentially at the two synapses.

Neuromodulation of Astrocytic K+ Clearance

Potassium homeostasis is fundamental for brain function. Therefore, effective removal of excessive K+ from the synaptic cleft during neuronal activity is paramount. Astrocytes play a key role in K+ clearance from the extracellular milieu using various mechanisms, including uptake via Kir channels and the Na⁺-K⁺ ATPase, and spatial buffering through the astrocytic gap-junction coupled network. Recently we showed that alterations in the concentrations of extracellular potassium ([K⁺]_o) or impairments of the astrocytic clearance mechanism affect the resonance and oscillatory behavior of both the individual and networks of neurons. These results indicate that astrocytes have the potential to modulate neuronal network activity, however, the cellular effectors that may affect the astrocytic K+ clearance process are still unknown. In this study, we have investigated the impact of neuromodulators, which are known to mediate changes in network oscillatory behavior, on the astrocytic clearance process. Our results suggest that while some neuromodulators (5-HT; NA) might affect astrocytic spatial buffering via gap-junctions, others (DA; Histamine) primarily affect the uptake mechanism via Kir channels. These results suggest that neuromodulators can affect network oscillatory activity through parallel activation of both neurons and astrocytes, establishing a synergistic mechanism to maximize the synchronous network activity.

The differential contribution of pacemaker neurons to synaptic transmission in the pyloric network of the Jonah crab, Cancer borealis

Many neurons receive synchronous input from heterogeneous presynaptic neurons with distinct properties. An instructive example is the crustacean stomatogastric pyloric circuit pacemaker group, consisting of the anterior burster (AB) and pyloric dilator (PD) neurons, which are active synchronously and exert a combined synaptic action on most pyloric follower neurons. Previous studies in lobster have indicated that AB is glutamatergic, whereas PD is cholinergic. However, although the stomatogastric system of the crab Cancer borealis has become a preferred system for exploration of cellular and synaptic basis of circuit dynamics, the pacemaker synaptic output has not been carefully analyzed in this species. We examined the synaptic properties of these neurons using a combination of single-cell mRNA analysis, electrophysiology, and pharmacology. The crab PD neuron expresses high levels of choline acetyltransferase and the vesicular acetylcholine transporter mRNAs, hallmarks of cholinergic neurons. In contrast, the AB neuron expresses neither cholinergic marker but expresses high levels of vesicular glutamate transporter mRNA, consistent with a glutamatergic phenotype. Notably, in the combined synapses to follower neurons, 70-75% of the total current was blocked by putative glutamatergic blockers, but short-term synaptic plasticity remained unchanged, and although the total pacemaker current in two follower neuron types was different, this difference did not contribute to the phasing of the follower neurons. These findings provide a guide for similar explorations of heterogeneous synaptic connections in other systems and a baseline in this system for the exploration of the differential influence of neuromodulators.NEW & NOTEWORTHY The pacemaker-driven pyloric circuit of the Jonah crab stomatogastric nervous system is a well-studied model system for exploring circuit dynamics and neuromodulation, yet the understanding of the synaptic properties of the two pacemaker neuron types is based on older analyses in other species. We use single-cell PCR and electrophysiology to explore the neurotransmitters used by the pacemaker neurons and their distinct contribution to the combined synaptic potentials.

Short-term synaptic dynamics control the activity phase of neurons in an oscillatory network

In oscillatory systems, neuronal activity phase is often independent of network frequency. Such phase maintenance requires adjustment of synaptic input with network frequency, a relationship that we explored using the crab, Cancer borealis, pyloric network. The burst phase of pyloric neurons is relatively constant despite a > two fold variation in network frequency. We used noise input to characterize how input shape influences burst delay of a pyloric neuron, and then used dynamic clamp to examine how burst phase depends on the period, amplitude, duration, and shape of rhythmic synaptic input. Phase constancy across a range of periods required a proportional increase of synaptic duration with period. However, phase maintenance was also promoted by an increase of amplitude and peak phase of synaptic input with period. Mathematical analysis shows how short-term synaptic plasticity can coordinately change amplitude and peak phase to maximize the range of periods over which phase constancy is achieved.

Phase-locking and bistability in neuronal networks with synaptic depression

We consider a recurrent network of two oscillatory neurons that are coupled with inhibitory synapses. We use the phase response curves of the neurons and the properties of short-term synaptic depression to define Poincaré maps for the activity of the network. The fixed points of these maps correspond to phase-locked modes of the network. Using these maps, we analyze the conditions that allow short-term synaptic depression to lead to the existence of bistable phase-locked, periodic solutions. We show that bistability arises when either the phase response curve of the neuron or the short-term depression profile changes steeply enough. The results apply to any Type I oscillator and we illustrate our findings using the Quadratic Integrate-and-Fire and Morris-Lecar neuron models.

Mechanisms of generation of membrane potential resonance in a neuron with multiple resonant ionic currents

Neuronal membrane potential resonance (MPR) is associated with subthreshold and network oscillations. A number of voltage-gated ionic currents can contribute to the generation or amplification of MPR, but how the interaction of these currents with linear currents contributes to MPR is not well understood. We explored this in the pacemaker PD neurons of the crab pyloric network. The PD neuron MPR is sensitive to blockers of H- (I_H) and calcium-currents (I_Ca). We used the impedance profile of the biological PD neuron, measured in voltage clamp, to constrain parameter values of a conductance-based model using a genetic algorithm and obtained many optimal parameter combinations. Unlike most cases of MPR, in these optimal models, the values of resonant- (f_res) and phasonant- (f_{ϕ = 0}) frequencies were almost identical. Taking advantage of this fact, we linked the peak phase of ionic currents to their amplitude, in order to provide a mechanistic explanation the dependence of MPR on the I_Ca gating variable time constants. Additionally, we found that distinct pairwise correlations between I_Ca parameters contributed to the maintenance of f_res and resonance power (Q_Z). Measurements of the PD neuron MPR at more hyperpolarized voltages resulted in a reduction of f_res but no change in Q_Z. Constraining the optimal models using these data unmasked a positive correlation between the maximal conductances of I_H and I_Ca. Thus, although I_H is not necessary for MPR in this neuron type, it contributes indirectly by constraining the parameters of I_Ca.

Many neuron types exhibit membrane potential resonance (MPR) in which the neuron produces the largest response to oscillatory input at some preferred (resonant) frequency and, in many systems, the network frequency is correlated with neuronal MPR. MPR is captured by a peak in the impedance vs. frequency curve (Z-profile), which is shaped by the dynamics of voltage-gated ionic currents. Although neuron types can express variable levels of ionic currents, they may have a stable resonant frequency. We used the PD neuron of the crab pyloric network to understand how MPR emerges from the interplay of the biophysical properties of multiple ionic currents, each capable of generating resonance. We show the contribution of an inactivating current at the resonant frequency in terms of interacting time constants. We measured the Z-profile of the PD neuron and explored possible combinations of model parameters that fit this experimentally measured profile. We found that the Z-profile constrains and defines correlations among parameters associated with ionic currents. Furthermore, the resonant frequency and amplitude are sensitive to different parameter sets and can be preserved by co-varying pairs of parameters along their correlation lines. Furthermore, although a resonant current may be present in a neuron, it may not directly contribute to MPR, but constrain the properties of other currents that generate MPR. Finally, constraining model parameters further to those that modify their MPR properties to changes in voltage range produces maximal conductance correlations.

Functional roles of short-term synaptic plasticity with an emphasis on inhibition

Almost all synapses show activity-dependent dynamic changes in efficacy. Numerous studies have explored the mechanisms underlying different forms of short-term synaptic plasticity (STP), but the functional role of STP for circuit output and animal behavior is less understood. This is particularly true for inhibitory synapses that can play widely varied roles in circuit activity. We review recent findings on the role of synaptic STP in sensory, pattern generating, thalamocortical, and hippocampal networks, with a focus on synaptic inhibition. These studies show a variety of functions including sensory adaptation and gating, dynamic gain control and rhythm generation. Because experimental manipulations of STP are difficult and nonspecific, a clear demonstration of STP function often requires a combination of experimental and computational techniques.

The complexity of small circuits: the stomatogastric nervous system

The crustacean stomatogastric nervous system is a long-standing test bed for studies of circuit dynamics and neuromodulation. We give a brief update on the most recent work on this system, with an emphasis on the broader implications for understanding neural circuits. In particular, we focus on new findings underlining that different levels of dynamics taking place at different time scales all interact in multiple ways. Dynamics due to synaptic and intrinsic neuronal properties, neuromodulation, and long-term gene expression-dependent regulation are not independent, but influence each other. Extensive research on the stomatogastric system shows that these dynamic interactions convey robustness to circuit operation, while facilitating the flexibility of producing multiple circuit outputs.

Membrane potential resonance frequency directly influences network frequency through electrical coupling

Oscillatory networks often include neurons with membrane potential resonance, exhibiting a peak in the voltage amplitude as a function of current input at a nonzero (resonance) frequency (f_res). Although f_res has been correlated to the network frequency (f_net) in a variety of systems, a causal relationship between the two has not been established. We examine the hypothesis that combinations of biophysical parameters that shift f_res, without changing other attributes of the impedance profile, also shift f_net in the same direction. We test this hypothesis, computationally and experimentally, in an electrically coupled network consisting of intrinsic oscillator (O) and resonator (R) neurons. We use a two-cell model of such a network to show that increasing f_res of R directly increases f_net and that this effect becomes more prominent if the amplitude of resonance is increased. Notably, the effect of f_res on f_net is independent of the parameters that define the oscillator or the combination of parameters in R that produce the shift in f_res, as long as this combination produces the same impedance vs. frequency relationship. We use the dynamic clamp technique to experimentally verify the model predictions by connecting a model resonator to the pacemaker pyloric dilator neurons of the crab Cancer borealis pyloric network using electrical synapses and show that the pyloric network frequency can be shifted by changing f_res in the resonator. Our results provide compelling evidence that f_res and resonance amplitude strongly influence f_net, and therefore, modulators may target these attributes to modify rhythmic activity.

Tuning pathological brain oscillations with neurofeedback: a systems neuroscience framework

Neurofeedback (NFB) is emerging as a promising technique that enables self-regulation of ongoing brain oscillations. However, despite a rise in empirical evidence attesting to its clinical benefits, a solid theoretical basis is still lacking on the manner in which NFB is able to achieve these outcomes. The present work attempts to bring together various concepts from neurobiology, engineering, and dynamical systems so as to propose a contemporary theoretical framework for the mechanistic effects of NFB. The objective is to provide a firmly neurophysiological account of NFB, which goes beyond traditional behaviorist interpretations that attempt to explain psychological processes solely from a descriptive standpoint whilst treating the brain as a “black box”. To this end, we interlink evidence from experimental findings that encompass a broad range of intrinsic brain phenomena: starting from “bottom-up” mechanisms of neural synchronization, followed by “top-down” regulation of internal brain states, moving to dynamical systems plus control-theoretic principles, and concluding with activity-dependent as well as homeostatic forms of brain plasticity. In support of our framework, we examine the effects of NFB in several brain disorders, including attention-deficit hyperactivity (ADHD) and post-traumatic stress disorder (PTSD). In sum, it is argued that pathological oscillations emerge from an abnormal formation of brain-state attractor landscape(s). The central thesis put forward is that NFB tunes brain oscillations toward a homeostatic set-point which affords an optimal balance between network flexibility and stability (i.e., self-organised criticality (SOC)).