Transitions of Collective Motions Driven by Phase Resetting

Abrupt (i.e. step) environmental changes, such as natural disasters or the intervention of predators, can alter the internal dynamics of groups with active units, leading to the rapid destruction and/or restructuring of the group, with the emergence of new collective structures that endow the system with adaptability. Few studies, to date, have considered the influence of abrupt environmental changes on emergent behavior. Here, we use a model of active matter, the Belousov-Zhabotinsky (BZ) self-oscillating gel, to study the mechanism of formation and transition between modes of collective locomotion caused by changes of illumination intensity in arrays of interacting photosensitive active units. New forms of collective motion can be generated by step changes of illumination intensity. These transformations arise from the phase resetting and wave-signal regeneration induced by the abrupt parameter variation, while gradual change results in different evolution of collective motion. Our results not only suggest a novel mechanism for emergence, but also imply that new collective behaviors could be accessible via discontinuous parameter changes.

Epilepsy disrupts hippocampal phase precision and impairs working memory

OBJECTIVE

Working memory deficits are prevalent in childhood epilepsy. Working memory processing is thought to be supported by the phase of hippocampal neural oscillations. Disruptions in working memory have previously been linked to the occurrence of transient epileptic activity. This study aimed to resolve the associations between oscillatory neural activity, transient epileptiform events, and working memory in children with epilepsy.

METHODS

Intracranial recordings were acquired from stereotactically-implanted electrodes in the hippocampi, epileptogenic zones, and working memory-related networks of children with drug-resistant epilepsy during a 1-back working memory task. Interictal epileptic activity was captured using automated detectors. Hippocampal phase and interregional connectivity within working memory networks were indexed by Rayleigh Z and the phase difference derivative respectively. Trials with and without transient epileptiform events were compared.

RESULTS

Twelve children (mean age of 14.3 ± 2.8 years) with drug-resistant epilepsy were included in the study. In the absence of transient epileptic activity, significant delta and theta hippocampal phase resetting occurred in response to working memory stimulus presentation (Rz = 9, Rz = 8). Retrieval trials that were in-phase with the preferred phase angle were associated with faster reaction times (p = 0.01, p = 0.03). Concurrently, delta and theta coordinated interactions between the hippocampi and working memory-related networks were enhanced (PDD z-scores = 6-11). During retrieval trials with pre-encoding or pre-retrieval transient epileptic activity, phase resetting was attenuated (Rz = 5, Rz = 1), interregional connectivity was altered (PDD z-scores = 1-3), and reaction times were prolonged (p = 0.01, p = 0.03).

SIGNIFICANCE

This work highlights the role of hippocampal phase in working memory. We observe post-stimulus hippocampal phase resetting coincident with enhanced interregional connectivity. The precision of hippocampal phase predicts optimal working memory processing, and transient epileptic activity prolongs working memory processing. These findings can help guide future treatments aimed at restoring memory function in this patient population.

θ-Band Cortical Tracking of the Speech Envelope Shows the Linear Phase Property

When listening to speech, low-frequency cortical activity tracks the speech envelope. It remains controversial, however, whether such envelope-tracking neural activity reflects entrainment of neural oscillations or superposition of transient responses evoked by sound features. Recently, it is suggested that the phase of envelope-tracking activity can potentially distinguish entrained oscillations and evoked responses. Here, we analyze the phase of envelope-tracking in humans during passive listening, and observe that the phase lag between cortical activity and speech envelope tends to change linearly across frequency in the θ band (4–8 Hz), suggesting that the θ-band envelope-tracking activity can be readily modeled by evoked responses.

Phase Resetting in the Anterior Cingulate Cortex Subserves Childhood Attention and Is Impaired by Epilepsy

The neural mechanisms that underlie selective attention in children are poorly understood. By administering a set-shifting task to children with intracranial electrodes stereotactically implanted within anterior cingulate cortex (ACC) for epilepsy monitoring, we demonstrate that selective attention in a set-shifting task is dependent upon theta-band phase resetting immediately following stimulus onset and that the preferred theta phase angle is predictive of reaction time during attentional shift. We also observe selective enhancement of oscillatory coupling between the ACC and the dorsal attention network and decoupling with the default mode network during task performance. When transient focal epileptic activity occurs around the time of stimulus onset, phase resetting is impaired, connectivity changes with attentional and default mode networks are abolished, and reaction times are prolonged. The results of the present work highlight the fundamental mechanistic role of oscillatory phase in ACC in supporting attentional circuitry and present novel opportunities to remediate attention deficits in children with epilepsy.

Corrigendum: [A Comparative Study of Adaptive Interlimb Coordination Mechanisms for Self-Organized Robot Locomotion]

[This corrects the article DOI: 10.3389/frobt.2021.638684.].

A Comparative Study of Adaptive Interlimb Coordination Mechanisms for Self-Organized Robot Locomotion

Walking animals demonstrate impressive self-organized locomotion and adaptation to body property changes by skillfully manipulating their complicated and redundant musculoskeletal systems. Adaptive interlimb coordination plays a crucial role in this achievement. It has been identified that interlimb coordination is generated through dynamical interactions between the neural system, musculoskeletal system, and environment. Based on this principle, two classical interlimb coordination mechanisms (continuous phase modulation and phase resetting) have been proposed independently. These mechanisms use decoupled central pattern generators (CPGs) with sensory feedback, such as ground reaction forces (GRFs), to generate robot locomotion autonomously without predefining it (i.e., self-organized locomotion). A comparative study was conducted on the two mechanisms under decoupled CPG-based control implemented on a quadruped robot in simulation. Their characteristics were compared by observing their CPG phase convergence processes at different control parameter values. Additionally, the mechanisms were investigated when the robot faced various unexpected situations, such as noisy feedback, leg motor damage, and carrying a load. The comparative study reveals that the phase modulation and resetting mechanisms demonstrate satisfactory performance when they are subjected to symmetric and asymmetric GRF distributions, respectively. This work also suggests a strategy for the appropriate selection of adaptive interlimb coordination mechanisms under different conditions and for the optimal setting of their control parameter values to enhance their control performance.

The Auditory Steady-State Response: Electrophysiological Index for Sensory Processing Dysfunction in Psychiatric Disorders

Sensory processing is disrupted in several psychiatric disorders, including schizophrenia, bipolar disorder, and autism spectrum disorder. In this review, we focus on the electrophysiological auditory steady-state response (ASSR) driven by high-frequency stimulus trains as an index for disease-associated sensory processing deficits. The ASSR amplitude is suppressed within the gamma band (≥30 Hz) among these patients, suggesting an imbalance between GABAergic and N-methyl-D-aspartate (NMDA) receptor-mediated neurotransmission. The reduced power and synchronization of the 40-Hz ASSR are robust in patients with schizophrenia. In recent years, similar ASSR deficits at gamma frequencies have also been reported in patients with bipolar disorder and autism spectrum disorder. We summarize ASSR abnormalities in each of these psychiatric disorders and suggest that the observed commonalities reflect shared pathophysiological mechanisms. We reviewed studies on phase resetting in which a salient sensory stimulus affects ASSR. Phase resetting induces the reduction of both the amplitude and phase of ASSR. Moreover, phase resetting is also affected by rare auditory stimulus patterns or superimposed stimuli of other modalities. Thus, sensory memory and multisensory integration can be investigated using phase resetting of ASSR. Here, we propose that ASSR amplitude, phase, and resetting responses are sensitive indices for investigating sensory processing dysfunction in psychiatric disorders.

Theta Phase Synchrony Is Sensitive to Corollary Discharge Abnormalities in Early Illness Schizophrenia but Not in the Psychosis Risk Syndrome

BACKGROUND

Prior studies have shown that the auditory N1 event-related potential component elicited by self-generated vocalizations is reduced relative to played back vocalizations, putatively reflecting a corollary discharge mechanism. Schizophrenia patients and psychosis risk syndrome (PRS) youth show deficient N1 suppression during vocalization, consistent with corollary discharge dysfunction. Because N1 is an admixture of theta (4-7 Hz) power and phase synchrony, we examined their contributions to N1 suppression during vocalization, as well as their sensitivity, relative to N1, to corollary discharge dysfunction in schizophrenia and PRS individuals.

METHODS

Theta phase and power values were extracted from electroencephalography data acquired from PRS youth (n = 71), early illness schizophrenia patients (ESZ; n = 84), and healthy controls (HCs; n = 103) as they said "ah" (Talk) and then listened to the playback of their vocalizations (Listen). A principal component analysis extracted theta intertrial coherence (ITC; phase consistency) and event-related spectral power, peaking in the N1 latency range. Talk-Listen suppression scores were analyzed.

RESULTS

Talk-Listen suppression was greater for theta ITC (Cohen's d = 1.46) than for N1 in HC (d = 0.63). Both were deficient in ESZ, but only N1 suppression was deficient in PRS. When deprived of variance shared with theta ITC suppression, N1 suppression no longer differentiated ESZ and PRS individuals from HC. Deficits in theta ITC suppression were correlated with delusions (P = .007) in ESZ. Theta power suppression did not differentiate groups.

CONCLUSIONS

Theta ITC-suppression during vocalization is a more sensitive index of corollary discharge-mediated auditory cortical suppression than N1 suppression and is more sensitive to corollary discharge dysfunction in ESZ than in PRS individuals.

Contribution of Phase Resetting to Adaptive Rhythm Control in Human Walking Based on the Phase Response Curves of a Neuromusculoskeletal Model

Humans walk adaptively in varying environments by manipulating their complicated and redundant musculoskeletal system. Although the central pattern generators in the spinal cord are largely responsible for adaptive walking through sensory-motor coordination, it remains unclear what neural mechanisms determine walking adaptability. It has been reported that locomotor rhythm and phase are regulated by the production of phase shift and rhythm resetting (phase resetting) for periodic motor commands in response to sensory feedback and perturbation. While the phase resetting has been suggested to make a large contribution to adaptive walking, it has only been investigated based on fictive locomotion in decerebrate cats, and thus it remains unclear if human motor control has such a rhythm regulation mechanism during walking. In our previous work, we incorporated a phase resetting mechanism into a motor control model and demonstrated that it improves the stability and robustness of walking through forward dynamic simulations of a human musculoskeletal model. However, this did not necessarily verify that phase resetting plays a role in human motor control. In our other previous work, we used kinematic measurements of human walking to identify the phase response curve (PRC), which explains phase-dependent responses of a limit cycle oscillator to a perturbation. This revealed how human walking rhythm is regulated by perturbations. In this study, we integrated these two approaches using a physical model and identification of the PRC to examine the hypothesis that phase resetting plays a role in the control of walking rhythm in humans. More specifically, we calculated the PRC using our neuromusculoskeletal model in the same way as our previous human experiment. In particular, we compared the PRCs calculated from two different models with and without phase resetting while referring to the PRC for humans. As a result, although the PRC for the model without phase resetting did not show any characteristic shape, the PRC for the model with phase resetting showed a characteristic phase-dependent shape with trends similar to those of the PRC for humans. These results support our hypothesis and will improve our understanding of adaptive rhythm control in human walking.

Indirect pathway control of firing rate and pattern in the substantia nigra pars reticulata

Unitary pallido-nigral synaptic currents were measured using optogenetic stimulation, which activated up to three unitary synaptic inputs to each substantia nigra pars reticulata (SNr) cell. Episodic barrages of synaptic conductances were generated based on in vivo firing patterns of globus pallidus pars externa (GPe) cells and applied to SNr cells using conductance clamp. Barrage inputs were compared to continuous step conductances with the same mean. Barrage inputs and steps both slowed SNr neuron firing and produced disinhibition responses seen in peristimulus histograms. Barrages were less effective than steps at producing inhibition and disinhibition responses. Barrages, but not steps, produced irregular firing during the inhibitory response. Phase models of SNr neurons were constructed from their phase-resetting curves. The phase models reproduced the inhibition and disinhibition responses to the same inputs applied to the neurons. The disinhibition response did not require rebound currents but arose from reset of the cells' oscillation. The differences in firing rate and irregularity in response to barrage and step inhibition resulted from the high sensitivity of SNr neurons to inhibition at late phases in their intrinsic oscillation. During step inhibition, cells continued rhythmic firing at a reduced rate. During barrages, brief bouts of intense inhibition stalled the cells' phase evolution late in their cycle, close to firing, and even very brief respites from inhibition rapidly released single action potentials. The SNr cell firing pattern reflected the fine structure of the synaptic barrage from GPe, as well as its onset and offset.NEW & NOTEWORTHY The pallido-nigral pathway connects the striatum to spontaneously active basal ganglia output neurons in the substantia nigra. Each substantia nigra neuron receives powerful inhibitory synaptic connections from a small group of globus pallidus cells and may fire during pauses in pallidal activity. Despite lacking any hyperpolarization-activated rebound currents, they fire quickly to even brief pauses in the pallido-nigral inhibition. The mechanism of their rapid disinhibitory response is explained by features of their phase-resetting curves.

Change-Related Acceleration Effects on Auditory Steady State Response

Rapid detection of sensory changes is important for survival. We have previously used change-related cortical responses to study the change detection system and found that the generation of a change-related response was based on sensory memory and comparison processes. However, it remains unclear whether change-related cortical responses reflect processing speed. In the present study, we simultaneously recorded the auditory steady-state response (ASSR) and change-related response using magnetoencephalography to investigate the acceleration effects of sensory change events. Overall, 13 healthy human subjects (four females and nine males) completed an oddball paradigm with a sudden change in sound pressure used as the test stimulus, i.e., the control stimulus was a train of 25-ms pure tones at 75 dB for 1,200 ms, whereas the 29th sound at 700 ms of the test stimulus was replaced with a 90-dB tone. Thereafter, we compared the latency of ASSR among four probabilities of test stimulus (0, 25, 75, and 100%). For both the control and test stimulus, stronger effects of acceleration on ASSR were observed when the stimulus was rarer. This finding indicates that ASSR and change-related cortical response depend on physical changes as well as sensory memory and comparison processes. ASSR was modulated without changes in peripheral inputs, and brain areas higher than the primary cortex could be involved in exerting acceleration effects. Furthermore, the reduced latency of ASSR clearly indicated that a new sensory event increased the speed of ongoing sensory processing. Therefore, changes in the latency of ASSR are a sensitive index of accelerated processing.

Frequency-dependent entrainment of striatal fast-spiking interneurons

Striatal fast-spiking interneurons (FSIs) fire in variable-length runs of action potentials at 20-200 spikes/s separated by pauses. In vivo, or with fluctuating applied current, both runs and pauses become briefer and more variable. During runs, spikes are entrained specifically to gamma-frequency components of the input fluctuations. We stimulated parvalbumin-expressing striatal FSIs in mouse brain slices with broadband noise currents added to direct current steps and measured spike entrainment across all frequencies. As the constant current level was increased, FSIs produced longer runs and showed sharper frequency tuning, with best entrainment at the stimulus frequency matching their intrarun firing rate. We separated the contributions of previous spikes from that of the fluctuating stimulus, revealing a strong contribution of previous action potentials to gamma-frequency entrainment. In contrast, after subtraction of the effect inherited from the previous spike, the remaining stimulus contribution to spike generation was less sharply tuned, showing a larger contribution of lower frequencies. The frequency specificity of entrainment within a run was reproduced with a phase resetting model based on experimentally measured phase resetting curves of the same FSIs. In the model, broadly tuned phase entrainment for the first spike in a run evolved into sharply tuned gamma entrainment over the next few spikes. The data and modeling results indicate that for FSIs firing in brief runs and pauses firing within runs is entrained by gamma-frequency components of the input, whereas the onset timing of runs may be sensitive to a wider range of stimulus frequency components.NEW & NOTEWORTHY Specific types of neurons entrain their spikes to particular oscillation frequencies in their synaptic input. This entrainment is commonly understood in terms of the subthreshold voltage response, but how this translates to spiking is not clear. We show that in striatal fast-spiking interneurons, entrainment to gamma-frequency input depends on rhythmic spike runs and is explained by the phase resetting curve, whereas run initiation can be triggered by a broad range of input frequencies.

Oxygen and Carbon Dioxide Rhythms Are Circadian Clock Controlled and Differentially Directed by Behavioral Signals

Daily rhythms in animal physiology are driven by endogenous circadian clocks in part through rest-activity and feeding-fasting cycles. Here, we examined principles that govern daily respiration. We monitored oxygen consumption and carbon dioxide release, as well as tissue oxygenation in freely moving animals to specifically dissect the role of circadian clocks and feeding time on daily respiration. We found that daily rhythms in oxygen and carbon dioxide are clock controlled and that time-restricted feeding restores their rhythmicity in clock-deficient mice. Remarkably, day-time feeding dissociated oxygen rhythms from carbon dioxide oscillations, whereby oxygen followed activity, and carbon dioxide was shifted and aligned with food intake. In addition, changes in carbon dioxide levels altered clock gene expression and phase shifted the clock. Collectively, our findings indicate that oxygen and carbon dioxide rhythms are clock controlled and feeding regulated and support a potential role for carbon dioxide in phase resetting peripheral clocks upon feeding.

Resetting the Respiratory Rhythm with a Spinal Central Pattern Generator

There is evidence that a variety of central and afferent stimuli, including swallowing, can produce phase resetting in the respiratory rhythmicity. Also, there are reports about the intrinsic linkage between locomotion and respiration. However, little is known about the interaction between the central pattern generators (CPGs) for scratching and respiration. The present study aims to examine whether the activation of scratching CPG produces phase resetting of the respiratory rhythm. We employed decerebrate cats to apply brief tactile stimuli to the pinna during the inspiratory-expiratory transition. We observed that those stimuli to the pinna not eliciting fictive scratching did not reset the respiratory rhythm. However, when the pinna stimuli elicited fictive scratching, then the respiratory rhythm exhibited a significant phase resetting. We also found interneurons in the medulla oblongata exhibiting phase resetting related to scratching-CPG episodes. This second finding suggests that this type of resetting involves brainstem components of the respiratory CPG. These results shed new light on the resetting action from a spinal CPG on the respiratory rhythm.

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

We show how to predict whether a neural network will exhibit global synchrony (a one-cluster state) or a two-cluster state based on the assumption of pulsatile coupling and critically dependent upon the phase response curve (PRC) generated by the appropriate perturbation from a partner cluster. Our results hold for a monotonically increasing (meaning longer delays as the phase increases) PRC, which likely characterizes inhibitory fast-spiking basket and cortical low-threshold-spiking interneurons in response to strong inhibition. Conduction delays stabilize synchrony for this PRC shape, whereas they destroy two-cluster states, the former by avoiding a destabilizing discontinuity and the latter by approaching it. With conduction delays, stronger coupling strength can promote a one-cluster state, so the weak coupling limit is not applicable here. We show how jitter can destabilize global synchrony but not a two-cluster state. Local stability of global synchrony in an all-to-all network does not guarantee that global synchrony can be observed in an appropriately scaled sparsely connected network; the basin of attraction can be inferred from the PRC and must be sufficiently large. Two-cluster synchrony is not obviously different from one-cluster synchrony in the presence of noise and may be the actual substrate for oscillations observed in the local field potential (LFP) and the electroencephalogram (EEG) in situations where global synchrony is not possible. Transitions between cluster states may change the frequency of the rhythms observed in the LFP or EEG. Transitions between cluster states within an inhibitory subnetwork may allow more effective recruitment of pyramidal neurons into the network rhythm. NEW & NOTEWORTHY We show that jitter induced by sparse connectivity can destabilize global synchrony but not a two-cluster state with two smaller clusters firing alternately. On the other hand, conduction delays stabilize synchrony and destroy two-cluster states. These results hold if each cluster exhibits a phase response curve similar to one that characterizes fast-spiking basket and cortical low-threshold-spiking cells for strong inhibition. Either a two-cluster or a one-cluster state might provide the oscillatory substrate for neural computations.

Neuronal Dynamics Underlying Communication Signals in a Weakly Electric Fish: Implications for Connectivity in a Pacemaker Network

Neuronal networks can produce stable oscillations and synchrony that are under tight control yet flexible enough to rapidly switch between dynamical states. The pacemaker nucleus in the weakly electric fish comprises a network of electrically coupled neurons that fire synchronously at high frequency. This activity sets the timing for an oscillating electric organ discharge with the lowest cycle-to-cycle variability of all known biological oscillators. Despite this high temporal precision, pacemaker activity is behaviorally modulated on millisecond time-scales for the generation of electrocommunication signals. The network mechanisms that allow for this combination of stability and flexibility are not well understood. In this study, we use an in vitro pacemaker preparation from Apteronotus leptorhynchus to characterize the neural responses elicited by the synaptic inputs underlying electrocommunication. These responses involve a variable increase in firing frequency and a prominent desynchronization of neurons that recovers within 5 oscillation cycles. Using a previously developed computational model of the pacemaker network, we show that the frequency changes and rapid resynchronization observed experimentally are most easily explained when model neurons are interconnected more densely and with higher coupling strengths than suggested by published data. We suggest that the pacemaker network achieves both stability and flexibility by balancing coupling strength with interconnectivity and that variation in these network features may provide a substrate for species-specific evolution of electrocommunication signals.

Disruption in neural phase synchrony is related to identification of inattentional deafness in real-world setting

Individuals often have reduced ability to hear alarms in real world situations (e.g., anesthesia monitoring, flying airplanes) when attention is focused on another task, sometimes with devastating consequences. This phenomenon is called inattentional deafness and usually occurs under critical high workload conditions. It is difficult to simulate the critical nature of these tasks in the laboratory. In this study, dry electroencephalography is used to investigate inattentional deafness in real flight while piloting an airplane. The pilots participating in the experiment responded to audio alarms while experiencing critical high workload situations. It was found that missed relative to detected alarms were marked by reduced stimulus evoked phase synchrony in theta and alpha frequencies (6-14 Hz) from 120 to 230 ms poststimulus onset. Correlation of alarm detection performance with intertrial coherence measures of neural phase synchrony showed different frequency and time ranges for detected and missed alarms. These results are consistent with selective attentional processes actively disrupting oscillatory coherence in sensory networks not involved with the primary task (piloting in this case) under critical high load conditions. This hypothesis is corroborated by analyses of flight parameters showing greater maneuvering associated with difficult phases of flight occurring during missed alarms. Our results suggest modulation of neural oscillation is a general mechanism of attention utilizing enhancement of phase synchrony to sharpen alarm perception during successful divided attention, and disruption of phase synchrony in brain networks when attentional demands of the primary task are great, such as in the case of inattentional deafness.

Inappropriate Timing of Swallow in the Respiratory Cycle Causes Breathing-Swallowing Discoordination

Rationale: Swallowing during inspiration and swallowing immediately followed by inspiration increase the chances of aspiration and may cause disease exacerbation. However, the mechanisms by which such breathing–swallowing discoordination occurs are not well-understood.

Objectives: We hypothesized that breathing–swallowing discoordination occurs when the timing of the swallow in the respiratory cycle is inappropriate. To test this hypothesis, we monitored respiration and swallowing activity in healthy subjects and in patients with dysphagia using a non-invasive swallowing monitoring system.

Measurements and Main Results: The parameters measured included the timing of swallow in the respiratory cycle, swallowing latency (interval between the onset of respiratory pause and the onset of swallow), pause duration (duration of respiratory pause for swallowing), and the breathing–swallowing coordination pattern. We classified swallows that closely follow inspiration (I) as I-SW, whereas those that precede I as SW-I pattern. Patients with dysphagia had prolonged swallowing latency and pause duration, and tended to have I-SW or SW-I patterns reflecting breathing–swallows discoordination.

Conclusions: We conclude that swallows at inappropriate timing in the respiratory cycle cause breathing–swallowing discoordination, and the prolongation of swallowing latency leads to delayed timing of the swallow, and results in an increase in the SW-I pattern in patients with dysphagia.

An Unstable Singularity Underlies Stochastic Phasing of the Circadian Clock in Individual Cyanobacterial Cells

The endogenous circadian clock synchronizes with environmental time by appropriately resetting its phase in response to external cues. Of note, some resetting stimuli induce attenuated oscillations of clock output, which has been observed at the population-level in several organisms and in studies of individual humans. To investigate what is happening in individual cellular clocks, we studied the unicellular cyanobacterium S. elongatus. By measuring its phase-resetting responses to temperature changes, we found that population-level arrhythmicity occurs when certain perturbations cause stochastic phases of oscillations in individual cells. Combining modeling with experiments, we related stochastic phasing to the dynamical structure of the cyanobacterial clock as an oscillator and explored the physiological relevance of the oscillator structure for accurately timed rhythmicity in changing environmental conditions. Our findings and approach can be applied to other biological oscillators.

Predicting the response of striatal spiny neurons to sinusoidal input

Spike-timing effects of small-amplitude sinusoidal currents were measured in mouse striatal spiny neurons firing repetitively. Spike-timing reliability varied with the stimulus frequency. For frequencies near the cell's firing rate, the cells altered firing rate to match the stimulus and became phase locked to it. The stimulus phase of firing during lock depended on the stimulus frequency relative to the cell's unperturbed firing rate. Interspike intervals during sinusoidal stimulation were predicted using an iterative map constructed from the cells' phase-resetting curve. Variability of interspike intervals was reduced by stimulation at all frequencies higher than about half the cell's unperturbed rate, and interspike intervals were accurately predicted by the map. Long sequences of spike times were predicted by iterating on the map. The accuracy of that prediction varied with frequency. Spike time predictability was highest near and during phase lock. The map predicted the phase of firing on the input and its dependence on stimulus frequency. Prediction errors, when they occurred, were of two kinds: unpredicted variation in interspike interval from intrinsic cell noise and accumulation of prediction errors from previous interspike intervals. Each type of prediction error arose from a different mechanism, and their impact was also predicted from the phase model. When two oscillatory input currents were presented simultaneously, striatal neurons responded selectively to only one of them, the one closest in frequency to the cell's unperturbed firing rate. Their spike times encoded the frequency and phase of that single oscillatory input.NEW & NOTEWORTHY During repetitive firing, the timing of action potentials is determined by the interaction between the input and voltage-sensitive currents throughout the interspike interval. This interaction is encapsulated in the neuron's phase-resetting curve. The phase-resetting curve predicted spike timing to small sinusoidal currents over a wide range of stimulus frequencies. Firing patterns were most sensitive to oscillatory components near the cell's own firing rate, even in the presence of noise and other inputs.

The Art of Grid Fields: Geometry of Neuronal Time

The discovery of grid cells in the entorhinal cortex has both elucidated our understanding of spatial representations in the brain, and germinated a large number of theoretical models regarding the mechanisms of these cells' striking spatial firing characteristics. These models cross multiple neurobiological levels that include intrinsic membrane resonance, dendritic integration, after hyperpolarization characteristics and attractor dynamics. Despite the breadth of the models, to our knowledge, parallels can be drawn between grid fields and other temporal dynamics observed in nature, much of which was described by Art Winfree and colleagues long before the initial description of grid fields. Using theoretical and mathematical investigations of oscillators, in a wide array of mediums far from the neurobiology of grid cells, Art Winfree has provided a substantial amount of research with significant and profound similarities. These theories provide specific inferences into the biological mechanisms and extraordinary resemblances across phenomenon. Therefore, this manuscript provides a novel interpretation on the phenomenon of grid fields, from the perspective of coupled oscillators, postulating that grid fields are the spatial representation of phase resetting curves in the brain. In contrast to prior models of gird cells, the current manuscript provides a sketch by which a small network of neurons, each with oscillatory components can operate to form grid cells, perhaps providing a unique hybrid between the competing attractor neural network and oscillatory interference models. The intention of this new interpretation of the data is to encourage novel testable hypotheses.

Oscillators and Oscillations in the Basal Ganglia

What is the meaning of an action potential? There must be different answers for neurons that fire spontaneously, even in the absence of synaptic input, and those driven to fire from a resting membrane potential. In spontaneously firing neurons, the occurrence of the next action potential is guaranteed; only variations in its timing can carry the message. In the basal ganglia, the globus pallidus, the substantia nigra, and the subthalamic nucleus consist of neurons firing spontaneously. They each receive thousands of synaptic inputs, but these are not required to maintain their background firing. Instead, synaptic interactions among basal ganglia nuclei comprise a system of coupled oscillators that produces a complex resting pattern of activity. Normally, this pattern is highly irregular and uncorrelated, so that the firing of each cell is statistically independent of the others. This maximizes the potential information that may be transmitted by the basal ganglia to its target structures. In Parkinson's disease, the resting pattern of activity is dominated by a slow oscillation shared by nearly all of the neurons. Treatment with deep brain stimulation may gain its therapeutic value by disrupting this shared pathological oscillation, and restoring independent action by each neuron in the network.

The proportion of light-responsive neurons determines the limit cycle properties of the suprachiasmatic nucleus

In mammals, the central clock in the suprachiasmatic nucleus (SCN) controls physiological and behavioral circadian rhythms and is entrained to the external light-dark cycle. The ability of the SCN to entrain can be measured by exposing the animal to a light-dark cycle with a duration that deviates from 24 h (T-cycles); a wider entrainment range reflects a higher ability to entrain. The neurons of the SCN are either light responsive or light unresponsive and are mutually synchronized. The coupling and synchronization between individual SCN neurons and between groups of neurons within the SCN influence the SCN's ability to entrain. Some studies suggest that enhanced coupling decreases the entrainment range, whereas others suggest that enhanced coupling increases the entrainment range. The latter results are surprising, as they are not consistent with the prevalent assumption that the SCN is a limit cycle oscillator that has larger phase shifts when the amplitude is smaller. Here, we used the Poincaré and Goodwin models to test entrainment properties using various proportions of neurons that are responsive to an external stimulus. If all neurons receive external input, the SCN shows limit cycle behavior in all conditions. If all neurons do not receive light input, we found that the entrainment range of the SCN was positively related to coupling strength when coupling was weak. When coupling strength was stronger and above a critical value, the entrainment range was negatively correlated with coupling strength. The results obtained from our simulations were confirmed by analytical studies. Thus, the limit cycle behavior of the SCN appears to be critically dependent on the coupling strength among the neurons and the proportion of neurons that respond to the entraining stimulus.

Effect of phase response curve skew on synchronization with and without conduction delays

A central problem in cortical processing including sensory binding and attentional gating is how neurons can synchronize their responses with zero or near-zero time lag. For a spontaneously firing neuron, an input from another neuron can delay or advance the next spike by different amounts depending upon the timing of the input relative to the previous spike. This information constitutes the phase response curve (PRC). We present a simple graphical method for determining the effect of PRC shape on synchronization tendencies and illustrate it using type 1 PRCs, which consist entirely of advances (delays) in response to excitation (inhibition). We obtained the following generic solutions for type 1 PRCs, which include the pulse-coupled leaky integrate and fire model. For pairs with mutual excitation, exact synchrony can be stable for strong coupling because of the stabilizing effect of the causal limit region of the PRC in which an input triggers a spike immediately upon arrival. However, synchrony is unstable for short delays, because delayed inputs arrive during a refractory period and cannot trigger an immediate spike. Right skew destabilizes antiphase and enables modes with time lags that grow as the conduction delay is increased. Therefore, right skew favors near synchrony at short conduction delays and a gradual transition between synchrony and antiphase for pairs coupled by mutual excitation. For pairs with mutual inhibition, zero time lag synchrony is stable for conduction delays ranging from zero to a substantial fraction of the period for pairs. However, for right skew there is a preferred antiphase mode at short delays. In contrast to mutual excitation, left skew destabilizes antiphase for mutual inhibition so that synchrony dominates at short delays as well. These pairwise synchronization tendencies constrain the synchronization properties of neurons embedded in larger networks.

Oscillatory activity, phase differences, and phase resetting in the inferior olivary nucleus

The generation of temporal patterns is one of the most fascinating functions of the brain. Unlike the response to external stimuli temporal patterns are generated within the system and recalled for a specific use. To generate temporal patterns one needs a timing machine, a “master clock” that determines the temporal framework within which temporal patterns can be generated and implemented. Here we present the concept that in this putative “master clock” phase and frequency interact to generate temporal patterns. We define the requirements for a neuronal “master clock” to be both reliable and versatile. We introduce this concept within the inferior olive nucleus which at least by some scientists is regarded as the source of timing for cerebellar function. We review the basic properties of the subthreshold oscillation recorded from olivary neurons, analyze the phase relationships between neurons and demonstrate that the phase and onset of oscillation is tightly controlled by synaptic input. These properties endowed the olivary nucleus with the ability to act as a “master clock.”

Estimation of the transmission time of stimulus-locked responses: modelling and stochastic phase resetting analysis

A model of two coupled phase oscillators is studied, where both oscillators are subject to random forces but only one oscillator is repetitively stimulated with a pulsatile stimulus. A pulse causes a reset, which is transmitted to the other oscillator via the coupling. The transmission time of the cross-trial (CT) averaged responses, i.e. the difference in time between the maxima of the CT averaged responses of both oscillators differs from the time difference between the maxima of the oscillators' resets. In fact, the transmission time of the CT averaged responses directly corresponds to the phase difference in the stable synchronized state with integer multiples of the oscillators' mean period added to it. With CT averaged responses it is impossible to reliably estimate the time elapsing, owing to the stimulus' action being transmitted between the two oscillators.

Midbrain raphe modulation of nonphotic circadian clock resetting and 5-HT release in the mammalian suprachiasmatic nucleus

Serotonin (5-HT) is an important regulator of the mammalian circadian clock of the suprachiasmatic nucleus (SCN); however, critical questions remain concerning the control of serotonergic activity in the SCN and how this relates to the putative clock-resetting actions of 5-HT. Previously, we reported that electrical stimulation of the dorsal raphe nucleus (DRN) or median raphe nucleus (MRN) in hamsters evoked 5-HT release in the SCN. This DRN-stimulated 5-HT release was blocked by systemic injection of 5-HT antagonists, indicating a 5-HT receptor-mediated pathway from the DRN to the SCN. In the present study, targeted injections of the 5-HT1,2,7 antagonist metergoline or the selective 5-HT7 antagonist DR4004 into the DRN or MRN attenuated DRN-electrically stimulated SCN 5-HT release, supporting a multisynaptic DRN-->MRN-->SCN route. Intra-DRN and intra-MRN injections of the GABA(A) antagonist bicuculline significantly stimulated SCN 5-HT release, whereas intra-DRN or intra-MRN injections of the GABAA agonist muscimol suppressed this release. The 5-HT release induced by intra-DRN bicuculline was also blocked by co-injection of DR4004. In complementary behavioral trials, SCN 5-HT release associated with a phase-advancing sleep deprivation stimulus at midday was prevented by intra-DRN injection of metergoline. Also, phase-advance shifts induced by novel wheel access at midday were suppressed, but not blocked, by intra-DRN injection of DR4004 or muscimol. These results indicate that 5-HT7 and GABAergic receptors of the DRN and MRN regulate behaviorally induced 5-HT release in the SCN, and that DRN output modulates nonphotic phase-resetting responses.