While oscillations of the local field potential (LFP) are commonly attributed to the synchronization of neuronal firing rate on the same time scale, their relationship to coincident spiking in the millisecond range is unknown. Here, we present experimental evidence to reconcile the notions of synchrony at the level of spiking and at the mesoscopic scale. We demonstrate that only in time intervals of significant spike synchrony that cannot be explained on the basis of firing rates, coincident spikes are better phase locked to the LFP than predicted by the locking of the individual spikes. This effect is enhanced in periods of large LFP amplitudes. A quantitative model explains the LFP dynamics by the orchestrated spiking activity in neuronal groups that contribute the observed surplus synchrony. From the correlation analysis, we infer that neurons participate in different constellations but contribute only a fraction of their spikes to temporally precise spike configurations. This finding provides direct evidence for the hypothesized relation that precise spike synchrony constitutes a major temporally and spatially organized component of the LFP.
motor cortex; oscillation; population signals; synchrony
Neural activity in the brain of parkinsonian patients is characterized by the intermittently synchronized oscillatory dynamics. This imperfect synchronization, observed in the beta frequency band, is believed to be related to the hypokinetic motor symptoms of the disorder. Our study explores potential mechanisms behind this intermittent synchrony. We study the response of a bursting pallidal neuron to different patterns of synaptic input from subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe) neuron is sensitive to the phase of the input from the STN cell and can exhibit intermittent phase-locking with the input in the beta band. The temporal properties of this intermittent phase-locking show similarities to the intermittent synchronization observed in experiments. We also study the synchronization of GPe cells to synaptic input from the STN cell with dependence on the dopamine-modulated parameters. Earlier studies showed how the strengthening of dopamine-modulated coupling may lead to transitions from non-synchronized to partially synchronized dynamics, typical in Parkinson's disease. However, dopamine also affects the cellular properties of neurons. We show how the changes in firing patterns of STN neuron due to the lack of dopamine may lead to transition from a lower to a higher coherent state, roughly matching the synchrony levels observed in basal ganglia in normal and parkinsonian states. The intermittent nature of the neural beta band synchrony in Parkinson's disease is achieved in the model due to the interplay of the timing of STN input to pallidum and pallidal neuronal dynamics, resulting in sensitivity of pallidal output to the phase of the arriving STN input. Thus the mechanism considered here (the change in firing pattern of subthalamic neurons through the dopamine-induced change of membrane properties) may be one of the potential mechanisms responsible for the generation of the intermittent synchronization observed in Parkinson's disease.
We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase-lock spike-to-spike for strong mutual coupling. But the shared input can desynchronize the locked spike-pairs by selectively eliminating the lagging spike or modulating its timing with respect to the leading spike depending on their separation time window. Such loss of synchrony is also found in a large network of sparsely coupled heterogeneous spiking neurons receiving shared input.
Ongoing interactions among cortical neurons often manifest as network-level synchrony. Understanding the spatiotemporal dynamics of such spontaneous synchrony is important because it may 1) influence network response to input, 2) shape activity-dependent microcircuit structure, and 3) reveal fundamental network properties, such as an imbalance of excitation (E) and inhibition (I). Here we delineate the spatiotemporal character of spontaneous synchrony in rat cortex slice cultures and a computational model over a range of different E-I conditions including disfacilitated (antagonized AMPA, NMDA receptors), unperturbed, and disinhibited (antagonized GABAA receptors). Local field potential was recorded with multi-electrode arrays during spontaneous burst activity. Synchrony among neuronal groups was quantified based on phase-locking among recording sites. As network excitability was increased from low to high, we discovered three phenomena at an intermediate excitability level: 1) onset of synchrony, 2) maximized variability of synchrony, and 3) neuronal avalanches. Our computational model predicted that these three features occur when the network operates near a unique balanced E-I condition called ‘criticality’. These results were invariant to changes in the measurement spatial extent, spatial resolution, and frequency bands. Our findings indicate that moderate average synchrony, which is required to avoid pathology, occurs over a limited range of E-I conditions and emerges together with maximally variable synchrony. If variable synchrony is detrimental to cortical function, this is a cost paid for moderate average synchrony. However, if variable synchrony is beneficial, then by operating near criticality the cortex may doubly benefit from moderate mean and maximized variability of synchrony.
multi-site electrode recording; synchrony; phase synchrony; entropy; neuronal avalanches; neural excitability; critical phenomena
A phase-locked loop (PLL) model of the response of the postural control system to periodic platform motion is proposed. The PLL model is based on the hypothesis that quiet standing (QS) postural sway can be characterized as a weak sinusoidal oscillation corrupted with noise. Because the signal to noise ratio is quite low, the characteristics of the QS oscillator are not measured directly from the QS sway, instead they are inferred from the response of the oscillator to periodic motion of the platform. When a sinusoidal stimulus is applied, the QS oscillator changes speed as needed until its frequency matches that of the platform, thus achieving phase lock in a manner consistent with a PLL control mechanism. The PLL model is highly effective in representing the frequency, amplitude, and phase shift of the sinusoidal component of the phase-locked response over a range of platform frequencies and amplitudes. Qualitative analysis of the PLL control mechanism indicates that there is a finite range of frequencies over which phase lock is possible, and that the size of this capture range decreases with decreasing platform amplitude. The PLL model was tested experimentally using nine healthy subjects and the results reveal good agreement with a mean phase shift error of 13.7° and a mean amplitude error of 0.8 mm.
Mathematical model; phase-locked loop; postural control
The goal of this research was to investigate the changes in neural processing in mild cognitive impairment. We measured phase synchrony, amplitudes, and event-related potentials in veridical and false memory to determine whether these differed in participants with mild cognitive impairment compared with typical, age-matched controls. Empirical mode decomposition phase locking analysis was used to assess synchrony, which is the first time this analysis technique has been applied in a complex cognitive task such as memory processing. The technique allowed assessment of changes in frontal and parietal cortex connectivity over time during a memory task, without a priori selection of frequency ranges, which has been shown previously to influence synchrony detection. Phase synchrony differed significantly in its timing and degree between participant groups in the theta and alpha frequency ranges. Timing differences suggested greater dependence on gist memory in the presence of mild cognitive impairment. The group with mild cognitive impairment had significantly more frontal theta phase locking than the controls in the absence of a significant behavioural difference in the task, providing new evidence for compensatory processing in the former group. Both groups showed greater frontal phase locking during false than true memory, suggesting increased searching when no actual memory trace was found. Significant inter-group differences in frontal alpha phase locking provided support for a role for lower and upper alpha oscillations in memory processing. Finally, fronto-parietal interaction was significantly reduced in the group with mild cognitive impairment, supporting the notion that mild cognitive impairment could represent an early stage in Alzheimer’s disease, which has been described as a ‘disconnection syndrome’.
Neuronal interactions form the basis for our brain function, and oscillations and synchrony are the principal candidates for mediating them in the cortical networks. Phase synchrony, where oscillatory neuronal ensembles directly synchronize their phases, enables precise integration between separated brain regions. However, it is unclear how neuronal interactions are dynamically coordinated in space and over time. Cross-scale effects have been proposed to be responsible for linking levels of processing hierarchy and to regulate neuronal dynamics. Most notably, nested oscillations, where the phase of a neuronal oscillation modulates the amplitude of a faster one, may locally integrate neuronal activities in distinct frequency bands. Yet, hierarchical control of inter-areal synchrony could provide a more comprehensive view to the dynamical structure of oscillatory interdependencies in the human brain. In this study, the notion of nested oscillations is extended to a cross-frequency and inter-areal model of oscillatory interactions. In this model, the phase of a slower oscillation modulates inter-areal synchrony in a higher frequency band. This would allow cross-scale integration of global interactions and, thus, offers a mechanism for binding distributed neuronal activities. We show that inter-areal phase synchrony can be modulated by the phase of a slower neuronal oscillation using magnetoencephalography (MEG). This effect is the most pronounced at frequencies below 35 Hz. Importantly, changes in oscillation amplitudes did not explain the findings. We expect that the novel cross-frequency interaction could offer new ways to understand the flexible but accurate dynamic organization of ongoing neuronal oscillations and synchrony.
neuronal oscillations; magnetoencephalography; nested oscillations; oscillation synchrony
The hippocampus, a structure required for many types of memory, connects to the medial prefrontal cortex, an area that helps direct neuronal information streams during intentional behaviors. Increasing evidence suggests that oscillations regulate communication between these two regions. Theta rhythms may facilitate hippocampal inputs to the medial prefrontal cortex during mnemonic tasks and may also integrate series of functionally relevant gamma-mediated cell assemblies in the medial prefrontal cortex. During slow-wave sleep, temporal coordination of hippocampal sharp wave-ripples and medial prefrontal cortex spindles may be an important component of the process by which memories become hippocampus-independent. Studies using rodent models indicate that oscillatory phase-locking is disturbed in schizophrenia, emphasizing the need for more studies of oscillatory synchrony in the hippocampal–prefrontal network.
A current challenge is to develop computational approaches to infer gene network regulatory relationships based on multiple types of large-scale functional genomic data. We find that single-layer feed-forward artificial neural network (ANN) models can effectively discover gene network structure by integrating global in vivo protein:DNA interaction data (ChIP/Array) with genome-wide microarray RNA data. We test this on the yeast cell cycle transcription network, which is composed of several hundred genes with phase-specific RNA outputs. These ANNs were robust to noise in data and to a variety of perturbations. They reliably identified and ranked 10 of 12 known major cell cycle factors at the top of a set of 204, based on a sum-of-squared weights metric. Comparative analysis of motif occurrences among multiple yeast species independently confirmed relationships inferred from ANN weights analysis. ANN models can capitalize on properties of biological gene networks that other kinds of models do not. ANNs naturally take advantage of patterns of absence, as well as presence, of factor binding associated with specific expression output; they are easily subjected to in silico “mutation” to uncover biological redundancies; and they can use the full range of factor binding values. A prominent feature of cell cycle ANNs suggested an analogous property might exist in the biological network. This postulated that “network-local discrimination” occurs when regulatory connections (here between MBF and target genes) are explicitly disfavored in one network module (G2), relative to others and to the class of genes outside the mitotic network. If correct, this predicts that MBF motifs will be significantly depleted from the discriminated class and that the discrimination will persist through evolution. Analysis of distantly related Schizosaccharomyces pombe confirmed this, suggesting that network-local discrimination is real and complements well-known enrichment of MBF sites in G1 class genes.
A current challenge is to develop computational approaches to infer gene network regulatory relationships by integrating multiple types of large-scale functional genomic data. This paper shows that simple artificial neural networks (ANNs) employed in a new way do this very well. The ANN models are well-suited to capitalize on natural properties of gene networks in ways that many previous methods do not. Resulting gene network connections inferred between transcription factors and RNA output patterns are robust to noise in large-scale input datasets and to differences in RNA clustering class inputs. This was shown by using the yeast cell cycle gene network as a test case. The cycle has multiple classes of oscillatory RNAs, and Hart, Mjolsness, and Wold show that the ANNs identify key connections that associate genes from each cell cycle phase group with known and candidate regulators. Comparative analysis of network connectivity across multiple genomes showed strong conservation of basic factor-to-output relationships, although at the greatest evolutionary distances the specific target genes have mainly changed identity.
A critical function of the brain’s orienting response is to evaluate novel environmental events in order to prepare for potential behavioral action. Here, measures of synchronization (power, coherence) and nonlinear cross-frequency phase coupling (m:n phase locking measured with bicoherence and cross-bicoherence) were computed on 62-channel electroencephalographic (EEG) data during a paradigm in which unexpected, highly-deviant, novel sounds were randomly intermixed with frequent standard and infrequent target tones. Low frequency resolution analyses showed no significant changes in phase coupling for any stimulus type, though significant changes in power and synchrony did occur. High frequency resolution analyses, on the other hand, showed significant differences in phase coupling, but only for novel sounds compared to standard tones. Novel sounds elicited increased power and coherence in the delta band together with m:n phase locking (bicoherence) of delta:theta (1:3) and delta:alpha (1:4) rhythms in widespread fronto-central, right parietal, temporal, and occipital regions. Cross-bicoherence revealed that globally synchronized delta oscillations were phase coupled to theta oscillations in central regions and to alpha oscillations in right parietal and posterior regions. These results suggest that globally synchronized low frequency oscillations with phase coupling to more localized higher frequency oscillations provide a neural mechanism for the orienting response.
Bicoherence; cross-frequency coupling; orienting response; novelty; P3; coherence
Synchronous oscillatory dynamics is frequently observed in the human brain. We analyze the fine temporal structure of phase-locking in a realistic network model and match it with the experimental data from parkinsonian patients. We show that the experimentally observed intermittent synchrony can be generated just by moderately increased coupling strength in the basal ganglia circuits due to the lack of dopamine. Comparison of the experimental and modeling data suggest that brain activity in Parkinson’s disease resides in the large boundary region between synchronized and nonsynchronized dynamics. Being on the edge of synchrony may allow for easy formation of transient neuronal assemblies.
The basolateral complex of the amygdala (BLA) is a critical component of the neural circuit regulating fear learning. During fear learning and recall, the amygdala and other brain regions, including the hippocampus and prefrontal cortex, exhibit phase-locked oscillations in the high delta/low theta frequency band (∼2–6 Hz) that have been shown to contribute to the learning process. Network oscillations are commonly generated by inhibitory synaptic input that coordinates action potentials in groups of neurons. In the rat BLA, principal neurons spontaneously receive synchronized, inhibitory input in the form of compound, rhythmic, inhibitory postsynaptic potentials (IPSPs), likely originating from burst-firing parvalbumin interneurons. Here we investigated the role of compound IPSPs in the rat and rhesus macaque BLA in regulating action potential synchrony and spike-timing precision. Furthermore, because principal neurons exhibit intrinsic oscillatory properties and resonance between 4 and 5 Hz, in the same frequency band observed during fear, we investigated whether compound IPSPs and intrinsic oscillations interact to promote rhythmic activity in the BLA at this frequency. Using whole-cell patch clamp in brain slices, we demonstrate that compound IPSPs, which occur spontaneously and are synchronized across principal neurons in both the rat and primate BLA, significantly improve spike-timing precision in BLA principal neurons for a window of ∼300 ms following each IPSP. We also show that compound IPSPs coordinate the firing of pairs of BLA principal neurons, and significantly improve spike synchrony for a window of ∼130 ms. Compound IPSPs enhance a 5 Hz calcium-dependent membrane potential oscillation (MPO) in these neurons, likely contributing to the improvement in spike-timing precision and synchronization of spiking. Activation of the cAMP-PKA signaling cascade enhanced the MPO, and inhibition of this cascade blocked the MPO. We discuss these results in the context of spike-timing dependent plasticity and modulation by neurotransmitters important for fear learning, such as dopamine.
The increase of induced gamma-band responses (iGBRs; oscillations >30 Hz) elicited by familiar (meaningful) objects is well established in electroencephalogram (EEG) research. This frequency-specific change at distinct locations is thought to indicate the dynamic formation of local neuronal assemblies during the activation of cortical object representations. As analytically power increase is just a property of a single location, phase-synchrony was introduced to investigate the formation of large-scale networks between spatially distant brain sites. However, classical phase-synchrony reveals symmetric, pair-wise correlations and is not suited to uncover the directionality of interactions. Here, we investigated the neural mechanism of visual object processing by means of directional coupling analysis going beyond recording sites, but rather assessing the directionality of oscillatory interactions between brain areas directly. This study is the first to identify the directionality of oscillatory brain interactions in source space during human object recognition and suggests that familiar, but not unfamiliar, objects engage widespread reciprocal information flow. Directionality of cortical information-flow was calculated based upon an established Granger-Causality coupling-measure (partial-directed coherence; PDC) using autoregressive modeling. To enable comparison with previous coupling studies lacking directional information, phase-locking analysis was applied, using wavelet-based signal decompositions. Both, autoregressive modeling and wavelet analysis, revealed an augmentation of iGBRs during the presentation of familiar objects relative to unfamiliar controls, which was localized to inferior-temporal, superior-parietal and frontal brain areas by means of distributed source reconstruction. The multivariate analysis of PDC evaluated each possible direction of brain interaction and revealed widespread reciprocal information-transfer during familiar object processing. In contrast, unfamiliar objects entailed a sparse number of only unidirectional connections converging to parietal areas. Considering the directionality of brain interactions, the current results might indicate that successful activation of object representations is realized through reciprocal (feed-forward and feed-backward) information-transfer of oscillatory connections between distant, functionally specific brain areas.
Oscillations in chemical reactions and metabolic pathways have historically served as prototypes for understanding the dynamics of complex nonlinear systems. This chapter reviews the oscillatory behavior of mitochondria, with a focus on the mitochondrial oscillator dependent on reactive oxygen species (ROS), as first described in heart cells. Experimental and theoretical evidence now indicates that mitochondrial energetic variables oscillate autonomously as part of a network of coupled oscillators under both physiological and pathological conditions. The physiological domain is characterized by small-amplitude oscillations in mitochondrial membrane potential (ΔΨm) showing correlated behavior over a wide range of frequencies, as determined using Power Spectral Analysis and Relative Dispersion Analysis of long term recordings of ΔΨm. Under metabolic stress, when the balance between ROS generation and ROS scavenging is perturbed, the mitochondrial network throughout the cell locks to one main low-frequency, high-amplitude oscillatory mode. This behavior has major pathological implications because the energy dissipation and cellular redox changes that occur during ΔΨm depolarization result in suppression of electrical excitability and Ca2+ handling, the two main functions of the cardiac cell. In an ischemia/reperfusion scenario these alterations scale up to the level of the whole organ, giving rise to fatal arrhythmias.
In networks of excitatory and inhibitory neurons with mutual synaptic coupling, specific drive to sub-ensembles of cells often leads to gamma-frequency (25–100 Hz) oscillations. When the number of driven cells is too small, however, the synaptic interactions may not be strong or homogeneous enough to support the mechanism underlying the rhythm. Using a combination of computational simulation and mathematical analysis, we study the breakdown of gamma rhythms as the driven ensembles become too small, or the synaptic interactions become too weak and heterogeneous. Heterogeneities in drives or synaptic strengths play an important role in the breakdown of the rhythms; nonetheless, we find that the analysis of homogeneous networks yields insight into the breakdown of rhythms in heterogeneous networks. In particular, if parameter values are such that in a homogeneous network, it takes several gamma cycles to converge to synchrony, then in a similar, but realistically heterogeneous network, synchrony breaks down altogether. This leads to the surprising conclusion that in a network with realistic heterogeneity, gamma rhythms based on the interaction of excitatory and inhibitory cell populations must arise either rapidly, or not at all. For given synaptic strengths and heterogeneities, there is a (soft) lower bound on the possible number of cells in an ensemble oscillating at gamma frequency, based simply on the requirement that synaptic interactions between the two cell populations be strong enough. This observation suggests explanations for recent experimental results concerning the modulation of gamma oscillations in macaque primary visual cortex by varying spatial stimulus size or attention level, and for our own experimental results, reported here, concerning the optogenetic modulation of gamma oscillations in kainate-activated hippocampal slices. We make specific predictions about the behavior of pyramidal cells and fast-spiking interneurons in these experiments.
Gamma-frequency (25–100 Hz) oscillations in the brain often arise as a result of an interaction between excitatory and inhibitory cell populations. For this mechanism to work, the interaction must be sufficiently strong, and connectivity and external drives to participating neurons must be sufficiently homogeneous. As the interactions become weaker, either because the neuronal ensembles become smaller or because synapses weaken, the rhythms deteriorate, and eventually break down. This fact, by itself, is not surprising, but details of how the breakdown occurs are subtle. In particular, our analysis leads to the conclusion that in realistically heterogeneous networks, gamma rhythms must arise quickly, within a small number of oscillation periods, if they arise at all. Our findings suggest explanations for recent experimental findings concerning the minimal spatial extent of stimuli eliciting gamma oscillations in the primary visual cortex, the modulation of gamma oscillations in the primary visual cortex by attention, as well as our own experimental results, reported here, concerning the minimal light intensity below which optogenetic drive to pyramidal cells in a kainate-activated hippocampal slice results in disruption of an ongoing gamma oscillation. Our analysis leads to experimentally testable predictions about the behavior of the excitatory and inhibitory cells in these experiments.
Microarrays are widely used to investigate the blood stage of Plasmodium falciparum infection. Starting with synchronized cells, gene expression levels are continually measured over the 48-hour intra-erythrocytic cycle (IDC). However, the cell population gradually loses synchrony during the experiment. As a result, the microarray measurements are blurred. In this paper, we propose a generalized deconvolution approach to reconstruct the intrinsic expression pattern, and apply it to P. falciparum IDC microarray data.
We develop a statistical model for the decay of synchrony among cells, and reconstruct the expression pattern through statistical inference. The proposed method can handle microarray measurements with noise and missing data. The original gene expression patterns become more apparent in the reconstructed profiles, making it easier to analyze and interpret the data. We hypothesize that reconstructed gene expression patterns represent better temporally resolved expression profiles that can be probabilistically modeled to match changes in expression level to IDC transitions. In particular, we identify transcriptionally regulated protein kinases putatively involved in regulating the P. falciparum IDC.
By analyzing publicly available microarray data sets for the P. falciparum IDC, protein kinases are ranked in terms of their likelihood to be involved in regulating transitions between the ring, trophozoite and schizont developmental stages of the P. falciparum IDC. In our theoretical framework, a few protein kinases have high probability rankings, and could potentially be involved in regulating these developmental transitions.
This study proposes a new methodology for extracting intrinsic expression patterns from microarray data. By applying this method to P. falciparum microarray data, several protein kinases are predicted to play a significant role in the P. falciparum IDC. Earlier experiments have indeed confirmed that several of these kinases are involved in this process. Overall, these results indicate that further functional analysis of these additional putative protein kinases may reveal new insights into how the P. falciparum IDC is regulated.
The mechanism of the self-regulation of gene expression in living cells is generally explained by considering complicated networks of key-lock relationships, and in fact there is a large body of evidence on a hugenumber of key-lock relationships. However, in the present article we stress that with the network hypothesis alone it is impossible to fully explain the mechanism of self-regulation in life. Recently, it has been established that individual giant DNA molecules, larger than several tens of kilo base pairs, undergo a large discrete transition in their higher-order structure. It has become clear that nonspecific weak interactions with various chemicals, suchas polyamines, small salts, ATP and RNA, cause on/off switching in the higher-order structure of DNA. Thus, the field parameters of the cellular environment should play important roles in the mechanism of self-regulation, in addition to networks of key and locks. This conformational transition induced by field parameters may be related to rigid on/off regulation, whereas key-lock relationships may be involved in a more flexible control of gene expression.
DNA condensation; environmental parameter; first-order phase transition of DNA; higher-order structure of DNA; on/off regulation; segregation in a chain
The paired Teleost Mauthner (M-) cells and their associated network serve as an excellent system to study the biophysical basis of decision making. In teleosts, an abrupt sound evokes a M-spike, triggering a C-start escape that is usually directed away from a sound source. The response latency is minimized by electrical synapses between auditory afferents and the M-cell lateral dendrite. Here, we demonstrate that the electrical synapses also mediate phase encoding. Ramped sound pressure waves (150-250 Hz) evoked electrotonic postsynaptic potentials in the M-cell locked to two diametrically opposed phase angles that were frequency dependent but intensity independent. Phase encoding was also evident at the behavioral level underwater, as the stimuli evoked directional C-starts with an onset that was phase locked to the sound wave. In interneurons inhibitory to the M-cell these same stimuli also evoked phase locked electrotonic postsynaptic potentials and action potentials. The resulting chemical and electrical, i.e field effect, inhibitions functioned tonically and phasically respectively. Phase encoding could be important in underwater sound source localization, which is thought to require a neural computation involving a phase comparison between the pressure and the directional particle motion components of sound. This computation may be implemented by an inter-play between phase dependent afferent excitation and feedforward inhibition that activates the appropriate M-cell and directs the C-start away from the sound source.
startle response; synaptic integration; excitatory-inhibitory balance; field effect (ephaptic) interactions; time coding; directional hearing
Our goal is to understand how nearly synchronous modes arise in heterogenous networks of neurons. In heterogenous networks, instead of exact synchrony, nearly synchronous modes arise, which include both 1:1 and 2:2 phase-locked modes. Existence and stability criteria for 2:2 phase-locked modes in reciprocally coupled two neuron circuits were derived based on the open loop phase resetting curve (PRC) without the assumption of weak coupling. The PRC for each component neuron was generated using the change in synaptic conductance produced by a presynaptic action potential as the perturbation. Separate derivations were required for modes in which the firing order is preserved and for those in which it alternates. Networks composed of two model neurons coupled by reciprocal inhibition were examined to test the predictions. The parameter regimes in which both types of nearly synchronous modes are exhibited were accurately predicted both qualitatively and quantitatively provided that the synaptic time constant is short with respect to the period and that the effect of second order resetting is considered. In contrast, PRC methods based on weak coupling could not predict 2:2 modes and did not predict the 1:1 modes with the level of accuracy achieved by the strong coupling methods. The strong coupling prediction methods provide insight into what manipulations promote near-synchrony in a two neuron network and may also have predictive value for larger networks, which can also manifest changes in firing order. We also identify a novel route by which synchrony is lost in mildly heterogenous networks.
Synchrony; phase response curve; network oscillation
The period of complex signals is encoded in the bullfrog’s eighth nerve by a synchrony code based on phase-locked responding. We examined how these arrays of phase-locked activity are represented in different subnuclei of the auditory midbrain, the torus semicircularis (TS). Recording sites in different areas of the TS differ in their ability to synchronize to the envelope of complex stimuli, and these differences in synchronous activity are related to response latency. Cells in the caudal principal nucleus (cell sparse zone) have longer latencies, and show little or no phase-locked activity, even in response to low modulation rates, while some cells in lateral areas of the TS (magnocellular nucleus, lateral part of principal nucleus) synchronize to rates as high as 90–100 Hz. At midlevels of the TS, there is a lateral-to-medial gradient of synchronization ability: cells located more laterally show better phase-locking than those located more medially. Pooled all-order interval histograms from short latency cells located in the lateral TS represent the waveform periodicity of a biologically relevant complex harmonic signal at different stimulus levels, and in a manner consistent with behavioral data from vocalizing male frogs. Long latency cells in the caudal parts of the TS (cell sparse zone, caudal magnocellular nucleus) code stimulus period by changes in spike rate, rather than by changes in synchronized activity. These data suggest that neural codes based on rate processing and time domain processing are represented in anatomically different areas of the TS. They further show that a population-based analysis can increase the precision with which temporal features are represented in the central auditory system.
auditory; midbrain; temporal coding; periodicity coding; synchrony; complex sounds
Although Salmonella enterica serovar Typhimurium can undergo phase variation to alternately express two different types of flagellin subunit proteins, FljB or FliC, no biological function for this phenomenon has been described. In this investigation, we constructed phase-locked derivatives of S. enterica serovar Typhimurium that expressed only FljB (termed locked-ON) or FliC (termed locked-OFF). The role of phase variation in models of enteric and systemic pathogenesis was then evaluated. There were no differences between the wild-type parent strain and the two phase-locked derivatives in adherence and invasion of mouse epithelial cells in vitro, survival in mouse peritoneal macrophages, or in a bovine model of gastroenteritis. By contrast, the locked-OFF mutant was virulent in mice following oral or intravenous (i.v.) inoculation but the locked-ON mutant was attenuated. When these phase-locked mutants were compared in studies of i.v. kinetics in mice, similar numbers of the two strains were isolated from the blood and spleens of infected animals at 6 and 24 h. However, the locked-OFF mutant was recovered from the blood and spleens in significantly greater numbers than the locked-ON strain by day 2 of infection. By 5 days postinfection, a majority of the mice infected with the locked-OFF mutant had died compared with none of the mice infected with the locked-ON mutant. These results suggest that phase variation is not involved in the intestinal stage of infection but that once S. enterica serovar Typhimurium reaches the spleens of susceptible mice those organisms in the FliC phase can grow and/or survive better than those in the FljB phase. Additional experiments with wild-type S. enterica serovar Typhimurium, fully capable of switching flagellin type, supported this hypothesis. We conclude that organisms that have switched to the FliC+ phase have a selective advantage in the mouse model of typhoid fever but have no such advantage in invasion of epithelial cells or the induction of enteropathogenesis.
Theoretical studies and robotic experiments have shown that asymptotically stable periodic walking may emerge from nonlinear limit-cycle oscillators in the neuro-mechanical periphery. We recently reported entrainment of human gait to periodic mechanical perturbations with two essential features: 1) entrainment occurred only when the perturbation period was close to the original (preferred) walking period, and 2) entrainment was always accompanied by phase locking so that the perturbation occurred at the end of the double-stance phase. In this study, we show that a highly-simplified state-determined walking model can reproduce several salient nonlinear limit-cycle behaviors of human walking: 1) periodic gait that is 2) asymptotically stable; 3) entrainment to periodic mechanical perturbations only when the perturbation period is close to the model's unperturbed period; and 4) phase-locking to locate the perturbation at the end of double stance. Importantly, this model requires neither supra-spinal control nor an intrinsic self-sustaining neural oscillator such as a rhythmic central pattern generator. Our results suggest that several prominent limit-cycle features of human walking may stem from simple afferent feedback processes without significant involvement of supra-spinal control or a self-sustaining oscillatory neural network.
Cortical neurons are capable of generating trains of action potentials in response to current injections. These discharges can take different forms, e.g. repetive firing that adapts during the period of current injection or bursting behaviors. We have used a combined experimental and computational approach to characterize the dynamics leading to action potential responses in single neurons. Specifically we investigated the origin of complex firing patterns in response to sinusoidal current injections. Using a reduced model, the theta neuron, alongside recordings from cortical pyramidal cells we show that both real and simulated neurons show phase locking to sine wave stimuli up to a critical frequency, above which period skipping and 1-to-x phase locking occurs. The locking behavior follows a complex “devil’s staircase” phenomena, where locked modes are interleaved with irregular firing. We further show that the critical frequency depends on the time scale of spike generation and on the level of spike frequency adaptation. These results suggest that phase locking of neuronal responses to complex input patterns can be explained by basic properties of the spike generating machinery.
bifurcation theory; devil’s staircase; endogenous oscillators
Acoustically communicating animals often have to cope with ambient noise that has the potential to interfere with the perception of conspecific signals. Here we use the synchronous display of mating signals in males of the tropical katydid Mecopoda elongata in order to assess the influence of nocturnal rainforest noise on signal perception. Loud background noise may disturb chorus synchrony either by masking the signals of males or by interaction of noisy events with the song oscillator. Phase-locked synchrony of males was studied under various signal-to-noise ratios (SNRs) using either native noise or the audio component of noise (<9 kHz). Synchronous entrainment was lost at a SNR of −3 dB when native noise was used, whereas with the audio component still 50 % of chirp periods matched the pacer period at a SNR of −7 dB. Since the chirp period of solo singing males remained almost unaffected by noise, our results suggest that masking interference limits chorus synchrony by rendering conspecific signals ambiguous. Further, entrainment with periodic artificial signals indicates that synchrony is achieved by ignoring heterospecific signals and attending to a conspecific signal period. Additionally, the encoding of conspecific chirps was studied in an auditory neuron under the same background noise regimes.
Acoustic communication; Background noise; Chorus synchrony; Signal detection; Entrainment
A new method for assessing group synchrony is introduced as being potentially useful for objectively determining degree of group cohesiveness or entitativity. The cluster-phase method of Frank and Richardson (2010) was used to analyze movement data from the rocking chair movements of six-member groups who rocked their chairs while seated in a circle facing the center. In some trials group members had no information about others' movements (their eyes were shut) or they had their eyes open and gazed at a marker in the center of the group. As predicted, the group level synchrony measure was able to distinguish between situations where synchrony would have been possible and situations where it would be impossible. Moreover, other aspects of the analysis illustrated how the cluster phase measures can be used to determine the type of patterning of group synchrony, and, when integrated with multi-level modeling, can be used to examine individual-level differences in synchrony and dyadic level synchrony as well.
cluster phase method; group synchrony; interpersonal coordination; group processes; multivariate analysis