Fig 5 - uploaded by Lakshmi Chandrasekaran
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Importance of Second Order Resetting. Comparison of |λ max | for the case in which f 2 (φ) is neglected (without f 2 (φ), open circles) and the case in which it is considered (with f 2 (φ), filled diamonds) plotted against the synaptic conductance strength. For both cases, |λ max | is less than one up to .07 mS/cm 2 , predicting stability for the two cluster solution. In this range, the eigenvalue with the largest absolute value is |λ 1 |, which does not include a contribution from f 2 (φ). Beyond .07 mS/cm 2 when f 2 (φ) is considered (filled diamonds), the eigenvalue with the the largest absolute value is λ 2 , which correctly predicts that the cluster mode loses stability for conductances greater than .08 mS/cm 2 . This diverges from the case where f 2 (φ) is ignored (open circles); neglecting f 2 (φ) incorrectly predicts stability up to .18 mS/cm 2 (circles).
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Phase response curves (PRCs) have been widely used to study synchronization in neural circuits comprised of pacemaking neurons. They describe how the timing of the next spike in a given spontaneously firing neuron is affected by the phase at which an input from another neuron is received. Here we study two reciprocally coupled clusters of pulse cou...
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In the nervous system, a network of neurons shows interesting population activities. One example is a various frequency of synchronized oscillations which are thought to be important to sensory functions. In particular, it has been reported that gamma frequency rhythms (30∼70Hz) in the cortex can significantly regulate the responses...
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... can enforce synchrony within each cluster, even if neither cluster is capable of 379 synchronizing in isolation [32]. The key is the multiplicative nature of the factors that scale 380 the perturbation in separate intervals. ...
Previously, our group used phase response curves under a pulsatile coupling assumption to determine the stability of synchrony within a cluster of neural oscillators and between two clusters of oscillators. The interactions of the within and between cluster terms were considered, demonstrating how an alternating firing pattern between clusters could stabilize within cluster synchrony- even in clusters unable to synchronize themselves in isolation. In addition, criteria were derived for synchrony between two pulse coupled oscillators with synaptic delays. In this study, we update our previous work on one and two clusters of coupled oscillators to include delays and demonstrate the validity of the results using a map of the firing intervals based on the phase resetting curve. We use self-connected neurons to represent clusters and derive conditions under which an oscillator can phase-lock itself with a delayed input. Although this analysis only strictly applies to identical neurons receiving identical synapses from the same number of neurons, the principles are general and can be used to understand how to promote or impede synchrony in physiological networks of neurons. Heterogeneity can be interpreted as a form of frozen noise, and approximate synchrony can be sustained despite heterogeneity. The pulse-coupled oscillator model can not only be used to describe biological neuronal networks but also cardiac pacemakers, lasers, fireflies, artificial neural networks, social self-organization, and wireless sensor networks.
... The high and stable classification results observed in our experiment for the β frequency band might be related to the unique role of these oscillations in global neural network synchronization. Strong long-range connections in β and γ have been found to be highly stable [45][46][47], less prone to interferences, and less energetically demanding [45][46][47]. ...
... The high and stable classification results observed in our experiment for the β frequency band might be related to the unique role of these oscillations in global neural network synchronization. Strong long-range connections in β and γ have been found to be highly stable [45][46][47], less prone to interferences, and less energetically demanding [45][46][47]. ...
The paper is devoted to the study of EEG-based people verification. Analyzed solutions employed shallow artificial neural networks using spectral EEG features as input representation. We investigated the impact of the features derived from different frequency bands and their combination on verification results. Moreover, we studied the influence of a number of hidden neurons in a neural network. The datasets used in the analysis consisted of signals recorded during resting state from 29 healthy adult participants performed on different days, 20 EEG sessions for each of the participants. We presented two different scenarios of training and testing processes. In the first scenario, we used different parts of each recording session to create the training and testing datasets, and in the second one, training and testing datasets originated from different recording sessions. Among single frequency bands, the best outcomes were obtained for the beta frequency band (mean accuracy of 91 and 89% for the first and second scenarios, respectively). Adding the spectral features from more frequency bands to the beta band features improved results (95.7 and 93.1%). The findings showed that there is not enough evidence that the results are different between networks using different numbers of hidden neurons. Additionally, we included results for the attack of 23 external impostors whose recordings were not used earlier in training or testing the neural network in both scenarios. Another significant finding of our study shows worse sensitivity results in the second scenario. This outcome indicates that most of the studies presenting verification or identification results based on the first scenario (dominating in the current literature) are overestimated when it comes to practical applications.
... Theoretical considerations indicate that strong EEG connectivity in the beta-2 band is highly stable 44,45 , less prone to disturbance 44,46 and consequently results in less dynamic processing and behavior 47,48 . This lower reconfiguration capability is also in line with our previous investigation which showed that subjects with stronger PLVs exhibited less flexible connection patterns 49 . ...
Here we attempted to define the relationship between: EEG activity, personality and coping during lockdown. We were in a unique situation since the COVID-19 outbreak interrupted our independent longitudinal study. We already collected a significant amount of data before lockdown. During lockdown, a subgroup of participants willingly continued their engagement in the study. These circumstances provided us with an opportunity to examine the relationship between personality/cognition and brain rhythms in individuals who continued their engagement during lockdown compared to control data collected well before pandemic. The testing consisted of a one-time assessment of personality dimensions and two sessions of EEG recording and deductive reasoning task. Participants were divided into groups based on the time they completed the second session: before or during the COVID-19 outbreak ‘Pre-pandemic Controls’ and ‘Pandemics’, respectively. The Pandemics were characterized by a higher extraversion and stronger connectivity, compared to Pre-pandemic Controls. Furthermore, the Pandemics improved their cognitive performance under long-term stress as compared to the Pre-Pandemic Controls matched for personality traits to the Pandemics. The Pandemics were also characterized by increased EEG connectivity during lockdown. We posit that stronger EEG connectivity and higher extraversion could act as a defense mechanism against stress-related deterioration of cognitive functions.
... Theoretical analyses have shown that the stability and robustness of strong beta-phase correlations are characteristic of long, interregional connections [34][35][36] . Since participants with higher gB2rest were characterized by stronger resting-state PLVs (intrinsic connectivity) between frontal and parietal and between frontal and occipital sites in the beta-2 band (Figs. 2 and S2), we hypothesized that participants with stronger ties might be less prone to modification of their connections strength and therefore the smaller number of significant gB2rest-PLV correlations in the retest session observed in both tasks would result mostly from the change of connections' strength in the participants with lower PLVs. ...
... This notion seems to be well grounded in theoretical investigations. Strong long-range connections were found to be highly stable [34][35][36] , less prone to disturbance and less energetically demanding 34,36 . Stronger phase correlations were also postulated to lower network complexity, resulting in less flexible processing 37,38 and worse behavioral performance 39 . ...
... This notion seems to be well grounded in theoretical investigations. Strong long-range connections were found to be highly stable [34][35][36] , less prone to disturbance and less energetically demanding 34,36 . Stronger phase correlations were also postulated to lower network complexity, resulting in less flexible processing 37,38 and worse behavioral performance 39 . ...
Mounting evidence indicates that resting-state EEG activity is related to various cognitive functions. To trace physiological underpinnings of this relationship, we investigated EEG and behavioral performance of 36 healthy adults recorded at rest and during visual attention tasks: visual search and gun shooting. All measures were repeated two months later to determine stability of the results. Correlation analyses revealed that within the range of 2–45 Hz, at rest, beta-2 band power correlated with the strength of frontoparietal connectivity and behavioral performance in both sessions. Participants with lower global beta-2 resting-state power (gB2rest) showed weaker frontoparietal connectivity and greater capacity for its modifications, as indicated by changes in phase correlations of the EEG signals. At the same time shorter reaction times and improved shooting accuracy were found, in both test and retest, in participants with low gB2rest compared to higher gB2rest values. We posit that weak frontoparietal connectivity permits flexible network reconfigurations required for improved performance in everyday tasks.
... By clustering we do not mean spatial clustering (cultures that exhibit YMO occur in well-mixed bioreactors), but temporal clustering -cohorts of cells traversing the CDC in near synchrony (see Figure 1). The mathematical results in Boczko et al. (2010) are similar to those in Chandrasekaran, Achuthan, and Canavier (2011) where, in a different context, it was observed that reciprocal coupling can stabilize a 2-cluster solution by enforcing synchrony within clusters that would not synchronize in isolation. ...
We investigate the possibility that slow metabolic, cell-cycle-related oscillations in yeast and associated temporal clustering of cells within the cell cycle could be due to an interplay between near-critical metabolism and cell cycle checkpoints. We construct a dynamical model of the cell cycles of a large culture of cells that incorporates checkpoint gating and metabolic mode switching that are triggered by resource thresholds. We investigate the model analytically and prove that there exist open sets of parameter values for which the model possesses stable periodic solutions that exhibit metabolic oscillations with cell cycle clustering. Simulations of the model give evidence that such solutions exist for large sets of parameter values. This demonstrates that checkpoint gating coupled with critical resources can be a robust mechanism for producing the phenomena observed in experiments.
... By clustering we do not mean spatial clustering (cultures that exhibit YMO occur in well-mixed bioreactors), but temporal clustering -cohorts of cells traversing the CDC in near synchrony (see Figure 1). The mathematical results in Boczko et al. (2010) are similar to those in Chandrasekaran, Achuthan, and Canavier (2011) where, in a different context, it was observed that reciprocal coupling can stabilize a 2-cluster solution by enforcing synchrony within clusters that would not synchronize in isolation. ...
We investigate the possibility that slow metabolic, cell-cycle-related oscillations in yeast and associated temporal clustering of cells within the cell cycle could be due to an interplay between near-critical metabolism and cell cycle checkpoints. We construct a dynamical model of the cell cycles of a large culture of cells that incorporates checkpoint gating and metabolic mode switching that are triggered by resource thresholds. We investigate the model analytically and prove that there exist open sets of parameter values for which the model possesses stable periodic solutions that exhibit metabolic oscillations with cell cycle clustering. Simulations of the model give evidence that such solutions exist for large sets of parameter values. This demonstrates that checkpoint gating coupled with critical resources can be a robust mechanism for producing the phenomena observed in experiments.
... Finally, we show the activity phases ϕ* of neuron A in Figure 5D. These are the actual phases (13) of neuron A at the steady state. ...
... The techniques derived in this paper build on the work of many other researchers who have used maps, based on inter-spike intervals, to derive conditions for phase locking (see, e.g., [11,13,17,41]). As in the present study, in most of these studies, qualitative as well as quantitative properties of the PRC are used to conduct the analysis. Oprisan [39] developed similar geometric methods that depended on the shape of the PRC in order to assess phase locking, but synaptic plasticity was not considered. ...
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 Poincare´ 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.
... The PRC can be calculated numerically or measured experimentally for oscillatory systems of different origin [4]. These properties made it a useful tool for the study of forced or coupled oscillators [5][6][7][8][9][10][11], and it is especially effective in neuroscience where the interactions are mediated by pulses. If the pulse arrivals are separated by sufficiently long time intervals, the transient caused by a pulse vanishes before the next one comes. ...
... To verify the developed theory we stimulated various oscillators by doublets of pulses at different phases ϕ 1 and ϕ 2 and measured the PRF Z 2 (ϕ 1 , ϕ 2 ) directly. Then we checked whether the correction term is given by Z 2 (ϕ 1 , ϕ 2 ) − Z(ϕ 1 ) = ε 2 F (ϕ 2 )G(ϕ 1 )μ ϕ2−ϕ1 as it should be according to (8). Our tests for several popular oscillatory models -FitzHugh-Nagumo, Morris-Lecar, Hodgkin-Huxley and Van der Pol-showed remarkable accuracy of this approximation. ...
Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Here we develop a framework for studying the response to a series of pulses which are frequent or/and strong so that the standard PRC fails. We show that in this case, the phase shift caused by each pulse depends on the history of several previous pulses. We call the corresponding function which measures this shift the phase response function (PRF). As a result of the introduction of the PRF, a variety of oscillatory systems with pulse interaction, such as neural systems, can be reduced to phase systems. The main assumption of the classical PRC model, i.e. that the effect of the stimulus vanishes before the next one arrives, is no longer a restriction in our approach. However, as a result of the phase reduction, the system acquires memory, which is not just a technical nuisance but an intrinsic property relevant to strong stimulation. We illustrate the PRF approach by its application to various systems, such as Morris-Lecar, Hodgkin-Huxley neuron models, and others. We show that the PRF allows predicting the dynamics of forced and coupled oscillators even when the PRC fails.
... As described above, the intersection point g 2,δ (ϕ 1 ) = 2(ϕ 1 − δ P 2,δ ) − 1 determines the phase ϕ * 1 = ϕ AP at which and input is received by each cluster in the antiphase mode. Stability of the two-cluster mode can be calculated by treating the two clusters as two oscillators, provided synchrony within each cluster is stable [37]; otherwise a more complicated analysis applies [38]. Since we are only interested in cases in which synchrony is stable, this caveat is not relevant. ...
The synchronization tendencies of networks of oscillators have been studied intensely. We assume a network of all-to-all pulse-coupled oscillators in which the effect of a pulse is independent of the number of oscillators that simultaneously emit a pulse and the normalized delay (the phase resetting) is a monotonically increasing function of oscillator phase with the slope everywhere less than 1 and a value greater than 2φ−1, where φ is the normalized phase. Order switching cannot occur; the only possible solutions are globally attracting synchrony and cluster solutions with a fixed firing order. For small conduction delays, we prove the former stable and all other possible attractors nonexistent due to the destabilizing discontinuity of the phase resetting at a phase of 0.
... In regimes that lead to bistability of in-phase and anti-phase locking according to our analysis of pairs, the simulated networks break up into two clusters of synchronized neurons. Recently it has been shown that a stable two cluster state of pulse coupled neural oscillators can exist even when synchrony of individual pairs is unsta-ble (Chandrasekaran et al. 2011). Such cluster states have been invoked to explain population rhythms measured in vitro, where the involved neurons spike at about half of the population frequency (Pervouchine et al. 2006). ...
Cognitive processing is linked to the activation of neurons in the brain, and specific cognitive tasks are often correlated with certain activity patterns of individual neurons and neuronal networks. Of major relevance are the temporal relationships between successive neuronal spikes and, in particular, the concerted spiking activity across small groups and large populations of coupled neurons, which often exhibit oscillatory overall dynamics due to synchronization. It is therefore important to understand the mechanisms which underlie and control the spiking activity of individual neurons and their collective dynamics in networks.
A prominent mechanism which alters neuronal excitability involves adaptation currents through specific types of potassium channels in the neuronal membrane. These currents cause spike rate adaptation in many types of neurons and are regulated by neuromodulators such as acetylcholine. In this thesis, we employ computational models and mathematical methods to shed light on the role of that mechanism in controlling neuronal dynamics at different spatial levels, ranging from single neurons to large networks. Specifically, we characterize how distinct types of adaptation currents affect (i) spike rates, interspike interval variability and phase response properties of single neurons, (ii) spike synchronization and spike-to-spike locking in small networks, and (iii) the dynamics of spike rates across large populations of coupled neurons.
We take a bottom-up approach based on an experimentally validated neuron model of the integrate-and-fire type, effectively covering spikes, the fast subthreshold membrane voltage and slow adaptation current dynamics. We use this model across the three spatial levels, which facilitates to relate the respective findings. To obtain robust results in an efficient way we extend different suitable methods from statistical physics and nonlinear dynamics – including mean-field, phase reduction and master stability function techniques – for that model class, and complement them by (stochastic) numerical simulations. This approach allows to examine the relationships between microscopic interactions (neuron biophysics) and macroscopic features (network dynamics) in a direct way and simplifies bridging scales.
Applying these tools we demonstrate that at the level of single cells adaptation currents change threshold, gain and variability of spiking, as well as the neuronal phase responses to transient inputs, in type-dependent ways. At the network level adaptation currents engage in mechanisms that generate low-frequency oscillations for excitation dominated synaptic interaction, stabilizing spike synchrony (small networks) or promoting sparse synchronization (large networks), and they can facilitate and modulate faster rhythms which heavily rely on synaptic inhibition. Thereby, we show that neuromodulatory regulation of adaptation currents allows to stabilize biologically relevant synchronized and asynchronous network states and switch between them, by changing the neuronal spiking characteristics in particular ways. This work demonstrates the benefits of unified mathematical bottom-up modeling and analyses in contributing to our understanding of neuronal dynamics across different scales.
