Role of frequency mismatch in neuronal communication through coherence

Neuronal gamma oscillations have been described in local field potentials of different brain regions of multiple species. Gamma oscillations are thought to reflect rhythmic synaptic activity organized by inhibitory interneurons. While several aspects of gamma rhythmogenesis are relatively well understood, we have much less solid evidence about how gamma oscillations contribute to information processing in neuronal circuits. One popular hypothesis states that a flexible routing of information between distant populations occurs via the control of the phase or coherence between their respective oscillations. Here, we investigate how a mismatch between the frequencies of gamma oscillations from two populations affects their interaction. In particular, we explore a biophysical model of the reciprocal interaction between two cortical areas displaying gamma oscillations at different frequencies, and quantify their phase coherence and communication efficiency. We observed that a moderate excitatory coupling between the two areas leads to a decrease in their frequency detuning, up to ～6 Hz, with no frequency locking arising between the gamma peaks. Importantly, for similar gamma peak frequencies a zero phase difference emerges for both LFP and MUA despite small axonal delays. For increasing frequency detunings we found a significant decrease in the phase coherence (at non-zero phase lag) between the MUAs but not the LFPs of the two areas. Such difference between LFPs and MUAs behavior is due to the misalignment between the arrival of afferent synaptic currents and the local excitability windows. To test the efficiency of communication we evaluated the success of transferring rate-modulations between the two areas. Our results indicate that once two populations lock their peak frequencies, an optimal phase relation for communication appears. However, the sensitivity of locking to frequency mismatch suggests that only a precise and active control of gamma frequency could enable the selection of communication channels and their directionality.     

Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling

This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.     

Effect of the topology and delayed interactions in neuronal networks synchronization

As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish well-defined temporal relations among firing of their action potentials. This ability of a population of neurons to produce and maintain a millisecond-precise coordinated firing (either evoked by external stimuli or internally generated) is central to neural codes exploiting precise spike timing for the representation and communication of information. Our results, based on extensive simulations of conductance-based type of neurons in an oscillatory regime, indicate that only certain topologies of networks allow for a coordinated firing at a local and long-range scale simultaneously. Besides network architecture, axonal conduction delays are also observed to be another important factor in the generation of coherent spiking. We report that such communication latencies not only set the phase difference between the oscillatory activity of remote neural populations but determine whether the interconnected cells can set in any coherent firing at all. In this context, we have also investigated how the balance between the network synchronizing effects and the dispersive drift caused by inhomogeneities in natural firing frequencies across neurons is resolved. Finally, we show that the observed roles of conduction delays and frequency dispersion are not particular to canonical networks but experimentally measured anatomical networks such as the macaque cortical network can display the same type of behavior.     

Multiple origins of the cortical γ rhythm

Gamma rhythms (30-80 Hz) are a near-ubiquitous feature of neuronal population activity in mammalian cortices. Their dynamic properties permit the synchronization of neuronal responses to sensory input within spatially distributed networks, transient formation of local neuronal "cell assemblies," and coherent response patterns essential for intercortical regional communication. Each of these phenomena form part of a working hypothesis for cognitive function in cortex. All forms of physiological gamma rhythm are inhibition based, being characterized by rhythmic trains of inhibitory postsynaptic potentials in populations of principal neurons. It is these repeating periods of relative enhancement and attenuation of the responsivity of major cell groups in cortex that provides a temporal structure shared across many millions of neurons. However, when considering the origins of these repeating trains of inhibitory events considerable divergence is seen depending on cortical region studied and mode of activation of gamma rhythm generating networks. Here, we review the evidence for involvement of multiple subtypes of interneuron and focus on different modes of activation of these cells. We conclude that most massively parallel brain regions have different mechanisms of gamma rhythm generation, that different mechanisms have distinct functional correlates, and that switching between different local modes of gamma generation may be an effective way to direct cortical communication streams. Finally, we suggest that developmental disruption of the endophenotype for certain subsets of gamma-generating interneuron may underlie cognitive deficit in psychiatric illness.     

Activation and inhibitory types of brain neuronal sinchronisation: genesis and functional significance

The generalization of studies of the systemic work of cortical neurons during the information processing initiated in Livanov's laboratory allows us to make the following conclusions in terms of the modem state of the problem. In different brain structures, there is a considerable degree of correlation between neuronal activities and slow potential oscillations. In the state of rest or deep extinction, the synchronization of brain neurons increases by the inhibitory type. In the active state of the brain, the degree of neuronal synchronization increases by the activation type. Both processes are determined by the involvement of the whole brain inhibitory or activation systems, respectively. A relative augmentation of inhibitory processes results in a restriction of information transmission in the cortex and prevents its fixation in memory of the system. A decrease in inhibition facilitates the excitation thransmission in the interconnected brain structures. Synchronous convergence of ordered polse flows ensures the information fixation during learning.     

Communication through Resonance in Spiking Neuronal Networks

The cortex processes stimuli through a distributed network of specialized brain areas. This processing requires mechanisms that can route neuronal activity across weakly connected cortical regions. Routing models proposed thus far are either limited to propagation of spiking activity across strongly connected networks or require distinct mechanisms that create local oscillations and establish their coherence between distant cortical areas. Here, we propose a novel mechanism which explains how synchronous spiking activity propagates across weakly connected brain areas supported by oscillations. In our model, oscillatory activity unleashes network resonance that amplifies feeble synchronous signals and promotes their propagation along weak connections (“communication through resonance”). The emergence of coherent oscillations is a natural consequence of synchronous activity propagation and therefore the assumption of different mechanisms that create oscillations and provide coherence is not necessary. Moreover, the phase-locking of oscillations is a side effect of communication rather than its requirement. Finally, we show how the state of ongoing activity could affect the communication through resonance and propose that modulations of the ongoing activity state could influence information processing in distributed cortical networks.     

Neuronal coherence during selective attentional processing and sensory-motor integration.

Groups of neurons synchronize their activities during a variety of conditions, but whether this synchronization is functionally relevant has remained a matter of debate. Here, we survey recent findings showing that synchronization is dynamically modulated during cognitive processes. Based on this evidence, synchronization appears to reflect a general mechanism that renders interactions among selective subsets of neurons effective. We show that neuronal synchronization predicts which sensory input is processed and how efficient it is transmitted to postsynaptic target neurons during sensory-motor integration. Four lines of evidence are presented supporting the hypothesis that rhythmic neuronal synchronization, also called neuronal coherence, underlies effective and selective neuronal communication. (1) Findings from intracellular recordings strongly suggest that postsynaptic neurons are particularly sensitive to synaptic input that is synchronized in the gamma-frequency (30-90 Hz) range. (2) Neurophysiological studies in awake animals revealed enhanced rhythmic synchronization among neurons encoding task-relevant information. (3) The trial-by-trial variation in the precision of neuronal synchronization predicts part of the trial-by-trial variation in the speed of visuo-motor integration. (4) The planning and selection of specific movements can be predicted by the strength of coherent oscillations among local neuronal groups in frontal and parietal cortex. Thus, neuronal coherence appears as a neuronal substrate of an effective neuronal communication structure that dynamically links neurons into functional groups processing task-relevant information and selecting appropriate actions during attention and effective sensory-motor integration.     

Spontaneously active cells induce state transitions in a model of olfactory cortex

The existence of neurons with intrinsic oscillations does not in itself explain the synchronization of local populations of neurons, but it is likely to pace population rhythms when the neurons are suitably coupled by chemical and/or electrical synapses. In the present study, we have investigated the role of spontaneously active cells as noisy or pacemaker units in setting global oscillations in a three-layered cortical model. The presence of a small number of noisy (spontaneously active) units induce oscillations at the network level in the range of the gamma rhythm. The number of noisy units in the network and their type (excitatory or inhibitory or excitatory and inhibitory together) determines the emergence of regular oscillations or aperiodic (chaotic) behaviour. It also determines the onset of the global behaviour. On replacing a noisy unit by a pacemaker unit, similar gamma oscillations were generated. With both noisy and pacemaker units, we found that certain characteristics of the spontaneous activity determine the delay period for the onset of global activity. Preliminary studies have been carried out with spontaneously active units having a chaotic dynamics but the results are much similar to that with a noisy burst. Different functional roles have been suggested for cortical oscillations, such as determining global functional states and specifying connectivity during development. Oscillations at different frequency bands, in particular in the gamma band (around 40 Hz), have also been associated with memory and attention. The presence of spontaneously active neurons, either with noisy or oscillatory activity, could be responsible for global oscillations in the absence of external stimuli in certain cortical areas in the mature brain.     

A method for the estimation of functional brain connectivity from time-series data

A central issue in cognitive neuroscience is which cortical areas are involved in managing information processing in a cognitive task and to understand their temporal interactions. Since the transfer of information in the form of electrical activity from one cortical region will in turn evoke electrical activity in other regions, the analysis of temporal synchronization provides a tool to understand neuronal information processing between cortical regions. We adopt a method for revealing time-dependent functional connectivity. We apply statistical analyses of phases to recover the information flow and the functional connectivity between cortical regions for high temporal resolution data. We further develop an evaluation method for these techniques based on two kinds of model networks. These networks consist of coupled Rössler attractors or of coupled stochastic Ornstein–Uhlenbeck systems. The implemented time-dependent coupling includes uni- and bi-directional connectivities as well as time delayed feedback. The synchronization dynamics of these networks are analyzed using the mean phase coherence, based on averaging over phase-differences, and the general synchronization index. The latter is based on the Shannon entropy. The combination of these with a parametric time delay forms the basis of a connectivity pattern, which includes the temporal and time lagged dynamics of the synchronization between two sources. We model and discuss potential artifacts. We find that the general phase measures are remarkably stable. They produce highly comparable results for stochastic and periodic systems. Moreover, the methods proves useful for identifying brief periods of phase coupling and delays. Therefore, we propose that the method is useful as a basis for generating potential functional connective models.     

Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses

Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.     

Dynamic effective connectivity of inter-areal brain circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities.     

Synaptic Plasticity Controls Sensory Responses through Frequency-Dependent Gamma Oscillation Resonance

Synchronized gamma frequency oscillations in neural networks are thought to be important to sensory information processing, and their effects have been intensively studied. Here we describe a mechanism by which the nervous system can readily control gamma oscillation effects, depending selectively on visual stimuli. Using a model neural network simulation, we found that sensory response in the primary visual cortex is significantly modulated by the resonance between “spontaneous” and “stimulus-driven” oscillations. This gamma resonance can be precisely controlled by the synaptic plasticity of thalamocortical connections, and cortical response is regulated differentially according to the resonance condition. The mechanism produces a selective synchronization between the afferent and downstream neural population. Our simulation results explain experimental observations such as stimulus-dependent synchronization between the thalamus and the cortex at different oscillation frequencies. The model generally shows how sensory information can be selectively routed depending on its frequency components.     

Neural Coding of Finger and Wrist Movements

Previous work (Schieber and Hibbard, 1993) has shown that single motor cortical neurons do not discharge specifically for a particular flexion-extension finger movement but instead are active with movements of different fingers. In addition, neuronal populations active with movements of different fingers overlap extensively in their spatial locations in the motor cortex. These data suggested that control of any finger movement utilizes a distributed population of neurons. In this study we applied the neuronal population vector analysis (Georgopoulos et al., 1983) to these same data to determine (1) whether single cells are tuned in an abstract, three-dimensional (3D) instructed finger and wrist movement space with hand-like geometry and (2) whether the neuronal population encodes specific finger movements. We found that the activity of 132/176 (75%) motor cortical neurons related to finger movements was indeed tuned in this space. Moreover, the population vector computed in this space predicted well the instructed finger movement. Thus, although single neurons may be related to several disparate finger movements, and neurons related to different finger movements are intermingled throughout the hand area of the motor cortex, the neuronal population activity does specify particular finger movements.     

Multisynaptic activity in a pyramidal neuron model and neural code

The highly irregular firing of mammalian cortical pyramidal neurons is one of the most striking observation of the brain activity. This result affects greatly the discussion on the neural code, i.e. how the brain codes information transmitted along the different cortical stages. In fact it seems to be in favor of one of the two main hypotheses about this issue, named the rate code. But the supporters of the contrasting hypothesis, the temporal code, consider this evidence inconclusive. We discuss here a leaky integrate-and-fire model of a hippocampal pyramidal neuron intended to be biologically sound to investigate the genesis of the irregular pyramidal firing and to give useful information about the coding problem. To this aim, the complete set of excitatory and inhibitory synapses impinging on such a neuron has been taken into account. The firing activity of the neuron model has been studied by computer simulation both in basic conditions and allowing brief periods of over-stimulation in specific regions of its synaptic constellation. Our results show neuronal firing conditions similar to those observed in experimental investigations on pyramidal cortical neurons. In particular, the variation coefficient (CV) computed from the inter-spike intervals (ISIs) in our simulations for basic conditions is close to the unity as that computed from experimental data. Our simulation shows also different behaviors in firing sequences for different frequencies of stimulation.     

Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators

Gamma oscillations can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices. How synchronization can take place over long distances in a stable manner is considered an open question. The phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike, depending upon where in the cycle it is received. We use PRCs under the assumption of pulsatile coupling to derive existence and stability criteria for 1:1 phase-locking that arises via bidirectional pulse coupling of two limit cycle oscillators with a conduction delay of any duration for any 1:1 firing pattern. The coupling can be strong as long as the effect of one input dissipates before the next input is received. We show the form that the generic synchronous and anti-phase solutions take in a system of two identical, identically pulse-coupled oscillators with identical delays. The stability criterion has a simple form that depends only on the slopes of the PRCs at the phases at which inputs are received and on the number of cycles required to complete the delayed feedback loop. The number of cycles required to complete the delayed feedback loop depends upon both the value of the delay and the firing pattern. We successfully tested the predictions of our methods on networks of model neurons. The criteria can easily be extended to include the effect of an input on the cycle after the one in which it is received.     

Emergence of Metastable State Dynamics in Interconnected Cortical Networks with Propagation Delays

The importance of the large number of thin-diameter and unmyelinated axons that connect different cortical areas is unknown. The pronounced propagation delays in these axons may prevent synchronization of cortical networks and therefore hinder efficient information integration and processing. Yet, such global information integration across cortical areas is vital for higher cognitive function. We hypothesized that delays in communication between cortical areas can disrupt synchronization and therefore enhance the set of activity trajectories and computations interconnected networks can perform. To evaluate this hypothesis, we studied the effect of long-range cortical projections with propagation delays in interconnected large-scale cortical networks that exhibited spontaneous rhythmic activity. Long-range connections with delays caused the emergence of metastable, spatio-temporally distinct activity states between which the networks spontaneously transitioned. Interestingly, the observed activity patterns correspond to macroscopic network dynamics such as globally synchronized activity, propagating wave fronts, and spiral waves that have been previously observed in neurophysiological recordings from humans and animal models. Transient perturbations with simulated transcranial alternating current stimulation (tACS) confirmed the multistability of the interconnected networks by switching the networks between these metastable states. Our model thus proposes that slower long-range connections enrich the landscape of activity states and represent a parsimonious mechanism for the emergence of multistability in cortical networks. These results further provide a mechanistic link between the known deficits in connectivity and cortical state dynamics in neuropsychiatric illnesses such as schizophrenia and autism, as well as suggest non-invasive brain stimulation as an effective treatment for these illnesses.     

Cellularly-driven differences in network synchronization propensity are differentially modulated by firing frequency

Spatiotemporal pattern formation in neuronal networks depends on the interplay between cellular and network synchronization properties. The neuronal phase response curve (PRC) is an experimentally obtainable measure that characterizes the cellular response to small perturbations, and can serve as an indicator of cellular propensity for synchronization. Two broad classes of PRCs have been identified for neurons: Type I, in which small excitatory perturbations induce only advances in firing, and Type II, in which small excitatory perturbations can induce both advances and delays in firing. Interestingly, neuronal PRCs are usually attenuated with increased spiking frequency, and Type II PRCs typically exhibit a greater attenuation of the phase delay region than of the phase advance region. We found that this phenomenon arises from an interplay between the time constants of active ionic currents and the interspike interval. As a result, excitatory networks consisting of neurons with Type I PRCs responded very differently to frequency modulation compared to excitatory networks composed of neurons with Type II PRCs. Specifically, increased frequency induced a sharp decrease in synchrony of networks of Type II neurons, while frequency increases only minimally affected synchrony in networks of Type I neurons. These results are demonstrated in networks in which both types of neurons were modeled generically with the Morris-Lecar model, as well as in networks consisting of Hodgkin-Huxley-based model cortical pyramidal cells in which simulated effects of acetylcholine changed PRC type. These results are robust to different network structures, synaptic strengths and modes of driving neuronal activity, and they indicate that Type I and Type II excitatory networks may display two distinct modes of processing information.     

Neuronal population activity and functional imaging.

Human functional brain imaging detects blood flow changes that are thought to reflect the activity of neuronal populations and, thus, the responses of neurons that carry behaviourally relevant information. Since this relationship is poorly understood, we explored the link between the activity of single neurons and their neuronal population. The functional imaging results were in good agreement with levels of population activation predicted from the known effects of sensory stimulation, learning and attention on single cortical neurons. However, the nature of the relationship between population activation and single neuron firing was very surprising. Population activation was strongly influenced by those neurons firing at low rates and so was very sensitive to the baseline or 'spontaneous' firing rate. When neural representations were sparse and neurons were tuned to several stimulus dimensions, population activation was hardly influenced by the few neurons whose firing was most strongly modulated by the task or stimulus. Measures of population activation could miss changes in information processing given simultaneous changes in neurons' baseline firing, response modulation or tuning width. Factors that can modulate baseline firing, such as attention, may have a particularly large influence on population activation. The results have implications for the interpretation of functional imaging signals and for cross-calibration between different methods for measuring neuronal activity.