The generation of phase differences and frequency changes in a network model of inferior olive subthreshold oscillations

It is commonly accepted that the Inferior Olive (IO) provides a timing signal to the cerebellum. Stable subthreshold oscillations in the IO can facilitate accurate timing by phase-locking spikes to the peaks of the oscillation. Several theoretical models accounting for the synchronized subthreshold oscillations have been proposed, however, two experimental observations remain an enigma. The first is the observation of frequent alterations in the frequency of the oscillations. The second is the observation of constant phase differences between simultaneously recorded neurons. In order to account for these two observations we constructed a canonical network model based on anatomical and physiological data from the IO. The constructed network is characterized by clustering of neurons with similar conductance densities, and by electrical coupling between neurons. Neurons inside a cluster are densely connected with weak strengths, while neurons belonging to different clusters are sparsely connected with stronger connections. We found that this type of network can robustly display stable subthreshold oscillations. The overall frequency of the network changes with the strength of the inter-cluster connections, and phase differences occur between neurons of different clusters. Moreover, the phase differences provide a mechanistic explanation for the experimentally observed propagating waves of activity in the IO. We conclude that the architecture of the network of electrically coupled neurons in combination with modulation of the inter-cluster coupling strengths can account for the experimentally observed frequency changes and the phase differences.     

A spiking neuron model for synchronous flashing of fireflies

Certain species of fireflies show a group behavior of synchronous flashing. Their synchronized and rhythmic flashing has received much attention among many researchers, and there has been a study of biological models for their entrainment of flashing. The synchronous behavior of fireflies resembles the firing synchrony of integrate-and-fire neurons with excitatory or inhibitory connections. This paper shows an analysis of spiking neurons specialized for a firefly flashing model, and provides simulation results of multiple neurons with various transmission delays and coupling strengths. It also explains flashing patterns of some firefly species and examines the synchrony conditions depending on transmission delays and coupling strengths.     

Clustering in small networks of excitatory neurons with heterogeneous coupling strengths

Excitatory coupling with a slow rise time destabilizes synchrony between coupled neurons. Thus, the fully synchronous state is usually unstable in networks of excitatory neurons. Phase-clustered states, in which neurons are divided into multiple synchronized clusters, have also been found unstable in numerical studies of excitatory networks in the presence of noise. The question arises as to whether synchrony is possible in networks of neurons coupled through slow, excitatory synapses. In this paper, we show that robust, synchronous clustered states can occur in such networks. The effects of non-uniform distributions of coupling strengths are explored. Conditions for the existence and stability of clustered states are derived analytically. The analysis shows that a multi-cluster state can be stable in excitatory networks if the overall interactions between neurons in different clusters are stabilizing and strong enough to counter-act the destabilizing interactions between neurons within each cluster. When heterogeneity in the coupling strengths strengthens the stabilizing inter-cluster interactions and/or weakens the destabilizing in-cluster interactions, robust clustered states can occur in excitatory networks of all known model neurons. Numerical simulations were carried out to support the analytical results.     

Pacemaker and network mechanisms of rhythm generation: cooperation and competition

The origin of rhythmic activity in brain circuits and CPG-like motor networks is still not fully understood. The main unsolved questions are (i) What are the respective roles of intrinsic bursting and network based dynamics in systems of coupled heterogeneous, intrinsically complex, even chaotic, neurons? (ii) What are the mechanisms underlying the coexistence of robustness and flexibility in the observed rhythmic spatio-temporal patterns? One common view is that particular bursting neurons provide the rhythmogenic component while the connections between different neurons are responsible for the regularisation and synchronisation of groups of neurons and for specific phase relationships in multi-phasic patterns. We have examined the spatio-temporal rhythmic patterns in computer-simulated motif networks of H-H neurons connected by slow inhibitory synapses with a non-symmetric pattern of coupling strengths. We demonstrate that the interplay between intrinsic and network dynamics features either cooperation or competition, depending on three basic control parameters identified in our model: the shape of intrinsic bursts, the strength of the coupling and its degree of asymmetry. The cooperation of intrinsic dynamics and network mechanisms is shown to correlate with bistability, i.e., the coexistence of two different attractors in the phase space of the system corresponding to different rhythmic spatio-temporal patterns. Conversely, if the network mechanism of rhythmogenesis dominates, monostability is observed with a typical pattern of winnerless competition between neurons. We analyse bifurcations between the two regimes and demonstrate how they provide robustness and flexibility to the network performance.     

Phase resetting of the mammalian circadian clock relies on a rapid shift of a small population of pacemaker neurons

The circadian pacemaker of the suprachiasmatic nuclei (SCN) contains a major pacemaker for 24 h rhythms that is synchronized to the external light-dark cycle. In response to a shift in the external cycle, neurons of the SCN resynchronize with different pace. We performed electrical activity recordings of the SCN of rats in vitro following a 6 hour delay of the light-dark cycle and observed a bimodal electrical activity pattern with a shifted and an unshifted component. The shifted component was relatively narrow as compared to the unshifted component (2.2 h and 5.7 h, respectively). Curve fitting and simulations predicted that less than 30% of the neurons contribute to the shifted component and that their phase distribution is small. This prediction was confirmed by electrophysiological recordings of neuronal subpopulations. Only 25% of the neurons exhibited an immediate shift in the phase of the electrical activity rhythms, and the phases of the shifted subpopulations appeared significantly more synchronized as compared to the phases of the unshifted subpopulations (p<0.05). We also performed electrical activity recordings of the SCN following a 9 hour advance of the light-dark cycle. The phase advances induced a large desynchrony among the neurons, but consistent with the delays, only 19% of the neurons peaked at the mid of the new light phase. The data suggest that resetting of the central circadian pacemaker to both delays and advances is brought about by an initial shift of a relatively small group of neurons that becomes highly synchronized following a shift in the external cycle. The high degree of synchronization of the shifted neurons may add to the ability of this group to reset the pacemaker. The large desynchronization observed following advances may contribute to the relative difficulty of the circadian system to respond to advanced light cycles.     

Spontaneous activity of olfactory bulb neurons in awake rabbits, with some observations on the effects of pentobarbital anaesthesia

A specially adapted microelectrode driver device has been used to record the spontaneous activity of neurons in the olfactory bulb of awake rabbits. Several parameters of this activity were studied in 78 neurons of conscious animals. A second experiment was performed to investigate anaesthetic-induced modifications of the spike discharge initially recorded in awake animals. 1. In unanaesthetized animals, the interspike interval distribution of all cells was found to be stable over short as well as long periods of time. 2. A periodical change in firing probability, correlated with respiratory activity, was observed in a high percentage of neurons. During inspiration, the discharge was markedly increased ("well synchronized" neurons, n = 2), slightly increased ("poorly synchronized" neurons, n = 15); or unchanged ("not synchronized" neurons, n = 8). 3. The passage from the awake to the anaesthetized state resulted in more regular cell activity with sudden changes from one steady firing level to another, without affecting the cell classification. As anaesthesia wore off, the cell units recovered the characteristic discharge pattern initially observed.     

Local synchronized activity of neurons of different classes in cat primary visual cortex

The goal of the present study was to investigate the local synchronized neuronal activity in the cat visual cortex and the role of different classes of neurons in neural synchrony. Four classes of neurons were identified on the basis of electrophysiological properties of extracellularly recorded cells: RS, FS, IB, and FRB. It was revealed that neurons with short spikes and FRB type of activity were first engaged in synchronization. The model study revealed that neurons with the short action potential had more stable synchronized activity.     

Dispersed activity during passive movement in the globus pallidus of the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP)-treated primate

Parkinson's disease is a neurodegenerative disorder manifesting in debilitating motor symptoms. This disorder is characterized by abnormal activity throughout the cortico-basal ganglia loop at both the single neuron and network levels. Previous neurophysiological studies have suggested that the encoding of movement in the parkinsonian state involves correlated activity and synchronized firing patterns. In this study, we used multi-electrode recordings to directly explore the activity of neurons from the globus pallidus of parkinsonian primates during passive limb movements and to determine the extent to which they interact and synchronize. The vast majority (80/103) of the recorded pallidal neurons responded to periodic flexion-extension movements of the elbow. The response pattern was sinusoidal-like and the timing of the peak response of the neurons was uniformly distributed around the movement cycle. The interaction between the neuronal activities was analyzed for 123 simultaneously recorded pairs of neurons. Movement-based signal correlation values were diverse and their mean was not significantly different from zero, demonstrating that the neurons were not activated synchronously in response to movement. Additionally, the difference in the peak responses phase of pairs of neurons was uniformly distributed, showing their independent firing relative to the movement cycle. Our results indicate that despite the widely distributed activity in the globus pallidus of the parkinsonian primate, movement encoding is dispersed and independent rather than correlated and synchronized, thus contradicting current views that posit synchronous activation during Parkinson's disease.     

Modeling stability in neuron and network function: the role of activity in homeostasis

Individual neurons display characteristic firing patterns determined by the number and kind of ion channels in their membranes. We describe experimental and computational studies that suggest that neurons use activity sensors to regulate the number and kind of ion channels and receptors in their membrane to maintain a stable pattern of activity and to compensate for ongoing processes of degradation, synthesis and insertion of ion channels and receptors. We show that similar neuronal and network outputs can be produced by a number of different combinations of ion channels and synapse strengths. This suggests that individual neurons of the same class may each have found an acceptable solution to a genetically determined pattern of activity, and that networks of neurons in different animals may produce similar output patterns by somewhat variable underlying mechanisms.     

Synchronized oscillations in the visual cortex — a synergetic model

We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model's behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.     

Pollen coupling of forest trees: forming synchronized and periodic reproduction out of chaos

Many of the tree species in mature forests show masting; their reproductive activity has a large variance between years and is often synchronized between different individuals. In this paper, we analyse a globally coupled map model in which trees accumulate photosynthate every year, produce flowers when the energy reserve level exceeds a threshold, and set seeds and fruits at a rate limited by pollen availability. Without pollen limitation, the trees in the forest show independent chaotic fluctuation. Coupling of trees via pollen exchange results in reproduction being synchronized partially or completely over the forest. The whole forest shows diverse dynamical behaviors determined by the values of two essential parameters; the depletion coefficient k and the coupling strength beta. We find perfectly synchronized periodic reproduction, synchronized reproduction with a chaotic time series, clustering phenomena, and chaotic reproduction of trees without synchronization over individuals. There are many parameter windows in which synchronized reproduction of trees shows a stable periodic fluctuation. For perfectly synchronized forests, we can calculate all the Lyapunov exponents analytically. They show that synchronized reproduction of all the trees in the forest can only occur when trees flower at low (but positive) levels in a significant fraction of years, resulting in small fruit sets due to outcrossed pollen limitation. This is consistent with the observation that the distinction between mast years and non-mast years is often not clear cut.     

Modelling Feedback Excitation,Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.     

Dynamics of Time Delay-Induced Multiple Synchronous Behaviors in Inhibitory Coupled Neurons

The inhibitory synapse can induce synchronous behaviors different from the anti-phase synchronous behaviors, which have been reported in recent studies. In the present paper, synchronous behaviors are investigated in the motif model composed of reciprocal inhibitory coupled neurons with endogenous bursting and time delay. When coupling strength is weak, synchronous behavior appears at a single interval of time delay within a bursting period. When coupling strength is strong, multiple synchronous behaviors appear at different intervals of time delay within a bursting period. The different bursting patterns of synchronous behaviors, and time delays and coupling strengths that can induce the synchronous bursting patterns can be well interpreted by the dynamics of the endogenous bursting pattern of isolated neuron, which is acquired by the fast-slow dissection method, combined with the inhibitory coupling current. For an isolated neuron, when a negative impulsive current with suitable strength is applied at different phases of the bursting, multiple different bursting patterns can be induced. For a neuron in the motif, the inhibitory coupling current, of which the application time and strength is modulated by time delay and coupling strength, can cause single or multiple synchronous firing patterns like the negative impulsive current when time delay and coupling strength is suitable. The difference compared to the previously reported multiple synchronous behaviors that appear at time delays wider than a period of the endogenous firing is discussed. The results present novel examples of synchronous behaviors in the neuronal network with inhibitory synapses and provide a reasonable explanation.     

'Non-synaptic' mechanisms in seizures and epileptogenesis

The role of 'non-synaptic' mechanisms (i.e. those mechanisms that are independent of active chemical synpases) in the synchronization of neuronal activity during seizures and their possible contribution to chronic epileptogenesis are summarized. These 'non-synaptic' mechanisms include electrotonic coupling through gap junctions, electrical field effects (i.e. ephaptic transmission), and ionic interactions (e.g. increases in the extracellular concentration of K(+)). Several lines of evidence indicate that granule cells and pyramidal cells of the hippocampus, and probably other cortical neurons, can generate synchronized electrical activity after active chemical synaptic transmission has been blocked. This synchronized activity is sensitive to alterations in the size of the extracellular space, thus suggesting that electrical field effects and ionic mechanisms contribute to this synchronized activity. Recent studies also indicate that 'non-synaptic' synchronization is quite prominent early in development. Electrophysiological data from hippocampal and neocortical slices have led to a re-interpretation of the fast prepotentials (i.e. partial spikes) recorded in cortical pyramidal cells, suggesting that they may not be due to dendritic spike generation. Improvement in freeze-fracture ultrastructural techniques have led to a re-assessment of previous data on gap junctions in the nervous system and opened new approaches to the quantitative analysis and characterization of gap junctions on glia and neurons. Finally, new methods of dye/tracer coupling have the potential to provide a more rigorous basis for evaluating gap junctions and electrotonic communication between neurons in the mammalian central nervous system. Therefore, recent data continue to suggest that gap junctions and electrotonic coupling play an important role in neural integration, although additional studies using new techniques will be needed to address some of the controversial issues that have arisen over the last several decades.     

Synchronized oscillations in the visual cortex — a synergetic model

 We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model’s behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model. Received: 15 February 1995/Accepted in revised form: 18 July 1995     

Unit responses of the superior olives in bats to single and paired ultrasonic stimuli

Single unit responses in the superior olive of the greater horseshoe bat to ultrasonic stimuli with a filling frequency within the echolocation range were investigated. Some neurons were found to have three completely unconnected response regions with characteristic frequencies of 1/2 and 1/3 of the basic frequency, which was within the 80–86 kHz band. An increase in strength of the stimulus with filling frequency equal to the characteristic frequency of the neuron changed the tonic regime of activity into phasic. Presentation of two stimuli, overlapping in time, replaced the phasic regime by tonic. The frequency of the tonic response corresponded exactly to the beating frequency up to 1200 Hz (synchronization of unit discharges with each beating cycle). The synchronized tonic regime was preserved to definite strengths and filling frequencies of the two stimuli.A. A. Zhdanov State University, Leningrad. Translated from Neirofiziologiya, Vol. 8, No. 1, pp. 30–38, January–February, 1976.     

Dispersion and time delay effects in synchronized spike–burst networks

We study spike–burst neural activity and investigate its transitions to synchronized states under electrical coupling. Our reported results include the following: (1) Synchronization of spike–burst activity is a multi-time scale phenomenon and burst synchrony is easier to achieve than spike synchrony. (2) Synchrony of networks with time-delayed connections can be achieved at lower coupling strengths than within the same network with instantaneous couplings. (3) The introduction of parameter dispersion into the network destroys the existence of synchrony in the strict sense, but the network dynamics in major regimes of the parameter space can still be effectively captured by a mean field approach if the couplings are excitatory. Our results on synchronization of spiking networks are general of nature and will aid in the development of minimal models of neuronal populations. The latter are the building blocks of large scale brain networks relevant for cognitive processing.     

Associative recognition and storage in a model network of physiological neurons

We consider a neural network model in which the single neurons are chosen to closely resemble known physiological properties. The neurons are assumed to be linked by synapses which change their strength according to Hebbian rules on a short time scale (100ms). The dynamics of the network — the time evolution of the cell potentials and the synapses — is investigated by computer simulation. As in more abstract network models (Cooper 1973; Hopfield 1982; Kohonen 1984) it is found that the local dynamics of the cell potentials and the synaptic strengths result in global cooperative properties of the network and enable the network to process an incoming flux of information and to learn and store patterns associatively. A trained net can associate missing details of a pattern, can correct wrong details and can suppress noise in a pattern. The network can further abstract the prototype from a series of patterns with variations. A suitable coupling constant connecting the dynamics of the cell potentials with the synaptic strengths is derived by a mean field approximation. This coupling constant controls the neural sensitivity and thereby avoids both extremes of the network state, the state of permanent inactivity and the state of epileptic hyperactivity.     

Bioluminescence imaging of individual fibroblasts reveals persistent, independently phased circadian rhythms of clock gene expression

Circadian (ca. 24 hr) oscillations in expression of mammalian "clock genes" are found not only in the suprachiasmatic nucleus (SCN), the central circadian pacemaker, but also in peripheral tissues. Under constant conditions in vitro, however, rhythms of peripheral tissue explants or immortalized cells damp partially or completely. It is unknown whether this reflects an inability of peripheral cells to sustain rhythms, as SCN neurons can, or a loss of synchrony among cells. Using bioluminescence imaging of Rat-1 fibroblasts transfected with a Bmal1::luc plasmid and primary fibroblasts dissociated from mPer2(Luciferase-SV40) knockin mice, we monitored single-cell circadian rhythms of clock gene expression for 1-2 weeks. We found that single fibroblasts can oscillate robustly and independently with undiminished amplitude and diverse circadian periods. Cells were partially synchronized by medium changes at the start of an experiment, but due to different intrinsic periods, their phases became randomly distributed after several days. Closely spaced cells in the same culture did not have similar phases, implying a lack of functional coupling among cells. Thus, like SCN neurons, single fibroblasts can function as independent circadian oscillators; however, lack of oscillator coupling in dissociated cell cultures leads to a loss of synchrony among individual cells and damping of the ensemble rhythm at the population level.     

Helix neurons invovled in control of rhythmic movement in the pneumostome

Three neurons capable of generating coordinated bursting activity or synchronized slow-wave fluctuations in membrane potential (MP) were identified in the left parietal ganglion ofHelix pomatia. The function of these units contributes to regulating rhythmic opening and closing movements in the pneumostome. Both bursting activity and slow-wave neuronal MP synchronize with rhythmic movements of the pneumostome. Onset of bursting activity and fluctuations in MP on the one hand or suppression of these effects due to different influences on the cells on the other leads to initiation or extinction of pneumostome movements respectively. These neurons do not exhibit endogenous bursting activity but do produce a fairly high rate of firing activity without bursting pattern and without slow-waves in MP in isolation. Bursting activity occurs in these neurons in the intact central nervous system (CNS) as a result of gigantic synchronized IPSP in some cases and due to the aforementioned slow waves in MP and in others. No direct chemically- or electrically-operated synaptic connections exist between the three cells. Serotonin triggers both waves in MP and bursting activity in all three neurons in the intact CNS and exerts a pronounced hyperpolarizing action on each of these factors in isolation.N. K. Kol'tsov Institute of Developmental Biology, Academy of Sciences of the USSR. Moscow. Balaton Limnological Research Institute of the Hungarian Academy of Sciences, Tihany. Translated from Neirofiziologiya, Vol. 20, No. 4, pp. 509–517, July–August, 1988.