Desynchronization in Networks of Globally Coupled Neurons with Dendritic Dynamics

Effective desynchronization can be exploited as a tool for probing the functional significance of synchronized neural activity underlying perceptual and cognitive processes or as a mild treatment for neurological disorders like Parkinson’s disease. In this article we show that pulse-based desynchronization techniques, originally developed for networks of globally coupled oscillators (Kuramoto model), can be adapted to networks of coupled neurons with dendritic dynamics. Compared to the Kuramoto model, the dendritic dynamics significantly alters the response of the neuron to the stimulation. Under medium stimulation amplitude a bistability of the re- sponse of a single neuron is observed. When stimulated at some initial phases, the neuron displays only modulations of its firing, whereas at other initial phases it stops oscillating entirely. Significant alterations in the duration of stimulation-induced transients are also observed. These transients endure after the end of the stimulation and cause maximal desynchronization to occur not during the stimulation, but with some delay after the stimulation has been turned off. To account for this delayed desynchronization effect, we have designed a new calibration procedure for finding the stimulation parameters that result in optimal desynchronization. We have also developed a new desynchronization technique by low frequency entrainment. The stimulation techniques originally developed for the Kuramoto model, when using the new calibration procedure, can also be applied to networks with dendritic dynamics. However, the mechanism by which desynchronization is achieved is substantially different than for the network of Kuramoto oscillators. In particular, the addition of dendritic dynamics significantly changes the timing of the stimulation required to obtain desynchronization. We propose desynchronization stimulation for experimental analysis of synchronized neural processes and for the therapy of movement disorders.     

Optimal open-loop desynchronization of neural oscillator populations

Deep brain stimulation (DBS) is an increasingly used medical treatment for various neurological disorders. While its mechanisms are not fully understood, experimental evidence suggests that through application of periodic electrical stimulation DBS may act to desynchronize pathologically synchronized populations of neurons resulting desirable changes to a larger brain circuit. However, the underlying mathematical mechanisms by which periodic stimulation can engender desynchronization in a coupled population of neurons is not well understood. In this work, a reduced phase-amplitude reduction framework is used to characterize the desynchronizing influence of periodic stimulation on a population of coupled oscillators. Subsequently, optimal control theory allows for the design of periodic, open-loop stimuli with the capacity to destabilize completely synchronized solutions while simultaneously stabilizing rotating block solutions. This framework exploits system nonlinearities in order to strategically modify unstable Floquet exponents. In the limit of weak neural coupling, it is shown that this method only requires information about the phase response curves of the individual neurons. The effects of noise and heterogeneity are also considered and numerical results are presented. This framework could ultimately be used to inform the design of more efficient deep brain stimulation waveforms for the treatment of neurological disease.

     

A model of event-related EEG synchronization changes in beta and gamma frequency bands

During preparation, execution and recovery from simple movements, the EEG power spectrum undergoes a sequence of changes. The power in the beta band (13-25 Hz) decreases during preparation and execution of movement, but during recovery it reaches a level higher than that in the reference period (not affected by the event). These effects are known as event-related beta desynchronization and beta rebound. The power in the gamma band (>30 Hz) increases significantly just before the onset of the movement. This effect is known as event-related gamma synchronization. There are numerous observations concerning these effects but the underlying physiological mechanisms and functional role are not clear. We propose a lumped computational model of a cortical circuit. The model consists only of a pyramidal and an interneuronal population. Each population represents averaged properties of constituting neurons. The output of the model represents a local field potential, with a power spectrum peak either in the beta or in the gamma band. The model elucidates the mechanisms of transition between slower and faster rhythms, gamma synchronization and beta desynchronization and rebound effects. The sufficient conditions to observe the effects in the model are changes of the external excitation level and of the connection strength between excitatory and inhibitory populations attributed to short-time plasticity. The present model presents the role of the pyramidal neurons to interneuron connection in the oscillatory behavior of the two populations. We conclude that the pronounced facilitation of the pyramidal to fast spiking interneuron connections, initiated by robust excitation of the motor cortex neurons, may be essential for the effect of beta rebound. Further experiments concerning short-time plasticity during behavioral tasks would be of great value in studies of functional local cortical circuits.     

Neural population codes

In many regions of the brain, information is represented by patterns of activity occurring over populations of neurons. Understanding the encoding of information in neural population activity is important both for grasping the fundamental computations underlying brain function, and for interpreting signals that may be useful for the control of prosthetic devices. We concentrate on the representation of information in neurons with Poisson spike statistics, in which information is contained in the average spike firing rate. We analyze the properties of population codes in terms of the tuning functions that describe individual neuron behavior. The discussion centers on three computational questions: first, what information is encoded in a population; second, how does the brain compute using populations; and third, when is a population optimal? To answer these questions, we discuss several methods for decoding population activity in an experimental setting. We also discuss how computation can be performed within the brain in networks of interconnected populations. Finally, we examine questions of optimal design of population codes that may help to explain their particular form and the set of variables that are best represented. We show that for population codes based on neurons that have a Poisson distribution of spike probabilities, the behavior and computational properties of the code can be understood in terms of the tuning properties of individual cells.     

Phase model-based neuron stabilization into arbitrary clusters

Deep brain stimulation (DBS) is a common method of combating pathological conditions associated with Parkinson’s disease, Tourette syndrome, essential tremor, and other disorders, but whose mechanisms are not fully understood. One hypothesis, supported experimentally, is that some symptoms of these disorders are associated with pathological synchronization of neurons in the basal ganglia and thalamus. For this reason, there has been interest in recent years in finding efficient ways to desynchronize neurons that are both fast-acting and low-power. Recent results on coordinated reset and periodically forced oscillators suggest that forming distinct clusters of neurons may prove to be more effective than achieving complete desynchronization, in particular by promoting plasticity effects that might persist after stimulation is turned off. Current proposed methods for achieving clustering frequently require either multiple input sources or precomputing the control signal. We propose here a control strategy for clustering, based on an analysis of the reduced phase model for a set of identical neurons, that allows for real-time, single-input control of a population of neurons with low-amplitude, low total energy signals. After demonstrating its effectiveness on phase models, we apply it to full state models to demonstrate its validity. We also discuss the effects of coupling on the efficacy of the strategy proposed and demonstrate that the clustering can still be accomplished in the presence of weak to moderate electrotonic coupling.     

Stabilization of metapopulation cycles: toward a classification scheme

The stability of population oscillations in ecological systems is considered. Experiments suggest that in many cases the single patch dynamics of predator-prey or host-parasite systems is extinction prone, and stability is achieved only when the spatial structure of the population is expressed via desynchronization between patches. A few mechanisms have been suggested so far to explain the inability of dispersal to synchronize the system. Here we compare a recently discovered mechanism, based on the dependence of the angular velocity on the oscillation amplitude, with other, already known conditions for desynchronization. Using a toy model composed of diffusively coupled oscillators we suggest a classification scheme for stability mechanisms, a scheme that allows for either a priori (based on the system parameters) or a posteriori (based on local measurements) identification of the dominant process that yields desynchronization.     

Dynamic representation of odours by oscillating neural assemblies

Stimulus evoked oscillatory synchronization of neural assemblies has been most clearly documented in the olfactory and visual systems. Recent results with the olfactory system of locusts show that information about odour identity is contained in spatial and temporal aspects of an oscillatory population response. This suggests that brain oscillations may reflect a common reference for messages encoded in time. Although stimulus-evoked oscillatory phenomena are reliable, their roles in perception, memory and pattern recognition remain to be demonstrated. Using honey bees, we demonstrated that odour encoding involves, as in locusts, the oscillatory synchronization of assemblies of neurons, and that this synchronization is, here also, selectively abolished by the GABA receptor antagonist picrotoxin. In collaboration with Dr Brian Smith's laboratory, we showed, using a behavioural learning paradigm, that picrotoxin-induced desynchronization impairs the discrimination of molecularly similar odourants, but not that of dissimilar odours. It appears, therefore, that oscillatory synchronization of neuronal assemblies is relevant, and essential for fine odour discrimination. Finally, experiments with locust mushroom body neurons, two synapses downstream from the antennal lobe, indicate that their responses to odours become less specific when antennal lobe neurons are desynchronized by picrotoxin injection. These results suggest that oscillatory synchronization and the kind of temporal encoding it affords provide an additional dimension by which the brain can segment spatially overlapping stimulus representations.     

Identification of Drosophila type II neuroblast lineages containing transit amplifying ganglion mother cells

Mammalian neural stem cells generate transit amplifying progenitors that expand the neuronal population, but these type of progenitors have not been studied in Drosophila. The Drosophila larval brain contains approximately 100 neural stem cells (neuroblasts) per brain lobe, which are thought to bud off smaller ganglion mother cells (GMCs) that each produce two post-mitotic neurons. Here, we use molecular markers and clonal analysis to identify a novel neuroblast cell lineage containing "transit amplifying GMCs" (TA-GMCs). TA-GMCs differ from canonical GMCs in several ways: each TA-GMC has nuclear Deadpan, cytoplasmic Prospero, forms Prospero crescents at mitosis, and generates up to 10 neurons; canonical GMCs lack Deadpan, have nuclear Prospero, lack Prospero crescents at mitosis, and generate two neurons. We conclude that there are at least two types of neuroblast lineages: a Type I lineage where GMCs generate two neurons, and a type II lineage where TA-GMCs have longer lineages. Type II lineages allow more neurons to be produced faster than Type I lineages, which may be advantageous in a rapidly developing organism like Drosophila.     

Partial phase synchronization of neural populations due to random Poisson inputs

We show that populations of identical uncoupled neurons exhibit partial phase synchronization when stimulated with independent, random unidirectional current spikes with interspike time intervals drawn from a Poisson distribution. We characterize this partial synchronization using the phase distribution of the population, and consider analytical approximations and numerical simulations of phase-reduced models and the corresponding conductance-based models of typical Type I (Hindmarsh-Rose) and Type II (Hodgkin-Huxley) neurons, showing quantitatively how the extent of the partial phase synchronization depends on the magnitude and mean interspike frequency of the stimulus. Furthermore, we present several simple examples that disprove the notion that phase synchrony must be strongly related to spike synchrony. Instead, the importance of partial phase synchrony is shown to lie in its influence on the response of the population to stimulation, which we illustrate using first spike time histograms.     

Optimal feedback control to describe multiple representations of primary motor cortex neurons

Primary motor cortex (M1) neurons are tuned in response to several parameters related to motor control, and it was recently reported that M1 is important in feedback control. However, it remains unclear how M1 neurons encode information to control the musculoskeletal system. In this study, we examined the underlying computational mechanisms of M1 based on optimal feedback control (OFC) theory, which is a plausible hypothesis for neuromotor control. We modelled an isometric torque production task that required joint torque to be regulated and maintained at desired levels in a musculoskeletal system physically constrained by muscles, which act by pulling rather than pushing. Then, a feedback controller was computed using an optimisation approach under the constraint. In the presence of neuromotor noise, known as signal-dependent noise, the sensory feedback gain is tuned to an extrinsic motor output, such as the hand force, like a population response of M1 neurons. Moreover, a distribution of the preferred directions (PDs) of M1 neurons can be predicted via feedback gain. Therefore, we suggest that neural activity in M1 is optimised for the musculoskeletal system. Furthermore, if the feedback controller is represented in M1, OFC can describe multiple representations of M1, including not only the distribution of PDs but also the response of the neuronal population.     

Sensitivity of firing rate to input fluctuations depends on time scale separation between fast and slow variables in single neurons

Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f–I curve. We introduce a novel classification of neurons into Types A, B−, and B+ according to how f–I curves are modulated by input fluctuations. In Type A neurons, the f–I curves display little sensitivity to input fluctuations when the mean current is large. In contrast, Type B neurons display sensitivity to fluctuations throughout the entire range of input means. Type B− neurons do not fire repetitively for any constant input, whereas Type B+ neurons do. We show that Type B+ behavior results from a separation of time scales between a slow and fast variable. A voltage-dependent time constant for the recovery variable can facilitate sensitivity to input fluctuations. Type B+ firing rates can be approximated using a simple “energy barrier” model.     

An In-vitro Preparation of Isolated Enteric Neurons and Glia from the Myenteric Plexus of the Adult Mouse

The enteric nervous system is a vast network of neurons and glia running the length of the gastrointestinal tract that functionally controls gastrointestinal motility. A procedure for the isolation and culture of a mixed population of neurons and glia from the myenteric plexus is described. The primary cultures can be maintained for over 7 days, with connections developing among the neurons and glia. The longitudinal muscle strip with the attached myenteric plexus is stripped from the underlying circular muscle of the mouse ileum or colon and subjected to enzymatic digestion. In sterile conditions, the isolated neuronal and glia population are preserved within the pellet following centrifugation and plated on coverslips. Within 24-48 hr, neurite outgrowth occurs and neurons can be identified by pan-neuronal markers. After two days in culture, isolated neurons fire action potentials as observed by patch clamp studies. Furthermore, enteric glia can also be identified by GFAP staining. A network of neurons and glia in close apposition forms within 5 - 7 days. Enteric neurons can be individually and directly studied using methods such as immunohistochemistry, electrophysiology, calcium imaging, and single-cell PCR. Furthermore, this procedure can be performed in genetically modified animals. This methodology is simple to perform and inexpensive. Overall, this protocol exposes the components of the enteric nervous system in an easily manipulated manner so that we may better discover the functionality of the ENS in normal and disease states.     

Long-term anti-kindling effects of desynchronizing brain stimulation: a theoretical study

In a modeling study we show that desynchronization stimulation may have powerful anti-kindling effects. For this, we incorporate spike-timing-dependent plasticity into a generic network of coupled phase oscillators, which serves as a model network of synaptically interacting neurons. Two states may coexist under spontaneous conditions: a state of uncorrelated firing and a state of pathological synchrony. Appropriate stimulation protocols make the network learn or unlearn the pathological synaptic interactions, respectively. Low-frequency periodic pulse train stimulation causes a kindling. Permanent high-frequency stimulation, used as golden standard for deep brain stimulation in medically refractory movement disorders, basically freezes the synaptic weights. In contrast, desynchronization stimulation, e.g., by means of a multi-site coordinated reset, has powerful long-term anti-kindling effects and enables the network to unlearn pathologically strong synaptic interactions. We propose desynchronization stimulation for the therapy of movement disorders and epilepsies.     

Frequency and topography in monkey electroencephalogram during action observation: possible neural correlates of the mirror neuron system

The observation of actions executed by others results in desynchronization of electroencephalogram (EEG) in the alpha and beta frequency bands recorded from the central regions in humans. On the other hand, mirror neurons, which are thought to be responsible for this effect, have been studied only in macaque monkeys, using single-cell recordings. Here, as a first step in a research programme aimed at understanding the parallels between human and monkey mirror neuron systems (MNS), we recorded EEG from the scalp of two monkeys during action observation. The monkeys were trained to fixate on the face of a human agent and subsequently to fixate on a target upon which the agent performed a grasping action. We found that action observation produced desynchronization in the 19–25 Hz band that was strongest over anterior and central electrodes. These results are in line with human data showing that specific frequency bands within the power spectrum of the ongoing EEG may be modulated by observation of actions and therefore might be a specific marker of MNS activity.     

The post-embryonic development of cell properties and synaptic drive underlying locomotor rhythm generation in Xenopus larvae.

In the first 24 h of post-embryonic development, the motor rhythm underlying swimming in Xenopus laevis tadpoles changes from brief (ca. 7 ms) ventral root discharge in each cycle to bursts of activity lasting around 20 ms (Sillar et al. 1991). Because individual motoneurons in the spinal cord of newly hatched embryos normally fire only a single impulse per cycle, two possible changes underly the transition to motor bursts seen in larval ventral roots; desynchronization of neurons in a given ventral root which continue to fire once per cycle, or the developmental acquisition of a multiple spike capability in individual motoneurons. Here we have recorded intracellularly from ventrally positioned spinal neurons, presumed to be myotomal motoneurons, in stage 37/38 embryos and 24 h later in development in stage 42 larvae. We find that (i) larval neurons are able to fire more than one impulse per cycle of fictive swimming activity; (ii) unlike in the embryo, they generally will fire multiple impulses in response to injected depolarizing current; (iii) the synaptic drive to motoneurons during swimming increases dramatically in complexity, although it still consists of alternating phases of synaptic excitation and chloride-dependent inhibition, superimposed upon tonic synaptic depolarization. The results therefore suggest a developmental change in the membrane properties of rhythmically active neurons as a major factor in the post-embryonic development of swimming in Xenopus larvae. This change appears to occur in premotor rhythm generating interneurons as well as in the motoneurons themselves and may satisfy a demand for behavioural flexibility that allows larvae to survive in a complex and changing environment.     

A model of stimulus-specific neural assemblies in the insect antennal lobe

It has been proposed that synchronized neural assemblies in the antennal lobe of insects encode the identity of olfactory stimuli. In response to an odor, some projection neurons exhibit synchronous firing, phase-locked to the oscillations of the field potential, whereas others do not. Experimental data indicate that neural synchronization and field oscillations are induced by fast GABA(A)-type inhibition, but it remains unclear how desynchronization occurs. We hypothesize that slow inhibition plays a key role in desynchronizing projection neurons. Because synaptic noise is believed to be the dominant factor that limits neuronal reliability, we consider a computational model of the antennal lobe in which a population of oscillatory neurons interact through unreliable GABA(A) and GABA(B) inhibitory synapses. From theoretical analysis and extensive computer simulations, we show that transmission failures at slow GABA(B) synapses make the neural response unpredictable. Depending on the balance between GABA(A) and GABA(B) inputs, particular neurons may either synchronize or desynchronize. These findings suggest a wiring scheme that triggers stimulus-specific synchronized assemblies. Inhibitory connections are set by Hebbian learning and selectively activated by stimulus patterns to form a spiking associative memory whose storage capacity is comparable to that of classical binary-coded models. We conclude that fast inhibition acts in concert with slow inhibition to reformat the glomerular input into odor-specific synchronized neural assemblies.     

A synchronization-desynchronization code for natural communication signals

Synchronous spiking of neural populations is hypothesized to play important computational roles in forming neural assemblies and solving the binding problem. Although the opposite phenomenon of desynchronization is well known from EEG studies, it is largely neglected on the neuronal level. We here provide an example of in vivo recordings from weakly electric fish demonstrating that, depending on the social context, different types of natural communication signals elicit transient desynchronization as well as synchronization of the electroreceptor population without changing the mean firing rate. We conclude that, in general, both positive and negative changes in the degree of synchrony can be the relevant signals for neural information processing.