Oscillatory mechanisms in pairs of neurons connected with fast inhibitory synapses

The contribution of the basal ganglia and cerebellum to motor learning: A neuro-computational approach

Motor learning involves a widespread brain network including the basal ganglia, cerebellum, motor cortex, and brainstem. Despite its importance, little is known about how this network learns motor tasks and which role different parts of this network take. We designed a systems-level computational model of motor learning, including a cortex-basal ganglia motor loop and the cerebellum that both determine the response of central pattern generators in the brainstem. First, we demonstrate its ability to learn arm movements toward different motor goals. Second, we test the model in a motor adaptation task with cognitive control, where the model replicates human data. We conclude that the cortex-basal ganglia loop learns via a novelty-based motor prediction error to determine concrete actions given a desired outcome, and that the cerebellum minimizes the remaining aiming error.

Neural Circuit Mechanism Underlying the Feeding Controlled by Insula-Central Amygdala Pathway

The Central nucleus of amygdala (CeA) contains distinct populations of neurons that play opposing roles in feeding. The circuit mechanism of how CeA neurons process information sent from their upstream inputs to regulate feeding is still unclear. Here we show that activation of the neural pathway projecting from insular cortex neurons to the CeA suppresses food intake. Surprisingly, we find that the inputs from insular cortex form excitatory connections with similar strength to all types of CeA neurons. To reconcile this puzzling result, and previous findings, we developed a conductance-based dynamical systems model for the CeA neuronal network. Computer simulations showed that both the intrinsic electrophysiological properties of individual CeA neurons and the overall synaptic organization of the CeA circuit play a functionally significant role in shaping CeA neural dynamics. We successfully identified a specific CeA circuit structure that reproduces the desired circuit output consistent with existing experimentally observed feeding behaviors.

•

Activation of the insular cortex→central amygdala (CeA) pathway suppresses feeding

•

Insular cortex neurons send similar excitatory inputs to different types of CeA neurons

•

Model suggests a required circuit with both late firing and regular spiking cells

•

The circuit model can explain current and previous CeA-mediated feeding behaviors

Learning of Central Pattern Generator Coordination in Robot Drawing

How do robots learn to perform motor tasks in a specific condition and apply what they have learned in a new condition? This paper proposes a framework for motor coordination acquisition of a robot drawing straight lines within a part of the workspace. Then, it addresses transferring the acquired coordination into another area of the workspace while performing the same task. Motor patterns are generated by a Central Pattern Generator (CPG) model. The motor coordination for a given task is acquired by using a multi-objective optimization method that adjusts the CPGs' parameters involved in the coordination. To transfer the acquired motor coordination to the whole workspace we employed (1) a Self-Organizing Map that represents the end-effector coordination in the Cartesian space, and (2) an estimation method based on Inverse Distance Weighting that estimates the motor program parameters for each SOM neuron. After learning, the robot generalizes the acquired motor program along the SOM network. It is able therefore to draw lines from any point in the 2D workspace and with different orientations. Aside from the obvious distinctiveness of the proposed framework from those based on inverse kinematics typically leading to a point-to-point drawing, our approach also permits of transferring the motor program throughout the workspace.

Hebbian Plasticity in CPG Controllers Facilitates Self-Synchronization for Human-Robot Handshaking

It is well-known that human social interactions generate synchrony phenomena which are often unconscious. If the interaction between individuals is based on rhythmic movements, synchronized and coordinated movements will emerge from the social synchrony. This paper proposes a plausible model of plastic neural controllers that allows the emergence of synchronized movements in physical and rhythmical interactions. The controller is designed with central pattern generators (CPG) based on rhythmic Rowat-Selverston neurons endowed with neuronal and synaptic Hebbian plasticity. To demonstrate the interest of the proposed model, the case of handshaking is considered because it is a very common, both physically and socially, but also, a very complex act in the point of view of robotics, neuroscience and psychology. Plastic CPGs controllers are implemented in the joints of a simulated robotic arm that has to learn the frequency and amplitude of an external force applied to its effector, thus reproducing the act of handshaking with a human. Results show that the neural and synaptic Hebbian plasticity are working together leading to a natural and autonomous synchronization between the arm and the external force even if the frequency is changing during the movement. Moreover, a power consumption analysis shows that, by offering emergence of synchronized and coordinated movements, the plasticity mechanisms lead to a significant decrease in the energy spend by the robot actuators thus generating a more adaptive and natural human/robot handshake.

A modeling approach on why simple central pattern generators are built of irregular neurons

The crustacean pyloric Central Pattern Generator (CPG) is a nervous circuit that endogenously provides periodic motor patterns. Even after about 40 years of intensive studies, the rhythm genesis is still not rigorously understood in this CPG, mainly because it is made of neurons with irregular intrinsic activity. Using mathematical models we addressed the question of using a network of irregularly behaving elements to generate periodic oscillations, and we show some advantages of using non-periodic neurons with intrinsic behavior in the transition from bursting to tonic spiking (as found in biological pyloric CPGs) as building components. We studied two- and three-neuron model CPGs built either with Hindmarsh-Rose or with conductance-based Hodgkin-Huxley-like model neurons. By changing a model’s parameter we could span the neuron’s intrinsic dynamical behavior from slow periodic bursting to fast tonic spiking, passing through a transition where irregular bursting was observed. Two-neuron CPG, half center oscillator (HCO), was obtained for each intrinsic behavior of the neurons by coupling them with mutual symmetric synaptic inhibition. Most of these HCOs presented regular antiphasic bursting activity and the changes of the bursting frequencies was studied as a function of the inhibitory synaptic strength. Among all HCOs, those made of intrinsic irregular neurons presented a wider burst frequency range while keeping a reliable regular oscillatory (bursting) behavior. HCOs of periodic neurons tended to be either hard to change their behavior with synaptic strength variations (slow periodic burster neurons) or unable to perform a physiologically meaningful rhythm (fast tonic spiking neurons). Moreover, 3-neuron CPGs with connectivity and output similar to those of the pyloric CPG presented the same results.

Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots

In this paper, we present an extended mathematical model of the central pattern generator (CPG) in the spinal cord. The proposed CPG model is used as the underlying low-level controller of a humanoid robot to generate various walking patterns. Such biological mechanisms have been demonstrated to be robust in locomotion of animal. Our model is supported by two neurophysiological studies. The first study identified a neural circuitry consisting of a two-layered CPG, in which pattern formation and rhythm generation are produced at different levels. The second study focused on a specific neural model that can generate different patterns, including oscillation. This neural model was employed in the pattern generation layer of our CPG, which enables it to produce different motion patterns-rhythmic as well as non-rhythmic motions. Due to the pattern-formation layer, the CPG is able to produce behaviors related to the dominating rhythm (extension/flexion) and rhythm deletion without rhythm resetting. The proposed multi-layered multi-pattern CPG model (MLMP-CPG) has been deployed in a 3D humanoid robot (NAO) while it performs locomotion tasks. The effectiveness of our model is demonstrated in simulations and through experimental results.

Switching mechanisms and bout times in a pair of reciprocally inhibitory neurons

Within the appropriate parameter regime, a deterministic model of a pair of mutually inhibitory neurons receiving excitatory driving currents exhibits bistability-each of the two stable states corresponds to one neuron being active and the other being quiescent. The presence of noise in the driving currents results in a system that randomly switches back and forth between these two states, causing alternating bouts of spiking activity. In this work, we examine the random bout durations of the two neurons and dependence on system parameters. We find that bout durations of each neuron are exponentially distributed, with changes in system parameters altering only the mean of the distribution. Synaptic inhibition independently controls the bout durations of the two neurons-the mean bout time of a neuron is a function of efferent (or outgoing) inhibition, and is independent of afferent (or incoming) inhibition. Furthermore, we find that the mean bout time of a neuron exhibits a critical dependence on the time course (rather than amplitude) of efferent inhibition-mean bout time of a neuron grows exponentially with the time course of efferent inhibition, and the growth rate of this exponential function depends only on the excitatory driving current to that neuron (and not on any other system parameters). We discuss the relevance of our results to the regulation of sleep-wake cycling by medullary and pontine structures within the brain.

Phase response properties of half-center oscillators

We examine the phase response properties of half-center oscillators (HCOs) that are modeled by a pair of Morris-Lecar-type neurons connected by strong fast inhibitory synapses. We find that the two basic mechanisms for half-center oscillations, "release" and "escape", give rise to strikingly different phase response curves (PRCs). Release-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the active to the suppressed state, and PRCs are dominated by a large negative peak (phase delays) at corresponding phases. On the other hand, escape-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the suppressed to the active state, and PRCs are dominated by a large positive peak (phase advances) at corresponding phases. By analyzing the phase space structure of Morris-Lecar-type HCO models with fast synaptic dynamics, we identify the dynamical mechanisms underlying the shapes of the PRCs. To demonstrate the significance of the different shapes of the PRCs for the release-type and escape-type HCOs, we link the shapes of the PRCs to the different frequency modulation properties of release-type and escape-type HCOs, and we show that the different shapes of the PRCs for the release-type and escape-type HCOs can lead to fundamentally different phase-locking dynamics.

On the role of sensory feedbacks in rowat-selverston CpG to improve robot legged locomotion

This paper presents the use of Rowat and Selverston-type of central pattern generator (CPG) to control locomotion. It focuses on the role of afferent exteroceptive and proprioceptive signals in the dynamic phase synchronization in CPG legged robots. The sensori-motor neural network architecture is evaluated to control a two-joint planar robot leg that slips on a rail. Then, the closed loop between the CPG and the mechanical system allows to study the modulation of rhythmic patterns and the effect of the sensing loop via sensory neurons during the locomotion task. Firstly simulations show that the proposed architecture easily allows to modulate rhythmic patterns of the leg, and therefore the velocity of the robot. Secondly, simulations show that sensori-feedbacks from foot/ground contact of the leg make the hip velocity smoother and larger. The results show that the Rowat–Selverston-type CPG with sensory feedbacks is an effective choice for building adaptive neural CPGs for legged robots.

Synaptic patterning of left-right alternation in a computational model of the rodent hindlimb central pattern generator

Establishing, maintaining, and modifying the phase relationships between extensor and flexor muscle groups is essential for central pattern generators in the spinal cord to coordinate the hindlimbs well enough to produce the basic walking rhythm. This paper investigates a simplified computational model for the spinal hindlimb central pattern generator (CPG) that is abstracted from experimental data from the rodent spinal cord. This model produces locomotor-like activity with appropriate phase relationships in which right and left muscle groups alternate while extensor and flexor muscle groups alternate. Convergence to this locomotor pattern is slow, however, and the range of parameter values for which the model produces appropriate output is relatively narrow. We examine these aspects of the model's coordination of left-right activity through investigation of successively more complicated subnetworks, focusing on the role of the synaptic architecture in shaping motoneuron phasing. We find unexpected sensitivity in the phase response properties of individual neurons in response to stimulation and a need for high levels of both inhibition and excitation to achieve the walking rhythm. In the absence of cross-cord excitation, equal levels of ipsilateral and contralateral inhibition result in a strong preference for hopping over walking. Inhibition alone can produce the walking rhythm, but contralateral inhibition must be much stronger than ipsilateral inhibition. Cross-cord excitatory connections significantly enhance convergence to the walking rhythm, which is achieved most rapidly with strong crossed excitation and greater contralateral than ipsilateral inhibition. We discuss the implications of these results for CPG architectures based on unit burst generators.

Parameter space structure of continuous-time recurrent neural networks

A fundamental challenge for any general theory of neural circuits is how to characterize the structure of the space of all possible circuits over a given model neuron. As a first step in this direction, this letter begins a systematic study of the global parameter space structure of continuous-time recurrent neural networks (CTRNNs), a class of neural models that is simple but dynamically universal. First, we explicitly compute the local bifurcation manifolds of CTRNNs. We then visualize the structure of these manifolds in net input space for small circuits. These visualizations reveal a set of extremal saddle node bifurcation manifolds that divide CTRNN parameter space into regions of dynamics with different effective dimensionality. Next, we completely characterize the combinatorics and geometry of an asymptotically exact approximation to these regions for circuits of arbitrary size. Finally, we show how these regions can be used to calculate estimates of the probability of encountering different kinds of dynamics in CTRNN parameter space.

On the dynamics of electrically-coupled neurons with inhibitory synapses

We study the dynamics and bifurcations of noise-free neurons coupled by gap junctions and inhibitory synapses, using both delayed delta functions and alpha functions to model the latter. We focus on the case of two cells, as in the studies of Chow and Kopell (2000) and Lewis and Rinzel (2003), but also show that stable asynchronous splay states exist for globally coupled networks of N cells dominated by subthreshold electrical coupling. Our results agree with those of Lewis and Rinzel (2003) in the weak coupling range, but our Poincaré map analysis yields more information about global behavior and domains of attraction, and we show that the explicit discontinuous maps derived using delayed delta functions compare well with the continuous history-dependent, implicitly-defined maps derived from alpha functions. We find that increased bias currents, super-threshold electrical coupling and synaptic delays promote synchrony, while sub-threshold electrical coupling and fast synapses promote asynchrony. We compare our analytical results with simulations of an ionic current model of spiking cells, and briefly discuss implications for stimulus response modes of locus coeruleus and for central pattern generators.

Oscillations in a Simple Neuromechanical System: Underlying Mechanisms

A half-center neural oscillator was coupled to a simple mechanical system to study the closed-loop interactions between a central pattern generator and its effector muscles. After a review of the open-loop mechanisms that were previously introduced by Skinner et al. (1994), we extend their geometric approach and introduce four additional closed-loop mechanisms by the inclusion of an antagonistic muscle pair acting on a mass and connected to the half-center neural oscillator ipsilaterally. Two of the closed-loop mechanisms, mechanical release mechanisms, have close resemblance to open-loop release mechanisms whereas the latter two, afferent mechanisms, have a strong dependence on the mechanical properties of the system. The results also show that stable oscillations can emerge in the presence of sensory feedback even if the neural system is not oscillatory. Finally, the feasibility of the closed-loop mechanisms was shown by weakening the idealized assumptions of the synaptic and the feedback connections as well as the rapidity of the oscillations.

Local network parameters can affect inter-network phase lags in central pattern generators

Weakly coupled phase oscillators and strongly coupled relaxation oscillators have different mechanisms for creating stable phase lags. Many oscillations in central pattern generators combine features of each type of coupling: local networks composed of strongly coupled relaxation oscillators are weakly coupled to similar local networks. This paper analyzes the phase lags produced by this combination of mechanisms and shows how the parameters of a local network, such as the decay time of inhibition, can affect the phase lags between the local networks. The analysis is motivated by the crayfish central pattern generator used for swimming, and uses techniques from geometrical singular perturbation theory.

Mechanisms underlying fictive feeding in aplysia: coupling between a large neuron with plateau potentials activity and a spiking neuron

The buccal ganglia of Aplysia contain a central pattern generator (CPG) that organizes the rhythmic movements of the radula and buccal mass during feeding. Many of the cellular and synaptic elements of this CPG have been identified and characterized. However, the roles that specific cellular and synaptic properties play in generating patterns of activity are not well understood. To examine these issues, the present study developed computational models of a portion of this CPG and used simulations to investigate processes underlying the initiation of patterned activity. Simulations were done with the SNNAP software package. The simulated network contained two neurons, B31/B32 and B63. The development of the model was guided and constrained by the available current-clamp data that describe the properties of these two protraction-phase interneurons B31/B32 and B63, which are coupled via electrical and chemical synapses. Several configurations of the model were examined. In one configuration, a fast excitatory postsynaptic potential (EPSP) from B63 to B31/B32 was implemented in combination with an endogenous plateau-like potential in B31/B32. In a second configuration, the excitatory synaptic connection from B63 to B31/B32 produced both fast and slow EPSPs in B31/B32 and the plateau-like potential was removed from B31/B32. Simulations indicated that the former configuration (i.e., electrical and fast chemical coupling in combination with a plateau-like potential) gave rise to a circuit that was robust to changes in parameter values and stochastic fluctuations, that closely mimicked empirical observations, and that was extremely sensitive to inputs controlling the onset of a burst. The coupling between the two simulated neurons served to amplify exogenous depolarizations via a positive feedback loop and the subthreshold activation of the plateau-like potential. Once a burst was initiated, the circuit produced the program in an all-or-none fashion. The slow kinetics of the simulated plateau-like potential played important roles in both initiating and maintaining the burst activity. Thus the present study identified cellular and network properties that contribute to the ability of the simulated network to integrate information over an extended period before a decision is made to initiate a burst of activity and suggests that similar mechanisms may operate in the buccal ganglia in initiating feeding movements.

Synchronization of coupled assemblies of relaxation oscillatory electrode pairs

Spatiotemporal patterns emerging through coupling of identical relaxation oscillatory electrode pairs are studied. Each pair, consisting of an iron anode and a copper cathode, oscillates periodically under fixed applied potential difference conditions. It is shown that the system synchronizes rapidly (within few oscillatory cycles) and differences of natural frequencies as well as boundary effects are compensated. The effect of the geometrical configuration on the dynamic modes is investigated for relatively large assemblies of such oscillatory pairs. When oscillators are coupled through neighboring electrodes, the response is synchronized by a simultaneous formation of groups. The formation of groups due to enhancement or inhibition of the oscillations depends on the relative position of interacting anodes and cathodes. The behavior of the system is compared with the response of coupled relaxation cells of neurophysiological interest.

Analysis of oscillations in a reciprocally inhibitory network with synaptic depression

We present and analyze a model of a two-cell reciprocally inhibitory network that oscillates. The principal mechanism of oscillation is short-term synaptic depression. Using a simple model of depression and analyzing the system in certain limits, we can derive analytical expressions for various features of the oscillation, including the parameter regime in which stable oscillations occur, as well as the period and amplitude of these oscillations. These expressions are functions of three parameters: the time constant of depression, the synaptic strengths, and the amount of tonic excitation the cells receive. We compare our analytical results with the output of numerical simulations and obtain good agreement between the two. Based on our analysis, we conclude that the oscillations in our network are qualitatively different from those in networks that oscillate due to postinhibitory rebound, spike-frequency adaptation, or other intrinsic (rather than synaptic) adaptational mechanisms. In particular, our network can oscillate only via the synaptic escape mode of Skinner, Kopell, and Marder (1994).

Geometric analysis of population rhythms in synaptically coupled neuronal networks

We develop geometric dynamical systems methods to determine how various components contribute to a neuronal network's emergent population behaviors. The results clarify the multiple roles inhibition can play in producing different rhythms. Which rhythms arise depends on how inhibition interacts with intrinsic properties of the neurons; the nature of these interactions depends on the underlying architecture of the network. Our analysis demonstrates that fast inhibitory coupling may lead to synchronized rhythms if either the cells within the network or the architecture of the network is sufficiently complicated. This cannot occur in mutually coupled networks with basic cells; the geometric approach helps explain how additional network complexity allows for synchronized rhythms in the presence of fast inhibitory coupling. The networks and issues considered are motivated by recent models for thalamic oscillations. The analysis helps clarify the roles of various biophysical features, such as fast and slow inhibition, cortical inputs, and ionic conductances, in producing network behavior associated with the spindle sleep rhythm and with paroxysmal discharge rhythms. Transitions between these rhythms are also discussed.

Network oscillations generated by balancing graded asymmetric reciprocal inhibition in passive neurons

We describe a novel mechanism by which network oscillations can arise from reciprocal inhibitory connections between two entirely passive neurons. The model was inspired by the activation of the gastric mill rhythm in the crab stomatogastric ganglion by the modulatory commissural ganglion neuron 1 (MCN1), but it is studied here in general terms. One model neuron has a linear current-voltage (I-V) curve with a low (L) resting potential, and the second model neuron has a linear current-voltage curve with a high (H) resting potential. The inhibitory connections between them are graded. There is an extrinsic modulatory excitatory input to the L neuron, and the L neuron presynaptically inhibits the modulatory neuron. Activation of the extrinsic modulatory neuron elicits stable network oscillations in which the L and H neurons are active in alternation. The oscillations arise because the graded reciprocal synapses create the equivalent of a negative-slope conductance region in the I-V curves for the cells. Geometrical methods are used to analyze the properties of and the mechanism underlying these network oscillations.

A 'sticky' interhemispheric switch in bipolar disorder?

Despite years of research into bipolar disorder (manic depression), its underlying pathophysiology remains elusive. It is widely acknowledged that the disorder is strongly heritable, but the genetics are complex with less than full concordance in monozygotic twins and at least four susceptibility loci identified. We propose that bipolar disorder is the result of a genetic propensity for slow interhemispheric switching mechanisms that become 'stuck' in one or the other state. Because slow switches are also 'sticky' when compared with fast switches, the clinical manifestations of bipolar disorder may be explained by hemispheric activation being 'stuck' on the left (mania) or on the right (depression). Support for this 'sticky' interhemispheric switching hypothesis stems from our recent observation that the rate of perceptual alternation in binocular rivalry is slow in euthymic subjects with bipolar disorder (n = 18, median = 0.27 Hz) compared with normal controls (n = 49, median = 0.60 Hz, p < 0.0005). We have presented evidence elsewhere that binocular rivalry is itself an interhemispheric switching phenomenon. The rivalry alternation rate (putative interhemispheric switch rate) is robust in a given individual, with a test-retest correlation of more than 0.8, making it suitable for genetic studies. The interhemispheric switch rate may provide a trait-dependent biological marker for bipolar disorder.

Synchronous bursting can arise from mutual excitation, even when individual cells are not endogenous bursters

Mutual excitation between two neurons is generally thought to raise the excitation level of each neuron or, if they are both bursty, to act to synchronize their bursts. If only one is bursty, it can induce synchronized bursts in the other cell. Here we show that two nonbursty cells can be induced to burst in synchrony by mutual excitatory synaptic connections, provided the presynaptic threshold for graded synaptic transmission at each synapse is at a different level. This mechanism may operate in a recently discovered network in the lobster Homarus gammarus. By a duality between presynaptic threshold and injected current, we also show that two identical, nonbursty, mutual excitatory cells could be induced to burst in synchrony by injecting differing amounts of current in the two cells. Finally we show that differential oscillations between two mutual excitatory cells could be stopped by a slow-tailed hyperpolarizing current pulse into one cell or a slow-tailed depolarizing pulse into the other.