A Codimension-2 Bifurcation Controlling Endogenous Bursting Activity and Pulse-Triggered Responses of a Neuron Model

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals–the duration of the burst and the duration of latency to spiking–are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of oscillators

Mechanisms of the Coregulation of Multiple Ionic Currents for the Control of Neuronal Activity

An open question in contemporary neuroscience is how neuromodulators coregulate multiple conductances to maintain functional neuronal activity. Neuromodulators enact changes to properties of biophysical characteristics, such as the maximal conductance or voltage of half-activation of an ionic current, which determine the type and properties of neuronal activity. We apply dynamical systems theory to study the changes to neuronal activity that arise from neuromodulation. Neuromulators can act on multiple targets within a cell. The coregulation of mulitple ionic currents extends the scope of dynamic control on neuronal activity. Different aspects of neuronal activity can be independently controlled by different currents. The coregulation of multiple ionic currents provides precise control over the temporal characteristics of neuronal activity. Compensatory changes in multiple ionic currents could be used to avoid dangerous dynamics or maintain some aspect of neuronal activity. The coregulation of multiple ionic currents can be used as bifurcation control to ensure robust dynamics or expand the range of coexisting regimes. Multiple ionic currents could be involved in increasing the range of dynamic control over neuronal activity. The coregulation of multiple ionic currents in neuromodulation expands the range over which biophysical parameters support functional activity

Contributions of Identifiable Neurons and Neuron Classes to Lamprey Vertebrate Neurobiology

Among the advantages offered by the lamprey brainstem and spinal cord for studies of the structure and function of the nervous system is the unique identifiability of several pairs of reticulospinal neurons in the brainstem. These neurons have been exploited in investigations of the patterns of sensory input to these cells and the patterns of their outputs to spinal neurons, but no doubt these cells could be used much more effectively in exploring their roles in descending control of the spinal cord. The variability of cell positions of neurons in the spinal cord has precluded the recognition of unique spinal neurons. However, classes of nerve cells can be readily defined and characterized within the lamprey spinal cord and this has led to progress in understanding the cellular and synaptic mechanisms of locomotor activity. In addition, both the identifiable reticulospinal cells and the various spinal nerve cell classes and their known synaptic interactions have been used to demonstrate the degree and specificity of regeneration within the lamprey nervous system. The lack of uniquely identifiable cells within the lamprey spinal cord has hampered progress in these areas, especially in gaining a full understanding of the locomotor network and how neuromodulation of the network is accomplished

Ion homeostasis in rhythmogenesis : the interplay between neurons and astroglia

Proper function of all excitable cells depends on ion homeostasis. Nowhere is this more critical than in the brain where the extracellular concentration of some ions determines neurons' firing pattern and ability to encode information. Several neuronal functions depend on the ability of neurons to change their firing pattern to a rhythmic bursting pattern, whereas, in some circuits, rhythmic firing is, on the contrary, associated to pathologies like epilepsy or Parkinson's disease. In this review, we focus on the four main ions known to fluctuate during rhythmic firing: calcium, potassium, sodium, and chloride. We discuss the synergistic interactions between these elements to promote an oscillatory activity. We also review evidence supporting an important role for astrocytes in the homeostasis of each of these ions and describe mechanisms by which astrocytes may regulate neuronal firing by altering their extracellular concentrations. A particular emphasis is put on the mechanisms underlying rhythmogenesis in the circuit forming the central pattern generator (CPG) for mastication and other CPG systems. Finally, we discuss how an impairment in the ability of glial cells to maintain such homeostasis may result in pathologies like epilepsy and Parkinson's disease

Duty Cycle Maintenance in an Artificial Neuron

Neuroprosthetics is at the intersection of neuroscience, biomedical engineering, and physics. A biocompatible neuroprosthesis contains artificial neurons exhibiting biophysically plausible dynamics. Hybrid systems analysis could be used to prototype such artificial neurons. Biohybrid systems are composed of artificial and living neurons coupled via real-time computing and dynamic clamp. Model neurons must be thoroughly tested before coupled with a living cell. We use bifurcation theory to identify hazardous regimes of activity that may compromise biocompatibility and to identify control strategies for regimes of activity desirable for functional behavior. We construct real-time artificial neurons for the analysis of hybrid systems and demonstrate a mechanism through which an artificial neuron could maintain duty cycle independent of variations in period

Hydrodynamics of Biomimetic Marine Propulsion and Trends in Computational Simulations

[Abstract] The aim of the present paper is to provide the state of the works in the field of hydrodynamics and computational simulations to analyze biomimetic marine propulsors. Over the last years, many researchers postulated that some fish movements are more efficient and maneuverable than traditional rotary propellers, and the most relevant marine propulsors which mimic fishes are shown in the present work. Taking into account the complexity and cost of some experimental setups, numerical models offer an efficient, cheap, and fast alternative tool to analyze biomimetic marine propulsors. Besides, numerical models provide information that cannot be obtained using experimental techniques. Since the literature about trends in computational simulations is still scarce, this paper also recalls the hydrodynamics of the swimming modes occurring in fish and summarizes the more relevant lines of investigation of computational models

Neural Control of Interlimb Oscillations II. Biped and Quadruped Gaits and Bifurications

Behavioral data concerning animal and human gaits and gait transitions are simulated as emergent properties of a central pattern generator (CPG) model. The CPG model is a version of the Ellias-Grossberg oscillator. Its neurons obey Hodgkin-Huxley type equations whose excitatory signals operate on a faster time scale than their inhibitory signals in a recurrent on-center off-surround anatomy. A descending command or GO signal activates the gaits and triggers gait transitions as its amplitude increases. A single model CPG can generate both in-phase and anti-phase oscillations at different GO amplitudes. Phase transition from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases. Quadruped vertebrate gaits, including the amble, the walk, all three pairwise gaits (trot, pace, and gallop), and the pronk are simulated using this property. Rapid gait transitions are simulated in the order walk, trot, pace, and gallop that occurs in the cat, along with the observed increase in oscillation frequency. Precise control of quadruped gait switching uses GO-dependent. modulation of inhibitory interactions, which generates a different functional anatomy at different arousal levels. The primary human gaits (the walk and the run) and elephant gaits (the amble and the walk) are simulated, without modulation, by oscillations with the same phase relationships but different waveform shapes at different GO signal levels, much as the duty cycles of the feet are longer in the walk than in the run. Relevant neural data from spinal cord, globus palliclus, and motor cortex, among other structures, are discussedArmy Research Office (DAAL03-88-K-0088); Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-92-J-1309); Air Force Office of Scientific Research (F49620-92-J-0499, F49620-92-J-0225, 90-0128

Ionic currents and intrinsic properties of key interneurons and their influence on network activity in a chain of coupled oscillators

Post-inhibitory rebound (PIR) plays an important role in producing rhythmic network activity. By inducing new excitation, following a phase of inhibition it promotes the generation of rhythmic neuronal activity. I investigated this property in identified neurons of the swimmeret system. These neurons are characterized by membrane potential oscillations and create the well-coordinated Power- and Return-Stroke movements of four pairs of swimmerets at the abdomen of crayfish. I isolated the abdominal nervous system and performed current clamp recordings with sharp electrodes at the dendritic aborizations of the neurons. I tested whether the neurons are able to produce a PIR by injecting hyperpolarizing current pulses. All spiking neurons (PSE, RSE, ASCE and DSC) possessed the ability to produce a PIR, which was accompanied by a small sag potential. In contrast, not all neurons of the central pattern generator, IPS, generated a PIR. The only neuron receiving excitatory synaptic input, ComInt1, also produce a PIR. Different ionic currents are shown in various studies to account for the generation of a PIR. Those are the L-type calcium current (ICaL), the hyperpolarization activated cation current (IH), and in some systems the persistent sodium current (INaP). In the following experiments, I investigated the ionic basis of the PIR in the above described neuron groups. I could detect that both ICaL and IH and partially INaP generate PIR responses in the spiking neurons PSE, RSE, ASCE and DSC, while only IH seemed to be involved in generating the PIR in IPS. To test the significance of the identified ionic conductances for generation of rhythmic motor output, I blocked the respective ionic currents individually while monitoring fictive locomotion of the system on the network-, as well as on the single cell level. During this series of experiments also the contribution of the transient potassium current, IA, was investigated by application of 4-AP. Confirming the importance of the above identified currents (ICaL, IH and INaP), all ion channel blockers altered the ability of the entire system to produce a steady motor rhythm. Similar strong effects were observed when blocking IA. These results of this study demonstrate that PIR is an essential mechanism for the neurons in the swimmeret system to induce new excitability after a phase of inhibition. This suggests that PIR plays a crucial role in establishing rhythmic cellular activity. Furthermore, I could show that PIR responses were mediated by different ionic current depending on the neuron group

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