Experimental observation of multistability and dynamic attractors in silicon central pattern generators.

We report on the multistability of chaotic networks of silicon neurons and demonstrate how spatiotemporal sequences of voltage oscillations are selected with timed current stimuli. A three neuron central pattern generator was built by interconnecting Hodgkin-Huxley neurons with mutually inhibitory links mimicking gap junctions. By systematically varying the timing of current stimuli applied to individual neurons, we generate the phase lag maps of neuronal oscillators and study their dependence on the network connectivity. We identify up to six attractors consisting of triphasic sequences of unevenly spaced pulses propagating clockwise and anticlockwise. While confirming theoretical predictions, our experiments reveal more complex oscillatory patterns shaped by the ratio of the pulse width to the oscillation period. Our work contributes to validating the command neuron hypothesis.

[1]  J C Smith,et al.  Spatial and functional architecture of the mammalian brain stem respiratory network: a hierarchy of three oscillatory mechanisms. , 2007, Journal of neurophysiology.

[2]  E. Marder,et al.  The roles of co-transmission in neural network modulation , 2001, Trends in Neurosciences.

[3]  C. Wiersma,et al.  INTERNEURONS COMMANDING SWIMMERET MOVEMENTS IN THE CRAYFISH, PROCAMBARUS CLARKI (GIRARD). , 1964, Comparative biochemistry and physiology.

[4]  R. Douglas,et al.  A silicon neuron , 1991, Nature.

[5]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[6]  A. Ijspeert,et al.  From Swimming to Walking with a Salamander Robot Driven by a Spinal Cord Model , 2007, Science.

[7]  A. Selverston,et al.  The stomatogastric nervous system: Structure and function of a small neural network , 1976, Progress in Neurobiology.

[8]  C Daniel Meliza,et al.  Silicon central pattern generators for cardiac diseases , 2015, The Journal of physiology.

[9]  A. Selverston,et al.  Dynamical principles in neuroscience , 2006 .

[10]  R Huerta,et al.  Dynamical encoding by networks of competing neuron groups: winnerless competition. , 2001, Physical review letters.

[11]  Tetsuya Asai,et al.  An analog CMOS central pattern generator for interlimb coordination in quadruped locomotion , 2003, IEEE Trans. Neural Networks.

[12]  M. P. Nusbaum,et al.  A small-systems approach to motor pattern generation , 2002, Nature.

[13]  Mingzhou Ding,et al.  Transitions to synchrony in coupled bursting neurons. , 2004, Physical review letters.

[14]  S. Hestrin,et al.  Spike Transmission and Synchrony Detection in Networks of GABAergic Interneurons , 2001, Science.

[15]  W. Snodgrass Physiology , 1897, Nature.

[16]  John W. Clark,et al.  Control of multistability in ring circuits of oscillators , 1999, Biological Cybernetics.

[17]  K. Abbink,et al.  24 , 1871, You Can Cross the Massacre on Foot.

[18]  A. Selverston,et al.  Synchronous Behavior of Two Coupled Biological Neurons , 1998, chao-dyn/9811010.

[19]  K. Nakazawa,et al.  Multifunctional Laryngeal Premotor Neurons: Their Activities during Breathing, Coughing, Sneezing, and Swallowing , 2007, The Journal of Neuroscience.

[20]  Ramón Huerta,et al.  Dynamical encoding by networks of competing neuron groups: winnerless competition. , 2001 .

[21]  G. Laurent,et al.  Odor encoding as an active, dynamical process: experiments, computation, and theory. , 2001, Annual review of neuroscience.

[22]  K. Sillar,et al.  Neuromodulation of vertebrate locomotor control networks. , 2011, Physiology.

[23]  K. Lukowiak,et al.  The respiratory central pattern generator of Lymnaea: a model, measured and malleable. , 2000, Respiration physiology.

[24]  E. Marder,et al.  Invertebrate Central Pattern Generation Moves along , 2005, Current Biology.

[25]  Ronald L. Calabrese,et al.  The neural control of alternate heartbeat coordination states in the leech,Hirudo medicinalis , 2004, Journal of comparative physiology.

[26]  Andrey Shilnikov,et al.  Order parameter for bursting polyrhythms in multifunctional central pattern generators. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[28]  M. Gorassini,et al.  Activation patterns of hindlimb motor units in the awake rat and their relation to motoneuron intrinsic properties. , 1999, Journal of neurophysiology.

[29]  J. Cabelguen,et al.  Fictive rhythmic motor patterns induced by NMDA in an in vitro brain stem-spinal cord preparation from an adult urodele. , 1999, Journal of neurophysiology.

[30]  R. Clewley,et al.  Key Bifurcations of Bursting Polyrhythms in 3-Cell Central Pattern Generators , 2013, PloS one.

[31]  O. Shafer,et al.  The Drosophila Circadian Clock Is a Variably Coupled Network of Multiple Peptidergic Units , 2014, Science.

[32]  Farzan Nadim,et al.  Dynamic Interaction of Oscillatory Neurons Coupled with Reciprocally Inhibitory Synapses Acts to Stabilize the Rhythm Period , 2004, The Journal of Neuroscience.

[33]  Julian F R Paton,et al.  Brainstem: neural networks vital for life , 2009, Philosophical Transactions of the Royal Society B: Biological Sciences.

[34]  A. Selverston,et al.  Invertebrate central pattern generator circuits , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[35]  K. R. Weiss,et al.  The command neuron concept , 1978, Behavioral and Brain Sciences.

[36]  I. Rybak,et al.  Brainstem respiratory networks: building blocks and microcircuits , 2013, Trends in Neurosciences.

[37]  F. Delcomyn Neural basis of rhythmic behavior in animals. , 1980, Science.

[38]  Tim Gollisch,et al.  Modeling Single-Neuron Dynamics and Computations: A Balance of Detail and Abstraction , 2006, Science.

[39]  Alain Nogaret,et al.  Modulation of respiratory sinus arrhythmia in rats with central pattern generator hardware , 2013, Journal of Neuroscience Methods.