Modeling Small Oscillating Biological Networks in Analog VLSI
Authors: Sylvie Ryckebusch, James M. Bower, Carver Mead
Published in: Advances in Neural Information Processing Systems 1  (NIPS 1988) (Main Conference Track), 1988

Abstract: We  have used analog VLSI technology to model a class of small os(cid:173) cillating  biological neural circuits  known  as  central pattern  gener(cid:173) ators  (CPG). These circuits generate rhythmic patterns of activity  which drive locomotor behaviour in the animal.  We  have designed,  fabricated,  and tested a model neuron circuit which relies on many  of the  same  mechanisms  as  a  biological  central pattern  generator  neuron,  such  as  delays  and  internal feedback.  We  show  that  this  neuron can be used  to build several small circuits based on known  biological CPG circuits, and that these circuits produce patterns of  output which  are very similar to the observed biological patterns. 
To  date,  researchers  in  applied  neural  networks  have  tended  to  focus  on  mam(cid:173) malian systems  as  the  primary source  of  potentially  useful  biological  information.  However,  invertebrate systems may represent  a source  of ideas  in many ways  more  appropriate, given current levels of engineering sophistication in building neural-like  systems, and given the state of biological understanding of mammalian circuits.  In(cid:173) vertebrate  systems  are  based  on  orders  of magnitude  smaller  numbers  of neurons  than  are  mammalian  systems.  The  networks  we  will  consider  here,  for  example,  are  composed  of  about  a  dozen  neurons,  which  is  well  within  the  demonstrated  capabilities  of current  hardware  fabrication  techniques.  Furthermore,  since  much  more detailed structural information is  available about these systems than for  most  systems in  higher animals, insights can be guided by real information rather than by  guesswork.  Finally, even though they are constructed of small numbers of neurons,  these networks have  numerous interesting and  potentially even useful properties. 
CENTRAL PATTERN  GENERATORS 
Of  all  the  invertebrate  neural  networks  currently  being  investigated  by  neurobi(cid:173) ologists,  the  class  of  networks  known  as  central  pattern  generators  (CPGs)  may  be  especially  worthy  of attention.  A  CPG is  responsible  for  generating  oscillatory  neural  activity  that  governs  specific  patterns  of  motor  output,  and  can  generate  its  pattern  of activity  when  isolated  from  its  normal neuronal  inputs.  This  prop-
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erty, which greatly facilitates experiments, has enabled biologists to describe several  CPGs in  detail at  the cellular and synaptic level.  These networks have  been found  in all animals,  but have been extensively studied in invertebrates [Selverston,  1985]. 
We  chose to model several small CPG networks using analog VLSI technology.  Our  model differs from  most computer simulation models of biological networks [Wilson  and Bower, in press] in that we did not attempt to model the details of the individual  ionic currents,  nor did we  attempt to model each known connection in the networks.  Rather, our aim  was  to determine the basic  functionality  of a  set of CPG networks  by modeling them as  the minimum set of connections required to reproduce output  qualitatively similar to that produced by the real network under certain conditions. 
MODELING  CPG NEURONS 
The  basic  building  block  for  our  model  is  a  general  purpose  CPG  neuron  circuit.  This circuit, shown  in  Figure  1,  is  our model  for  a  typical neuron  found  in central  pattern  generators,  and  contains  some  of  the  essential  elements  of real  biological  neurons.  Like real neurons, this model integrates current and uses positive feedback  to  output  a  train  of pulses,  or  action  potentials,  whose  frequency  depends  on  the  magnitude of the current input.  The part of the circuit which generates these pulses  is  shown  in  Figure 2a [Mead,  19891. 
The second element in  the CPG neuron circuit is the synapse.  In Figure 1,  each pair  of transistors functions as a synapse.  The p-well transistors are. excitatory synapses,  whereas the n-well transistors are inhibitory synapses.  One of the transistors in the  pair sets the strength of the synapse,  while  the other transistor is  the  input of the  synapse.  Each  CPG neuron  has four  different synapses. 
The  third element of our model  CPG neuron  involves  temporal delays.  Delays  are  an essential element in the function of CPGs, and biology has evolved many different  mechanisms  to  introduce delays  into neural networks.  The membrane capacitance  of the  cell  body,  different  rates of chemical reactions,  and  axonal transmission  are  just  a  few  of the  mechanisms which  have  time constants  associated with  them.  In  our  model we  have  included  synaptic  delay  as  the  principle source of delay  in  the  network.  This  is  modeled  as  an  RC  delay,  implemented  by  the follower-integrator  circuit shown in Figure 2b [Mead,  19891.  The time constant of the delay is a function  of the  conductance  of  the  amplifier,  set  by  the  bias  G.  A  multiple  time  constant  delay line is  formed  by cascading several of these elements.  Our neuron circuit uses  a  delay  line  with  three  time  constants.  The  synapses  which  are  before  the  delay  element  are  slow synapses, whereas the  undelayed synapses  are  fa.st  synapses. 
We fabricated the circuit shown in Figure 1 using CMOS, VLSI technology.  Several  of these  circuits  were  put  on  each  chip,  with  all  of  the  inputs  and  controls  going  out  to pads, so  that these  cells  could  be externally connected  to form  the  network  of interest. 
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