{"title": "Lower Boundaries of Motoneuron Desynchronization via Renshaw Interneurons", "book": "Advances in Neural Information Processing Systems", "page_first": 535, "page_last": 542, "abstract": null, "full_text": "Lower  Boundaries  of Motoneuron \n\nDesynchronization  via  Renshaw  Interneurons \n\nMitchell  Gil  Maltenfort It \nDept. of Biomedical Engineering \n\nNorthwestern University \n\nEvanston, IT..  60201 \nc.  J.  Heckman \n\nV. A. Research Service \n\nLakeside Hospital \n\nand Dept. of Physiology \nNorthwestern University \n\nChicago, IT..  60611 \n\nRobert  E.  Druzinsky \n\nDept. of Physiology \n\nNorthwestern University \n\nChicago, IT..  60611 \n\nw.  Zev  Rymer \nDept. of Physiology \n\nand Biomedical Engineering \n\nNorthwestern University \n\nChicago, IT..  60611 \n\nAbstract \n\nUsing a quasi-realistic model of the feedback inhibition ofmotoneurons \n(MNs) by Renshaw cells, we show that weak inhibition is sufficient to \nmaximally  desynchronize MNs,  with  negligible  effects  on  total  MN \nactivity.  MN synchrony can produce a 20 - 30 Hz peak in  the force \npower spectrum, which may cause instability in feedback loops. \n\n1 \n\nINTRODUCTION \n\nThe  structure of the  recurrent inhibitory  connections  from  Renshaw  cells (RCs)  onto \nmotoneurons (MNs)  (Figure 1) suggests that the RC  forms  a  simple negative  feedback \n\n* send mail to: Mitchell G.  Maltenfort, SMPP room 1406, Rehabilitation Insitute of \nChicago, 345 East Superior Street, Chicago, IT.. 60611.  Email address is mgm@nwu.edu \n\n535 \n\n\f536 \n\nMaltenfort, Druzinsky, Heckman, and Rymer \n\nloop. Past theoretical work has examined possible roles of this feedback in smoothing or \ngain regulation of motor output (e.g.,  Bullock and Contreras-Vidal,  1991; Graham and \nRedman,  1993),  but  has  assumed  relatively  strong  inhibitory  effects  from  the  RC. \nExperimental observations (Granit et al.,1961) show that maximal RC activity can only \nreduce MN  frring  rates by a few  impulses per second. although  this  weak inhibition is \nsufficient to affect the timing of MN fuings, reducing the probability that any two MNs \nwill  fire  simultaneously  (Adam  et al.,  1978;  Windhorst et al.,  1978).  In  this  study, \nsimulations  were  used to examine the impact of RC inhibition on MN frring  synchrony \nand to predict the effects of such synchrony on force output. \n\n+ \n\nFigure 1:  Simplified Schematic of Recurrent Inhibition \n\n2 \n\nCONSTRUCTION  OF  THE  MODEL \n\n2.1  MODELING  OF  INDIVIDUAL  NEURONS \n\nThe integrate-and-fIre neuron model  of MacGregor (1987) adequately mimics specific \nfrring patterns.  Coupled first-order differential equations govern membrane potential and \nafterhyperpolarization (AHP) based on injected current and synaptic inputs.  A spike is \nfrred  when  the  membrane  potential  crosses a  threshold.  The  model  was  modified  to \ninclude a membrane resistance in order to model MN s of varying current thresholds. \nMembrane resistance and time constants of model MNs were set to match published data \n(Gustaffson and Pinter,  1984).  The parameters governing AHPs were adjusted to agree \nwith  observations  from  single  action  potentials  and  steady-state  current-rate  plOts \n(Heckman and Binder, 1991).  Realistic frring behavior could be generated for MNs with \ncurrent thresholds of 4 - 40 nA. \n\nAlthough  there  are  no  direct  measurements  of RC  membrane  properties  available, \nappropriate parameters were estimated by extrapolation from the MN parameter set.  The \nsimulated  RC  has  a  30  ms  AHP  and  a  current-rate  plot  matching  that  reported  by \nHultborn and Pierrot-Deseilligny (1979).  Spontaneous frring  of 8 pps is produced in  the \nmodel by  setting  the RC  firing  threshold  to  0.01  mV  below resting  potential;  in  vivo \n\n\fLower Boundaries of Motoneuron Desynchronization via Renshaw Intemeurons \n\n537 \n\nthis  fuing  is  likely  due  to  descending  inputs  (Hamm  et al.,  1987a),  but  there  is  no \nquantitative description of such inputs. The RCs are assumed to be homgeneous. \n\nCONNECTIVITY  OF  THE  POOL \n\n2.2 \nSimulated neurons  were  arranged along  a 16 by  16 grid.  The network consists of 256 \nMNs and 64 RCs, with the RCs ordered on even-numbered rows and columns; as a result, \nthe MN - RC connections are inhomogeneous along the pool.  For each trial, MN pools \nwere randomly generated following the distribution of MN current thresholds for a model \nof the cat medial gastrocnemius motor pool  (Heckman and Binder, 1991). \n\nCommunication between neurons is mediated by synaptic conductances which open when \na  presynaptic cell  fues,  then  decay  exponentially.  MN excitation  of RCs  was  set to \nproduce RC  fuing rates  S;  190 pps (Cleveland et aI.,  1981) which linearly increase with \nMN activity  (Cleveland and Ross,  1977). MN  activation  of RCs  scales  inversely with \nMN current threshold (Hultbom et al., 1988). \n\nConnectivity  is  based on observations that synapses from  RCs  to  MNs have  a  longer \nspatial range  than  the reverse (reviewed in Windhorst,  1990).  The  IPSPs produced by \nsingle  MN fIrings  are  4  - 6  times  larger  than  those  produced by  single  RC  fIrings \n(Hamm et al.,  1987b;  van  Kuelen,  1981).  In  the  model,  each MN  excites RCs  within \none column  or row  of itself,  and  each  RC  inhibits  MNs  up  to  two  rows  or columns \naway; thus, each MN excites 1 - 4 RCs (mean 2.25) and receives feedback from 4 - 9 RCs \n(mean 6.25). \n\nACTIVATION  OF  THE  POOL \n\n2.3 \nThe  MNs  are  activated by  applied  step currents.  Although  this  is  not realistic,  it is \ncomputationally efficient.  An  option in  the simulation program allows for the addition \nof bandlimited  noise  to  the  activation  current,  to  simulate  a  synchronizing  common \nsynaptic input.  This  signal has an rms  value of 3%  of the mean  applied current and is \nlOW-pass mtered with a cutoff of 30 Hz.  This allows us look at the effects due purely to \nRC  activity  and to  establish  which  effects persist when  the MN pool  is being actively \nsynchronized. \n\n3 \n\nEFFECTS  OF  RC  STRENGTH  ON  MN  SYNCHRONY \n\n3.1 \n\nDEFINITION  OF  SYNCHRONY  COEFFICIENT \n\nConsider  the  total  number of spikes  frred  by  the  MN pool as  a  time  series.  During \nsynchronous  firing,  the MN spikes  will  clump  together and  the  time  series  will  have \nregions of very many or very few  MN spikes.  When the MNs are de synchronized, the \nrange of spike counts in each time bin will contract towards the mean.  It follows  that a \nsimple measure of MN synchrony is the the coeffIcient of variation (c. v. = s.d. I mean) of \nthe  time  series formed  by  the  summed MN activity.  Figure 2  shows typical  MN pool \nfIring  before  and  after  RC  feedback  inhibition  is  added;  the  changes  in  \"clumping\" \ndescribed above are quite visible in the two plots. \n\n\f538 \n\nMaltenfort, Druzinsky, Heckman, and Rymer \n\n3.2 \n\n\"PLATEAU\"  OF  DESYNCHRONIZATION \n\nThe magnitude of the synaptic conductance from RCs onto MNs was changed from zero \nto  twice physiological in  order to compare  the  effects  of 'weak' and  'strong' recurrent \ninhibition.  At activation  levels  sufficient to  recruit  at least 70%  of MNs in the pool \n(mean  tiling  rate  ~ 15  pps),  a  surprising  plateau  effect  was  seen.  The  synchrony \ncoefficient  fell  off with  RC  synaptic  conductance  until  the  physiological  level  was \nreached,  and  then  no  further de synchronization  was  seen.  The effect persisted when \nsynchronizing noise was added (Figure  3).  At activation levels sufficient to  show  this \nplateau, this \"comer\" inhibition level was always the same. \n\nSynchronized Firing (no RC inhibition) \n\n50 \n\nO~~~u-~~~~~~~~~~~~~~~~~~ \n200 \n\n150 \n\n100 \n\n50 \n\no \n\nDesynchronized Firing (RC inhibition added) \n\n20 \n\no \n\nO~----~--~--------~~~----~u-~~~~ \n200 \nTime (ms) \n\n100 \n\n150 \n\n50 \n\nFigure 2:  Comparison of Synchronous and Asynchronous MN Firing \n\nAt  this  comer  level,  the  decrease  in  mean  MN  firing  rate  was  ~ 1  pps  and  not \nstatistically significant.  There was also no discernible change in  the percentage of the \nMN pool active. The c.v. of the interspike interval of single MN filings during constant \nactivation is  ~  2.5  % even with RCs  active  - this  implies that the RC  system finds  an \noptimal arrangement of the MN fuings and then performs few if any further shifts.  When \nsynchronizing noise is added, the RC effect on the interspike interval is swamped by the \neffect of the synchronizing random input. \n\nFigure 4  shows  the  effect of increasing  MN activation  on  the  synchrony  coefficients \nbefore and  after RC  inhibition  is  added.  The  change  is  statistically  significant at all \nlevels, but is only large at higber levels as discussed above.  As activation of the MNs \n\n\fLower Boundaries of Motoneuron Desynchronization via Renshaw Intemeurons \n\n539 \n\nincreases, the \"before\" level of synchrony increases while the \"after\" level seems to move \nasymptotically  towards a minimum  level  of about 0.35.  This  minimum  level of MN \nsynchrony,  as well as  the dependence of the effect on  the activation  level of the  pool, \nsuggests  that  a  certain  amount  of synchrony  becomes  inevitable  as  more  MNs  are \nactivated and fIre at higher rates. \n\n* \n\n1.4 \n\n1.2 \n\n1 \n\n0.8 \n\n0.6 \n\n0.4 \n\nsynchronizing noise added \n\no \n\n0.002 \n\n0.004 \n\n0.006 \n\n0.008 \n\n0.01 \n\nRC Synaptic Conductance ijJ.Siemens) \n\nFigure 3:  MN Firing Synchrony vs.  RC Strength \n\n4 \n\nEFFECTS  OF  MN  SYNCHRONY  ON  MUSCLE  FORCE \n\n4.1  MODELING  OF  FORCE  OUTPUT \nSingle  twitches  of motor units  are  modeled with  a second-order model,  f(t)  = Be-tit, \nwhere the amplitude F and time constant t  are matched to MN current threshold according \nto  the  model  of Heckman and  Binder (1991).  A rate-based gain  factor  adapted  from \nFuglevand (1989) produces fused tetanus at high fuing  rates.  The  tenfold difference in \ncurrent thresholds maps to a fifty-fold difference in twitch forces.  Twitch time constants \nrange 30-90 ms. \n\nt \n\n\f540 \n\nMaltenfort, Druzinsky, Heckman, and Rymer \n\n4.1 \n\nEFFECTS  OF  RECURRENT  INHmITION  ON  FORCE \n\nThe force model sharply low-pass fllters the neural input signal (S 5 Hz). As a result,  the \nc.v.  of the  force  output is  much lower than  that of the associated  MN input (S 0.01). \nAlthough  the plot of force  c.v.  vs.  RC strength during  constant activation  follows  the \ncurve in Figure 3, adding synchronizing noise removes any correlation between force .c.v. \nand magnitude of recurrent inhibition.  The effect of recurrent inhibition on mean force is \nsimilar  to  that  on  the  mean  firing  rate:  small  (S5  %  decrease)  and  generally  not \nstatistically significant \n\n0 \n\n1.8 \n\n1.6 \n\n1.4 \n\nbefore recurrent inhibition \n\n1.2 \n\n~ c \n~ u \n~ \n~ \nbO \n:5 \n0.8 \n~  0.6 \n\n1 \n\n~ \n\n0.4 \n\n0.2 \n\n5 \n\n10 \n\n15 \n\n20 \n\n25 \n\n30 \n\n35 \n\nActivation Current (nA) \n\nFigure 4: Effects of MN Activation on Synchrony Before and After Recurrent Inhibition \n\nWhen the change in synchrony due  to  RCs  is large, a  peak appears in the force  power \nspectrum in the range 20 - 30 Hz.  This peak is reduced by RCs even when the MN pool \nis being actively synchronized (Figure 5).  Peaks in the force spectrum match peaks in the \nspectrum of pooled MN activity, suggesting the effect is due to synchronous MN ruing. \n\nAlthough the magnitude of this peak is small (S 0.5% of mean force),  its relatively high \nfrequency suggests that in derivative feedback - where spectral components are multiplied \nby 21t times their frequency  - its impact could be substantial.  The feedback loop which \nmeasures muscle stretch contains such a derivative component (Hook and Rymer,  1981). \n\n\fLower Boundaries of Motoneuron Desynchronization via Renshaw Intemeurons \n\n541 \n\n5 \n\nDISCUSSION \n\nThe preceding shows that the ostensibly weak recurrent inhibition is sufficient to sharply \nreduce  the  maximum  number  of synchronous  Irrings  of a  neuron  population,  while \nhaving a negligible effect on the total population activity.  This has a broad implication \nfor neural networks in  that it suggests the existence of a \"switching mechanism\" which \nforces  the peaks  in  the output of an ensemble of neurons to  remain below a  threshold \nlevel without significantly suppressing the total ensemble activity. \n\nOne possible role  for  such  a mechanism  would be in  the  accommodation  to  a step or \nramp increase in a stimulus.  The initial increase synchronizes the neural signal from the \nreceptor,  which  is  then  desyncbronized by  the  recurrent inhibition.  The synchronized \nruing phase would be sufficient to excite a target neuron past its ruing threshold, but after \nthat, the desyncbronized neural signal would remain well below the target's threshold. \n\n0.2 \n\n0.15 \n\n0.1 \n\n0.05 \n\nO~--------~--------~----------~------~ \no \n40 \n\n20 \n\n10 \n\n30 \n\nFrequency (Hz) \n\nFigure 5:  Recurrent Inhibition Reduces  Spectral Peak.  95% confidence limit of means \nplotted, solid lines before recurrent inhibition and dashed lines after. \n\nAcknowledgments \nThe authors are indebted to Dr. Tom Buchanan for use of his IBM RS/6000 workstation. \nThis work was supported by NIH grants NS28076-02 and NS30295-01. \n\n\f542 \n\nMaltenfort, Druzinsky, Heckman, and Rymer \n\nReferences \n\nAdam  D,  Windhorst  U,  Inbar  GF:  The  effects  of recurrent  inhibition  on  the  cross(cid:173)\ncorrelated flring patterns of motoneurons (and their relation to signal transmission in  the \nspinal cord-muscle channel).  Bioi.  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Cybem., \n29:  221-227,  1978. \n\n\f", "award": [], "sourceid": 756, "authors": [{"given_name": "Mitchell", "family_name": "Maltenfort", "institution": null}, {"given_name": "Robert", "family_name": "Druzinsky", "institution": null}, {"given_name": "C.", "family_name": "Heckman", "institution": null}, {"given_name": "W.", "family_name": "Rymer", "institution": null}]}