Intrinsic Bursters Increase the Robustness of Rhythm Generation in Range

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					     Intrinsic Bursters Increase the
Robustness of Rhythm Generation in
              an Excitatory Network

  L. K. Purvis, J. C. Smith, H. Koizumi, and R. J. Butera
 Pre-Botzinger Complex (pBC)
    Network is critical for generating respiratory rhythm
    Contains intrinsic bursters (pacemakers, PMs)
        Cells capable of bursting in absence of synaptic input
        Two types: NaP dependent, Ca++ dependant
    Excitatory network coupling
        Neuromodulators change # of pacemakers in network

     How does the fraction of the network population that is composed of
                    intrinsic bursters affect measures of
                           rhythmogenic capacity?
Input range = size of parameter space where network wide rhythmic bursting occurs
Output range = range of bursting frequencies network produces over input range
The Model:
   Data is from Koizumi and Smith (2004)

   Heterogeneous excitatory network of 50 pBC neurons
       Single-compartment HH model
       Population distributions reflect range AND variability of experimental data
       Results presented from all-to-all coupling

   3 VG currents
       VG fast Na+ current (i_Na)
       K+ delayed rectifier (i_KDR)
       Slowly inactivating persistent Na+ (i_NaP)

   1 K+ dominated leak current (i_leak)

   Parameters varied:
       Fraction of Pacemakers
       Amount of excitatory drive (g_tonic) -> models tonic spiking population
       Strength of synaptic coupling (g_syn)
Membrane Potential

      (calculated for each of
      4 currents)

Ionic conductance dynamics:

Activation/inactivation function

Voltage dependant time constant
Pacemaker and Non-pacemaker cells have
different g_NaP / g_leak ratios:

    Experimentally measured

  Model parameter space
             Experimental data are corrected by increasing
                         gNaP values by 25%

corrected experimental data:     some data points fall outside the   randomly generated
Line is models boundary          boundary allowed for model          parameter distribution,
                                 parameters                          30 PMs and 20 NPMs

                                            Data                     Model
                   Conductance     Mean, nS     SD, %        Mean, nS     SD, %
            PM     g_NaP           2.43         31           2.44         31
                   g_leak          2.51         37           2.20         37
            NPM    g_NaP           1.10         27           1.11         27
                   g_leak          2.51         34           3.00         28
Model behavior as g_tonic is increased:
A: g_leak = 2.2nS g_NaP = 1.5nS silence -> tonic firing
B: g_leak = 2.2nS g_NaP = 2.5nS silence -> burst -> tonic
Three network activity modes:
       (top row = rasters, bottom row = histograms)
Only interested in regular bursting
Vary 3
report burst

   Black regions: could be silence, a few cells bursting, irregular bursting, or
   tonic firing.

   Variability: each point is a distinct simulation with different randomly
   generated parameters. (g_leak)
     Represents data from > 4,000 simulations
                 •Networks with g_syn= 0.15 or
                 0.2 span greatest input range

                     •Highest g_syn peaks, then
HIGH g               decreases

                     •Lowest g_syn requires >20
                     PMs to burst
         LOW g
        (output range)                 Variability

•Max = solid
•Min = empty circles

•As # PMs increases, output range increases

•If network bursts with no PMs, output range is small
(synaptic conductance
increases from 0.075 to
0.3 nS as each trace
progresses clockwise.)

(number of PMs
increases as each trace
progresses from left to right.)
Sparsely Connected Networks
   Probability of connection = 10%
   Synaptic strength varied:
       1, 1.5, 2nS
   Results are consistent with all-to-all coupling results
       Input and Output range increased as number of PMs increased.
       Magnitude of frequency range was similar.
   Optimal synaptic conductance level falls between 0.15nS
    and 0.2nS.

       Largest input and output range

   Authors ran additional simulations at these values

                           for 0.2nS

Bold = average of 5 runs
Increasing # of PMs increases bursting frequency range and reliability

                         Network can burst with fewer PMs, but less reliably
                 G_syn= 0.15nS

Model Prediction: Increasing # of PMs increases input and output range
Discussion and Predictions:
   Controllability:
       Increasing g_syn can increase input range, but at cost of output
       Increasing # of PMs increases input & output range

   PMs are not required for bursting
       But, their inclusion triples input and output ranges
   i_NaP is required for bursting
       Provides mechanism for single unit rhythmic bursting
       And population level synchronized bursts and termination

   Hypoxia increases NaP conductance density
       May increase PMs in network, increase burst frequency

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Description: Intrinsic Bursters Increase the Robustness of Rhythm Generation in Range