Background

1
747.4
Background
Results and Analysis

• The distribution of ISIs at generation (blue)
  should be broadened at arrival by noise
  (green)
• In reality, the distribution of ISIs at arrival
  (red) is much
• sharper than at generation (595 µs vs. 735
  µs) for shorter
• ISIs while remaining unchanged for longer
  ISIs

• In temporal coding schemes, information is
  encoded by the
• temporal pattern of spikes
• Therefore, any increase in the uncertainty of
  relative spike
• timing that originates during the
  propagation of spikes from
• the encoding site to the decoding site would
  manifest as
• channel noise in an information-theoretic
  sense
• Major Questions Addressed in this Study
• What is the magnitude of the channel noise
  originating from
• variance in spike propagation time between
  encoder and
• decoder?
• Is the magnitude of this noise component large
  enough to limit
• overall encoding accuracy?
• Previous Results of Relevance
• The maximum spike timing precision at the
  encoding site (spike-
• initiating zone or SIZ) of several sensory
  interneurons was
• calculated to range from 50-100 µs,
  depending on the cell
• (Dimitrov and Miller, 2000)

Variance of Propagation Time

• For each spike marked at recording site
• 1, the delay before a spike was marked
• at recording site 2 was determined
• This delay is the time taken by
• each action potential to travel
• between recording sites
• (about 1 cm apart)
• The black vertical band seen in
• the raster plot at right corresponds
• to the time most commonly taken
• for action potentials to propagate
• between the two recording sites
• The width of this band is the variance
• of this propagation time, and is
• shown in the histogram below

Summary and Conclusions

• The propagation of a spike along an axon
  introduces
• uncertainty to the timing of that spike at a
  post-synaptic
• target site
• In the cells studied here, the variance in spike
  timing intro-
• duced by propagation sets the lower bound on
  the intrinsic
• spike timing precision at the decoder. This
  uncertainty is
• consistent with theoretically-derived values
  for encoding
• precision in this system by Dimitrov and
  Miller (2000).
• The mean propagation time of a spike depends on
  the
• preceding interspike interval shorter
  interspike intervals
• are lengthened by propagation
• The variance of propagation times for different
  interspike
• intervals is relatively independent of the
  interval the variance
• of intervals is about twice the variance of
  propagation times
• for individual spikes (implying independent
  propagation noise
• for each spike.)

• ISI asymptotically approaches a minimum at 2
  ms, corresponding
• to the absolute refractory period for action
  potential generation
• The variance around the best-fit line in the
  logarithmic plot (right panel)
• is the variance in propagation time of
  second spikes for a given ISI
• Width (2s) is 70 µs (average for all ISIs lt 10
  ms)
• Single spikes (preceding ISI gt 10 ms) have
  smaller propagation
• time uncertainty than the second spikes in
  short doublets
• As ISI decreases, propagation time increases
  exponentially
• This effect is due to the relative refractory
  period and is predictable
• from reaction-diffusion models
• From this, we predict that ISIs that are very
  short at spike
• generation will be slightly longer at spike
  arrival (after propagation)

• The red line across the histogram is a
• Gaussian distribution fit to the data,
• although the data are clearly not
• distributed in a Gaussian manner
• The width of the Gaussian (2s) is
• 44 µs, representing the approximate
• variance of the spike propagation time

Effect of Propagation on Inter-Spike Interval
IMPLICATION This variance in propagation time
should accumulate for multi-spike words,
limiting the precision of temporal encoding as
the number of spikes per word increases. QUESTION
Is this the case? ANSWER Not so simple! OUR
APPROACH We measured the dependence of
inter-spike interval on propagation time, and
found that the propagation time variance
is decreased considerably in doublets. Details
Significance
Effect of Inter-Spike Interval on Propagation Time

• The s for an ISI is 29 µs for ISIs gt 10 ms, 43
  µs for ISIs lt 10 ms,
• both of which are compatible with
  independent propagation variances
• Shorter ISIs are lengthened by increased
  propagation time of the
• second spike while longer ISIs are
  unchanged, meaning that the
• distribution of ISIs could be sharper upon
  arrival than it was at
• generation

• Information channel capacity between processing
  stages in
• this system is limited by the biophysical
  processes underlying
• spike propagation.
• However, these properties may also act to
  compensate for
• limitations in the encoding apparatus.
  Specifically,
• the refractory nature of the axon acts to reduce
  uncertainty in
• the timing of spikes in the set which
  consists of short-interval
• doublets. This result has significant
  implications within the
• context of coding with codeword classes
  (Dimitrov and
• Miller, 2001).

• The plot below shows the actual recorded voltage
  traces at both
• recording sites for 5 ms before and after
  the occurrence of some
• selected (sequential) spikes in the
  intracellular recording

• A crickets two cerci contain mechanosensory
  hairs sensitive to
• air currents in the animal's immediate
  vicinity
• The afferent neurons from the hairs synapse with
  10 pairs of
• primary sensory interneurons in the terminal
  abdominal
• ganglion, just below recording site 1
• The interneurons carry the information about the
  air currents
• to the thoracic ganglia and brain, just
  above recording site 2
• Experimentally, perform simultaneous
  electrophysiological
• recordings at both ends of an axon (sites 1
  and 2)
• Determine individual action potential
  propagation times between
• those two ends and calculate the variance of
  those times

References Dimitrov, A.G. and J.P. Miller.
Natural time scales for neural encoding.
Neurocomputing 32-33 (2000) 1027-34. Dimitrov,
A.G. and J.P. Miller. Neural coding and
decoding communication channels and
quantization. Network 12(4) (2001)
441-72. Supported by NIH grants MH12159 (AGD)
and MH57179 (JPM, JAB) and NSF grant MRI 9871191.

• Every blue spike is a singlet or the first spike
  of a doublet, and every
• magenta spike is the second spike of a
  doublet
• The second spike of every doublet takes slightly
  longer to propagate
• These doublets are the source of the haze to
  the right of the black
• vertical band in the raster plot (top)