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Background

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Biophysical Constraints on the Precision of Neural Encoding ... Supported by NIH grants MH12159 (AGD) and MH57179 (JPM, JAB) and NSF grant MRI 9871191. ... – PowerPoint PPT presentation

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Title: 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)
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