Download How is the stimulus represented in the nervous system?

How is the stimulus represented in the nervous
system?
Eric Young
F. Rieke et al. Spikes MIT Press (1997). Especially chapter 2.
I. Nelken et al. Encoding stimulus information by spike numbers and
mean response time in primary auditory cortex. J Comput Neurosci
19:199-221 (2005).
The fundamental assumption is
that the representation is in
terms of spike times (as
opposed to subthreshold
potentials for example).
For the analysis, the spike train
is reduced to a series of time
points, the times at which action
potentials occur.
A basic analysis: how did the
neuron respond to the stimulus?
D.K. Ryugo
But there are two different problems:
(1) characterizing the response to a given stimulus
(2) inferring the stimulus given a particular response.
Note
they
are
different!
Characterizing
the response,
given the
stimulus
Characterizing
the stimulus
given the
response
The response
(number of spikes in
0.2 s)
The stimulus (optical
flow velocity)
Rieke et al 1997
In principal, the two kinds of descriptions are interconvertible using
Baye’s theorem:
measure in an
experiment
P(v n) =
P(n, v)
P(n)
and so
P(v n) =
P(n v)P(v)
P(n)
The problem comes in estimating P(v) and P(n) which may be difficult to
do meaningfully, especially for natural stimuli. Thus we often work on the
forward problem, estimating the response given an arbitrary stimulus,
and postpone the reverse problem.
There is another problem: what is the appropriate variable to use for n,
the response? Number of spikes is easy, but other measures which
include spike times may be more appropriate.
The stimulus is represented by the strength of firing (i.e. the discharge
rate) or by some aspect of spike timing. Usually there is more information in the
latter.
stimulus
spike train
time
rate code: different
number of spikes,
depending on the
stimulus
stimulus
(expanded
time scale)
spike train
(note phase locking of the
spikes to the stimulus
waveform)
Any representation is based on population
responses, i.e. on the distribution of activity in
the array of neurons. In hearing that means a
tonotopic representation, by frequency.
The idea of a tonotopic representation is
illustrated by the rate representation of sound
spectrum in the auditory nerve, in this case for
the vowel /eh/, as in met.
The plots show discharge rate in a large
population of auditory nerve fibers, plotted
versus best frequency. The lines are smoothed
versions of the data points.
individual fibers' rates
Sachs and Young, 1979
Spike timing in the stimulus response can contribute to the representation in the brain.
(1) Note the periodic responses at the frequencies of components of the stimulus (e.g.
F1, F2, and F3 for the /da/ below). Using this information requires a central processor
sensitive to temporal patterns.
(2) The transitions along the frequency axis from one component of the stimulus to the
next could serve as cues readable by central coincidence detectors.
(3) Similarly relative latency across BF could be used, discussed later.
Shamma 1985 from Miller and Sachs 1983
A temporal representation need not reflect the actual waveform of the stimulus, as in the
previous example. Neurons also code aspects of the stimulus by changing the overall
temporal patterns of response.
Neurons in auditory
cortex show different
patterns of response
depending on sound
source direction.
A neural network model was
trained to compute source
azimuth from PSTs of neurons’
responses.
This worked pretty well.
Middlebrooks et al. 1998
The analyses described above require
assumptions about the nature of the
representation.
To minimize the effects of assumptions,
search for the optimal stimulus for a neuron,
i.e. the stimulus to which the neuron
responds most strongly.
One approach to finding the optimal stimulus
is to use reverse correlation, in which the
neuron is presented with rich ensemble of
stimuli (noise) and signals its optimum by
where it spikes.
C
In auditory nerve fibers, averaging
the stimulus preceding spikes finds
short tone bursts at the BF of the
neuron, with Fourier transforms
that look like tuning curves, a
comforting result.
Young et al. 2005, Carney and Yin 1988
In the CNS, reverse correlation is applied by averaging the power spectrum of
the stimulus preceding spikes (called the spectro-temporal receptive field,
STRF). The results are more complex with excitatory and inhibitory areas.
This neuron did give strong responses
to downsweeping tones.
deCharms et al. 1998
Although it is a seductive idea, the optimal stimulus may not be so useful.
First, it may not produce a predictive model. Second, neurons may not have
a true optimum.
For example, if rate depends on both linear and 2nd order weighting of the
stimulus spectrum:
r = R0 + ! w j S( f j ) + ! ! m jk S( f j )S( fk )
j
j
k
Then the rate response can have a maximum, a saddle, or a ridge. In these
cases, the optimization method may fail in confusing ways.
DiMattina and Zhang, 2009
The saddle behavior occurs in neurons in the dorsal cochlear nucleus.
DiMattina, Anderson, Young, Zhang, 2010
Moreover, the optimal stimulus derived
in this way may be different depending
on the stimulus ensemble used to
derive it.
In these cases, the STRF is not a
unique characterization of the neuron,
probably because of the nonlinearity of
the neuron’s responses.
Theunissen et al. 2000
Everything up to now has been aimed at estimating P(n|v), the response given the
stimulus.
To approach the estimation of P(v|n), one approach is to use the neuron’s
responses to show how it maps the stimulus space. The stimulus dimensions that
the neuron represents are those that induce a change in its responses.
The stimuli
the spike trains
P1
P2
similar spike trains
P3
not
P4
.
.
.
This neuron considers
stimuli P1 and P3 to be
similar, but stimuli P3 and
P4 to be different.
Pn
A simple example: which auditory nerve fibers signal the difference between
two vowel spectra, based just on discharge rate? The answer is the fibers
with BFs near the formants, where the vowels differ.
Miller et al. 1999
It is useful to be able to measure the information that neurons’ responses provide
about the stimulus. Define information as the reduction in uncertainty about an
event, where uncertainty is measured by entropy
Which stimulus was presented?
?
The possibilities and their probabilities
P1
P2
The uncertainty about the
stimulus or entropy H is
n
H = ! " Pi log 2 Pi
i =1
P3
P4
.
.
.
Then the information provided by the
spike trains about the stimulus is the
reduction in entropy:
MI = H (S) ! H (S R)
Pn
called the mutual information or MI.
An example, trying to discover what
aspects of a stimulus neurons are
responding to, when the responses are
very poorly time-locked.
Responses in insula versus
A1 to a variety of natural
stimuli. The insula responses
bear only a general
relationship to the stimuli.
A monkey
call modified
in three ways
Insula neurons
provide more
information
about the calls
than the
modified ones
Remedios et al. 2009
Neurons can represent multiple cues in their discharge rates. This raises the
question of how different sources of information can be simultaneously represented
by a neuron. For example, in the inferior colliculus:
ILD and SN sensitive
SN, ILD and ITD sensitive
May, Davis, Ramachandran
Of course, neurons are encoding many features of the stimulus simultaneously
(frequency content, loudness, temporal parameters, modulation, . . .
But rate can only code one thing at a time!
confounded
information
Type I and O neurons
vary from SNdominated to ILDdominated.
All types can encode
ITD and vary in the
relative encoding of
ITD and ILD.
Type V neurons
devote little MI to
SN.
(BFs<4 kHz only)
Type V neurons
encode mainly ABI,
whereas type O and
type I units encode
ILD.
Which aspect of a neuron’s response provides the most information about the
stimulus?
1. discharge rate (previous slides)
2. latency of the first spike
3. temporal spiking patterns.
Note that these
are quite different.
Chase and Young 2006
The information contained in spike timing patterns can be analyzed using a method
due to Victor and Purpura, 1997.
1. Distances between spike trains are computed.
2. From the distances a cluster analysis can be done.
3. The result is a confusion matrix from which the MI can be calculated.
Chase and Young 2006
Considering spike timing patterns increases the information in spike trains over that
due to rate.
The extra
information encoded
in spike timing.
Chase and Young 2008
Population responses to two tones. Note
1.
Wide distribution of responses
along the BM.
2.
Two tone suppression of responses
to one tone by the other (*).
3.
Generation of combination tones at
frequencies f2-f1 and 2f1-f2.
Even though there is no energy in
the stimulus at these frequencies,
they distribute along the BM like
real tones. Presumably energy at
these frequencies is generated by
BM nonlinearity.
2.17 and 2.79 kHz at 65 dB SPL.
Kim et al. 1975
*
A better representation is provided by looking at the strength of phase locking at
various BFs. With this measure, it is possible to tell which of the many frequency
components of the vowel produces the response of a particular fiber.
Stimulus frequency
to which the fiber
responds
Strength of
the response
Where on the basilar membrane?
Miller et al. 1997