So this implies that for a good coding system, its input output function, this
function here, should be determined by the distribution of natural inputs.
So here's a classic study in which this idea was tested directly.
In the early 1980's, Simon Laughlin went out into the fields with a camera, and
measured the typical contrasts, that is deviations in the light level, divided by
the mean light level, that would be experienced in the natural world, for
example, by a fly. So, that's this distribution here.
If the response does indeed follow the distribution of natural inputs...
Then the response curve, here, should look like the cumultive probability
determined by integrating p of c. And in fact, that's a very good match to
what he did actually observe in the response properties of the fly large
mono-polar cells, the neurons that integrate signals from the fly's
photo-receptors. Now, a study like this poses a challenge.
While it makes sense that our sensory systems would, over evolution or
development, set up response codes that are adjusted to natural input statistics.
It seems that much more work is needed to handle the problems posed by this huge
natural variation, that stimuli take as one moves from indoors to outdoors or
even moves one's eyes around a room. The contrast distribution is varying
widely. Might sensory systems rather adjust
themselves on much shorter timescales to take these statistical variations into
account. So let's take a patch of the image, and
look at the, the variations in contrast in that image.
Here for example, that contrast distribution might take, might be narrow
like this. Wheras over here, it might be much
broader. What our code should do is take the
widths of these distributions into account in setting up a local.
Input, output curve, that accommodates this structure of the, currently measured
statistics of the input. So that's the question that we tested
here, in the h1 neuron. In this experiment, we took a white-noise
input, of the type that you used in the problem sets, so some s of t.
Looks like that. And we multiplied it by some time
varying, slowing time varying envelope. Call that sigma of t.
And that's what you see here. So we repeated the same sigma of t.
This is a 90 second long chunk of stimulus.
Repeated the same sigma of t. In every trial, but we changed the
specific white noise. Stimulus.
And that allowed us to pick out spikes that occurred at different time points
throughout this presentation of, of sigma of t, where in every trial the cell would
have seen a different specific stimulus. And to calculate the input output
function described by those spikes, in those different, in those different
windows of time. So now one, when one analyzes spikes
across these different windows, and pulls out their input output function using the
methods that we talked about in week two, one finds that for example, here in this
window, one gets a very broad input and output curve.
Where, when the stimulus is varying very little, one finds a very sharp input and
output curve. Now, it turns out that if one normalizes
the stimulus by its standard deviation, or by this envelope sigma of t, all of
these curves collapse onto the same curve.
What that says is that the code has the freedom to stretch its input access such
that it's accommodating these variations in the overall scale of the stimulus.
And it's able to do that in real time as this envelope is varying.
This is being seen in several other systems, including the retna and the
auditory system. But here's an example from rat barrel
cortex. This is somatosensory cortex of the rat.
In particular. The part that encodes the vibrations of
whiskers. So, from extracellular in vivo recordings
of responses to whisker motion, whiskers were stimulated with a velocity signal
again, s of t, that looked like this. So this is a slightly simpler experiment.
The standard deviation was varied between two different values.
And now one can pull out spikes that are generated in these two epochs that
presentation. The high variance case and the low
variance case. And one can compute input output curves
for spikes that occurred under these two different conditions.