Case 3
The business end of the mammalian brain is its huge mess of
interconnected neurons, all constantly sending signals to one
another in a massively-connected network. Each neuron is a single cell
with a rather complicated structure. The exact morphology varies
according to location and function, but there's generally a sprawling
3-dimensional collection of branched input channels, called
dendrites because of their tree-like appearance; a main body or
soma that contains the nucleus and organelles; and a long output
channel called the axon. The axon from each neuron intersects the
dendrites from many others at synapses. The neurons are not
exactly joined at the synapses, but they are very close together.
Neurons fire by sending an electrochemical action
potential down the axon, which triggers the release at the synapses
of small packets (vesicles) of chemicals called
neurotransmitters. Some of these released molecules will bind to
receptors on the other side of the synapse, which then allow passage of
particular ions into the interior of that neuron, which in turn
affect whether or not it fires.
There are a two basic kinds of neurotransmitter: inhibitory,
which reduce the likelihood of firing in the receiving neuron, and
excitatory, which increase it. At any moment, the firing rate of
each neuron acts as a kind of summation of all the excitatory and
inhibitory signals it is receiving from the hundreds or thousands of
neurons tickling its dendrites.
There are a bunch of different neurotransmitters at work in different
neurons, but the most common are glutamate, which is excitatory,
and gamma-aminobutyric acid (GABA), which is inhibitory. A given
neuron will generally have receptors for both, but will release only one
or the other at all its synapses; in other words, a neuron takes both
positive and negative inputs, but always gives only one kind of output.
Neurotransmitter receptors are ligand-gated ion channels --
protein complexes that float around in the cell membrane, ready to admit
ions when the appropriate chemical turns them on. For synapses -- and
hence the whole neural apparatus -- to function, the correct receptors
must be present in the membrane of the receiving cell in the area where
the neurotransmitter gets released. However, cell membranes are dynamic
-- seething seas of lipids and embedded proteins that get shoved this
way and that by all sorts of random forces. While some kind of order is,
on average, maintained, it is not at all clear how.
Membrane proteins are pretty small, making it rather difficult to see
just what's going on down there. However, it is possible to get some
idea by using confocal microscopy with single-photon fluorescence. If
you can bind an appropriate fluorophore to the receptors of interest,
you can image them as little specks of light in the wine-dark membrane.
There are a number of ways to do this, none of them perfect. Candidate
fluorophores include quantum dots, which are artificial
semiconductor beads whose emission spectrum depends on their size, and
GFP, a naturally-occurring jellyfish protein which has become one
of the great workhorses of biological imaging by virtue of being a
pretty stable fluorophore that can be manufactured by the genetic
machinery of the cell itself. In the former case, you need to attach the
quantum dot to specific antibodies that will seek out and bind
the proteins of the receptor. In the latter, you genetically engineer
the cell so that when it expresses the receptor proteins it adds the GFP
to them. (This is a potentially risky process, since protein function is
very dependent on shape and having a huge stack of alien peptides
plonked on the end could easily change the target's behaviour, but it
seems to work in a surprising number of cases. Presumably the failures
tend not to wind up in the literature: scientific journals almost
exclusively publish positive results rather than papers concluding "Um,
who knows?")
Both these approaches have been used to image receptor movement in the
post-synaptic membrane, but the problem doesn't end there. A video
sequence of the cell membrane obtained this way simply shows a pattern
of bright specks at successive time steps. It's quite difficult to go
from such an image sequence to a clear model of how the receptors are
actually moving.
Even if the data were ideal -- each image providing a perfect
identification of the positions of all the receptors at each instant --
it would be non-trivial to correctly identify the movements of the
receptors, because there are a lot of them and they all look the same;
it's a giant shell game. And -- of course -- the data are
not ideal.
Experimental measurements are always prone to instrumental noise, but in
this case there are also other confounding factors. The field of view is
limited, so the receptors may move in and out: those visible at one
instant may not be the same ones visible at the next. The resolving
power is also limited, so if two receptors are close together they may
be misread as one. Worse, the fluorophores are imperfect. GFPs degrade
and quantum dots blink -- getting trapped in quantum states from
which it isn't possible to drop to ground -- so only an indeterminate
subset of receptors may be visible in each frame. New receptors may be
made and added to the membrane, and ones already there may be removed by
invagination. Finally, there's the very effect we want to
measure: the motility of the receptors may vary across the field of
view, but we don't know where.
Fortunately, analytic methods exist to deal with such difficulties.
Unfortunately they can be very computationally expensive (as bad as
O(n!); problems can get harder than that, but not much).
Heuristics are available to help us along, but there's an element of
lossiness. Certainty -- as ever -- is the province of the dull.
The domains of science are weakness and imperfection.
It's early days yet, but individual receptors do indeed seem to wander
around stochastically while statistically maintaining sufficient
concentrations at the synapses for the neuron to function. One theory
for how this works involves scaffold proteins inside the cell,
anchored to the cytoskeleton, which encourage -- in a
thermodynamic sense, which is to say: make energetically favourable --
the localization of receptors in the nearby membrane.