The sense of smell is the ability
to detect molecules of different chemicals in the air. This happens via an
array of receptor molecules in your nose that bind to odour molecules and send
signals to your brain. A simple design would have one receptor for each
molecule. However it’s more complicated than that. Humans can detect over
2100 different molecules and can tell the difference between mixtures of up to
30 different molecules, using a much smaller number of distinct receptors.
Receptors therefore need to respond to more than one different molecule each and
the brain must put together all of the signals form the receptors to identify
the odour. A recent paper by David Zwicker, Arvind Murugan and Michael P.
Brenner discusses the optimal setup of receptors from an information-theoretic
perspective.
One important point to note is that
different odours are present in the natural environment with different
frequencies and this ought to be taken into account when designing your
receptor array. It is no use having an array that very accurately distinguishes
between two very rare odours if it can’t distinguish between two very common
odours. This is made more precise by Laughlin’s principle which says that an
optimal sensor (one that conveys the most information) should be such that all
possible outputs are equally likely in the natural environment.
Zwicker, Murugan and Brenner
construct a simple model of the response of the receptor array to different
mixtures of odour molecules in which the receptors respond proportionally to
the concentrations of the molecules. Each receptor has a different sensitivity
to each of the molecules and it transmits a binary signal that is 1 if the
excitation is above a threshold and 0 if it is below. They find that there are
two principles that are relevant to maximising the information:
(1) Any given receptor should be
active half the time, which maximises the amount of information provided by
that receptor in isolation.
(2) Each pair of receptors should
have as uncorrelated (non-matching) a response as possible, reducing the
redundancy between them.
They then go on to discuss to what
extent these principles can be satisfied in general and which parameters of
their model give the maximum information. The most interesting outcome is a
fundamental trade-off between being effective at identifying the presence or
not of as many molecules as possible, and being able to estimate the
concentrations of molecules accurately. This trade-off arises because the best
way to identify as many molecules as possible is for each to activate only a
single receptor, whereas to estimate concentration each molecule activate a
number of receptors with different thresholds.
This paper is a good example of one
of the ideas in in William Bialek’s paper that Tom McGrath wrote about in a previous
post. The authors are assuming that this biological process is operating near
to the optimum that physical limits allow and then they are trying to
find the parameters of the system that correspond to these limits. One
criticism of the paper might be that it takes no account of the fact that some
odours a more important than others, even if they are very rare. For example,
accurately identifying the smell of a poisonous substance that an animal
encounters occasionally might be more important than distinguishing between the
smells of two good food sources that are encountered more frequently.
