  Motivated by the fact that living cells use molecular circuits (i.e. a set of
chemical reactions) for information processing, this paper investigates the
problem of designing molecular circuits for demodulation. In our earlier work,
we use a Markovian approach to derive a demodulator for diffusion-based
molecular communication. The demodulation filters take the form of an ordinary
differential equation which computes the log-posteriori probability of a
transmission symbol being sent. This work considers the realisation of these
demodulation filters using molecular circuits assuming the transmission symbols
are rectangular pulses of the same duration but different amplitudes, i.e.
concentration modulation. This paper makes a number of contributions. First, we
use time-scale separation and renewal theory to analytically derive an
approximation of the demodulation filter from our earlier work. Second, we
present a method to turn this approximation into a molecular circuit. By using
simulation, we show that the output of the derived molecular circuit is
approximately equal to the log-posteriori probability calculated by the exact
demodulation filter if the log-posteriori probability is positive. Third, we
demonstrate that a biochemical circuit in yeast behaves similarly to the
derived molecular demodulation filter and is therefore a candidate for
implementing the derived filter.
