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Motivated by the fact that living cells use molecular circuits (i.e. a set ofchemical reactions) for information processing, this paper investigates theproblem of designing molecular circuits for demodulation. In our earlier work,we use a Markovian approach to derive a demodulator for diffusion-basedmolecular communication. The demodulation filters take the form of an ordinarydifferential equation which computes the log-posteriori probability of atransmission symbol being sent. This work considers the realisation of thesedemodulation filters using molecular circuits assuming the transmission symbolsare rectangular pulses of the same duration but different amplitudes, i.e.concentration modulation. This paper makes a number of contributions. First, weuse time-scale separation and renewal theory to analytically derive anapproximation of the demodulation filter from our earlier work. Second, wepresent a method to turn this approximation into a molecular circuit. By usingsimulation, we show that the output of the derived molecular circuit isapproximately equal to the log-posteriori probability calculated by the exactdemodulation filter if the log-posteriori probability is positive. Third, wedemonstrate that a biochemical circuit in yeast behaves similarly to thederived molecular demodulation filter and is therefore a candidate forimplementing the derived filter.

Designing molecular circuits for approximate maximum a posteriori demodulation of concentration modulated signals