Design and Analysis of Compact DNA Strand Displacement Circuits for Analog Computation Using Autocatalytic Amplifiers

A main goal in DNA computing is to
build DNA circuits to compute
designated functions using a minimal number of DNA strands. Here,
we propose a novel architecture to build compact DNA strand displacement
circuits to compute a broad scope of functions in an analog fashion.
A circuit by this architecture is composed of three autocatalytic
amplifiers, and the amplifiers interact to perform computation. We
show DNA circuits to compute functions sqrt­(x), ln­(x) and exp­(x) for x in
tunable ranges with simulation results. A key innovation in our architecture,
inspired by Napier’s use of logarithm transforms to compute
square roots on a slide rule, is to make use of autocatalytic amplifiers
to do logarithmic and exponential transforms in concentration and
time. In particular, we convert from the input that is encoded by
the initial concentration of the input DNA strand, to time, and then
back again to the output encoded by the concentration of the output
DNA strand at equilibrium. This combined use of strand-concentration
and time encoding of computational values may have impact on other
forms of molecular computation.