The structural similarity of neural networks and genetic regulatory networks
to digital circuits, and hence to each other, was noted from the
very beginning of their study [1, 2]. In this work, we propose a simple
biochemical system whose architecture mimics that of genetic regulation
and whose components allow for in vitro implementation of arbitrary
circuits. We use only two enzymes in addition to DNA and RNA
molecules: RNA polymerase (RNAP) and ribonuclease (RNase). We
develop a rate equation for in vitro transcriptional networks, and derive
a correspondence with general neural network rate equations [3].
As proof-of-principle demonstrations, an associative memory task and a
feedforward network computation are shown by simulation. A difference
between the neural network and biochemical models is also highlighted:
global coupling of rate equations through enzyme saturation can lead
to global feedback regulation, thus allowing a simple network without
explicit mutual inhibition to perform the winner-take-all computation.
Thus, the full complexity of the cell is not necessary for biochemical
computation: a wide range of functional behaviors can be achieved with
a small set of biochemical components
