An essential aspect of any digital logic gate is a high-quality nonlinearity. In essence, a digital gate must exhibit low gain for signals near a logical zero or one, while exhibiting high gain for signals within the transition regions.
The biological world utilizes two chemical techniques to achieve this highly nonlinear behavior.
The first technique is the use of protein dimers as the biologically active form. The active form of many enzymes, including the DNA binding proteins we propose using, is a bound combination of two copies of the protein. In equilibrium, the concentration of the dimer is proportional to the square of the protein concentration. Higher power nonlinearities can be achieved with tetramers, hexamers, or even higher multimers. Such multimers are common in biologically active protein complexes.
A similar power law behavior is obtained in cooperative binding of proteins to a substrate. Cooperative binding refers to mechanisms in which the first of several protein binding reactions occurs at a relatively low rate, while subsequent binding reactions occur more rapidly, because the presence of the already bound protein enhances the binding affinity.