Network analysis of biochemical logic for noise reduction and stability: a system of three coupled enzymatic and gates.

We develop an approach aimed at optimizing the parameters of a network of biochemical logic gates for reduction of the "analog" noise buildup. Experiments for three coupled enzymatic AND gates are reported, illustrating our procedure. Specifically, starch, one of the controlled network inputs, is converted to maltose by beta-amylase. With the use of phosphate (another controlled input), maltose phosphorylase then produces glucose. Finally, nicotinamide adenine dinucleotide (NAD(+)), the third controlled input, is reduced under the action of glucose dehydrogenase to yield the optically detected signal. Network functioning is analyzed by varying selective inputs and fitting standardized few-parameters "response-surface" functions assumed for each gate. This allows a certain probe of the individual gate quality, but primarily yields information on the relative contribution of the gates to noise amplification. The derived information is then used to modify our experimental system to put it in a regime of a less noisy operation.