A three-metabolite unbranched metabolic pathway and estimation results. (a) The pathway model diagram is given. The metabolites are denoted by xi and enzymes by e. S and P are the external metabolites. The first enzyme e1 is regulated through both transcriptional repression and allosteric inhibition by the third metabolite. Enzymes 1, 2, and 3 are encoded on the same operon. (b and c) GPR to simulated metabolite observations x1, x2, x3, mRNA, and enzymes e after the change in S from 0.1 to 1 at t = 0 is shown. The noisy metabolite observations are shown in dot, and the confidence intervals in gray represent the ± 2× SDs of the GP posterior distribution. To see this figure in color, go online.