Iteration | Perturbation | Measurement | Estimated error |
|---|
1 | Wild | Microarray | ∞ |
2 | Delete 1 | Proteins 3 and 4 | 4.7×107 |
3 | Over 1 | Microarray | 3.8×104 |
4 | Down 5 | Proteins 1 and 6 | 54 |
5 | Over 1 | Proteins 2 and 4 | 2.5×103 |
6 | Down 5 | Microarray | 1.5 |
7 | Over 4 | Proteins 2 and 4 | 1.2 |
8 | Down 1 | Proteins 2 and 6 | 1.1 |
9 | Delete 1 | Proteins 2 and 6 | 6.9×10−2 |
10 | Assay 1 | n/a | 2.2×10−2 |
11 | Down 5 | Proteins 3 and 4 | 1.5×10−2 |
12 | Assay 3 | n/a | 1.2×10−2 |
13 | Down 1 | Proteins 3 and 5 | 1.0×10−2 |
- We list the sequence of experiments for estimating the parameters for model 1 for a randomly chosen set of true parameters. Experiments consist of a perturbation and a measurement. “Wild” refers to the original, unperturbed model, while “Delete 1” indicates a deletion of gene 1, “Over 1” indicates an over-expression of gene 1, “Down 5” indicates a down-regulation of protein 5, and so forth. “Microarray” indicates a microarray measurement experiment of time series for all the mRNA concentrations, while “Protein 3 and 4” indicates a time series measurement of proteins 3 and 4, and similarly for the remaining measurements. Gel-shift assay experiments indicate a direct measurement of the Michaelis-Menten constant and Hill coefficients for a specific reaction in the model. The estimated error is calculated from Eq. (10) which is an estimate of the average variance in log-parameters, so that that 30% accuracy corresponds to an error of 0.1 and is achieved after about 9 experiments. An accuracy of 10% corresponds to an estimated error of 0.01 and is achieved after 13 experiments. After about six experiments, the marginal benefit of additional experiments becomes small. At this point, the experiments are no longer complimentary and most of the benefit is attributed to probing the same degrees of freedom with more data. Notice that the estimated error increases at the fifth iteration. This is due to the minimization algorithm not finding the best fit at this iteration. The subsequent success of the method is a demonstration of the robustness of this method for selecting experiments.
