Fig 1.
Flow charts describing the three steps for the MBDOE method.
These describe (a) how acceptable and representative parameters are identified, (b) the process for determining the optimal input vector, and (c) the selection of multiple measurement pairs associated with the optimal input vector.
Table 1.
Mapping of functions to equation numbers to efficiently estimate necessary expected values and variances.
Table 2.
Hes1 model parameters and definitions.
Table 3.
Optimal Experiment Design for Hes1 Example.
Fig 2.
An illustration of the optimal experiment design for the Hes1 example.
(a) The input sequence selected by the design for the duration of the experiment. (b) Model simulation of the output dynamics of the measurable species m and P1+P2 under an optimal input simulated with ΩRA. The red dots specify the selected optimal measurement points which are the mean values generated using nominal plant with additive 10% Gaussian noise. Error bars are also given by the standard deviation of the simulated data (three data points are generated for each time point). (c) The initial (grey) and final (blue) uncertainty in the target states dynamics. The designed experiment reduces the uncertainty region by 84%,81%, and 86% for mRNA, P1, and P2, respectively. The red line shows the simulated dynamics of the nominal plant.
Table 4.
Greedy Method for Hes1 Input Vector Design.
Fig 3.
Supporting details of optimal experiment design for Hes1 example.
(a) The measurement scenario tree representation for selecting optimal measurements. Each node defines, the measurement pairs with the predicted value of the distinguishability metric, ξ, target dynamical uncertainty, γ, and three estimated measurement values from simulation, G1, G2, and G3. The path along the scenario tree with predictions closest to the data from the nominal plant is shown in red. (b) Reduction of TDU and (c) individual variance of target states with each additional unique measurement from the scenario tree.
Table 5.
Comparison of Optimal Input MBDOE with Measurement Only MBDOE for the Hes1 Model.
Table 6.
Optimal Experiment Design for TCR Example.
Fig 4.
An illustration of the optimal experimental design for the TCR example.
(a) Model simulation of the output dynamics of the measurable species under the optimal input provided in Table 6 simulated with ΩRA. The red dots specify the selected optimal measurement points by the mean values generated by nominal plant with additive 10% Gaussian noise. Error bars are also given by the standard deviation of the simulated data (three data points are generated for each time point). (b) The initial (grey) and final (blue) uncertainty in the target states dynamics. The designed experiment reduces the uncertainty region by 46%,99%,85% and 59% for free SHP, ZAP, ppMEK and ppERK, respectively. The red line shows the simulated dynamics of the nominal plant.
Fig 5.
Supporting details of optimal experiment design for TCR example.
(a) The measurement scenario tree representation for selecting optimal measurements. Each node defines, the measurement pairs with the predicted value of the distinguishability metric, ξ, target dynamical uncertainty, γ, and three estimated measurement values from simulation, G1, G2, and G3. The path along the scenario tree with predictions closest to the data from the nominal plant is shown in red. (b) Reduction of TDU (blue line) and (c) individual variance of target states with each additional unique measurement from the scenario tree. In (b) the reduction in TDU for a measurement only MBDOE scenario (red line) is provided for comparison purposes.