Silicon concentration in the medium – fitting to experimental data.

<p>Data from the experiment and model output of silicon concentration in the culture medium is shown in points and a blue curve. This curve depicts the total silicon consumption by all cells. The red curve is the integration of uptake rate coming from term 1 in equation 5. After 150 minutes, the difference between this value and the total silicon consumption becomes big as a result of non-synchronized cell culture. Adding the black curve, integral of term 2, compensates for this difference.</p

Parameters of the computational model.

<p>The values for the range of parameters for the optimization search are approximate values, based on experimental measurements.</p

Model output of forward problem resulted from different solutions of the inverse problem.

<p>The temporal dynamics of 11 variables of the model in (A) case 1 with no penalty term and (B) case 2 with penalty terms. Even though there are different curves for variables of both cases, using penalty term made the silicon dynamics (1,4,7,10,11) much more unique and identified.</p

Relative error in conservation rules.

<p>(A) Conservation of nutrient (eq. 2), (B) Conservation of enzymes (eqs. 9–11)</p

Perturbation analysis.

<p>Changes in, (A) objective function and (B) intracellular dynamics of nutrients, due to perturbation of system by 10% change in parameters , and (solid line: original quantities - dotted lines: perturbed quantities).</p

Silicon uptake rates of diatoms versus silicic acid concentration in medium in different time steps.

<p>(A) Constant amount of total enzyme. (B) Considering changes in total amount of SIT enzymes. The uptake rates have saturated forms in high concentrations of dissolved silicon in water. 2 minutes after adding silicon to the starved cells, the uptake rate is very high (surge uptake). By passing time the uptake rate has a big drop in value. In (B) this drop accrues slower and the rate increases again during valve formation.</p

Objective function value.

<p>Best objective function during searching for optimized solution until the algorithm cannot find a better value for a long time. The simulation time was around 12 hours.</p

Dynamics of silicon concentrations in different compartments.

<p>(A) Silicon transport with the assumption of a constant amount of enzymes in all compartments. (B) Silicon transport considering a flux of proteins for SITs during the cell cycle.</p

A flowchart for finding solutions to the inverse (optimization) problem.

<p>After designing an optimization problem, the first step is to check structural identifiability of parameters: to test if the inverse problem is solvable assuming that data are accurate and significant. After that the optimization problem should be solved (globally or locally) and at the last step posteriori analysis should be applied to ensure the results are meaningful and the model is robust. In the end, if the model can be validated, it can predict the mechanisms in the system, which, in turn, can provide a better model and, therefore, a better understanding of the system.</p

Protein flux used in the model.

<p>The relative changes in SIT protein expression level during the cell cycle of diatoms that has been applied to the model. This curve is inferred using the data from the experiment [44 - Figure 3]. SITs are least expressed during S-phase when silicon deposition is almost stopped.</p