Scatter plot of accepted parameters.

<p>(A) Parameter values in the acceptance range of objective function for case 1, when there is no penalty term in the model. Most of parameters are scattered in this case, which means that there are many solutions to the optimization problem. (B) Parameter values in acceptance range of objective function for case 2, when penalty terms added to the objective function. In this case, besides and , most of the parameter values are not scattered much.</p

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

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

The relevant experimental measurements on diatom <i>T. pseudonana</i> measurements.

<p>The condition of the experiment: SD: starvation duration, T: temperature, : initial concentration of silicic acid after the starvation. The measurement values in this table are approximate.</p

Cell cycle and cell division of diatoms.

<p>(A) Schematic picture of different stages of the asexual cell cycle of a typical diatom: Silica wall is composed of valves and girdle bands. 1: a full-size diatom cell, 2: Cell during the DNA replication (S-phase), 3; immediately after this silica deposition in SDV starts, 4&5: the valve formation continues until it is ready for the new sibling cells and then the cell divides (G2+M-phase), 6: new cells grow accompanied with silica girdle bands formation (G1) until it achieves the full size. (B)&(C) SEM images of diatom <i>Thalassiosira pseudonana</i>. The image of silica frustules of one diatom including valves and girdle bands (B) and a diatom during cell division (C).</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

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

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