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. 2019 Sep 15;8(9):bio047175. doi: 10.1242/bio.047175

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© 2019. Published by The Company of Biologists Ltd

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution and reproduction in any medium provided that the original work is properly attributed.

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Fig. 4. — Mathematical modeling of the centriolar dynamics of Plk4, STIL and HsSAS6. (A) Schematic of the mathematical model. The definitions of rate constant k are as follows: k_p1 and k_p2 are the entry and dissociation rates of centiolar Plk4. k_p3 and k_p4 are the self- and trans-autophosphorylation rates of Plk4. k_p5 is the dissociation rate of centriolar phospho-Plk4. k_st1 and k_st2 are the entry and dissociation rates of centriolar STIL. k_cw is the rate of cartwheel assembly of HsSAS6. k_sas1 and k_sas2 are the entry and dissociation rates of centriolar HsSAS6. Plk4-p, STIL-p and HsSAS6-cw denote the phosphorylated forms of Plk4 and STIL, and HsSAS6 in the cartwheel structure, respectively. See the text and Materials and Methods for details. (B) Simulated time course of Plk4, STIL and HsSAS6 at a centriole. Total quantities (Plk4+Plk4-p, STIL+STIL-p, and HsSAS6+HsSAS6-cw) are shown. Note that quantity and time are all relative (dimensionless). (C) Changes in the quantity of Plk4 against that of STIL or HsSAS6. The simulation data have been plotted in the same way as in the graphs in Fig. 2. (D) Simulated effect of STIL or HsSAS6 depletion. Simulation results with the expression levels of STIL or HsSAS6 decreased to 10% and 1% of the normal levels, respectively, are shown. (E) Schematic of the model of the onset time course of procentriole formation. A.U., arbitrary units.