Is the model robust?
We have systematically tested the robustness of the model by changing the parameters in the basal parameter set individually to determine the range over which cyclic behavior persists. Matlab code and complete data on parameter sensitivity runs are available on request. (fcross@mail.rockefeller.edu).
(A) The model must execute the following events in order, or else the model is considered inviable.
- origin re-licensing (due to a drop in [Clb2]+[Clb5] below Kez);
- origin activation (due to a subsequent rise in [Clb2]+[Clb5], causing [ORI] to increase above 1);
- spindle alignment (due to a rise in [Clb2], causing [SPN] to increase above 1);
- Esp1 activation ([Esp1] to increase above 0.1, due to Pds1 proteolysis at anaphase);
- [Clb2] dropping below a threshold Kez to trigger nuclear division.
(B) The model is inviable if division occurrs in an "unbudded cell" (i.e. when [BUD] never reaches 1 in the cycle).
(C) The cell cycle should be stable such that the root mean square deviation of all variables is < 0.05 in subsequent divisions.
(D) Lastly, the model is considered inviable if the cell [mass] is > 10.
For assaying robustness, the model was transferred to MatLab v. 6.5 using the ode23s integrator. Each parameter was varied individually up to 256-fold in both directions by 1.414-fold increments, and the maximum tolerable variation was recorded.
We find that 72% of the parameters can be changed at least ten-fold in either direction. The 35 parameters that do not exhibit this flexibility are:
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Reactions |
Parameter sensitive to 10 fold change either up or down |
Parameter sensitive to 10 fold change up (but not down) |
Parameter sensitive to 10 fold change down (but not up) |
Reason(s) why the model is sensitive to parameter values |
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SBF activation |
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SBF does not turn on, the cell will be unbudded as in the triple-cln mutant (Stuart & Wittenberg, 1995). |
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Cln2 level |
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High Cln2 prevents mitotic exit due to Cdh1 and CKI inactivation. |
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MCM1 activation |
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Clb2 synthesis must be fast enough to hold post-START cells in the high-Clb state, but not so fast as to block cells in telophase. |
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Clb2 level |
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SWI5 activation |
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The cell will arrest in G1 if CKI is too high (Verma et al., 1997a). |
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Sic1 and Cdc6 level |
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Cdc20 activation |
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Insufficient Cdc20 causes metaphase arrest (Shirayama et al., 1998. |
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PPX level and activity |
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High PPX causes cells to arrest like GAL-PDS1-db∆ (Cohen-Fix et al., 1996; Tinker-Kulberg & Morgan, 1999). Low PPX, as described in the footnote, prevents Esp1 activation at mitotic exit. |
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Cdc14 release from RENT |
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The allowable range is 1 < Net1/Cdc14 <2.8. Telophase arrest occurs if the ratio is too high, whereas G1 arrest occurs if the ratio is too low. |
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Cdh1 activation |
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Esp1 activation |
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The model is sensitive to the ratio of Esp1 to Pds1. If the ratio is high, Esp1 will be active even before spindle alignment; if it is low, Esp1 will not be activated at mitosis, as in GAL-PDS1-db∆. |
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SPN alignment |
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The cell will arrest in metaphase, because [SPN] never exceeds 1. |
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BUD formation |
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The cell will be unbudded because [BUD] never exceeds 1. |
(2.8x up)
(0.35x dn)
(0.25x dn)
(5.7x up)
(0.25x dn)
(0.13x dn)
(8x up, 0.7x dn)
(2x up*)
(2x up)
(0.18x dn)
(2.8x up)
(2.8x up)
(0.18x dn*)
(0.13x dn)
(2x up)
(0.35x dn)
(8x up, 0.5x dn*)
(8x up, 0.5x dn*)
(2x up*)
(5.7x up*)
(5.7x up*)
(2x up, 0.13x dn)
(8x up, 0.35x dn)
(2x up, 0.5x dn)
(2x up, 0.5x dn)
(5.7x up*)
(1.4x up, 0.7x dn)
(1.4x up)
(4x up)
(0.7x dn)
(0.13x dn)
(1.4x up)
(0.7x dn)
(2.8x up)
(0.35x dn)†The maximum allowable fold of increase or decrease
is indicated in the parentheses.
* Mutants are considered inviable due to low [Esp1] activity
(<0.1) at mitosis exit. However, [Esp1] rises to 0.1 in a minute or so
after mitosis. If this problem is ignored, these mutants are insensitive
to parameter changes within the range tested. The main reason for the low [Esp1]
activity is that Cdh1 activates too soon after Cdc20 activation such that there is
not enough time for Pds1 to be degraded to sufficiently low levels before the condition for mitotic exit is met.
The cumulative distribution of parameters exhibiting a tolerance
for a given fold of increase or decrease is plotted below for WT,
APC-A (ka20=0; or equivalently ka,iep=0); cdh1∆ (kdb2"=0.001, kd3,pds"=0.001), cki∆ (synthesis rates for Sic1 and Cdc6 =0), cln3∆,
cln2∆, and clb5∆. Wild type and
cln3∆ mutant are most robust to parameter changes, whereas
cln2∆ and cdh1∆
are least robust.
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