Fig 1.
A simplified graphical description of the MEN and FEAR pathways.
A detailed description of both networks can be found in S1 Text. CDK, Cyclin-Dependent Kinase; FEAR, Cdc14 Early Anaphase Release; MEN, Mitotic Exit Network; SPB, Spindle Pole Body.
Fig 2.
The compartmental logical modelling framework and the MEN.
(A) The compartments present in the model. (B) Illustration showing how a simple biochemical motif can be interpreted as a set of logical rules, shown as a truth table. (C) Schematic showing how a logical network can be expanded across multiple compartments, with additional rules to describe the regulation of localisation. dSPB, daughter SPB; MEN, Mitotic Exit Network; mSPB, mother SPB.
Table 1.
Description of model versions.
Fig 3.
Refinement of the MEN model based on mutants that can release Cdc14 in metaphase.
All simulations are performed using the random asynchronous update scheme; 100 cells were simulated for each mutant starting from realistic initial conditions. In the original model, the CDC15-7A mutant has an intact SPoC, in contradiction to the experimental evidence. Introducing regulation of the Cdc15High SPB localisation node by CDK fixes this issue (Model 1); however, this model cannot fit the behaviour of the CDC15-7A MOB1-2A double mutant. This double mutant can exit mitosis in metaphase but only when the spindle aligns and an SPB enters the bud [67]. The inclusion of an ASC that limits Cdc15 loading in metaphase resolves this problem (Model 2). Deletion of either component of the Bub2-Bfa1 GAP complex also permits exit from mitosis in metaphase; however, simulations of Model 2 do not agree with this. Introducing 2 levels of Bub2, Bfa1, and Tem1 activity (Model 3) is sufficient to represent this effect. All simulation data can be found in S5 File. ASC, Anaphase Specific Component; CDK, Cyclin-Dependent Kinase; GAP, GTPase activating protein; MEN, Mitotic Exit Network; SPB, Spindle Pole Body; SPoC, Spindle Position Checkpoint. A green tick indicates that the simulated phenotype matches the phenotype from the literature, while a red cross indicates that the simulation deviates from the known phenotype.
Fig 4.
Refinement of the MEN model based on the phenotype of kin4Δ sp12Δ cells.
All simulations are performed using the random asynchronous update scheme; 100 cells were simulated for each mutant starting from realistic initial conditions. In Model 3, the double mutant kin4 spo12Δ did not have a SPoC, in disagreement with experimental evidence [46]. By introducing an additional level of regulation of Bfa1 by Lte1, this issue was resolved in Model 4. This change also allowed for identification of the ASC with Cdc5, while maintaining the correct behaviour of related phenotypes, such as CDC15-7A MOB1-2A, kin4Δ and cdc5-1. All simulation data can be found in S5 File. APC, Anaphase-Promoting Complex; ASC, Anaphase Specific Component; CDK, Cyclin-Dependent Kinase; MEN, Mitotic Exit Network; SPB, Spindle Pole Body; SPoC, Spindle Position Checkpoint. A green tick indicates that the simulated phenotype matches the phenotype from the literature, while a red cross indicates that the simulation deviates from the known phenotype.
Fig 5.
Validation of Model 5 against literature phenotypes.
(A) The model correctly predicted 81% of the 140 tested literature phenotypes (S6 File). (B) The model often failed at predicting the phenotype of cells with a genotype that mixes overexpression with other mutations, such as the rescue of the temperature-sensitive alleles cdc15-2 and dbf2-2 by overexpression of CDC5. (C) The model predicts that overexpression of CDC5 cannot rescue the mob1Δ mutation. (D) Spot test confirming the model prediction that overexpression of CDC5 cannot rescue full deletion of MOB1. A mob1Δ strain kept alive by provision of a CEN-MOB1 plasmid with uracil selection was transformed with either a 2−μm plasmid bearing MOB1 or CDC5 or an empty plasmid. The CEN-MOB1 plasmid was counterselected by addition of 5FOA, showing that moderate overexpression of CDC5 is not sufficient for rescue of the mob1Δ phenotype. (E) The localisation state of MEN proteins on the SPBs in the 3 physiological stages of mitotic exit in the model. Steady states determined from synchronous update scheme. (F) Comparison of (a)symmetry of SPBs in the steady states of wild-type and bfa1Δ cells. All simulation data can be found in S5 File. CDK, Cyclin-Dependent Kinase; MEN, Mitotic Exit Network; SC-LEU, Synthetic Complete media lacking leucine.; SPB, Spindle Pole Body.
Fig 6.
The role of FEAR in regulating anaphase length.
(A) We simulated 10,000 SPO12 and spo12Δ cells and the length of anaphase (time from model initiation until mitotic exit) was calculated and was normalised to the mean of the wild-type cells. (B) Schematic showing the key cell cycle events used to calculate the length of time spent in anaphase. (C) Time course showing mRuby2-Tub1 fluorescence in a representative cell during exit from mitosis. Images were taken at 2-minute intervals and used to determine the length of anaphase. The image at 0 minutes shows the final frame where the cell has an unextended spindle and spindle disassembly after 18 minutes. (D) Distribution of anaphase lengths in SPO12 and spo12Δ cells. Five time courses were performed, each with 3 fields of view per strain (SPO12 n = 281, spo12Δ n = 223). Due to differences in mean exit times between time courses, exit times from each time course were normalised to the mean exit time of SPO12 cells in that time course. (E) The coefficient of variation of exit times for SPO12 and spo12Δ cells in simulation and experiment. Raw data can be found in S7 File; example simulation data and the normalised data can be found in S8 File. FEAR, Cdc14 Early Anaphase Release.
Fig 7.
Use of the parameterised model to predict and explore cell–cell variability in SPoC mutants.
(A) Simulated exit times of bub2Δ and kin4Δ cells with misaligned spindles, from 10,000 runs of the model. (B) Schematic of a kar9Δ osTIR1 dyn1-AID cell, showing the spindle angle x(t) and the half-angular neck width, ϑ. (C) Simulations of x(t), the spindle angle starting from uniformly distributed initial conditions and varying as a Brownian motion. The time until alignment Ai is indicated for each simulation. A1 = 0 as in this case, the initial condition of the simulation is within the bud neck (), corresponding to the scenario where the spindle is aligned at the point of extension. A2 and A3 can be measured as the point where x(t) crosses either of the boundaries, as it is not important which SPB enters the bud. The final 2 simulations do not achieve alignment during the 60 minutes simulated so A4,A5>60. (D) The distribution of exit times, E, for a simulated bub2Δ mutant and the distribution of alignment times, A, for a simulated kar9Δ osTir1 dyn1-AID cell. These distributions were inferred from cubic spline interpolation of histograms generated from 10,000 runs of the model or 10,000 Brownian motion simulations respectively. (E) Distribution of the difference between exit time and alignment time, D, for the simulated bub2Δ kar9Δ osTir1 dyn1-AID. The area between the x-axis, the curve, and x = 0 gives the predicted probability of a given cell exiting mitosis before spindle alignment occurs, giving rise to a multinucleate cell. (F) Predicted proportions of multinucleate cells for various genetic backgrounds. Dotted lines show the measured proportions of multinucleate cells in Falk and colleagues [46]. *CDC15-7A MOB1-2A was not included in the assays of Falk and colleagues [46] and so no dotted line is included. Example data can be found in S9 File. SPB, Spindle Pole Body; SPoC, Spindle Position Checkpoint.
Fig 8.
Forced localisation phenotypes.
(A) Predicted phenotype of cells where each of the SPB-localised proteins in the model are forced to localise to the SPB. A question mark (?) indicates a phenotype that has not been experimentally verified in the literature. A star (*) is used to indicate that the MOB1-SPB phenotype differs from literature accounts due to factors beyond the scope of the model. (B) Predicted rescue of the CDK-SPB phenotype by bfa1Δ. (C) Spot tests showing growth defect of Nud1-GFP cells expressing a fusion Clb2-CDK-GBP protein from the MET3 promoter and rescue of this defect by bfa1Δ. Activity of the MET3p promoter was tuned by addition of 10-μM methionine to media. (D) Predicted phenotype of cells where Cdc15 or CDK are forced to either the mSPB or dSPB. All simulation data can be found in S5 File. CDK, Cyclin-Dependent Kinase; GBP, GFP-Binding Protein; GFP, Green Fluorescent Protein; SPB, Spindle Pole Body; WT, wild type.
Fig 9.
Model of the MEN including the developments contributed in this manuscript.
(A) Lte1 regulates Bub2-Bfa1 via 2 pathways, only one of which is dependent on Kin4. (B) Cdc5 is required for recruitment of Cdc15 to the SPB in the absence of Tem1 or CDK regulation. (C) FEAR breaks a Cdc15-Nud1-CDK negative feedback loop, leading to deterministic timing of mitosis. CDK, Cyclin-Dependent Kinase; FEAR, Cdc14 Early Anaphase Release; MEN, Mitotic Exit Network; SPB, Spindle Pole Body.