Unifying the mechanism of mitotic exit control in a spatio-temporal logical model

The transition from mitosis into the first gap phase of the cell cycle in budding yeast is controlled by the Mitotic Exit Network (MEN). The network interprets spatio-temporal cues about the progression of mitosis and ensures that release of Cdc14 phosphatase occurs only after completion of key mitotic events. The MEN has been studied intensively however a unified understanding of how localization and protein activity function together as a system is lacking. In this paper we present a compartmental, logical model of the MEN that is capable of representing spatial aspects of regulation in parallel to control of enzymatic activity. Through optimization of the model, we reveal insights into role of Cdc5 in Cdc15 localization and the importance of Lte1 regulation in control of Bfa1. We show that our model is capable of correctly predicting the phenotype of ∼ 80% of mutants we tested, including mutants representing mislocalizing proteins. We use a continuous time implementation of the model to demonstrate the role of Cdc14 Early Anaphase Release (FEAR) to ensure robust timing of anaphase and verify our findings in living cells. We show that our model can represent measured cell-cell variation in Spindle Position Checkpoint (SPoC) mutants. Finally, we use the model to predict the impact of forced localization of MEN proteins and validate these predictions experimentally. This model represents a unified view of the mechanism of mitotic exit control.

activates the alternative APC subunit, Cdh1, and the CDK inhibitor, Sic1, leading to cytokinesis and the 3.4 Simulation of mutants 163 To analyse the phenotypes of mutant strains, we placed all mutations into one of the following categories: USA). Linear products were created by PCR with primers from Sigma Life Science and Q5 Polymerase 214 (New England Biolabs, USA). The strains and plasmids used in Figure 5D were a gift from Gislene Pereira 215 (Caydasi et al. [2017]), with the exception of the empty plasmid, which was pWJ1468. mRuby2-TUB1 216 strains were constructed using a linearized plasmid, "pHIS3p:mRuby2-Tub1+3'UTR::URA3", which was  Table S2, strains are listed in Table S3. 225 3.8 Fluorescence microscopy 226 In the anaphase length assay, cells were grown, shaking, overnight in synthetic complete (SC) media at 227 30 • C, then diluted 1 in 10 in fresh SC media and left to grow for 3 hours. Cells were then transferred to 228 a -uracil agarose cube and placed into a sealed chamber. SPO12 and spo12 ∆ cells were placed in side-229 by-side chambers. The cells were pre-incubated at 30 • C for an hour before imaging. Cells were imaged 230 using a DeltaVision R Elite (GE Healthcare), with a 60x 1.42NA Oil Plan APO and an InsightSSI 7 231 Colour Combined Unit illumination system (CFP = 438nm, mRuby2 = 575nm). Images were captured 232 with a front illuminated sCMOS camera, 2560 x 2160 pixels, 6.5µm pixels, binned 2x2. Time lapse 233 videos were captured over 2 hours, with images captured at 2 minute intervals. Images were analysed 234 using FIJI (Schindelin et al. [2012]), with the Bio-formats plugin (Linkert et al. [2010]). For the forced 235 CDK localization experiments, cells were grown shaking overnight in -leucine media supplemented with 236 additional methionine at 23 • C. They were then transferred to -leucine -methionine media and grown 237 shaking for 4 hours at 23 • C and then imaged. For the NUD1-GBP forced localization experiments, 238 functionality of the SAC was assessed as desribed in Fraschini [2016]. Cells were grown shaking overnight 239 in 2% raffinose -leucine media. They were then transferred to 2% raffinose -leucine media for 2 hours 240 before being spun down and washed in water. They were resuspended in 2% galactose YP media 241 containing 3µg/ml alpha factor. They were transferred to incubate shaking for 2 hours before the alpha 242 factor (The Francis Crick Institute Peptide Chemistry STP) was washed out and the cells were washed 243 and resupended in 2% galactose YP media containing 15µg/ml nocodazole (Sigma-Aldrich) and incubated 244 shaking for 3 hours. In both assays cell were imaged with a Zeiss Axioimager Z2 microscope (Carl Zeiss 245 AG, Germany), with a 63x 1.4NA oil immersion lens and using a Zeiss Colibri LED illumination system 246 (RFP = 590 nm, GFP = 470 nm). Bright field images were obtained and visualized using differential 247 interference contrast (DIC) prisms. Images were captured using a Hamamatsu Flash 4 Lte. CMOS 248 camera containing a FL-400 sensor with 6.5 µm pixels, binned 2x2. Images were analysed with ICY  Due to the complexities of the spatial aspects of the model we combined an expertise-based approach 259 with a model-fitting approach to construct the model. The FEAR network, which acts only in the nucleus 260 was trained against a dataset of 50 mutant phenotypes using the CellNOptR tool (Terfve et al. [2012]). 261 The rest of the model was built from the literature, and the trained FEAR network was integrated into 262 it. 263 CellNOptR uses a genetic algorithm to train a Boolean model against known phenotypes (Saez- can be found in the Supplementary Information. We found that, due to the stochasticity of the genetic 270 algorithm, there was significant variation between the fit achieved by independent runs of the algorithm. 271 For this reason, we ran the algorithm 100 times, distributed in parallel and considered the optimal fits 272 achieved. We found that several phenotypes, in particular those relating to Cdc5 overexpression, were 273 difficult for the algorithm to fit. Cdc5 when expressed at a high level is clearly capable of releasing Cdc14 274 (see for example Visintin et al. [2003]), however the activity of Cdc5 is thought to be stable throughout 275 late mitosis, suggesting it is not part of the temporal signal initiating FEAR release. Therefore, we 276 reasoned that overexpression is likely to break the normal logic of Net1 inactivation. For this reason 277 we allowed overexpression of Cdc5 to "feed-forward" and regulate Net1 according to different rules than 278 those for physiological levels of Cdc5. Practically, this meant we introduced a node called "Cdc5OE" 279 which had the same outputs as Cdc5 in the PKN, this node was then treated as all the others in the 280 training process. We found this allowed for the identification of models which could fit 88% of the 281 training dataset. The "Cdc5OE" node was removed during integration with the MEN model but its Information. The model has five compartments: the nucleus, cytoplasm (mother compartment), bud, 290 mSPB and dSPB ( Figure 2A). In budding yeast, the old and new SPBs have some minor physiological 291 differences and it is the old SPB that enters the bud (Pereira et al. [2001]). However, it has been shown 292 that reversing this pattern has no significant effect on MEN signalling (Manzano-López et al. [2019]) and 293 therefore we consider the dSPB and mSPB to refer only to the destination of the SPB and not to their 294 age-related identity.

295
A key decision was how to model the activities of CDK and Cdc14. CDK activity depends on the 296 concentration of cyclins in the cell, early mitotic and S-phase cyclins such as Clb5 are largely degraded by 297 the Anaphase-Promoting Complex (APC) in its Cdc20 isoform at the metaphase-anaphase transition.

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Consequently, the level of CDK activity in the cell decreases, however late mitotic cyclins, such as 299 Clb2, remain present until activation of the alternative APC subunit, Cdh1, at mitotic exit. In the 300 interests of simplicity we do not distinguish specific cyclin contributions, instead the model has a high 301 and low level of activity for CDK, representing the metaphase and anaphase levels of CDK respectively.

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Similarly, the Cdc14 nodes are two-levelled, as although FEAR release of Cdc14 is largely limited to the 303 nucleus, its impact on MEN proteins means that a low level of Cdc14 must reach the cytoplasm in early 304 anaphase. We also used two levels for Cdc15 nodes. There is limited evidence that the activity of Cdc15 As 0 and the low (anaphase) level of CDK inhibits Cdc15 loading in absence of Tem1. 2 As 1 and the ASC inhibits Cdc15 loading in metaphase, in the absence of Tem1 and CDK. 3 As 2 and multi-level Tem1, Bub2 and Bfa1. 3a As 3 and identification of ASC as Cdc5. 4 As 3 and Lte1 can inhibit Bfa1 activity in a mechanism parallel to Kin4. 4a As 3 and Lte1 can activate Tem1 activity in a mechanism parallel to Bfa1 inhibition. 5 As 4 and identification of ASC as Cdc5 and above. 6 As 5 but Lte1 regulation of Bfa1 can influence speed of Tem1 activation (MaBoSS implementation).   propose that Cdc15 can load onto SPBs in the absence of CDK or Tem1, in a way that is dependent on 346 an Anaphase Specific Component (ASC). We introduced the ASC into a further model (Model 2) and 347 found that this model is now capable of correctly representing the behaviour of the single and double phospho-mutants ( Figure 3).

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Having established that the model requires both CDK inhibition of Cdc15 localization at the SPB 350 and an additional level of regulation from an unknown ASC, we decided to test whether the model 351 could predict the phenotype of bfa1 ∆. We found that Model 2 predicted that bfa1 ∆ cells would exit 352 mitosis in anaphase regardless of spindle alignment, but not in metaphase ( Figure 3). This     high frequency of cells with misaligned spindles. In some cases we found disagreement between papers 406 on particular mutants, in these cases we chose a single finding to include in the datatset, prioritising 407 experiments in the S288C/BY4741 genetic background, which were more numerous. 408 We simulated each of these mutants 100 times using the asynchronous update scheme and then 409 calculated the percentage that exited mitosis, as judged by full release of Cdc14 into the cytoplasm. We  5FOA, we found that the provision of CDC5 from a 2µm plasmid could not suppress the lethality of 430 MOB1 deletion ( Figure 5D), in agreement with the model's prediction ( Figure 5C). This demonstrates 431 that any effect caused by Cdc5 overexpression must rely on activation of at least the final part of the 432 MEN pathway. More broadly, it suggests suppression of partial or conditional lethality is a particular 433 issue for our logical model, in which activity must be set to one of a number of discrete states. 434 We found that many of the phenotypes which the model predicted incorrectly relate to overexpression structural information relating to how these proteins bind to the SPB. This is likely to be a general 445 problem when building compartmental logical models. 446 We found the steady states of the model fit closely with current understanding of the MEN. In the 447 wild type model there is a single steady state for each of the stages of mitotic exit: metaphase, early 448 anaphase (pre-spindle alignment) and late anaphase (post-spindle alignment). In these steady states, the 449 patterning of proteins on the SPBs matches the known localization patterns of MEN proteins ( Figure  5D). Disruption of the asymmetrical distribution of MEN proteins, such as by the bfa1 ∆ mutation is 451 accurately captured by the model ( Figure 5E). timings. Using MaBoSS we simulated wild type and spo12 ∆ cells in late anaphase ( Figure 6A). For these 468 simulations we did not modify the standard rate parameters, as we wish only to compare the mutants 469 to each other. We found that, as expected, the simulated FEAR mutant cells were significantly delayed 470 in exit from mitosis. Intriguingly, the distribution of exit times in the FEAR mutant is not just shifted 471 right, to longer times, but the shape of the distribution is also altered. The distribution of exit times 472 for spo12 ∆ has a long tail ( Figure S3), indicating that in addition to the increased mean, the variance 473 of the distribution is also increased. 474 We wanted to know whether this effect was detectable in real cells. Previous studies have used bulk  ). We hypothesised that these differences in timing may 501 explain the differences in outcome between these two mutants.

502
We modified the existing MaBoSS model to allow for the difference in time spent in anaphase for 503 bub2 ∆ and kin4 ∆ cells (Model 6). In this model, the wiring has not changed but the rate of Tem1 504 activation is higher in the presence of Lte1 (Figure 4). This choice was based on the earlier result that 505 Lte1 inhibits the activity of Bub2-Bfa1 towards Tem1. Note that just as before, this does not necessarily 506 indicate that Lte1 acts as a GEF for Tem1 but may act via a different or even indirect mechanism. To 507 dimensionalize the model, we defined three parameters representing the rate of Bfa1 inhibition in the 508 presence (ρ f ast ) or absence (ρ slow ) of Lte1 and the rate of all other variables (ρ) ( Table S1). We chose ρ 509 so that the average length of mitosis in a bub2 ∆ cell with a misaligned spindle is 25 minutes and ρ slow 510 so that it is 70 minutes for a kin4 ∆ cell ( Figure S4A&B). We found that varying ρ f ast had minimal 511 effect on the length of mitosis in any of the tested mutants so it was left at 1 ( Figure S4C). With these 512 parameters, we could simulate cells with accurate temporal resolution, allowing us to estimate the exit 513 time distributions of both mutant strains ( Figure 7A). We define the time taken for a cell to exit mitosis 514 as the random variable, E.

515
In order to determine whether mitotic exit or spindle alignment occurs first, we require an estimate according to the random motion within the cell. As a simplistic model of this process, we consider the 520 spindle to rotate around the centre of the mother compartment, with its angular displacement x(t) 521 behaving as a Brownian motion ( Figure 7B). If the SPB ever passes into the bud neck then we assume the spindle has aligned and cannot become misaligned again. Then, as it does not matter which of 523 the two SPBs eventually enters the bud, we consider x(t) ∈ (− π 2 , π 2 ), with alignment occurring if x 524 passes beyond either π 2 − θ or − π 2 − θ , where θ is half the angular neck width ( Figure 7B & S4E). We 525 assume the orientation of the spindle during metaphase is random, so that the initial value is distributed 526 uniformly x(0) ∼ U (− π 2 , π 2 ). Example trajectories of x(t) are shown in Figure 7C. We define the random   Overall, these findings suggest that the compartmental logical framework is capable of representing 547 the continuous properties of the system, and can distinguish between "strong" and "weak" SPoC mutants.  Kin4 is predicted to prevent mitotic exit when forced to localise at the SPB. We constructed strains expressing NUD1-GFP from the endogenous promoter and bearing plasmids 582 expressing either GBP or a fusion CLB2-CDC28-GBP protein from the MET3 promoter. We tuned the 583 expression of fusion protein by addition of 10µM methionine, to prevent high levels of CDK overexpression (Mao et al. [2002]). We found that forcible recruitment of CDK to the SPB caused a growth defect 585 ( Figure 8C) and that this growth defect was rescued by bfa1 ∆. Recruiting CDK to the SPB caused cells 586 to arrest in late anaphase, with a large bud and an extended spindle ( Figure S6C) and this phenotype 587 was rescued by bfa1 ∆ (Figure S6D, Supplementary File 9). This indicates a failure to exit from 588 mitosis, as our model predicts.

589
Forcible localization of proteins to both SPBs has been used as a tool to explore the impact of 590 localization for many years however forcing proteins to localize to a single SPB has not been explored 591 in the same detail. An optogenetic binding system has been used to target Clb2 to a single SPB example by addition of extra levels for these nodes, however it seems likely that some mechanisms will 612 never be fully captured by logical rules. We argue that despite these limitations, the simplicity of the 613 formalism make it a useful tool to explore networks like the MEN.

614
The steps taken to optimize and refine the model provide some insight into key aspects of MEN 615 regulation. We included two levels of Bub2-Bfa1 and Tem1 activation in order to accurately model the 616 effect of bub2 ∆ or bfa1 ∆ mutations. The necessity of this step shows the importance of Bub2-Bfa1 to tune the strength of MEN response throughout mitosis. In order for kin4 ∆spo12 ∆ cells to maintain a 618 SPoC, we required two parallel Bub2-Bfa1 regulation pathways (Figure 9). This mechanism was first  Cdc5 is controlled by the FEAR network, and this could be tested in future models.

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Our model predicted that the FEAR network is important not just for timely mitotic exit, but also 638 to even out variation in the length of mitosis (Figure 9). This finding was validated by experimental The authors declare no competing financial interests.      Simulations of x(t), the spindle angle starting from uniformly distributed initial conditions and varying as a Brownian motion. The time until alignment A i is indicated for each simulation. A 1 = 0 as in this case the initial condition of the simulation is within the bud neck (x(0) > π 2 − θ), corresponding to the scenario where the spindle is aligned at the point of extension. A 2 and A 3 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 two simulations do not achieve alignment during the 60 minutes simulated so A 4 , A 5 > 60. D: The distribution of exit times, E, for a simulated bub2 ∆ mutant and the distribution of alignment times, A, for a simulated kar9 ∆ 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 bub2 ∆ kar9 ∆ 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.      The closest to the target value (ρ slow = 0.012) was selected. C: We tried varying the fast rate of Bfa1 inhibition, ρ f ast over 2 orders of magnitude but found it had little effect on the length of mitosis in either mutant, so it was left at ρ f ast = 1. Mean exit times were derived from simulations of 10,000 anaphase cells with misaligned spindles. D: The parameter, σ, representing the rate of spindle alignment, was chosen to match both the measured proportions of multinucleate cell formation in bub2 ∆ (∼ 0.5) and kin4 ∆ (∼ 0.25). We tested 6 values of σ between 0.11 and 0.16. Fortunately, the value σ = 0.14 fits both proportions closely. Mean exit times were derived from simulations of 10,000 anaphase cells with misaligned spindles. E: Measurement of the half-angular bud width, θ, from a microscope image of a large-budded wild type cell. Based on this measurement we use a value of θ = 0.3.   MET3p-GBP-RFP CEN Leu/Met/Amp this study pHT795 MET3p-CLB2-CDC28-GBP-RFP CEN Leu/Met/Amp this study     the efficiency of spindle alignment is so high that it will generally occur prior to cytokinesis regardless of 793 whether it is monitored. There are two independent spindle orientation pathways, based on either Kar9 794 or Dyn1, loss of either of these proteins leads to a significant delay in spindle alignment and so these 795 mutants are used to detect SPoC defects (Scarfone and Piatti [2015]). In our model we assume that for 796 any SPoC phenotypes, we model a cell defective in one of these pathways.    Swedlow. Metadata matters: access to image data in the real world. The Journal of Cell Biology, 189 to data using multiple logic formalisms. BMC Systems Biology, 6(1):133, Oct. 2012.