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Computational modeling of chromosome re-replication in mutant strains of fission yeast

Typically cells replicate their genome only once per division cycle, but under some circumstances, both natural and unnatural, cells synthesize an overabundance of DNA, either in a disorganized manner (“overreplication”) or by a systematic doubling of chromosome number (“endoreplication”). These variations on the theme of DNA replication and division have been studied in strains of fission yeast, Schizosaccharomyces pombe, carrying mutations that interfere with the function of mitotic cyclin-dependent kinase (Cdk1:Cdc13) without impeding the roles of DNA-replication loading factor (Cdc18) and S-phase cyclin-dependent kinase (Cdk1:Cig2). Some of these mutations support endoreplication, and some overreplication. In this paper, we propose a dynamical model of the interactions among the proteins governing DNA replication and cell division in fission yeast. By computational simulations of the mathematical model, we account for the observed phenotypes of these re-replicating mutants, and by theoretical analysis of the dynamical system, we provide insight into the molecular distinctions between overreplicating and endoreplicating cells. In the case of induced overproduction of regulatory proteins, our model predicts that cells first switch from normal mitotic cell cycles to growth-controlled endoreplication, and ultimately to disorganized overreplication, parallel to the slow increase of protein to very high levels.

There are two forms of DNA replication uncoupled from cell division considered here, 'endoreplication' in which complete rounds of DNA replication occur periodically (so that DNA content goes 1C to 2C to 4C etc), and 'over-replication' in which this behavior is not observed, but DNA content per cell goes up steadily. Exactly what DNA is replicated and how evenly the genome is replicated in the latter situation has been only partially explored.
One molecular interaction that is not discussed at all here is the mechanism of the positive effect of cyclin-cdk on replication initiation on Mcm-loaded ('licensed') origins. Another is the mechanism by which cyclin-cdk blocks Mcm loading (though inhibition of cdc18 by cig2 is indicated, this is far from the whole story).
Another rather critical thing not modeled here is the replication origin itself. This is a major omission, though I can see that its inclusion is challenging since it may not lend itself well to the ODE approach where all variables are continuous, while a given origin is either loaded or it's not, and there are thousands of them. But I think this leads to problems with the paper.
There is a well-established qualitative molecular understanding of the difference between endo-and over-replication that goes as follows.
Replication origins with bound ORC and bound Mcm ('loaded') can be converted to active origins, driving bidirectional replication, upon cyclin-cdk activation (phosphorylating proteins such as Sld2; see work by Diffley and Araki). Bidirectional replication sends the Mcm helicase off with the replication fork, leaving behind an unloaded origin. This is an important feature since it most likely makes origin unloading an inevitable mechanical consequence of origin firing. cyclin-cdk activity simultaneously blocks RE-loading of the origin by multiple mechanisms (e.g. Nguyen 2000). So the origin will not re-load, therefore will not refire. After replication, mitotic cyclin-cdk promotes cell division and also degradation of mitotic cyclin; replication origins can reload (cyclin-cdk blockade removed) but will not fire until cyclin-cdk rises again. This gives once-per-cycle replication. Endoreplication requires cyclical activation AND inactivation of cyclin-cdk without cell division, to circumvent this control. One way to achieve this, discussed here, is that in the absence of mitotic cyclin cdc13, levels of S cyclin cig2 still cycle, due to a transcriptional oscillator. The mechanism of this oscillator is unknown, though the authors present an interesting theoretical case for a transcriptional oscillatory loop with involvement of nrm1 in combination with loops involving ste9, cdc18 and mik1.
There are other ways to achieve the same end. For example, preventing mitosis by depolymerizing microtubules, while eliminating the 'spindle assembly checkpoint', will result in repeated rounds of replication and polyploid nuclei. We assume (though I'm not sure about documentation) that such a situation entails essentially multiple complete cell cycles, where all that's missed is actual segregation of replicated sister chromosomes due to absence of microtubules.
Over-replication: this situation is understood as a case where the block to origin reloading after firing is weakened or blocked. Any individual origin then may fire, then reload and fire again, repeatedly, in a stochastic fashion. Mitosis in such cells is blocked, and this is not well understood though there is some evidence that multiple initiations without division from individual origins ('onion-skin replication') may activate DNA damage checkpoints that block cell division. There are two main ways to achieve this state. Mechanisms for cyclin-cdk blockade of origin reloading can be blocked, for example by mutation of ORC, MCM and CDC6 (Nguyen 2000); or, the cyclin-cdk requirement for firing can be blocked (by appropriate mutation of Sld2 and Sld3 for example; Araki, Diffley) in which case cells with no cyclin-cdk activity at all will continuously and stochastically fire and reload origins. Probably, overexpression of cdc18 gives over-replication by forcing origin reloading despite countering mechanisms from cyclin-cdk through mass action, though this is less well-understood to my knowledge. This is, I think, the consensus view of how cells replicate once per cycle, and how this can go wrong with endo-or over-replication. I find it a serious omission in the present paper that neither of these ideas (especially the latter one) is discussed at all. It is striking that the paper is expressed as being about control of DNA replication, but in no figure and in none of the equations is DNA replication itself actually even mentioned. (Leaving aside top left of Fig.5A, the idea that some unidentified 'Starter kinase' might be inhibited by DNA replication somehow -an idea for which no evidence is adduced, and an interaction that furthermore does not seem to be discussed in the text at all).
I think the paper does some useful theorizing about potential endogenous loops controlling cig2 and cdc18. Novak and Tyson have been leaders in explaining how negative and positive feedback loops can give interesting biological behavior, and this is here elucidated with another example. The equations and diagrams are dependent on parameter choices, most or all of which are underpowered with respect to experimental data from others; so these ideas really are theoretical.
(Some indication of parameter sensitivity of the models and claims would be welcome here). However, when the paper transitions to explaining endo-vs over-replication I think falls short. There are two sides to the controls preventing these two kinds of replication errors: the cyclin-cdk side (alternating high and low levels are essential), and the replication origin side (key features: loading is cyclin-cdk-inhibited, firing is cyclin-cdk-promoted, and firing likely immediately reverses loading). The complete absence of discussion of the origin side of the story in this manuscript just won't do.
The paper comes up with some experimental suggestions: that moderate overexpression of cdc18 will lead to endo-and not over-replication. I must say this seems highly unlikely to me, and something furthermore that almost surely would have been seen if a robust phenomenon, but that's just my opinion. I'm also doubtful about the suggestion that super-overexpression of rum1 and ste9 would lead to over-replication but again, that's just an opinion. It is, however, worth mentioning that the modeling for varying levels of overexpression was done assuming that published overexpression experiments were done with known degrees of overexpression. This is in general not the case (since it requires antibodies to native proteins not generally available) and was not done in several cases I checked specifically. This is related to the general question about parameter sensitivity raised above.
In general, I do think this kind of theoretical modeling can be quite useful, and certainly there are many unsolved mysteries (molecular and dynamic) that can benefit from these approaches. But I really can't get enthusiastic about a theoretical approach that leaves out perhaps the most central component (the replication origin, unloaded, loaded and firing). There are many mysteries there; for example, the conventional qualitative model gets into a muddle without quite sharp thresholds for cyclin-cdk to avoid the situation with slow but continuing origin reloading with refiring, before mitosis. The theoretical approaches here, if modified, could well lead to insight into such matters, with useful experimental predictions about thresholds, unidentified but needed controls, etc. But I just don't think the current manuscript is there yet. 1

Reviewer #1 (Remarks to the Author):
In this excellent manuscript Novak and Tyson describe a computational model for the endoreduplication cycles in fission yeast. During cell division, DNA replication (S-phase) and mitosis (M-phase) alternate in order to maintain a constant DNA ploidy. Under some circumstances, cells can increase ploidy by undergoing multiple rounds of S-phase in the absence of M-phase, generating large cells with a giant nucleus. In fission yeast, endoreplication cycles are generated in mutants with reduced levels of Cdk1/CyclinB activity, either by deleting the cdc13+ gene, encoding the mitotic Cyclin B, or by overexpressing rum1+, encoding a potent Cdk1/Cdc13 kinase inhibitor, or ste9+, and APC/C activator that promotes polyubiquitylation and degradation of Cdc13. In all of these cases, the Cdk1/Cdc13 protein kinase activity is reduced to very low levels and these cells are unable to enter mitosis from G2. However, they can initiate S-phase because the Cdk1/Cig2 protein kinase activity continues to oscillate and promotes multiple rounds of S-phase without intervening mitoses.
This manuscript is very well written and contains very clear diagrams. The authors have done a careful job to build a model based on a central regulatory network consisting of Cdc10, a transcription factor that, at the end of G1, activates the expression of Cig2 (an S-phase cyclin), Cdc18 (a licensing factor for DNA replication) and Nrm1 (a negative regulator of Cdc10 that switches off transcription once DNA replication is initiated). The Cdk1/Cig2 protein kinase triggers S-phase and inhibits APC/C-Ste9 by phosphorylation at multiple sites during S-phase and G2. This allows the accumulation of Nrm1, which inhibits Cdc10 in S-phase and G2. This network generates two negative feedback loops that contributes to the oscillation of the system (Fig. 1). Additional elements, such as Mik1 (Fig.2), another Cdc10 target that phosphorylates and inhibits Cdk1/Cig2, TFI (Whi5) (Fig. 4), a negative regulator of Cdc10 and a Starter Kinase (SF) (Fig.5) that couples the system to cell growth and DNA replication, are added to the model. Finally, they introduce the oscillation of Cdk1/Cdc13 to demonstrate that the model of endoreplication can also explain the alternation of DNA replication and mitosis in a normal cell cycle. Thank you for the endorsement of our work and of the way it is presented in this paper.
The model takes into consideration all the published information in this area. Therefore, I recommend accepting the manuscript after the following minor revisions: 1. Page 5, line 12. Cdk:Cig2 should be Cdk1:Cig2. corrected 2. Page 5, line 13. The authors should explain why they assume constant activity of Cdc25 and/or Pyp3 in the endoreplication cycles? We wanted to keep the model as simple as possible, and regulation of Mik1 seems to be sufficient to achieve this goal. Furthermore, Cdc25 only becomes activated at the G2/M transition, and nothing is known about Pyp3 regulation according to our knowledge. 3. Page 8, second paragraph (results) and page 11, second paragraph (discussion). It would be important to distinguish the outcome of rum1+ and ste9+ overexpression which lead to endoreplication and cdc18+ overexpression that induces over-replication. We have made significant modifications to the manuscript by extending the model with replication dynamics, which is described in details in our reply to Reviewer #2. We think the distinction between these phenotypes is now clearly described.

Reviewer #2 (Remarks to the Author):
This paper addresses a classic issue: alternation of DNA replication and mitosis and coordination of both with cell growth. The approach is entirely theoretical, and familiar from previous work from these authors. ODE models are analyzed for geometrical features that exhibit biology-mimicking behavior. The ODE models are populated with variables based on well-researched molecular biology. In the present case, where the model is fission yeast, these variables include the mitotic kinase cdc13-cdk1, the (dispensable) S kinase cig2-cdk1, cdc18 (loading factor for the Mcm helicase at sites with bound ORC complex; this loading is required for, and may constitute, replication origin 'licensing') and transcription factors such as Nrm1 thought to be responsible for oscillations in cig2 and cdc18 among other genes.
There are two forms of DNA replication uncoupled from cell division considered here, 'endo-replication' in which complete rounds of DNA replication occur periodically (so that DNA content goes 1C to 2C to 4C etc), and 'over-replication' in which this behavior is not observed, but DNA content per cell goes up steadily. Exactly what DNA is replicated and how evenly the genome is replicated in the latter situation has been only partially explored.
One molecular interaction that is not discussed at all here is the mechanism of the positive effect of cyclin-cdk on replication initiation on Mcm-loaded ('licensed') origins. Another is the mechanism by which cyclin-cdk blocks Mcm loading (though inhibition of cdc18 by cig2 is indicated, this is far from the whole story).
Another rather critical thing not modeled here is the replication origin itself. This is a major omission, though I can see that its inclusion is challenging since it may not lend itself well to the ODE approach where all variables are continuous, while a given origin is either loaded or it's not, and there are thousands of them. But I think this leads to problems with the paper. This is a valid criticism which we took very seriously. We agree that association of oscillatory and steady state dynamics of the Cdc18-Cig2 network with endo-and over-replication phenotypes is not convincing without a kinetic description of licensing and activation of replication origins. Although Cdc18 was degraded in a Cig2-dependent manner in the original model, Cdc18 is still present at significant levels for a period of time after replication initiation, which raises the possibility of rereplication. A safe-guarding mechanism against re-replication is provided by a Cdk1-dependent local protection of replicated origins from re-licensing by Cdc18, as suggested by the work of Wuarin et al.

(2002). To this end, we have developed an ODE-based model for the licensing and activation of replication-origins (Figure 4A, a new section on 'Control of replication origin dynamics', and
Supplement). This model shows robust temporal separation of origin licensing and firing under the control of the limit cycle oscillation driving endoreplication cycles ( Figure 4B), which is a necessary and sufficient requirement for 'once and only once' origin firing. We also show that, at high overexpression of Cdc18, the flux of replication-origin licensing and firing come to a steady state, which corresponds to continuous replication, i.e. over-replication (see Figure 8B). In summary, by extending the Cdk1 control system with a mathematical model of replication dynamics, we provide a detailed quantitative description of endo-and over-replication.
There is a well-established qualitative molecular understanding of the difference between endo-and over-replication that goes as follows.
Replication origins with bound ORC and bound Mcm ('loaded') can be converted to active origins, driving bidirectional replication, upon cyclin-cdk activation (phosphorylating proteins such as Sld2; see work by Diffley and Araki). Bidirectional replication sends the Mcm helicase off with the replication fork, leaving behind an unloaded origin. This is an important feature since it most likely makes origin unloading an inevitable mechanical consequence of origin firing. cyclin-cdk activity simultaneously blocks RE-loading of the origin by multiple mechanisms (e.g. Nguyen 2000). So the origin will not re-load, therefore will not refire. After replication, mitotic cyclin-cdk promotes cell division and also degradation of mitotic cyclin; replication origins can reload (cyclin-cdk blockade removed) but will not fire until cyclin-cdk rises again. This gives once-per-cycle replication. Endo-replication requires cyclical activation AND inactivation of cyclin-cdk without cell division, to circumvent this control. One way to achieve this, discussed here, is that in the absence of mitotic cyclin cdc13, levels of S cyclin cig2 still cycle, due to a transcriptional oscillator. The mechanism of this oscillator is unknown, though the authors present an interesting theoretical case for a transcriptional oscillatory loop with involvement of nrm1 in combination with loops involving ste9, cdc18 and mik1. We agree with this 'qualitative' understanding of endo-and over-replication, and we have cast it into precise mathematical (quantitative) terms in order to understand the consequences of a particular mechanism, constructed along these lines of qualitative reasoning. We think our contribution helps to make the informal molecular model more well-founded.
There are other ways to achieve the same end. For example, preventing mitosis by depolymerizing microtubules, while eliminating the 'spindle assembly checkpoint', will result in repeated rounds of replication and polyploid nuclei. We assume (though I'm not sure about documentation) that such a situation entails essentially multiple complete cell cycles, where all that's missed is actual segregation of replicated sister chromosomes due to absence of microtubules. We are not aware of endomitosis induced by inactivation of the 'spindle assembly checkpoint' (SAC) in fission yeast. A possible reason for lack of experimental evidence could be that inactivation of the SAC (mad2 − ) leads to septum formation that cuts the nucleus and the cell dies (He, Patterson & Sazer: PNAS, 1997).
Over-replication: this situation is understood as a case where the block to origin reloading after firing is weakened or blocked. Any individual origin then may fire, then reload and fire again, repeatedly, in a stochastic fashion. Mitosis in such cells is blocked, and this is not well understood though there is some evidence that multiple initiations without division from individual origins ('onion-skin replication') may activate DNA damage checkpoints that block cell division. There are two main ways to achieve this state. Mechanisms for cyclin-cdk blockade of origin reloading can be blocked, for example by mutation of ORC, MCM and CDC6 (Nguyen 2000); or, the cyclin-cdk requirement for firing can be blocked (by appropriate mutation of Sld2 and Sld3 for example; Araki, Diffley) in which case cells with no cyclin-cdk activity at all will continuously and stochastically fire and reload origins. Probably, overexpression of cdc18 gives over-replication by forcing origin reloading despite countering mechanisms from cyclin-cdk through mass action, though this is less well-understood to my knowledge. We completely agree with the last sentence of this paragraph, and our proposed replication model implements exactly this mechanism. We assume that Cdk1 activity maintains replicated origins in a refractory state, which is made available for another round of licensing by Cdc18 only after a drop of Cdk1 activity. The paper by Wuarin et al. (2002) confirms this assumption. In our new model, a high level of Cdc18 overcomes this control by competing with Cdk1 for replicated origins. This is, I think, the consensus view of how cells replicate once per cycle, and how this can go wrong with endo-or over-replication. The replication control mechanism only becomes compromised during over-replication; it remains intact during endoreplication. During endoreplication, cells execute a complete round of DNA replication in response to each oscillation of S-phase Cdk activity.
I find it a serious omission in the present paper that neither of these ideas (especially the latter one) is discussed at all. It is striking that the paper is expressed as being about control of DNA replication, but in no figure and in none of the equations is DNA replication itself actually even mentioned. In the revised version of the paper, we provide a mathematical model of DNA replication kinetics as suggested by the reviewer and explained in more detail above. We have also modified the text at multiple places in order to provide background information about eukaryotic replication control. All modifications are highlighted in the revised paper.
(Leaving aside top left of Fig.5A, the idea that some unidentified 'Starter kinase' might be inhibited by DNA replication somehow -an idea for which no evidence is adduced, and an interaction that furthermore does not seem to be discussed in the text at all).

DNA replication has an inhibitory effect on 'Starter kinase' (SK) because the number of chromatin binding sites for SK doubles over the course of S phase. This effect is already described in the text.
I think the paper does some useful theorizing about potential endogenous loops controlling cig2 and cdc18. Novak and Tyson have been leaders in explaining how negative and positive feedback loops can give interesting biological behavior, and this is here elucidated with another example. The equations and diagrams are dependent on parameter choices, most or all of which are underpowered with respect to experimental data from others; so these ideas really are theoretical. (Some indication of parameter sensitivity of the models and claims would be welcome here). We are presenting a 'proof-of-principle' model here. We are not trying to pin down parameter values by fitting the model to a host of experimental observations, so an exploration of parameter sensitivity would be inappropriate.
However, when the paper transitions to explaining endo-vs over-replication I think falls short. There are two sides to the controls preventing these two kinds of replication errors: the cyclin-cdk side (alternating high and low levels are essential), and the replication origin side (key features: loading is cyclin-cdk-inhibited, firing is cyclin-cdk-promoted, and firing likely immediately reverses loading). The complete absence of discussion of the origin side of the story in this manuscript just won't do. We agree with the two sides of the control, and in our revision we have provided a model for the replication origin side. The extension of the model with replication origin dynamics confirms that oscillating Cdc18-Cig2 drives endoreplication while steady state dynamics leads to over-replication.
The paper comes up with some experimental suggestions: that moderate overexpression of cdc18 will lead to endo-and not over-replication. I must say this seems highly unlikely to me, and something furthermore that almost surely would have been seen if a robust phenomenon, but that's just my opinion. I'm also doubtful about the suggestion that super-overexpression of rum1 and ste9 would lead to over-replication but again, that's just an opinion. It is, however, worth mentioning that the modeling for varying levels of overexpression was done assuming that published overexpression experiments were done with known degrees of overexpression. This is in general not the case (since it requires antibodies to native proteins not generally available) and was not done in several cases I checked specifically. This is related to the general question about parameter sensitivity raised above. We think that it is quite reasonable to propose (as is observed in simulations of our realistic model) that there is a dynamic sequence from mitotic cycles to endoreplication to over-replication as the level of overexpression of protein(s) increases on releasing the thiamine-block to gene transcription. Anecdotal-but unpublished-DNA microarray data from Nurse's lab indicate that Rum1 overexpressing cells, after two rounds of endoreplication, show continued DNA replication, like cdc18 op cells. This is not surprising since Rum1 and Cdc18 share the same degradation machinery (SCF), so it is likely that Rum1 overexpression leads to elevated levels of Cdc18 (Kominami & Toda, 1997).
In general, I do think this kind of theoretical modeling can be quite useful, and certainly there are many unsolved mysteries (molecular and dynamic) that can benefit from these approaches. But I really can't get enthusiastic about a theoretical approach that leaves out perhaps the most central component (the replication origin, unloaded, loaded and firing). There are many mysteries there; for example, the conventional qualitative model gets into a muddle without quite sharp thresholds for cyclin-cdk to avoid the situation with slow but continuing origin reloading with refiring, before mitosis. The theoretical approaches here, if modified, could well lead to insight into such matters, with useful experimental predictions about thresholds, unidentified but needed controls, etc. But I just don't think the current manuscript is there yet. The referee is correct that sharp Cdk1 thresholds are required to control origin firing and to block relicensing. In response to the referee's critique, we have presented a formal model of replication control, with sharp thresholds (implemented by Hill functions) for origin firing by Cdk1 and for Cdk1maintenance of a refractory state of fired-origins. We thank the referee for prompting us to make these changes, and we hope that our ODE-based model of replication control eliminates some of his/her reservations about our paper. 2nd Editorial Decision RE: Manuscript #E20-09-0610R TITLE: "Computational modelling of chromosome re-replication in mutant strains of fission yeast" Dear Bela: please address the remaining concerns of one of the reviewer, and I will accept the paper without further delay The review of your manuscript, referenced above, is now complete. The Monitoring Editor has decided that your manuscript requires minor revisions before it can be published in Molecular Biology of the Cell, as described in the Monitoring Editor's decision letter above and the reviewer comments (if any) below.
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Reviewer #2 (Remarks to the Author): I think the paper is considerably improved, in bringing in explicit consideration of the origin side of replication control. And in general I think this sort of modeling is helpful to crystallize qualitative insights and 'nail flags to the mast' -that is, if one really believes all the input ideas, then one must adhere to the prediction or state the reason why.
The authors are not concerned with parameter sensitivity of their model, according to their response letter -I personally think this is a mistake. It is, of course, OK for a model to be very sensitive to some parameter choice, but then that becomes an important prediction (that small changes in whatever gene/biochemical pathway drives that parameter should have major effects on output). And if a model is super-sensitive to too many parameters then it becomes a priori unlikely just because cells aren't that accurate. But this is my opinion, I state it for what it's worth. Some fairly minor issues: "carrying mutations that interfere with the function of mitotic cyclin-dependent kinase (Cdk1:Cdc13) without impeding the roles of DNA-replication loading-factor (Cdc18) and S-phase cyclin-dependent kinase (Cdk1:Cig2). Some of these mutations support endoreplication, and some over-replication". -This passage suggests there are mutations interfering with CDK1-CDC13 that cause over-replication, but I don't know what mutations these are. No mutations in CDK1 or CDC13 themselves will do this, to my knowledge. The paper assigns a role to mik1 in the phenomenon of re-replication in cdc13-null (at least this is my understanding). If the model predicts that cdc13 null mik1 will not re-replicate, then I think this is a prediction worth stating because it's an easy experiment (like a week's work) and would show that the replication checkpoint is indeed required to get the requisite delay for the Cig2 negative feedback loop to oscillate. Or maybe I have this all wrong, sorry if so.
The paper states 'During endoreplication, Cig2-kinase oscillations drive discrete rounds of DNA synthesis with the periodicity of cell mass doubling time (Kiang et al., 2009), which suggests a strong coupling between the oscillatory mechanism in Figure 3 and the nucleocytoplasmic ratio (NCR).' The general concept is OK, but it really should be DNA-cytoplasmic ratio or equivalent, since Nurse showed constant NCR volume ratio throughout the cell cycle and in many other situations. If the authors really want to say that ratio of nuclear to cytoplasmic volume is changing in a meaningful way then they have to deal with some contrary evidence.
The 'titration mechanism' for inactivating TFI is certainly at the least a close relative of the 'inhibitor dilution' mechanism of Schmoller et al. This similarity (and any key differences between Schmoller et al and the authors' views) should be discussed explicitly. This is especially to the point as Schmoller's view has come under some considerable attack (though in my mind it remains the best available model for G1 size control in budding yeast). "In addition to depletion of Cdc13 mitotic cyclin, multiple rounds of DNA replication in the absence of mitosis can be induced by overexpression of several cell cycle regulators (cdc18op, rum1op or ste9op) in cdc13+ genetic background (Moreno and Nurse, 1994;Yamaguchi et al., 1997;Kitamura et al., 1998)." None of the cited papers discuss cdc18-OP at all -a text search shows that 'cdc18' does not occur in their texts even once. A correct reference is Nishitani and Nurse (1995) -and that paper is notably cautious about calling the extra replication 'repeated rounds', distinguishing the phenotype from e.g. rum1-OP. Similarly see Yanow et al. 2001 for DNA over-replication (not endo-reduplication) upon cdc18-op. Kiang et al 2010 make the point that cdc18/cdt1-op induced over-replication is origin-specific, presumably reflecting some difference in sensitivity of different origins to enhancement of loading by cdc18, to inhibition of reloading by Cdk, or both. It is not reasonable to ask the authors to atomize their model by putting in different classes of origins, but this should at least be discussed (I believe there is similar data from budding yeast). The reason is that the experimental readout for 'over-replication' vs. endoreplication is whether replication goes in precise rounds; if there are different origin classes, though, then what looks like a mound of randomly over-replicated DNA might actually reflect precise once-per-cycle replication but applied variably to different populations of origins.
1 Reviewer #2 (Remarks to the Author): I think the paper is considerably improved, in bringing in explicit consideration of the origin side of replication control. And in general I think this sort of modeling is helpful to crystallize qualitative insights and 'nail flags to the mast' -that is, if one really believes all the input ideas, then one must adhere to the prediction or state the reason why. We are glad that the Reviewer appreciates our efforts to improve the manuscript.
The authors are not concerned with parameter sensitivity of their model, according to their response letter -I personally think this is a mistake. It is, of course, OK for a model to be very sensitive to some parameter choice, but then that becomes an important prediction (that small changes in whatever gene/biochemical pathway drives that parameter should have major effects on output). And if a model is super-sensitive to too many parameters then it becomes a priori unlikely just because cells aren't that accurate. But this is my opinion, I state it for what it's worth. Our proposed explanations of endo/over-replication are based ultimately on robust phase plane portraits and bifurcation diagrams that describe the dynamic behavior of the control systems. Dynamical systems theory assures that these behaviors are 'non-fragile,' i.e., they persist over a range of parameter values. So we are confident in the robustness of the qualitative features of our proposed mechanisms. Quantitative features (specific times and protein levels), of course, depend on specific parameter values. To carry out a detailed 'sensitivity analysis' of these features would require us to define meaningful physiological criteria beyond which the functionality of the system would be considered to be unacceptable. Such an analysis is outside the scope of our investigation.
Some fairly minor issues: "carrying mutations that interfere with the function of mitotic cyclin-dependent kinase (Cdk1:Cdc13) without impeding the roles of DNA-replication loading-factor (Cdc18) and S-phase cyclin-dependent kinase (Cdk1:Cig2). Some of these mutations support endoreplication, and some over-replication". -This passage suggests there are mutations interfering with CDK1-CDC13 that cause over-replication, but I don't know what mutations these are. No mutations in CDK1 or CDC13 themselves will do this, to my knowledge. The paper assigns a role to mik1 in the phenomenon of re-replication in cdc13-null (at least this is my understanding). If the model predicts that cdc13 null mik1 will not re-replicate, then I think this is a prediction worth stating because it's an easy experiment (like a week's work) and would show that the replication checkpoint is indeed required to get the requisite delay for the Cig2 negative feedback loop to oscillate. Or maybe I have this all wrong, sorry if so. We assume that the reviewer is referring to a cdc13-null mik1-null double mutant. It is a good suggestion, but there is a potential caveat, because the experiment can be done only with nmt-cdc13 strain in the presence of thiamine. This strain expresses low, residual level of Cdc13, which is targeted by Mik1 as well. In the absence of Mik1-kinase the activity of Cdc13-kinase should be increased, which might inhibit re-replication. This complication makes difficult even the interpretation of the positive result. Despite this difficulty, we added the following sentence to the MS: "Our model predicts that inhibitory phosphorylation of Cdk1:Cig2 by Mik1kinase could be an essential step in creating Cig2 oscillations and genome reduplication." We also added another experimentally testable prediction for rum1 op -induced endocycles: "According to our model, overproduction of Rum1 induces endoreplication with periodic appearance of the Cdc13 mitotic cyclin, which comes and goes because Ste9 periodically destroys it. This prediction could be tested by measuring Cdc13-GFP levels in single cells." The paper states 'During endoreplication, Cig2-kinase oscillations drive discrete rounds of DNA synthesis with the periodicity of cell mass doubling time (Kiang et al., 2009), which suggests a strong coupling between the oscillatory mechanism in Figure 3 and the nucleocytoplasmic ratio (NCR).' The general concept is OK, but it really should be DNA-cytoplasmic ratio or equivalent, since Nurse showed constant NCR volume ratio throughout the cell cycle and in many other situations. If the authors really want to say that ratio of nuclear to cytoplasmic volume is changing in a meaningful way then they have to deal with some contrary evidence. Although we were using the nucleocytoplasmic ratio (NCR) to refer to the 'nuclear DNA:protein ratio', we follow the advice of the reviewer and we have replaced NCR with 'DNA:protein ratio' at all places in the manuscript in order to avoid confusion.
The 'titration mechanism' for inactivating TFI is certainly at the least a close relative of the 'inhibitor dilution' mechanism of Schmoller et al. This similarity (and any key differences between Schmoller et al and the authors' views) should be discussed explicitly. This is especially to the point as Schmoller's view has come under some considerable attack (though in my mind it remains the best available model for G1 size control in budding yeast). Our 'titration' and 'inhibitor-dilution' mechanisms are indeed "distant" relatives, because both of them are based on strong complex formation between TF and the active (not SK-inactivated) fraction of TFI. The DNA:protein ratio (DPR) dictates the synthesis rate of TFI in the 'inhibitor-dilution' model, and its inverse (protein:DNA ratio) determines the rate of TFI inactivation in the 'titration' model. The activeTFI:TF ratio is declining during G1 progression in both mechanisms until the tipping point, when they reach stoichiometric balance. This leads to initiation of genome duplication and a corresponding doubling of TFI synthesis in the 'inhibitor-dilution' mechanism, and halving of TFI inactivation rate in the 'titration' model. Balanced growth and division requires that the activeTFI:TF ratio rapidly recovers to its maximal value in less than a mass doubling time. This requirement is easily satisfied by the 'titration' mechanism, where the number of SK molecules per chromatin is halved during the course of DNA replication. Resetting the ratio in the 'inhibitor dilution' mechanism requires that the half-life of the TFI is much shorter than the mass doubling time. This problem with the 'inhibitor dilution' mechanism is already explained in the paper.
"In addition to depletion of Cdc13 mitotic cyclin, multiple rounds of DNA replication in the absence of mitosis can be induced by overexpression of several cell cycle regulators (cdc18op, rum1op or ste9op) in cdc13+ genetic background (Moreno and Nurse, 1994;Yamaguchi et al., 1997;Kitamura et al., 1998)." None of the cited papers discuss cdc18-OP at all -a text search shows that 'cdc18' does not occur in their texts even once. A correct reference is Nishitani and Nurse (1995) -and that paper is notably cautious about calling the extra replication 'repeated rounds', distinguishing the phenotype from e.g. rum1-OP. Similarly see Yanow et al. 2001 for DNA overreplication (not endo-reduplication) upon cdc18-op. We have inserted the required references at the end of the cited sentence.
Kiang et al 2010 make the point that cdc18/cdt1-op induced over-replication is origin-specific, presumably reflecting some difference in sensitivity of different origins to enhancement of loading by cdc18, to inhibition of reloading by Cdk, or both. It is not reasonable to ask the authors to atomize their model by putting in different classes of origins, but this should at least be discussed (I believe there is similar data from budding yeast). The reason is that the experimental readout for 'over-replication' vs. endoreplication is whether replication goes in precise rounds; if there are different origin classes, though, then what looks like a mound of randomly overreplicated DNA might actually reflect precise once-per-cycle replication but applied variably to different populations of origins. We agree that our deterministic description of replication-origin dynamics ignores the heterogeneous characteristics of individual origins, but we think our simplified description is satisfactory for this investigation. Congratulations on the acceptance of your manuscript.
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