Newton's cradle: Cell cycle regulation by two mutually inhibitory oscillators.

The cell division cycle is a fundamental physiological process displaying a great degree of plasticity during the course of multicellular development. This plasticity is evident in the transition from rapid and stringently-timed divisions of the early embryo to subsequent size-controlled mitotic cycles. Later in development, cells may pause and restart proliferation in response to myriads of internal or external signals, or permanently exit the cell cycle following terminal differentiation or senescence. Beyond this, cells can undergo modified cell division variants, such as endoreplication, which increases their ploidy, or meiosis, which reduces their ploidy. This wealth of behaviours has led to numerous conceptual analogies intended as frameworks for understanding the proliferative program. Here, we aim to unify these mechanisms under one dynamical paradigm. To this end, we take a control theoretical approach to frame the cell cycle as a pair of arrestable and mutually-inhibiting, doubly amplified, negative feedback oscillators controlling chromosome replication and segregation events, respectively. Under appropriate conditions, this framework can reproduce fixed-period oscillations, checkpoint arrests of variable duration, and endocycles. Subsequently, we use phase plane and bifurcation analysis to explain the dynamical basis of these properties. Then, using a physiologically realistic, biochemical model, we show that the very same regulatory structure underpins the diverse functions of the cell cycle control network. We conclude that Newton's cradle may be a suitable mechanical analogy of how the cell cycle is regulated.

The bistable mitotic switch in fission yeast.

In favorable conditions, eukaryotic cells proceed irreversibly through the cell division cycle (G1-S-G2-M) in order to produce two daughter cells with the same number and identity of chromosomes of their progenitor. The integrity of this process is maintained by "checkpoints" that hold a cell at particular transition points of the cycle until all requisite events are completed. The crucial functions of these checkpoints seem to depend on irreversible bistability of the underlying checkpoint control systems. Bistability of cell cycle transitions has been confirmed experimentally in frog egg extracts, budding yeast cells and mammalian cells. For fission yeast cells, a recent paper by Patterson et al. (2021) provides experimental evidence for an abrupt transition from G2 phase into mitosis, and we show that these data are consistent with a stochastic model of a bistable switch governing the G2/M checkpoint. Interestingly, our model suggests that their experimental data could also be explained by a reversible/sigmoidal switch, and stochastic simulations confirm this supposition. We propose a simple modification of their experimental protocol that could provide convincing evidence for (or against) bistability of the G2/M transition in fission yeast.

The oscillation of mitotic kinase governs cell cycle latches in mammalian cells.

The mammalian cell cycle alternates between two phases - S-G2-M with high levels of A- and B-type cyclins (CycA and CycB, respectively) bound to cyclin-dependent kinases (CDKs), and G1 with persistent degradation of CycA and CycB by an activated anaphase promoting complex/cyclosome (APC/C) bound to Cdh1 (also known as FZR1 in mammals; denoted APC/C:Cdh1). Because CDKs phosphorylate and inactivate Cdh1, these two phases are mutually exclusive. This 'toggle switch' is flipped from G1 to S by cyclin-E bound to a CDK (CycE:CDK), which is not degraded by APC/C:Cdh1, and from M to G1 by Cdc20-bound APC/C (APC/C:Cdc20), which is not inactivated by CycA:CDK or CycB:CDK. After flipping the switch, cyclin E is degraded and APC/C:Cdc20 is inactivated. Combining mathematical modelling with single-cell timelapse imaging, we show that dysregulation of CycB:CDK disrupts strict alternation of the G1-S and M-G1 switches. Inhibition of CycB:CDK results in Cdc20-independent Cdh1 'endocycles', and sustained activity of CycB:CDK drives Cdh1-independent Cdc20 endocycles. Our model provides a mechanistic explanation for how whole-genome doubling can arise, a common event in tumorigenesis that can drive tumour evolution.

Reusable rule-based cell cycle model explains compartment-resolved dynamics of 16 observables in RPE-1 cells.

The mammalian cell cycle is regulated by a well-studied but complex biochemical reaction system. Computational models provide a particularly systematic and systemic description of the mechanisms governing mammalian cell cycle control. By combining both state-of-the-art multiplexed experimental methods and powerful computational tools, this work aims at improving on these models along four dimensions: model structure, validation data, validation methodology and model reusability. We developed a comprehensive model structure of the full cell cycle that qualitatively explains the behaviour of human retinal pigment epithelial-1 cells. To estimate the model parameters, time courses of eight cell cycle regulators in two compartments were reconstructed from single cell snapshot measurements. After optimisation with a parallel global optimisation metaheuristic we obtained excellent agreements between simulations and measurements. The PEtab specification of the optimisation problem facilitates reuse of model, data and/or optimisation results. Future perturbation experiments will improve parameter identifiability and allow for testing model predictive power. Such a predictive model may aid in drug discovery for cell cycle-related disorders.

Time-keeping and decision-making in the cell cycle.

Cell growth, DNA replication, mitosis and division are the fundamental processes by which life is passed on from one generation of eukaryotic cells to the next. The eukaryotic cell cycle is intrinsically a periodic process but not so much a 'clock' as a 'copy machine', making new daughter cells as warranted. Cells growing under ideal conditions divide with clock-like regularity; however, if they are challenged with DNA-damaging agents or mitotic spindle disrupters, they will not progress to the next stage of the cycle until the damage is repaired. These 'decisions' (to exit and re-enter the cell cycle) are essential to maintain the integrity of the genome from generation to generation. A crucial challenge for molecular cell biologists in the 1990s was to unravel the genetic and biochemical mechanisms of cell cycle control in eukaryotes. Central to this effort were biochemical studies of the clock-like regulation of 'mitosis promoting factor' during synchronous mitotic cycles of fertilized frog eggs and genetic studies of the switch-like regulation of 'cyclin-dependent kinases' in yeast cells. In this review, we uncover some secrets of cell cycle regulation by mathematical modelling of increasingly more complex molecular regulatory networks of cell cycle 'clocks' and 'switches'.

Mitotic kinase oscillation governs the latching of cell cycle switches.

In 1996, Kim Nasmyth1 proposed that the eukaryotic cell cycle is an alternating sequence of transitions from G1 to S-G2-M and back again. These two phases correlate to high activity of cyclin-dependent kinases (CDKs) that trigger S-G2-M events and CDK antagonists that stabilize G1 phase. We associated these "alternative phases" with the coexistence of two stable steady states of the biochemical reactions among CDKs and their antagonists.2,3 Transitions between these steady states (G1-to-S and M-to-G1) are driven by "helper" proteins. The fact that the transitions are irreversible is guaranteed by a "latching" property of the molecular switches, as we have argued in previous publications.4,5 Here, we show that if the latch is broken, then the biochemical reactions can swing back-and-forth across the transitions; either G1-S-G1-S … (periodic DNA replication without mitosis or cell division) or M-(G1)-M-(G1) … (periodic Cdc14 release, without fully exiting mitosis). Using mathematical modeling of the molecular control circuit in budding yeast, we provide a fresh account of aberrant cell cycles in mutant strains: endoreplication in the clb1-5Δ strain6 and periodic release and resequestration of Cdc14 (an "exit" phosphatase) in the CLB2kdΔ strain.7,8 In our opinion, these "endocycles" are not autonomous oscillatory modules that must be entrained by the CDK oscillator6,7 but rather inadvertent and deleterious oscillations that are normally suppressed by the CDK latching-gate mechanism.8.

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.

Mechanisms of signalling-memory governing progression through the eukaryotic cell cycle.

As cells pass through each replication-division cycle, they must be able to postpone further progression if they detect any threats to genome integrity, such as DNA damage or misaligned chromosomes. Once a 'decision' is made to proceed, the cell unequivocally enters into a qualitatively different biochemical state, which makes the transitions from one cell cycle phase to the next switch-like and irreversible. Each transition is governed by a unique signalling network; nonetheless, they share a common characteristic of bistable behaviour, a hallmark of molecular memory devices. Comparing the cell cycle signalling mechanisms acting at the restriction point, G1/S, G2/M and meta-to-anaphase transitions, we deduce a generic network motif of coupled positive and negative feedback loops underlying each transition.

Cyclin A triggers Mitosis either via the Greatwall kinase pathway or Cyclin B.

Two mitotic cyclin types, cyclin A and B, exist in higher eukaryotes, but their specialised functions in mitosis are incompletely understood. Using degron tags for rapid inducible protein removal, we analyse how acute depletion of these proteins affects mitosis. Loss of cyclin A in G2-phase prevents mitotic entry. Cells lacking cyclin B can enter mitosis and phosphorylate most mitotic proteins, because of parallel PP2A:B55 phosphatase inactivation by Greatwall kinase. The final barrier to mitotic establishment corresponds to nuclear envelope breakdown, which requires a decisive shift in the balance of cyclin-dependent kinase Cdk1 and PP2A:B55 activity. Beyond this point, cyclin B/Cdk1 is essential for phosphorylation of a distinct subset of mitotic Cdk1 substrates that are essential to complete cell division. Our results identify how cyclin A, cyclin B and Greatwall kinase coordinate mitotic progression by increasing levels of Cdk1-dependent substrate phosphorylation.

A Dynamical Paradigm for Molecular Cell Biology.

The driving passion of molecular cell biologists is to understand the molecular mechanisms that control important aspects of cell physiology, but this ambition is often limited by the wealth of molecular details currently known about these mechanisms. Their complexity overwhelms our intuitive notions of how molecular regulatory networks might respond under normal and stressful conditions. To make progress we need a new paradigm for connecting molecular biology to cell physiology. We suggest an approach that uses precise mathematical methods to associate the qualitative features of dynamical systems, as conveyed by 'bifurcation diagrams', with 'signal-response' curves measured by cell biologists.

A Single Light-Responsive Sizer Can Control Multiple-Fission Cycles in Chlamydomonas.

Most eukaryotic cells execute binary division after each mass doubling in order to maintain size homeostasis by coordinating cell growth and division. By contrast, the photosynthetic green alga Chlamydomonas can grow more than 8-fold during daytime and then, at night, undergo rapid cycles of DNA replication, mitosis, and cell division, producing up to 16 daughter cells. Here, we propose a mechanistic model for multiple-fission cycles and cell-size control in Chlamydomonas. The model comprises a light-sensitive and size-dependent biochemical toggle switch that acts as a sizer, guarding transitions into and exit from a phase of cell-division cycle oscillations. This simple "sizer-oscillator" arrangement reproduces the experimentally observed features of multiple-fission cycles and the response of Chlamydomonas cells to different light-dark regimes. Our model also makes specific predictions about the size dependence of the time of onset of cell division after cells are transferred from light to dark conditions, and we confirm these predictions by single-cell experiments. Collectively, our results provide a new perspective on the concept of a "commitment point" during the growth of Chlamydomonas cells and hint at intriguing similarities of cell-size control in different eukaryotic lineages.

Absolute quantification of cohesin, CTCF and their regulators in human cells.

The organisation of mammalian genomes into loops and topologically associating domains (TADs) contributes to chromatin structure, gene expression and recombination. TADs and many loops are formed by cohesin and positioned by CTCF. In proliferating cells, cohesin also mediates sister chromatid cohesion, which is essential for chromosome segregation. Current models of chromatin folding and cohesion are based on assumptions of how many cohesin and CTCF molecules organise the genome. Here we have measured absolute copy numbers and dynamics of cohesin, CTCF, NIPBL, WAPL and sororin by mass spectrometry, fluorescence-correlation spectroscopy and fluorescence recovery after photobleaching in HeLa cells. In G1-phase, there are ~250,000 nuclear cohesin complexes, of which ~ 160,000 are chromatin-bound. Comparison with chromatin immunoprecipitation-sequencing data implies that some genomic cohesin and CTCF enrichment sites are unoccupied in single cells at any one time. We discuss the implications of these findings for how cohesin can contribute to genome organisation and cohesion.

CDK1-CCNB1 creates a spindle checkpoint-permissive state by enabling MPS1 kinetochore localization.

Spindle checkpoint signaling is initiated by recruitment of the kinase MPS1 to unattached kinetochores during mitosis. We show that CDK1-CCNB1 and a counteracting phosphatase PP2A-B55 regulate the engagement of human MPS1 with unattached kinetochores by controlling the phosphorylation status of S281 in the kinetochore-binding domain. This regulation is essential for checkpoint signaling, since MPS1S281A is not recruited to unattached kinetochores and fails to support the recruitment of other checkpoint proteins. Directly tethering MPS1S281A to the kinetochore protein Mis12 bypasses this regulation and hence the requirement for S281 phosphorylation in checkpoint signaling. At the metaphase-anaphase transition, MPS1 S281 dephosphorylation is delayed because PP2A-B55 is negatively regulated by CDK1-CCNB1 and only becomes fully active once CCNB1 concentration falls below a characteristic threshold. This mechanism prolongs the checkpoint-responsive period when MPS1 can localize to kinetochores and enables a response to late-stage spindle defects. By acting together, CDK1-CCNB1 and PP2A-B55 thus create a spindle checkpoint-permissive state and ensure the fidelity of mitosis.

Two Interlinked Bistable Switches Govern Mitotic Control in Mammalian Cells.

Distinct protein phosphorylation levels in interphase and M phase require tight regulation of Cdk1 activity [1, 2]. A bistable switch, based on positive feedback in the Cdk1 activation loop, has been proposed to generate different thresholds for transitions between these cell-cycle states [3-5]. Recently, the activity of the major Cdk1-counteracting phosphatase, PP2A:B55, has also been found to be bistable due to Greatwall kinase-dependent regulation [6]. However, the interplay of the regulation of Cdk1 and PP2A:B55 in vivo remains unexplored. Here, we combine quantitative cell biology assays with mathematical modeling to explore the interplay of mitotic kinase activation and phosphatase inactivation in human cells. By measuring mitotic entry and exit thresholds using ATP-analog-sensitive Cdk1 mutants, we find evidence that the mitotic switch displays hysteresis and bistability, responding differentially to Cdk1 inhibition in the mitotic and interphase states. Cdk1 activation by Wee1/Cdc25 feedback loops and PP2A:B55 inactivation by Greatwall independently contributes to this hysteretic switch system. However, elimination of both Cdk1 and PP2A:B55 inactivation fully abrogates bistability, suggesting that hysteresis is an emergent property of mutual inhibition between the Cdk1 and PP2A:B55 feedback loops. Our model of the two interlinked feedback systems predicts an intermediate but hidden steady state between interphase and M phase. This could be verified experimentally by Cdk1 inhibition during mitotic entry, supporting the predictive value of our model. Furthermore, we demonstrate that dual inhibition of Wee1 and Gwl kinases causes loss of cell-cycle memory and synthetic lethality, which could be further exploited therapeutically.

Dilution and titration of cell-cycle regulators may control cell size in budding yeast.

The size of a cell sets the scale for all biochemical processes within it, thereby affecting cellular fitness and survival. Hence, cell size needs to be kept within certain limits and relatively constant over multiple generations. However, how cells measure their size and use this information to regulate growth and division remains controversial. Here, we present two mechanistic mathematical models of the budding yeast (S. cerevisiae) cell cycle to investigate competing hypotheses on size control: inhibitor dilution and titration of nuclear sites. Our results suggest that an inhibitor-dilution mechanism, in which cell growth dilutes the transcriptional inhibitor Whi5 against the constant activator Cln3, can facilitate size homeostasis. This is achieved by utilising a positive feedback loop to establish a fixed size threshold for the Start transition, which efficiently couples cell growth to cell cycle progression. Yet, we show that inhibitor dilution cannot reproduce the size of mutants that alter the cell's overall ploidy and WHI5 gene copy number. By contrast, size control through titration of Cln3 against a constant number of genomic binding sites for the transcription factor SBF recapitulates both size homeostasis and the size of these mutant strains. Moreover, this model produces an imperfect 'sizer' behaviour in G1 and a 'timer' in S/G2/M, which combine to yield an 'adder' over the whole cell cycle; an observation recently made in experiments. Hence, our model connects these phenomenological data with the molecular details of the cell cycle, providing a systems-level perspective of budding yeast size control.

Genome Stability during Cell Proliferation: A Systems Analysis of the Molecular Mechanisms Controlling Progression through the Eukaryotic Cell Cycle.

Well-nourished cells in a favorable environment (well supplied with growth factors, cytokines, and/or hormones and free from stresses, ionizing radiation, etc.) will grow, replicate their genome, and divide into two daughter cells, fully prepared to repeat the process. This cycle of DNA replication and division underlies all aspects of biological growth, reproduction, repair and development. As such, it is essential that the cell's genome be guarded against damage during the replication/division process, lest the error(s) be irrevocably passed down to all future generations of progeny. Hence, cell cycle progression is closely guarded against major sources of errors, in particular DNA damage and misalignment of replicated chromosomes on the mitotic spindle. In this review article we examine closely the molecular mechanisms that maintain genomic integrity during the cell division cycle, and we find an unexpected and intriguing arrangement of concatenated and nested bistable toggle switches. The topology of the network seems to play crucial roles in maintaining the stability of the genome during cell proliferation.

Systems-level feedback regulation of cell cycle transitions in Ostreococcus tauri.

Ostreococcus tauri is the smallest free-living unicellular organism with one copy of each core cell cycle genes in its genome. There is a growing interest in this green algae due to its evolutionary origin. Since O. tauri is diverged early in the green lineage, relatively close to the ancestral eukaryotic cell, it might hold a key phylogenetic position in the eukaryotic tree of life. In this study, we focus on the regulatory network of its cell division cycle. We propose a mathematical modelling framework to integrate the existing knowledge of cell cycle network of O. tauri. We observe that feedback loop regulation of both G1/S and G2/M transitions in O. tauri is conserved, which can make the transition bistable. This is essential to make the transition irreversible as shown in other eukaryotic organisms. By performing sequence analysis, we also predict the presence of the Greatwall/PP2A pathway in the cell cycle of O. tauri. Since O. tauri cell cycle machinery is conserved, the exploration of the dynamical characteristic of the cell division cycle will help in further understanding the regulation of cell cycle in higher eukaryotes.

A comprehensive model for the proliferation-quiescence decision in response to endogenous DNA damage in human cells.

Human cells that suffer mild DNA damage can enter a reversible state of growth arrest known as quiescence. This decision to temporarily exit the cell cycle is essential to prevent the propagation of mutations, and most cancer cells harbor defects in the underlying control system. Here we present a mechanistic mathematical model to study the proliferation-quiescence decision in nontransformed human cells. We show that two bistable switches, the restriction point (RP) and the G1/S transition, mediate this decision by integrating DNA damage and mitogen signals. In particular, our data suggest that the cyclin-dependent kinase inhibitor p21 (Cip1/Waf1), which is expressed in response to DNA damage, promotes quiescence by blocking positive feedback loops that facilitate G1 progression downstream of serum stimulation. Intriguingly, cells exploit bistability in the RP to convert graded p21 and mitogen signals into an all-or-nothing cell-cycle response. The same mechanism creates a window of opportunity where G1 cells that have passed the RP can revert to quiescence if exposed to DNA damage. We present experimental evidence that cells gradually lose this ability to revert to quiescence as they progress through G1 and that the onset of rapid p21 degradation at the G1/S transition prevents this response altogether, insulating S phase from mild, endogenous DNA damage. Thus, two bistable switches conspire in the early cell cycle to provide both sensitivity and robustness to external stimuli.

Cell-cycle transitions: a common role for stoichiometric inhibitors.

The cell division cycle is the process by which eukaryotic cells replicate their chromosomes and partition them to two daughter cells. To maintain the integrity of the genome, proliferating cells must be able to block progression through the division cycle at key transition points (called "checkpoints") if there have been problems in the replication of the chromosomes or their biorientation on the mitotic spindle. These checkpoints are governed by protein-interaction networks, composed of phase-specific cell-cycle activators and inhibitors. Examples include Cdk1:Clb5 and its inhibitor Sic1 at the G1/S checkpoint in budding yeast, APC:Cdc20 and its inhibitor MCC at the mitotic checkpoint, and PP2A:B55 and its inhibitor, alpha-endosulfine, at the mitotic-exit checkpoint. Each of these inhibitors is a substrate as well as a stoichiometric inhibitor of the cell-cycle activator. Because the production of each inhibitor is promoted by a regulatory protein that is itself inhibited by the cell-cycle activator, their interaction network presents a regulatory motif characteristic of a "feedback-amplified domineering substrate" (FADS). We describe how the FADS motif responds to signals in the manner of a bistable toggle switch, and then we discuss how this toggle switch accounts for the abrupt and irreversible nature of three specific cell-cycle checkpoints.

Interlinked bistable mechanisms generate robust mitotic transitions.

The transitions between phases of the cell cycle have evolved to be robust and switch-like, which ensures temporal separation of DNA replication, sister chromatid separation, and cell division. Mathematical models describing the biochemical interaction networks of cell cycle regulators attribute these properties to underlying bistable switches, which inherently generate robust, switch-like, and irreversible transitions between states. We have recently presented new mathematical models for two control systems that regulate crucial transitions in the cell cycle: mitotic entry and exit, 1 and the mitotic checkpoint. 2 Each of the two control systems is characterized by two interlinked bistable switches. In the case of mitotic checkpoint control, these switches are mutually activating, whereas in the case of the mitotic entry/exit network, the switches are mutually inhibiting. In this Perspective we describe the qualitative features of these regulatory motifs and show that having two interlinked bistable mechanisms further enhances robustness and irreversibility. We speculate that these network motifs also underlie other cell cycle transitions and cellular transitions between distinct biochemical states.