Interlinked bistable mechanisms generate robust mitotic transitions

Cyclin B3 is a dominant fast-acting cyclin that drives rapid early embryonic mitoses

Mitosis in early embryos often proceeds at a rapid pace, but how this pace is achieved is not understood. Here, we show that cyclin B3 is the dominant driver of rapid embryonic mitoses in the C. elegans embryo. Cyclins B1 and B2 support slow mitosis (NEBD to anaphase ∼600 s), but the presence of cyclin B3 dominantly drives the approximately threefold faster mitosis observed in wildtype. Multiple mitotic events are slowed down in cyclin B1 and B2-driven mitosis, and cyclin B3-associated Cdk1 H1 kinase activity is ∼25-fold more active than cyclin B1-associated Cdk1. Addition of cyclin B1 to fast cyclin B3-only mitosis introduces an ∼60-s delay between completion of chromosome alignment and anaphase onset; this delay, which is important for segregation fidelity, is dependent on inhibitory phosphorylation of the anaphase activator Cdc20. Thus, cyclin B3 dominance, coupled to a cyclin B1-dependent delay that acts via Cdc20 phosphorylation, sets the rapid pace and ensures mitotic fidelity in the early C. elegans embryo.

Cyclin B3 is a dominant fast-acting cyclin that drives rapid early embryonic mitoses

In many species, early embryonic mitoses proceed at a very rapid pace, but how this pace is achieved is not understood. Here we show that in the early C. elegans embryo, cyclin B3 is the dominant driver of rapid embryonic mitoses. Metazoans typically have three cyclin B isoforms that associate with and activate Cdk1 kinase to orchestrate mitotic events: the related cyclins B1 and B2 and the more divergent cyclin B3. We show that whereas embryos expressing cyclins B1 and B2 support slow mitosis (NEBD to Anaphase ~ 600s), the presence of cyclin B3 dominantly drives the ~3-fold faster mitosis observed in wildtype embryos. CYB-1/2-driven mitosis is longer than CYB-3-driven mitosis primarily because the progression of mitotic events itself is slower, rather than delayed anaphase onset due to activation of the spindle checkpoint or inhibitory phosphorylation of the anaphase activator CDC-20. Addition of cyclin B1 to cyclin B3-only mitosis introduces an ~60s delay between the completion of chromosome alignment and anaphase onset, which likely ensures segregation fidelity; this delay is mediated by inhibitory phosphorylation on CDC-20. Thus, the dominance of cyclin B3 in driving mitotic events, coupled to introduction of a short cyclin B1-dependent delay in anaphase onset, sets the rapid pace and ensures fidelity of mitoses in the early C. elegans embryo.

Cell cycle oscillations driven by two interlinked bistable switches

Regular transitions between interphase and mitosis during the cell cycle are driven by changes in the activity of the enzymatic protein complex cyclin B with cyclin-dependent kinase 1 (Cdk1). At the most basic level, this cell cycle oscillator is driven by negative feedback: active cyclin B-Cdk1 activates the anaphase-promoting complex/cyclosome, which triggers the degradation of cyclin B. Such cell cycle oscillations occur fast and periodically in the early embryos of the frog Xenopus laevis, where several positive-feedback loops leading to bistable switches in parts of the regulatory network have been experimentally identified. Here, we build cell cycle oscillator models to show how single and multiple bistable switches in parts of the underlying regulatory network change the properties of the oscillations and how they can confer robustness to the oscillator. We present a detailed bifurcation analysis of these models.

On the assembly of the mitotic spindle, bistability and hysteresis

During cell division, the transition from interphase to mitosis is dictated by activation of the cyclin B-cdk1 (Cdk1) complex, master mitotic kinase. During interphase, Cdk1 accumulates in an inactive state (pre-Cdk1). When Cdk1 overcomes a certain threshold of activity upon initial activation of pre-Cdk1, then the stockpiled pre-Cdk1 is rapidly converted into overshooting active Cdk1, and mitosis is established irreversibly in a switch-like fashion. This is granted by positive Cdk1 activation loops and the concomitant inactivation of Cdk1 counteracting phosphatases, empowering Cdk1 activity and favoring the Cdk1-dependent phosphorylations that are required to establish mitosis. These circuitries prevent backtracking and ensure unidirectionality so that interphase and mitosis are considered bistable states. Mitosis also shows hysteresis, meaning that the levels of Cdk1 activity needed to establish mitosis are higher than those required to maintain it; therefore, once in mitosis cells can tolerate moderate drops in Cdk1 activity without exiting mitosis. Whether these features have other functional implications in addition to the general action of preventing backtracking is unknown. Here, we contextualize these concepts in the view of recent evidence indicating that loss of activity of small and compartmentalized amounts of Cdk1 within mitosis is necessary to assemble the mitotic spindle, the structure required to segregate replicated chromosomes. We further propose that, in addition to prevent backtracking, the stability and hysteresis properties of mitosis are also essential to move forward in mitosis by allowing cells to bear small, localized, drops in Cdk1 activity that are necessary to build the mitotic spindle.

Structural, enzymatic and spatiotemporal regulation of PP2A-B55 phosphatase in the control of mitosis

Cells require major physical changes to induce a proper repartition of the DNA. Nuclear envelope breakdown, DNA condensation and spindle formation are promoted at mitotic entry by massive protein phosphorylation and reversed at mitotic exit by the timely and ordered dephosphorylation of mitotic substrates. This phosphorylation results from the balance between the activity of kinases and phosphatases. The role of kinases in the control of mitosis has been largely studied, however, the impact of phosphatases has long been underestimated. Recent data have now established that the regulation of phosphatases is crucial to confer timely and ordered cellular events required for cell division. One major phosphatase involved in this process is the phosphatase holoenzyme PP2A-B55. This review will be focused in the latest structural, biochemical and enzymatic insights provided for PP2A-B55 phosphatase as well as its regulators and mechanisms of action.

A general hypothesis of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A hypothesis is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present hypothesis makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the hypothesis holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

A general theory of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A theory is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present theory makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the theory holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

A general hypothesis of multistable systems in pathophysiology

Despite intensive investigations numerous diseases remain etiologically puzzling and recalcitrant to treatments. A hypothesis is proposed here assuming that these difficulties are due to an unsuitable approach to the mechanisms of life, which is subjugated by an apparent complexity and fails to grasp the uniformity that lays behind. The stability of metabolism, despite the enormous complex of chemical reactions, suggests that reciprocal control is a prerequisite of life. Negative feedback loops have been known for a long time to maintain homeostasis, while more recently, different life processes involved in transitions or changes have been modeled by positive loops giving rise to bistable switches, also including various diseases. The present hypothesis makes a generalization, by assuming that any functional element of a biological system is involved in a positive or a negative feedback loop. Consequently, the hypothesis holds that the starting mechanism of any disease that affects a healthy human can be conceptually reduced to a bistable or multistationary loop system, thus providing a unifying model leading to the discovery of critical therapeutic targets.

PP2A-B55: substrates and regulators in the control of cellular functions

PP2A is a major serine/threonine phosphatase class involved in the regulation of cell signaling through the removal of protein phosphorylation. This class of phosphatases is comprised of different heterotrimeric complexes displaying distinct substrate specificities. The present review will focus on one specific heterocomplex, the phosphatase PP2A-B55. Herein, we will report the direct substrates of this phosphatase identified to date, and its impact on different cell signaling cascades. We will additionally describe its negative regulation by its inhibitors Arpp19 and ENSA and their upstream kinase Greatwall. Finally, we will describe the essential molecular features defining PP2A-B55 substrate specificity that confer the correct temporal pattern of substrate dephosphorylation. The main objective of this review is to provide the reader with a unique source compiling all the knowledge of this particular holoenzyme that has evolved as a key enzyme for cell homeostasis and cancer development.

A modular approach for modeling the cell cycle based on functional response curves

Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way.

Bistability plays an important role in many biochemical processes and typically emerges from complex interaction patterns such as positive and double negative feedback loops. Here, we propose to theoretically study the effect of bistability in a larger interaction network. We explicitly incorporate a functional expression describing an S-shaped input-output curve in the model equations, without the need for considering the underlying biochemical events. This expression can be converted into a functional module for an ultrasensitive response, and a time delay is easily included as well. Exploiting the fact that several of these modules can easily be combined in larger networks, we construct a cell cycle model consisting of multiple bistable switches and show how this approach can account for a number of known properties of the cell cycle.

CDK control pathways integrate cell size and ploidy information to control cell division

Maintenance of cell size homeostasis is a property that is conserved throughout eukaryotes. Cell size homeostasis is brought about by the co-ordination of cell division with cell growth and requires restriction of smaller cells from undergoing mitosis and cell division, whilst allowing larger cells to do so. Cyclin-CDK is the fundamental driver of mitosis and therefore ultimately ensures size homeostasis. Here we dissect determinants of CDK activity in vivo to investigate how cell size information is processed by the cell cycle network in fission yeast. We develop a high-throughput single-cell assay system of CDK activity in vivo and show that inhibitory tyrosine phosphorylation of CDK encodes cell size information, with the phosphatase PP2A aiding to set a size threshold for division. CDK inhibitory phosphorylation works synergistically with PP2A to prevent mitosis in smaller cells. Finally, we find that diploid cells of equivalent size to haploid cells exhibit lower CDK activity in response to equal cyclin-CDK enzyme concentrations, suggesting that CDK activity is reduced by increased DNA levels. Therefore, scaling of cyclin-CDK levels with cell size, CDK inhibitory phosphorylation, PP2A, and DNA-dependent inhibition of CDK activity, all inform the cell cycle network of cell size, thus contributing to cell size homeostasis.

Dynamical modules in metabolism, cell and developmental biology

Modularity is an essential feature of any adaptive complex system. Phenotypic traits are modules in the sense that they have a distinguishable structure or function, which can vary (quasi-)independently from its context. Since all phenotypic traits are the product of some underlying regulatory dynamics, the generative processes that constitute the genotype-phenotype map must also be functionally modular. Traditionally, modular processes have been identified as structural modules in regulatory networks. However, structure only constrains, but does not determine, the dynamics of a process. Here, we propose an alternative approach that decomposes the behaviour of a complex regulatory system into elementary activity-functions. Modular activities can occur in networks that show no structural modularity, making dynamical modularity more widely applicable than structural decomposition. Furthermore, the behaviour of a regulatory system closely mirrors its functional contribution to the outcome of a process, which makes dynamical modularity particularly suited for functional decomposition. We illustrate our approach with numerous examples from the study of metabolism, cellular processes, as well as development and pattern formation. We argue that dynamical modules provide a shared conceptual foundation for developmental and evolutionary biology, and serve as the foundation for a new account of process homology, which is presented in a separate contribution by DiFrisco and Jaeger to this focus issue.

Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.

Many systems in nature show bistability, which means they can evolve to one of two stable steady states under exactly the same conditions. Which state they evolve to depends on where the system comes from. Such bistability underlies the switching behavior that is essential for cells to progress in the cell division cycle. A quick switch happens when the cell jumps from one steady state to another steady state. Typical of this switching behavior is its robustness and irreversibility. In this paper, we expand this viewpoint of the dynamics of the cell cycle by considering bistable switches which themselves are changing in time. This gives the cell an extra layer of control over transitions both in time and in space, and can make those transitions more robust. Such dynamically changing bistability can appear very naturally. We show this in a model of mitotic entry, in which we include a nuclear and cytoplasmic compartment. The activity of a crucial cell cycle protein follows a bistable switch in each compartment, but the shape of its response is changing in time as proteins are imported into and exported from the nucleus.

A distinct class of plant and animal viral proteins that disrupt mitosis by directly interrupting the mitotic entry switch Wee1-Cdc25-Cdk1

Many animal viral proteins, e.g., Vpr of HIV-1, disrupt host mitosis by directly interrupting the mitotic entry switch Wee1-Cdc25-Cdk1. However, it is unknown whether plant viruses may use this mechanism in their pathogenesis. Here, we report that the 17K protein, encoded by barley yellow dwarf viruses and related poleroviruses, delays G2/M transition and disrupts mitosis in both host (barley) and nonhost (fission yeast, Arabidopsis thaliana, and tobacco) cells through interrupting the function of Wee1-Cdc25-CDKA/Cdc2 via direct protein-protein interactions and alteration of CDKA/Cdc2 phosphorylation. When ectopically expressed, 17K disrupts the mitosis of cultured human cells, and HIV-1 Vpr inhibits plant cell growth. Furthermore, 17K and Vpr share similar secondary structural feature and common amino acid residues required for interacting with plant CDKA. Thus, our work reveals a distinct class of mitosis regulators that are conserved between plant and animal viruses and play active roles in viral pathogenesis.

Bistable switches as integrators and actuators during cell cycle progression

Progression through the cell cycle is driven by bistable switches-specialized molecular circuits that govern transitions from one cellular state to another. Although the mechanics of bistable switches are relatively well understood, it is less clear how cells integrate multiple sources of molecular information to engage these switches. Here, we describe how bistable switches act as hubs of information processing and examine how variability, competition, and inheritance of molecular signals determine the timing of the Rb-E2F bistable switch that controls cell cycle entry. Bistable switches confer both robustness and plasticity to cell cycle progression, ensuring that cell cycle events are performed completely and in the correct order, while still allowing flexibility to cope with ongoing stress and changing environmental conditions.

Triggering mitosis

Entry into mitosis is triggered by the activation of cyclin-dependent kinase 1 (Cdk1). This simple reaction rapidly and irreversibly sets the cell up for division. Even though the core step in triggering mitosis is so simple, the regulation of this cellular switch is highly complex, involving a large number of interconnected signalling cascades. We do have a detailed knowledge of most of the components of this network, but only a poor understanding of how they work together to create a precise and robust system that ensures that mitosis is triggered at the right time and in an orderly fashion. In this review, we will give an overview of the literature that describes the Cdk1 activation network and then address questions relating to the systems biology of this switch. How is the timing of the trigger controlled? How is mitosis insulated from interphase? What determines the sequence of events, following the initial trigger of Cdk1 activation? Which elements ensure robustness in the timing and execution of the switch? How has this system been adapted to the high levels of replication stress in cancer cells?

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.

Implications of alternative routes to APC/C inhibition by the mitotic checkpoint complex

The mitotic checkpoint (also called spindle assembly checkpoint) is a signaling pathway that ensures faithful chromosome segregation. Mitotic checkpoint proteins inhibit the anaphase-promoting complex (APC/C) and its activator Cdc20 to prevent precocious anaphase. Checkpoint signaling leads to a complex of APC/C, Cdc20, and checkpoint proteins, in which the APC/C is inactive. In principle, this final product of the mitotic checkpoint can be obtained via different pathways, whose relevance still needs to be fully ascertained experimentally. Here, we use mathematical models to compare the implications on checkpoint response of the possible pathways leading to APC/C inhibition. We identify a previously unrecognized funneling effect for Cdc20, which favors Cdc20 incorporation into the inhibitory complex and therefore promotes checkpoint activity. Furthermore, we find that the presence or absence of one specific assembly reaction determines whether the checkpoint remains functional at elevated levels of Cdc20, which can occur in cancer cells. Our results reveal the inhibitory logics behind checkpoint activity, predict checkpoint efficiency in perturbed situations, and could inform molecular strategies to treat malignancies that exhibit Cdc20 overexpression.

Cell division is a fundamental event in the life of cells. It requires that a mother cell gives rise to two daughters which carry the same genetic material of their mother. Thus, during each cell cycle the genetic material needs to be replicated, compacted into chromosomes and redistributed to the two daughter cells. Any mistake in chromosome segregation would attribute the wrong number of chromosomes to the progeny. Hence, the process of chromosome segregation is closely watched by a surveillance mechanism known as the mitotic checkpoint. The molecular players of the checkpoint pathway are well known: we know both the input (ie, the species to be inhibited and their inhibitors), and the output (ie, the inhibited species). However, we do not exactly know the path that leads from the former to the latter. In this manuscript, we use a mathematical approach to explore the properties of plausible mitotic checkpoint networks. We find that seemingly similar circuits show very different behaviors for high levels of the protein targeted by the mitotic checkpoint, Cdc20. Interestingly, this protein is often overexpressed in cancer cells. For physiological levels of Cdc20, instead, all the models we have analyzed are capable to mount an efficient response. We find that this is due to a series of consecutive protein-protein binding reactions that funnel Cdc20 towards its inhibited state. We call this the funneling effect. Our analysis helps understanding the inhibitory logics underlying the checkpoint, and proposes new concepts that could be applied to other inhibitory pathways.

Cyclin A-cdk1-Dependent Phosphorylation of Bora Is the Triggering Factor Promoting Mitotic Entry

Mitosis is induced by the activation of the cyclin B/cdk1 feedback loop that creates a bistable state. The triggering factor promoting active cyclin B/cdk1 switch has been assigned to cyclin B/cdk1 accumulation during G2. However, this complex is rapidly inactivated by Wee1/Myt1-dependent phosphorylation of cdk1 making unlikely a triggering role of this kinase in mitotic commitment. Here we show that cyclin A/cdk1 kinase is the factor triggering mitosis. Cyclin A/cdk1 phosphorylates Bora to promote Aurora A-dependent Plk1 phosphorylation and activation and mitotic entry. We demonstrate that Bora phosphorylation by cyclin A/cdk1 is both necessary and sufficient for mitotic commitment. Finally, we identify a site in Bora whose phosphorylation by cyclin A/cdk1 is required for mitotic entry. We constructed a mathematical model confirming the essential role of this kinase in mitotic commitment. Overall, our results uncover the molecular mechanism by which cyclin A/cdk1 triggers mitotic entry.

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.