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The coordination of growth, DNA replication and division in proliferating cells can be adequately explained by a ‘clock + checkpoint’ model. The clock is an underlying circular sequence of states; the checkpoints ensure that the cycle proceeds without mistakes. From the molecular complexities of the control system in modern eukaryotes, we isolate a simple network of positive and negative feedbacks that embodies a clock + checkpoints. The model accounts for the fundamental physiological properties of mitotic cell divisions, evokes a new view of the meiotic program, and suggests how the control system may have evolved in the first place.
The cell division cycle is the sequence of events by which a growing cell replicates all its components and divides them into two nearly identical daughter cells, so that each daughter cell receives all the machinery and information necessary to repeat the process [1, 2]. The cell division cycle can be thought of as a simple developmental process by which a newborn cell grows in size, replicates its chromosomes, segregates a full set of chromosomes to each of two new nuclei (a process called ‘mitosis’), and divides into newborn daughter cells (Figure 1).
Like any other developmental process, the cell division cycle is successful if the underlying steps take place in the right order . In particular, DNA replication and chromosome segregation should alternate in proliferating cells. If a cell attempts a second mitotic division before its chromosomes have been fully replicated, the daughter cells will inherit broken, incomplete or unbalanced chromosomes, which is almost always lethal [4, 5]. If a cell undergoes multiple rounds of DNA replication between mitoses, then its nuclei become polyploid [6, 7], which usually puts the cell at considerable disadvantage compared to diploid cells, especially during sexual reproduction.
Growing cells must satisfy a second requirement that the cycle time (period between two successive divisions) should be equal to the cytoplasmic mass doubling time. If this requirement is not satisfied, then during successive division cycles, cells become progressively smaller or larger depending on which process is faster [8, 9]. This instability of cell size is not compatible with long term perpetuation of life. The requirement of balanced growth and division is waived during oogenesis (and embryogenesis), when cells become extra large (progressively smaller).
The events of the cell division cycle are triggered by an underlying molecular machine that enforces the alternation of DNA replication and mitosis and that ensures balanced growth and division. If problems arise, feed-forward and feedback signals (‘checkpoint’ controls) inhibit further progression through the cell cycle until the problem(s) can be resolved [10, 11].
Checkpoint mechanisms govern crucial irreversible transitions of the cell cycle . A newborn cell with unreplicated chromosomes (G1 phase) must pass checkpoint controls before it can start DNA synthesis (i.e., enter S phase). A G2 phase cell (with replicated chromosomes) must pass a second checkpoint before it can enter M phase (mitosis) and attempt to segregate its chromosomes. Mitosis is a delicate process. The replicated chromosomes (called sister chromatids) are held together by cohesion complexes . During the first half of mitosis these replicated chromosomes are aligned on the bipolar mitotic spindle with sister chromatids attached to opposite poles of the spindle . The spindle assembly checkpoint prevents progression to the next stage (anaphase) until all chromosomes are properly aligned on the spindle . When this requirement is satisfied, the cohesins are destroyed and the spindle drags the sister chromatids to opposite sides of the cell . Then the cell divides in the middle (other mechanisms check the location of the division plane), and the newborn cells are assured to inherit one and only one copy of each chromosome.
These crucial cell-cycle transitions are triggered by transient signals that appear when the checkpoint conditions are satisfied. As the transition is carried out, the triggering signal disappears, and yet the cell never reverts to an earlier stage in the cycle. The irreversibility of these transitions is crucial to provide directionality to the cell cycle . It is our intention to describe the basic molecular logic controlling these cell cycle transitions. This logic underlies the temporal organization of the cell cycle and is absolutely fundamental to all processes of growth, development and reproduction in living organisms.
For the purposes of this review we will focus on the two most important transitions of the cell cycle: Start , when a cell leaves G1 phase and commits to a new round of DNA synthesis and mitosis, and Exit, when a cell with properly aligned chromosomes commits to finish the division process and create two new G1 cells . Of course, as we have suggested, cell cycle regulation is more complex, but this simplified view is appropriate to our goal of describing the fundamental molecular logic of cell cycle progression. Another caveat: this is our very personal view of the ‘fundamental molecular logic’, shaped by our experiences as mathematical modelers of cell cycle controls. For other perspectives, consult [20–23].
Cell cycle progression is a curious mixture of clocklike periodicity (G1-S-G2-M-G1-…) and of switch-like ‘checkpoints’ (yes-or-no decisions about the next event). Before attacking this issue, we must pause to consider what we mean by ‘clocks’ and ‘switches’. Our approach is inspired by Chapter 3 (The Rules of the Ring) of Winfree’s The Geometry of Biological Time .
Figure 2A gives a simple analogy for the checkpoint action of a bistable switch [25–27]. The bold horizontal lines are tracks on which a vehicle moves in the direction indicated by the black arrows. On the upper track, there are two stable rest points of the vehicle at the black circles. The white circle is an unstable rest point. (At the white point the vehicle has zero velocity, but if the vehicle should deviate slightly from the rest point to the right or to the left, then its velocity will carry it further away from the white point.) The U shape may be interpreted as a barrier (a ‘checkpoint’). As the barrier is raised (green arrow), the stable and unstable rest points merge and disappear (bottom), and the vehicle can proceed toward the rightmost rest point (its goal, or perhaps another checkpoint). After the vehicle passes the checkpoint, the barrier is automatically lowered (red arrow).
Figure 2B illustrates a simple clock. The vehicle proceeds around the circular track at constant speed. Events might be triggered in order as the vehicle passes certain ‘milestones’ (e.g., arise at 6, lunch at 12, seminar at 16, to bed at 23). Under constant favorable conditions, cells can progress through the DNA replication-division cycle with clocklike regularity, but the cell ‘cycle’ lacks many characteristic features of biological ‘clocks’.
Figure 2C is a more accurate representation cell cycle progression, in terms of movement around a circular track (G1-S-G2-M-G1) that is restricted by checkpoints. The Start checkpoint governs the G1-to-S transition, and Exit governs the metaphase-anaphase-telophase sequence of events. Most cells also have a third checkpoint in late G2, controlling entry into mitosis . The G2/M transition is controlled by a gate (a U shaped barrier) analogous to Start and Exit, but we are ignoring this checkpoint (for the time being) to keep our story simple.
The dynamical structure of cell cycle progression (Figure 2C) must be put in place by biochemical machinery, namely interacting genes and proteins. We know, in broad strokes, that the basic events of the cell cycle are triggered by fluctuations in the activities of specific cyclin-dependent kinases (CDK) (see Figure 1, center). CDK activities are governed, in general, by three distinct mechanisms . (1) Cyclin availability. Kinase subunits are present in excess during the cell cycle, but they have no activity until they bind to a cyclin partner. The availability of cyclin subunits is strictly controlled by transcription factors that regulate the expression of cyclin genes, and by ubiquitin-dependent proteolysis systems (e.g., the APC—anaphase promoting complex ) that can rapidly degrade cyclin proteins in response to specific signals. (2) Phosphorylation of kinase subunits. Active cyclin:CDK dimers can be inactivated by phosphorylation on a specific tyrosine residue close to the N-terminus of the kinase polypeptide chain. This tyrosine residue is phosphorylated by kinases of the Wee1-class and dephosphorylated by phosphatases of the Cdc25-class . (3) Active cyclin:CDK dimers can also be inactivated by binding to inhibitors, called CKIs [30–32]. CKIs come and go, depending on their production rate (governed by regulated transcription factors) and destruction rate (phosphorylated CKIs are rapidly ubiquitinated and degraded [33, 34]).
The basic logic of CDK regulation is diagrammed in Figure 3. For simplicity, we lump together cyclin A- and cyclin B-dependent kinase activities into one class. When CDK activity is low, the cell is in G1 phase. At Start, CDK activity rises and the cell carries out, in sequence, DNA synthesis, preparation for mitosis (G2), and early mitosis (chromosome condensation, spindle assembly, chromosome alignment). At Exit, CDK activity falls, the cell finishes mitosis and divides, and the daughter cells enter G1 phase . Whether CDK activity is low or high depends on the state of CDK’s ‘Enemies’: those protein factors that mitigate against CDK activity, namely APC, Wee1 and CKI. When these Enemies are active, CDK activity is low and the cell is ‘resting’. When the Enemies are inactive, CDK activity is high and the cell is progressing through S-G2-M up to metaphase .
The molecular mechanism we are describing here is highly stylized and deliberately over simplified, in order to draw into sharp relief certain aspects of eukaryotic cell cycle control that we think are crucially important. In Table 1 we indicate more precisely which molecules we have in mind when speaking of CDK, Enemies, etc.
As indicated in Figure 3, not only do the Enemies inhibit CDK activity, but CDKs down-regulate their Enemies. Active CDK phosphorylates a specific APC component (Cdh1) and thereby inactivates cyclin degradation [36–38]. CDK phosphorylates and inactivates Wee1 [39, 40]. And CDK phosphorylation of CKIs initiates their degradation [33, 34]. The mutual antagonism between the class of CDK proteins and the class of CDK Enemies creates a bistable switch [25, 27]. The off state of the switch corresponds to potent Enemies and low CDK activity; the on state to high CDK activity and impotent Enemies. Bistability is indicated in the lower part of Figure 3A. At the center of this unusual graph, we find two stable states of CDK activity (low and high, indicated by the black circles), separated by an unstable state of intermediate CDK activity (indicated by the white circles). A ‘neutral’ cell can be in either stable state, i.e., in G1 phase (low CDK) or in S-G2-M phase (high CDK). A newborn (G1) cell is in the neutral-low CDK state; a metaphase cell is in the neutral-high CDK state. In this picture, Start is the transition from the low branch of stable states to the high branch, and Exit is the reverse transition. How are these transitions brought about?
As indicated in Figure 3A (top), there exist ‘Starter Kinases’ (SK) that are active in late G1 and promote the Start transition by down-regulating CDK’s Enemies. As SK activity increases (to the left in the lower part of Figure 3A), the stable off state (the branch of low CDK activity) begins to rise and the unstable intermediate state falls, until the two steady states coalesce and annihilate each other at the turning point of the -shaped curve (as in Figure 2C). At this level of SK activity, the CDK control system must leave the lower branch of stable states and transition irreversibly to the upper branch of on states. The cell begins progression through S, G2 and early M. High CDK activity down-regulates SK  (Figure 3A, top), and the cell returns to the neutral state, but now it is on the upper branch (Figure 3A, bottom). Bistability of the CDK regulatory system in yeast cells has been tested and confirmed in Fred Cross’s laboratory .
The transition from metaphase back to G1 (Exit) is promoted by ‘Exit Proteins’ (EP, in Figure 3A, top). The jobs of EP (see Table 1) are to up-regulate CDK’s Enemies [43, 44], thereby promoting the transition to the off state, and to dephosphorylate the numerous proteins that had been phosphorylated by CDKs during S-G2-M. By these actions, the cell can divide and the daughter cells be reestablished in G1 phase. EP activation is promoted by CDK [45–47], as soon as all chromosomes are properly aligned on the mitotic spindle. Then, as EP activity increases (to the right in the lower part of Figure 3A, the stable on state (the branch of high CDK activity) begins to fall and the unstable intermediate state rises, until the two steady states coalesce and annihilate each other at the turning point of the -shaped curve. At this level of EP activity, the CDK control system must leave the upper branch of stable states and transition irreversibly to the lower branch of off states . The cell divides as CDK activity abruptly vanishes. With CDK activity now low, EP activity cannot be sustained (Figure 3A, top) and the cell returns to the neutral state, but now it is back on the lower branch, in G1 phase (Figure 3A, bottom).
As Figure 3A (bottom) illustrates, the unperturbed mitotic cell cycle is a ‘hysteresis’ loop, switching alternately between two alternative stable states (G1 and S-G2-M) . As a growing-dividing cell transits repeatedly around the hysteresis loop, the intracellular concentrations of CDK, Enemies, SK and EP execute periodic, temporal oscillations, illustrated schematically in Figure 3B. Notice how (CDK, Enemies) flip periodically between the (off, on) and (on, off) states, and how SK and EP show peaks of activity at Start and Exit, respectively.
The large changes of CDK activity at Start and Exit are important for ensuring the strict alternation of DNA synthesis and cell division. In order to trigger a new round of DNA replication, CDK activity must first be reduced to a very low value so that origins of replication on the DNA can receive ‘licenses’ . Then CDK activity must increase sufficiently to phosphorylate licensed origins, causing them to begin the replication process. Newly replicating origins lose their licenses, so a second round of replication cannot occur until, at some later time, CDK activity drops low enough for re-licensing to occur . Cell division follows an inverse rule . CDK activity must first rise to sufficiently high value to prime the ‘mitotic exit network’. Then CDK activity must be abruptly destroyed in order for telophase and cell separation to occur .
Balanced growth and division is assured by a checkpoint requirement in G1: SK cannot be activated until cells grow to a critical size, x [53, 54]. After satisfying this condition, the time it takes for a growing cell to proceed through S-G2-M and cell division is less than the mass-doubling time of the cell. Hence, when the cell divides, its size is less than 2x and its offspring are born at size less than x. They must grow sufficiently in the next cell cycle to reach the critical size x, and only then may they initiate the next round of DNA replication and division. Because cells divide in half, the time between successive achievements of the critical size is just exactly the mass-doubling time.
The other checkpoints of the cell cycle are implemented, as well, by inhibiting either SK or EP activation. DNA damage in G1 phase induces proteins that interfere with SK activation . Chromosome alignment problems in M phase induce proteins that interfere with EP activation . These checkpoint mechanisms may be very complicated in their molecular details, but their control logic is quite simple and elegant. For example, some checkpoint pathways block cell cycle progression at the G2/M transition, which we have ignored until now. The G2 control point is implemented by the same logic as Start and Exit. During G2 phase, CDK is involved in a struggle with another protein kinase, Wee1. The two kinases phosphorylate and inactivate each other, creating a bistable system with (CDK, Wee1) in either the (off, on) or the (on, off) state. When conditions are right for entry into M phase, a helper protein (the phosphatase, Cdc25) shifts the balance of (CDK, Wee1) in favor of the (on, off) state. Bistability of the Wee1-CDK-Cdc25 control system in frog egg cells has been convincingly demonstrated in Jill Sible’s lab  and in Jim Ferrell’s lab .
If this general framework is a fruitful way to think about mitotic division cycles, then it should shed light on alternative modes of cell division. For example, during oogenesis, the egg cell grows without dividing because it is blocked solidly at the G2 checkpoint (presumably by activating Wee1 or inhibiting Cdc25). The fertilized egg, on the other hand, undergoes a series of rapid mitotic cycles without growth, because all checkpoints have been removed and the CDK control system executes spontaneous ‘limit cycle’ oscillations, which are a kind of abbreviated version of the hysteresis loop in Figure 3A . Endoreplication refers to repeated rounds of DNA synthesis without mitosis or cell division, creating highly polyploid cells. Endoreplication occurs when mitotic CDK activity is absent and the cell exhibits periodic bursts of S-phase CDK activity (CDKS). Models of endoreplication  rely on the same mechanism in Figure 3A, without the Exit Proteins. The SK-CDKS-Enemies control system is unique in that the upper steady state (CDKS large) is not stable, but spontaneously reverts to the lower state (G1) when SK activity drops.
Meiosis is an alternative mode of cell division by which a diploid G2 cell undergoes two successive divisions without an intervening DNA synthesis phase to create haploid G1 cells , called gametes (or spores) (see Figure 4). At fertilization, two gametes combine to form a diploid egg in G1 phase. After a round of DNA synthesis, the developing egg is back to the diploid G2 phase of the mitotic cell cycle. (In fungi and ferns, spores germinate to form the haploid (gametophytic) stage of the life cycle.) In the next section we explore a possible control strategy for meiotic division.
Events surrounding the first meiotic division differ considerably from mitosis . In preparation for meiosis I, homologous chromosomes (i.e., DNA molecules containing the same sets of genes, inherited originally from ‘mom’ and ‘dad’) must find each other and pair up (they do so by comparing DNA sequences). At this stage, the homologous chromosomes interchange large tracts of DNA in a process called recombination, which serves the important evolutionary role of increasing genetic diversity of the population and the quite practical role of holding the two homologous chromosomes together. At metaphase, the homologous chromosomes align on the spindle with the homologs attached to opposite poles. At anaphase, the arm-cohesins are destroyed and the homologous chromosomes can be separated from one another, but centromeric cohesins are protected from degradation and, hence, sister chromatids stay together at anaphase [61–63]. Daughter nuclei generated by the first meiotic division are haploid with replicated chromosomes. They skip S phase and enter the second meiotic division, which is (in essence) a normal mitosis, in which sister chromatids are segregated to opposite poles of the spindle.
How might it be that the mitotic CDK program is modified to generate the two distinctive meiotic cell divisions?
To address this question, we return to our generic picture of mitotic cell divisions in Figure 3A. During mitotic cycling, EP is absent at the Start transition [64, 65], so we can diagram Start on a two-dimensional graph of CDK activity versus SK activity (bottom left of Figure 3A). The newborn cell begins life in ‘neutral’ (low EP and low SK), and ends up in metaphase in neutral again. The cell exits mitosis with low SK, so we can diagram this transition on a two-dimensional graph of CDK activity versus EP activity (bottom right of Figure 3A). The mitotic cell switches back to the state of low CDK activity and returns to the neutral conditions for SK and EP. To understand meiosis, we propose to extend these pictures to three dimensions (CDK versus both SK and EP) because both SK and EP are active simultaneously during the first meiotic division.
To this end, we take the flat diagram at the bottom of Figure 3 and fold it along the CDK axis to an angle of 90°, as in Figure 5A. We can still see the characteristic and ⊃ shaped curves in the faces of the cube spanned by CDK-SK and by CDK-EP, respectively. Next, we must imagine filling in the interior of the cube with a continuous surface. It is a mathematical theorem that this surface will be a pleated sheet , as illustrated in Figure 5A. The folds of the pleat come together at a cusp. The upper layer of the pleat is the state of high CDK activity, the lower layer is the state of low CDK activity, and the middle level of the pleat is the unstable state of intermediate CDK activity. Beyond the cusp point, the surface is no longer multi-valued, and CDK activity can pass smoothly from high to medium to low values.
It is convenient to project the CDK surface in Figure 5A onto the SK-EP plane (Figure 5B), exactly as if one were using an iron to press a pleated skirt. The pleat itself projects onto a region (white) bounded by two fold lines that come together in a pointed cusp. Outside the bistable region, the CDK surface is single-valued, and we use color to indicate whether CDK activity is high (blue), medium (purple) or low (red). Figure 5B effectively represents the CDK response surface as a function of the signals it receives from SK and EP simultaneously.
Now we are ready to plot mitotic cycles and the meiotic program on the CDK response surface (Figure 6). During mitotic cycles (Figure 6, left panel), the cell’s trajectory (the black dashed curve) stays close to the axes of the diagram. From G1 to S-G2 to metaphase, the trajectory stays close to EP = 0, as SK rises and falls. From metaphase to anaphase to telophase and back to G1, the trajectory stays close to SK = 0, as EP rises and falls. The two meiotic divisions must follow a different trajectory on this surface. As the cell exits meiosis I, it is important that CDK activity does not drop to a very low value characteristic of G1 phase . CDK activity falls only to medium values, so the origins of DNA replication cannot be re-licensed and, hence, a second round of DNA synthesis will not be initiated when CDK activity rises again.
A simple way to imagine this state of affairs is to postulate a meiosis-specific protein X that is synthesized early in meiosis I and prevents the down-regulation of SK by CDK (see Figure 6, right panel, top), so that SK remains high during the first meiotic interphase. # We also assume that X is destroyed by EP, so that X is absent during the second meiotic interphase. As a cell enters the first meiotic division in the presence of X, it does not destroy SK as usual. Rather it enters metaphase of meiosis I with high SK activity. It exits meiosis I by activating EP, but now, because SK activity is still high, CDK activity drops only to intermediate levels as EP rises and falls (see the black, dashed trajectory in Figure 6, right panel, bottom diagram). The transient activation of EP as the cell exits meiosis I removes X, and so, as CDK activity rises, SK is down-regulated. Skipping S phase, the cell enters prophase and metaphase of meiosis II with low SK and low EP, exactly as if it were a mitotic division. Exit from meiosis II is a normal transition to the G1-state of low CDK activity, which permits re-licensing of replication origins on the DNA.
Other scenarios are possible. For example, X may inhibit the ability of EP to activate CDK’s Enemies. In this case, when the cell enters meiosis I, the bistable zone (the white region in Figure 6) extends to much larger concentrations of EP. Hence, when EP rises at the end of meiosis I, the control system does not cross the fold-line and jump to the lower surface (G1). Instead, the trajectory stays on the upper surface and goes to a G2-state (EP large, SK large, CDK medium) before entering meiosis II with EP small, SK small, and X small (because it was destroyed by the burst of EP as cells left meiosis I). Now, when EP rises at the end of meiosis II, the cell crosses the fold-line and enters G1 phase.
Our description of progression through meiosis is appropriate for yeast cells but not for animal oocytes, which typically arrest at metaphase of meiosis II, where they await fertilization. Metaphase arrest of mature oocytes is a separate issue altogether. It is enforced by special ‘checkpoint’ proteins that prevent activation of the Enemies after chromosome alignment at meiosis II .
In principle, four novel functions are needed  to convert mitotic division into the special events surrounding meiosis I: recombination of homologous chromosomes, attachment of sister kinetochores to the same pole of the spindle (and homologous chromosomes to opposite poles), protection of centromeric cohesins from degradation during anaphase, and remodeling the CDK response to prevent DNA replication after meiosis I. Given our expertise in regulatory dynamics, we have concentrated on the fourth function. Is there a gene/protein that corresponds to our hypothetical X? In budding yeast, SPO13 encodes a protein that is involved in functions 2-3-4 , and SPO11 encodes a protein essential for recombination. The double mutant, spo11 spo13, converts meiosis I into a normal mitosis. In light of these facts, we predict that, among its many functions, Spo13 must have some of the properties we have postulated for X.
What is a proper understanding of temporal organization in the cell cycle? Under constant favorable conditions, cells progress through the DNA replication-division cycle with clocklike regularity, but the cell ‘cycle’ is not a ‘clock’. Clocks set the time for events (e.g., lunch at noon) and continue ticking regardless of whether the events actually occur or not. Clocks are easily reset (by pushing their hands ahead or behind), and they are periodically synchronized to some standard time-giver (e.g., Greenwich Mean Time). In order to keep good time, clocks are carefully buffered against external conditions (e.g., temperature fluctuations). The circadian rhythm of organisms has all these clocklike properties . It persists under conditions of constant illumination and temperature (autonomy), it is easily reset (phase advance or phase delay) by pulses of light, it is readily entrained to external light/dark cycles with period close to 24 h, and the period of the autonomous circadian oscillator is remarkably independent of temperature in the physiological range 18–32°C.
The cell cycle, on the other hand, has none of these properties. Progression through the cell cycle is not easily pushed past checkpoints either forward or in reverse; the cell cycle does not readily entrain to external periodic signals; interdivision time is strongly dependent on the cell’s rate of growth (not on its ‘autonomous’ rate of DNA synthesis and mitotic progression) and, hence, the cell cycle period is sensitively dependent on temperature. For all of these reasons, the cell cycle should not be thought of as a clock.
Progression through the cell cycle is more like the cycle of a clothes washing machine . Events must occur in a specific order: load, fill, wash, empty, fill, rinse, empty, spin, unload. The time it takes to fill depends on water pressure and load setting (small, medium, large), and the wash cycle must wait until the fill operation is completed. The time from Start to Finish of a wash cycle depends on the machine, but the time interval between successive Starts depends on how fast the dirty laundry is accumulating. Crucial events of the wash cycle are guarded by checkpoints: e.g., if the load is unbalanced then progression to spin must be arrested. If this checkpoint fails, the whole machine can be destroyed. Clearly, the correct analogy for the cell cycle is a sequential machine (Figure 2C) rather than an autonomous clock (Figure 2B).
Is Figure 2C only an analogy? Can we take it more seriously? In this review, we have tried to show that the molecular controls over cyclin-dependent kinase activities (Figure 3A, top) create a dynamical system with exactly the same topology as the cartoon (compare Figure 2C and Figure 3A, bottom). Although we have not given any of the technical details, they can be found in the publications to which we refer. The experimental papers contain justifications for the topology of the control network (Figure 3A, top) and the theoretical papers prove the dynamical properties of the control system (Figure 3A, bottom).
The control network is centered on a fundamental molecular antagonism between cyclin-dependent kinases (CDKs) and their Enemies (inhibitors and cyclin-destroyers). This antagonism creates a dynamical system with two, alternative, self-maintaining states: G1 (low CDK activity) and S-G2-M (high CDK activity). Transitions between these states are controlled by two negative feedback loops. The Start transition (G1 to S) is triggered by a class of ‘starter kinases’ that are down-regulated by the very species they are aiding: SK —┤ Enemies—┤CDK —┤SK . The Exit transition (M to G1) is promoted by a class of ‘exit proteins’ that kill the very species they depend on: CDK ➔ EP ➔ Enemies —┤CDK . This topology creates a dynamic of irreversible transitions (Figure 3A, bottom) that drives a cell through the DNA replication-division cycle .
Figure 3 is no cartoon: it is a rigorous representation of the dynamical system that governs progression through the eukaryotic cell cycle. It is based on well-documented experimental evidence (mostly from budding yeast, to be sure) and solid mathematical reasoning. Figure 3 immediately accounts for the fundamental properties of cell cycle regulation:
Not only is Figure 3 perfectly consistent with the basic ‘rules’ of cell proliferation, but it is also in agreement with the ‘exceptions’. For example, cell division cycles during early embryonic development proceed rapidly, without growth and without checkpoints. During this stage of development, the most powerful, G1-stabilizing Enemies (APCG1 and CKIs) are absent, and the starter kinases are not in operation. The control system is stripped down to a positive feedback loop (CDK —┤ Wee1 —┤CDK) and a negative feedback loop (CDK ➔ EP —┤CDK). This topology generates robust limit-cycle oscillations that drive rapid cycles of S and M without gaps (rather like the autonomous clock in Figure 2B). Later in development (at the midblastula transition), the embryo expresses CKIs and G1-components of the APC, and the clocklike early division cycles are replaced by the standard checkpoint-regulated division cycles of somatic cells.
Meiosis is the other grand exception to the standard mitotic division cycle. During meiosis, the nucleus divides twice without an intervening S phase, in order to reduce its DNA content two-fold (diploid-to-haploid transition). The dynamical interrelations of CDK, Enemies, SK and EP during meiosis cannot be visualized on the flat diagram at the bottom of Figure 3A. But, with a little imagination, we can generalize Figure 3 to accommodate meiotic progression. We must recognize that the two-dimensional graphs in Figure 3A are limited views of a three-dimensional surface characterizing the activity of CDK as a function of both SK and EP. This surface (Figure 4) introduces new states of the control system, where SK and EP are simultaneously elevated and CDK reaches intermediate levels that are unstable and unachievable during mitotic cell cycles. The intermediate CDK state is just the ticket for the unusual phase after meiosis I, when the developing gamete skips S phase and goes directly into the second meiotic division.
This envisioning of meiotic progression on a pleated CDK-response surface (Figure 5) is not only an appealing view of meiosis but also suggestive of the molecular machinery needed to convert mitotic cycles into meiotic divisions. We propose that, early in meiosis I, the developing gamete synthesizes a novel protein X that blocks down-regulation of SK by CDK (or blocks activation of CDK’s Enemies by EP). Furthermore, X should be down-regulated by EP on exit from meiosis I.
Finally, our view of cell cycle control, stripped as it is of all the idiosyncratic details of CDK regulation in modern eukaryotes, suggests how the control system may have evolved in the first place. The generic requirements are really quite simple: (1) CDK and an Enemy, to create a bistable switch, and (2) SK and EP functions, to flip the switch back and forth. The SK function can be carried out by the low-activity state of CDK, and remarkably we see vestiges of this dual role of mitotic cyclin in fission yeast cells, where a single B-type cyclin (cdc13) can carry out both SK and CDK functions. It is easy to imagine an early gene duplication that separated these roles to two different cyclins. The EP function, as well, is currently carried out (in fission yeast) by an APCM component (slp1) that is homologous to an Enemy (the APCG1 component encoded by ste9). In the beginning, these two roles may have been played by the same gene product. Following this line of reasoning, it is easy to imagine a simple control system governing the alternation of S and M phases and ensuring balanced growth and division. Checkpoints could be added later to make the system more reliable in the face of common threats, like ionizing radiation. Finally, as we have shown, meiosis is only a short step away from mitotic cell divisions. With meiosis come all the joys of sex, which we know played a crucial role in the evolution of eukaryotes.
JJT acknowledges support from the NIH (R01-GM078989 and R01-GM079207), and BN acknowledges support from the BBSRC (UK) and from the EC FP7 (201142). JJT also thanks Merton College, Oxford, for support during the composition of this review. Our views of cell cycle regulation have been greatly influenced by conversations with Kim Nasmyth, Paul Nurse, Fred Cross, Frank Uhlmann, Wolfgang Zachariae and Kathy Chen.
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This paper is dedicated to the memory of Arthur Winfree (1942–2002), whose book, The Geometry of Biological Time, laid out new ways of thinking about how living organisms keep track of time.
#The Starter Kinase of the meiotic program need not be the same molecule used during mitotic cycles. Indeed, in yeast the SK role seems to be played by Ime2 during meiosis I. In addition, during meiosis in yeast, a different cyclin (Clb1) is used, in combination with Cdc28, to trigger M phase.