Modelling the fission yeast cell cycle Akos Sveiczer, John J. Tyson and Bela Novak Date received (in revised form): 20th October, 2003

Akos Sveiczer is a Reader in the Department of Agricultural Chemical Technology at Budapest University of Technology and Economics. John J. Tyson is a University Distinguished Professor in the Department of Biology at Virginia Polytechnic Institute and State University. Bela Novak is a professor in both the Department of Agricultural Chemical Technology at Budapest University of Technology and Economics, and the Molecular Network Dynamics Research Group of the Hungarian Academy of Sciences. Keywords: functional proteomics, cell cycle, fission yeast, mathematical modelling, molecular network, endoreplication Akos Sveiczer, 1111 Budapest, Szt. Gellert ter 4, Hungary Tel: +36 1 463 2349 Fax: +36 1 463 2598 E-mail: asveiczer@mail.bme.hu Modelling the fission yeast cell cycle Akos Sveiczer, John J. Tyson and Bela Novak Date received (in revised form): 20th October, 2003 Abstract The molecular networks regulating basic physiological processes in a cell can be converted into mathematical equations (eg differential equations) and solved by a computer. The division cycle of eukaryotic cells is an important example of such a control system, and fission yeast is an excellent test organism for the computational modelling approach. The mathematical model is tested by simulating wild-type cells and many known cell cycle mutants. This paper describes an example where this approach is useful in understanding multiple rounds of DNA synthesis (endoreplication) in fission yeast cells that lack the main (B-type) mitotic cyclin, Cdc13. It is proposed that the key physiological variable driving progression through the cell cycle during balanced growth and division is the mass/dna ratio, rather than the mass/nucleus ratio. INTRODUCTION The goal of molecular cell biology is to understand the physiology of cells in terms of the information encoded in their genomes. This information is first transcribed into messenger RNAs and then translated into proteins, which fold into functional three-dimensional shapes. These proteins then assemble spontaneously into macromolecular complexes that are responsible for most of a cell s properties (shape, movement, energy transduction, transport, growth and reproduction, gene expression, etc). In particular, some of these assemblies are molecular reaction networks that process information from inside and outside the cell and determine appropriate responses. 1,2 These computational modules regulate various aspects of cell physiology, such as chemotaxis, 3 circadian rhythms, 4,5 cell division 6 and development. 7,8 In pursuit of this goal, functional genomics and proteomics provide quantitative analyses of complex networks of interacting genes and proteins. From the experimental characterisation of these signal-processing systems, the underlying regulatory network must be reverse engineered. One approach to this problem, suitable for mechanisms of moderate complexity, is to draw a diagram of the hypothesised interactions among the main components (genes and proteins) of the control module, then convert this diagram into a set of dynamic equations (ordinary differential equations, stochastic differential equations, partial differential equations, cellular automata, etc, depending on what is most appropriate for the problem). These equations, which determine how the concentration of each component changes in time and space, usually contain a host of parameters (rate constants, Michaelis constants, transport coefficients, etc), whose numerical values are often unknown. Reverse engineering entails estimation of these parameters as well as confirmation of the wiring diagram. Brute force estimation involves a parameter refinement loop: an initial set of parameter values is assigned and the dynamic equations are solved on a computer. The simulations are compared quantitatively with experimental results; if the comparison is unsatisfactory, then the parameter assignments are adjusted to achieve a better fit. This loop can be automated, and there are many strategies for searching for the optimum parameter set. There is often no satisfactory parameter set for a model, presumably 298 & HENRY STEWART PUBLICATIONS 1473-9550. BRIEFINGS IN FUNCTIONAL GENOMICS AND PROTEOMICS. VOL 2. NO 4. 298 307. FEBRUARY 2004

Modelling the fission yeast cell cycle Mathematical models improve our understanding of cellular physiology The eukaryotic cell cycle is driven by a molecular engine based on cyclin-dependent protein kinases because the dynamical equations themselves are incorrect (although it is always possible that there are inconsistencies in the experimental data). In this case, the modeller must reconsider the kinetic assumptions made in writing the equations and in drawing the wiring diagram. 7 There are also parameter-free approaches for reverse engineering the topological connectivity of molecular regulatory systems, which are reviewed elsewhere. 9 Why is this approach useful and informative? First, any regulatory system of real physiological significance contains too many important genes and proteins for their interactions to be comprehended by intuitive reasoning alone. Mathematical equations and computer simulations to keep track of the precise consequences of all the interactions are required. It is not possible to be confident of understanding how a control system works until a comprehensive mathematical model that accurately reproduces the relevant characteristics of the living cell in quantitative detail is possessed. Secondly, once researchers have confidence in a model, it can be used to compute the complete behaviour of every component in time (and space) information which is tedious or impossible to obtain experimentally and it can be used to predict the response of the control system to challenges that have yet to be characterised experimentally. Sometimes, models predict the existence of novel proteins or interactions because without such a hypothesis the model cannot properly describe the cell s behaviour. 7,10 The power of this approach can be illustrated with a model of cell cycle regulation in fission yeast. EUKARYOTIC CELL CYCLE The cell cycle is the sequence of events whereby a cell duplicates all its constituents and divides into two nearly identical progeny cells. The cell cycle is the fundamental process of reproduction of all cells, and hence is essential to the development, growth, repair and reproduction of complex organisms. Moreover, it has a bearing on important health concerns, like cancer and wound healing. In all eukaryotic cells (protists, fungi, plants and animals), the regulatory motifs and the genes involved in cell cycle regulation are similar. During the last three decades, the scientific literature has revealed a complex molecular mechanism driving DNA synthesis, mitosis and cell division, 11 making the cell cycle an ideal test case for analysis by computer modelling. For the purposes of this paper, attention will be limited to the cell cycle of fission yeast, Schizosaccharomyces pombe. The logic of the cell cycle engine in fission yeast The eukaryotic cell cycle is traditionally divided into four phases: G1, S (DNA synthesis), G2 and M (mitosis). G1 and G2 are gaps, when the cell presumably prepares for the major events of DNA replication (S) and sister chromatid segregation (M), which must occur in alternation. Nearly all the other constituents of a cell are synthesised continuously. The temporal duration of G1 and G2 ensure that all the main components of a cell (collectively referred to as cell mass) are doubled between two consecutive cell divisions. 12 The alternation of S- and M-phases and the coordination of growth and division are accomplished by a molecular engine, whose most important components are dimers of cyclins and cyclin-dependent protein kinases (Cdks) (Figure 1). The catalytic subunit (Cdk) phosphorylates Ser/Thr residues on its substrates. Phosphorylation of specific target proteins is required at the onset of both S- and M- phases. The regulatory subunit (cyclin) is necessary for Cdk activity and also plays a role in targeting the Cdk to specific substrates. Unlike higher eukaryotes, fission yeast has only one essential Cdk (namely Cdc2). Although fission yeast cells have four cyclins (Cdc13, Cig1, Cig2 and Puc1), only Cdc13 is essential to & HENRY STEWART PUBLICATIONS 1473-9550. BRIEFINGS IN FUNCTIONAL GENOMICS AND PROTEOMICS. VOL 2. NO 4. 298 307. FEBRUARY 2004 299

Sveiczer, Tyson and Novak Checkpoints ensure that the main events of the cell cycle follow each other in the correct order Fission yeast s central cyclin-dependent kinase (Cdc2) is regulated in three different ways Figure 1: The main events, transitions and checkpoints of the eukaryotic cell cycle. The correct order of cell cycle phases is ensured by regulation of cyclin-dependent kinases (the dimers Cdc2/Cig2 and Cdc2/Cdc13 in the figure). In fission yeast, Cdc2/Cdc13 drives the cell through the G1/S (Start) and G2/M transitions, but prevents mitotic exit. Cdc2/Cdc13 is negatively regulated by four proteins Slp1, Ste9, Rum1 and Wee1 and activated by Cdc25. In G1-phase, the Cig2 cyclin in complex with Cdc2 helps Cdc2/Cdc13 to start DNA replication. (All these proteins are evolutionary conserved in eukaryotes; they are named here after genes in fission yeast.) Three checkpoints supervise these three transitions. If certain problems are detected (as indicated on the figure), a checkpoint mechanism halts further progression through the cell cycle until the problem is resolved progression through the cell cycle (the triple mutant, cig1 cig2 puc1,is viable). This suggests that a single species of Cdk/cyclin dimer can trigger both S- and M-phases, 13 and raises the question of how a fission yeast cell knows whether to prepare for DNA replication or mitosis. The answer seems to be that Cdc2/Cdc13 activity is very low in G1-phases, then rises to an intermediate level, sufficient to phosphorylate the substrates necessary for DNA replication. 14 This intermediate level is also sufficient to prevent rereplication of DNA or premature cell division. Later in the cycle, Cdc2/Cdc13 activity rises to a very high value, which is necessary to trigger entry into mitosis. In order to divide, Cdc2/Cdc13 activity must be reduced to the very low level characteristic of G1 cells. To create this pattern of activity, Cdc2/Cdc13 is regulated in three ways: cyclin degradation by the anaphasepromoting complex (APC); 15,16 binding to a reversible stoichiometric inhibitor (the Rum1 protein in fission yeast); 17 and reversible inhibitory phosphorylation of the Tyr15 residue of Cdc2 by the Wee1 tyrosine kinase. 18 These three enemies of Cdc2 (APC, Rum1 and Wee1) are regulated by Cdc2/Cdc13 itself, as described in the next section. 300 & HENRY STEWART PUBLICATIONS 1473-9550. BRIEFINGS IN FUNCTIONAL GENOMICS AND PROTEOMICS. VOL 2. NO 4. 298 307. FEBRUARY 2004

Modelling the fission yeast cell cycle In G2 phase, Cdc2 is controlled by reversible phosphorylation by Wee1 kinase and Cdc25 phosphatase In G1 phase, Cdc2 is controlled by two antagonists, Ste9 and Rum1 To avoid genetic and physiological abnormalities, checkpoints operate during the cell cycle. 19 Generally speaking, eukaryotic cells have three cell-cycle checkpoints: at the G1/S transition (also called Start in yeasts), the G2/M transition and the metaphase/anaphase transition in mitosis (Figure 1). Before starting S-phase, a G1 yeast cell checks if it has enough nutrients; if not, the cell stays in G1. At the same time, if mating pheromones are present, the cell may start sexual differentiation instead of executing a mitotic cycle. Moreover, a small G1 yeast cell must wait until it grows to a critical size. This size control at G1/S is cryptic in rapidly growing, wild-type fission yeast cells, 20 which measure their size instead at the G2/M transition. If the cell is too small, the G2/M checkpoint delays entry into mitosis. Another mechanism working at the G2/M checkpoint makes sure that mitosis is delayed if the DNA is damaged or incompletely replicated. The third checkpoint guarantees that sister chromatid segregation (anaphase) never occurs before all the chromosomes are correctly aligned on the mitotic spindle (metaphase). These checkpoints block progression through the cell cycle by interfering with the cell cycle engine, ie with the interactions that activate or inactivate Cdc2/Cdc13. The molecular network controlling the cell cycle engine in fission yeast The molecular interactions described in the previous section are used to build a proposed wiring diagram of the control system, as shown in Figure 2. The central component of the cell cycle engine is the Cdc2/Cdc13 dimer, also known as M- phase promoting factor (MPF). Since the Cdc2 subunit is in excess during the cycle and Cdc13 binding to Cdc2 is very fast, the production and destruction of Cdc2/ Cdc13 complexes follow that of Cdc13 itself. Cdc13 is continuously synthesised from amino acids in the cytoplasm, where it binds to Cdc2, and then the dimer moves into the nucleus. The larger the cell, the larger its rate of cyclin synthesis, and the more Cdc2/Cdc13 dimers enter the nucleus per unit time. A walk through the cell cycle can be considered from early G2, when Cdc2/ Cdc13 dimers accumulate in the nucleus in an inactive form, phosphorylated on the Cdc2 subunit by Wee1 kinase. The inactivating phosphate group is removed by Cdc25 phosphatase at the end of G2. 21 Since MPF activates its friend, Cdc25, and inactivates its enemy, Wee1, these two positive feedback loops ensure that the slowly accumulating pool of phosphorylated Cdc2/Cdc13 dimers suddenly generates a high peak of MPF activity at the G2/M transition. 22 Destruction of MPF activity, as cells exit mitosis, depends on Cdc13 degradation by the APC. Cdc13 is targeted to the APC by two auxiliary APC-binding proteins, Slp1 and Ste9. Slp1/APC 23 is activated by MPF itself, after a time delay. This negative feedback loop is primarily responsible for the degradation of Cdc13 as wild-type cells re-enter G1. Because MPF activity drops, Slp1 activity also falls off; however, Ste9 becomes active and Ste9/APC takes over the degradation of Cdc13 in G1-phase. At the same time, a stoichiometric inhibitor (Rum1) appears and binds to the few Cdc2/Cdc13 dimers present in G1. It can be seen in Figure 2 that Ste9/ APC and Rum1 are in mutually antagonistic relationships with Cdc2/ Cdc13. Ste9 and Rum1 outcompete Cdc2/Cdc13 only in very small cells. Wild-type cells larger than 6 7 ìm have sufficient Cdc2 activity (some of it provided by the alternative cyclins, Cig1, Cig2 and Puc1) to inactivate Ste9 and remove Rum1. Cdc13 s primary helper is Cig2. The cig2 gene is actively transcribed in G1-phase by its transcription factor, Cdc10. Cdc2/Cig2 activity rises in G1, because it is not degraded by Ste9/APC 16 and it is not so effectively inhibited by Rum1. 24 When Cdc2/Cig2 and Cdc2/ Cdc13 together switch off the G1 enemies, they phosphorylate some & HENRY STEWART PUBLICATIONS 1473-9550. BRIEFINGS IN FUNCTIONAL GENOMICS AND PROTEOMICS. VOL 2. NO 4. 298 307. FEBRUARY 2004 301

Sveiczer, Tyson and Novak Three regulatory modules govern the major cell cycle transitions in fission yeast Computers solve the differential equations that describe the regulatory modules Figure 2: A molecular network for the fission yeast cell cycle. Solid lines represent biochemical reactions and dotted lines represent enzymatic effects of proteins on these reactions. The three transitions of the cell cycle (Figure 1) are controlled by separate modules, as the shading indicates. The Start module is characterised by antagonistic relationships between Cdc2/Cdc13 and its enemies, Rum1 and Ste9. The cell passes through this transition when Cdc2/Cdc13 (with some help from Cdc2/Cig2) outcompetes Rum1 and Ste9. Negative feedback of Cdc2/Cig2 on Cdc10 activity plays a crucial role in endoreplication cycles in cdc13 mutants. The G2/M module is characterised by the reversible phosphorylation of Cdc2, catalysed by Wee1 kinase and Cdc25 phosphatase. These enzymes are involved in two positive feedback loops with Cdc2/Cdc13. The cell passes from G2 to M when Cdc2/Cdc13 activation by Cdc25 overcomes its inhibition by Wee1. Mitotic exit is achieved by a timedelayed negative feedback loop, whereby Cdc2/Cdc13 activates Slp1, which destroys Cdc13 unknown protein(s) at the origin of replication, and S-phase starts. When DNA replication is complete, the cell is in early G2, where the walk was started. COMPUTER SIMULATIONS The mathematical model A mechanism like that given in Figure 2 can be converted into a set of ordinary differential equations (ODEs) by using standard principles of biochemical kinetics. 25,26 A differential equation is written for the concentration of each component, where synthesis and activation increase the concentration and degradation and inactivation decrease it. It is also often assumed that certain dynamic variables are in pseudo-steady state; therefore, some ODEs are replaced by algebraic equations. After specifying the numerical values of numerous rate constants and Michaelis constants in these equations, the dynamical system can be solved numerically to determine the concentrations of all variables as functions of time. In the authors ODEs, the concentration variables are expressed in arbitrary units (AUs) and can be interpreted as relative levels. The activity of a protein in a biochemical reaction is determined by its relative level and the appropriate rate constant. 302 & HENRY STEWART PUBLICATIONS 1473-9550. BRIEFINGS IN FUNCTIONAL GENOMICS AND PROTEOMICS. VOL 2. NO 4. 298 307. FEBRUARY 2004

Modelling the fission yeast cell cycle The computer model is tested against the phenotypes of wild-type and mutant cells Cells lacking mitotic cyclin (Cdc13) cannot divide, but they increase their DNA content in discrete rounds of replication Post-translational modifications (eg phosphorylation) may also alter the activity of a protein; in this case, the model contains both the active form with large rate constant and the inactive form with small (or zero) rate constant. These two forms may be reversibly converted into each other. Numerical values of the parameters (eg rate constants) of the models were chosen so that the concentration profiles of the cell cycle regulators are consistent with experiments on wild-type cells and cell cycle mutants (see later). Several models for the fission yeast cell cycle have been developed during the last decade, 27 32 and a new, very comprehensive, model is currently under construction (A. Sveiczer, A. Csikasz-Nagy, J. J. Tyson and B. Novak, unpublished results). Wild-type cells A simulation of wild-type cells (Figure 3) shows the relative concentrations of some important proteins as functions of time during a cell cycle. Cell mass increases exponentially between two consecutive nuclear divisions, which occur every 140 minutes. The short (20 minute) G1- phase is characterised by high Ste9/APC and Rum1 and very low MPF levels. When Cdc2/Cdc13 and Cdc2/Cig2 dimers switch off Rum1, and then Ste9/ APC as well, the cell passes Start and DNA replication takes place (notice that the mass/dna ratio is halved in early S- phase). Since Wee1 activity is relatively high in mid-cycle, it keeps the cell in G2- phase for about three-quarters of the total cycle, 33 until the cell grows to a relatively large mass. During G2-phase, MPF activity can increase only slowly with cell growth, but when the positive feedback loops via Cdc25 and Wee1 turn on, MPF activity rises abruptly and the cell enters mitosis. Mitosis is short because the negative feedback loop activates Slp1, which destroys Cdc13. When MPF activity drops below a critical level, the cell completes nuclear division and about 20 30 minutes later undergoes cytokinesis (cell separation). 33 (Notice that these events have no effect on the mass/dna ratio.) To be worthy of consideration, a mathematical model of the fission yeast cell cycle should be able to describe the physiology of a broad set of cell cycle mutants. Laboratory collections maintain many mutant strains in which one or more genes are deleted, overexpressed or point mutated, with either loss or gain of function. The phenotypes of all these mutants are known, and it should be possible to simulate them with the model. To simulate a mutant strain, the parameter set from wild-type values has to be changed. For example, in the case of a gene deletion, the synthesis of the protein encoded by that gene is set to zero and the simulated time course should be comparable to experiments. The model is able to simulate at least 60 different types of fission yeast mutants (A. Sveiczer, A. Csikasz-Nagy, J. J. Tyson and B. Novak, unpublished results); 27 30 in this paper, only one is described. cdc13 mutant cells What happens if the gene encoding the main cyclin (Cdc13) is deleted? Since cdc13 is a lethal mutant, the answer to this question requires a genetic trick; putting a special promoter before the cdc13 gene that can be switched either on or off by altering the growth medium. After the promoter has been switched off, the cells elongate abnormally and finally die (cdc phenotype), because in the absence of Cdc13 they never enter mitosis and cannot divide. Their nuclei also become extremely large, and the DNA content in the nucleus increases 32-fold or more before they die. 34 In comparison with other cdc mutants, the large DNA content of cdc13 cells is unusual and unexpected, as lack of mitosis should prevent any further rounds of DNA replication by invoking a checkpoint (Figure 1). Apparently, cdc13 cells abnormally re-enter G1 from G2, leading to endoreplication cycles (consecutive S- phases without intervening mitoses). It is worth mentioning that endoreplication & HENRY STEWART PUBLICATIONS 1473-9550. BRIEFINGS IN FUNCTIONAL GENOMICS AND PROTEOMICS. VOL 2. NO 4. 298 307. FEBRUARY 2004 303

Sveiczer, Tyson and Novak Figure 3: Simulated time courses of cell-cycle control proteins in a wild-type fission yeast cell. Mass/DNA is divided by two at DNA replication, and grows exponentially between two consecutive S- phases. The Cdc13 symbol represents the sum of all the existing forms of Cdc2/Cdc13 complexes, either active or inactive, either free or bound to Rum1. The Cdc2/Cdc13 symbol represents only the active complex. A similar convention is used in the case of Cig2. The short G1 phase is characterised by high Cdc10, Ste9 and Rum1 activity and the lack of any Cdk/cyclin activity. S/G2 phases are characterised by low Cdc10, Ste9 and Rum1 activities, and a high level of total Cdc2/Cdc13, which is mostly inactive (phosphorylated). M- phase is characterised by high Cdc2/Cdc13 activity. M-phase is short because Cdc2/Cdc13 activates Slp1, which degrades Cdc13. Based on Tyson et al. 32 au, arbitary units often occurs normally during the development of higher eukaryotes, so this fission yeast mutant mimics a fundamental phenomenon. This unusual behaviour can be explained by the dynamics of Cig2 in our model (Figure 2). Since Cdc13 is absent, S-phase must be driven by Cdc2/Cig2. Cdc2/Cig2 apparently switches off its transcription factor, Cdc10, 35 and this 304 & HENRY STEWART PUBLICATIONS 1473-9550. BRIEFINGS IN FUNCTIONAL GENOMICS AND PROTEOMICS. VOL 2. NO 4. 298 307. FEBRUARY 2004

Modelling the fission yeast cell cycle The mass/dna ratio is a crucial regulator of the eukaryotic cell cycle negative feedback can return G2 cells to G1 after successive rounds of DNA replication. Computer simulations show that this might be the case (Figure 4). After replication, there is a short G2-like state when Cdc10 is off and Cdc2/Cig2 is Figure 4: Simulated time courses of cell-cycle control proteins in a cdc13 mutant cell. In the absence of Cdc13, the cell never enters mitosis and therefore dies; however, a negative feedback loop in the mechanism (Figure 2), whereby Cdc2/Cig2 inactivates its own transcription factor (Cdc10), results in an abnormal transition from G2 back to G1, leading to endoreplication (repeated S-phases) at intervals close to the mass doubling time. At every S-phase, the control system is reset (mass/dna is divided by two) (A. Sveiczer, A. Csikasz-Nagy, J. J. Tyson and B. Novak, unpublished results). au, arbitary units on; however, Cdc2 activity is dropping because Cig2 is being degraded and not synthesised. Eventually, Rum1 returns, inhibiting the remaining Cdc2/Cig2 and allowing Cdc10 to make a comeback. This G1 state lasts until enough Cdc2/ Cig2 accumulates in the nucleus, parallel with cell growth, to initiate a new round of DNA replication. This process is repeated at time intervals very close to the normal mean cycle time, as observed. To describe this endoreplicative cdc phenotype properly, we have had to assume that Cdc2/cyclin dimers accumulate in the nucleus proportionally to the mass/dna ratio instead of the mass/nucleus ratio. The mass/dna ratio halves at S-phase when DNA is doubled and grows exponentially (together with mass) between two consecutive S-phases. This alteration in the model means that the cell cycle control system is reset at replication (rather than at cell division, as assumed in most of the authors previous papers), because DNA synthesis is the only notable event occurring during the endoreplicative cycles. For many years, the mass/dna ratio has been implicated as a crucial regulatory signal in the cell cycles of a variety of organisms. 36 41 CONCLUSIONS The authors aim is to make connections between molecular control systems and cell physiology. 26 This requires that the problem is looked at from three different points of view: the molecular network of the control mechanism, its transformation into differential equations and its analysis by dynamical systems theory. These three points of view complement each other, and together they provide an in-depth understanding of the dynamics of the network and how it really plays out in the physiology of the cell. The molecular network is the natural view of molecular geneticists. Ideas from the theory of dynamical systems, like bistability and hysteresis, are the natural language of modellers. The differential equations provide a machine-readable form of these ideas, allowing both experimentalists and & HENRY STEWART PUBLICATIONS 1473-9550. BRIEFINGS IN FUNCTIONAL GENOMICS AND PROTEOMICS. VOL 2. NO 4. 298 307. FEBRUARY 2004 305

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