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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
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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...
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... 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 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. 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. 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). 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. 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 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 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 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 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 ...
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... 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 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 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 re- replication 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 anaphase- promoting 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. 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 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 ...
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... 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 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 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 re- replication 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 anaphase- promoting 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. 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 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 ì m 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 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. 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. 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. ...
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... 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 time- delayed negative feedback loop, whereby Cdc2/Cdc13 activates Slp1, which destroys Cdc13
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An analysis was made of cell length and cycle time in time-lapse films of the fission yeast Schizosaccharomyces pombe using wild-type (WT) cells and those of various mutants. The more important conclusions about 'size controls' are: (1) there is a marker in G2 in WT cells provided by a rate change point (RCP) where the linear rate of length growth...
Citations
... Cell cycle regulation is governed by cyclin-dependent kinase (CDK) complex comprising cyclin and CDK [1][2][3]. The fission yeast, Schizosaccharomyces pombe, encodes six CDKs, Cdc2 being the essential one [4,5]. Several cyclins bind to and activate Cdc2 during mitosis, but only Cdc13 is essential [4]. ...
Cyclins are degraded by the anaphase-promoting complex/cyclosome (APC/C)-mediated proteasome in normal mitosis. We showed that Cdc13 (cyclin B) is also degraded by macroautophagy/autophagy in sulfur-deficient fission yeast. Sulfur depletion causes G2 cell cycle arrest and reduces cell size; however, the associated mechanisms are unknown. We found that autophagy is required for the degradation of Cdc13, which is associated with cell cycle arrest and reduced cell size, by examining cell morphology under sulfur depletion. The analysis of the Cdc13-GFP fusion protein supported the conclusion that Cdc13 is degraded by autophagy. Moreover, we showed that sulfur depletion results in the inactivation of target of rapamycin complex 1 (TORC1) activity via Ecl1-family proteins. Our data indicate that the cyclin is degraded by two different systems: APC/C-mediated proteasome and autophagy. The latter is induced under nutrient-depleted situations. This switch in degradation systems will contribute to appropriate cell cycle arrest when resources are depleted.
Abbreviations: APC, anaphase-promoting complex; CDK, cyclin-dependent kinase; DB, destruction box; EMM, Edinburgh minimal medium; GFP, green fluorescent protein; PCR, polymerase chain reaction; TOR, target of rapamycin; UPS, ubiquitin-proteasome system
... It is a crucial point to determine the most adequate mathematical function which best describes the fission yeast cells' growth patterns, because it can be an important stepping-stone to investigate the underlying molecular background. Moreover, knowing the growth regularities would help to establish robust in silico models describing the biochemical network of the cell cycle [29,30]. Many years ago, it was observed that fission yeast cells grow for about 75% of the cycle. ...
Fission yeast is commonly used as a model organism in eukaryotic cell growth studies. To describe the cells' length growth patterns during the mitotic cycle, different models have been proposed previously as linear, exponential, bilinear and biexponential ones. The task of discriminating among these patterns is still challenging. Here, we have analyzed 298 individual cells altogether , namely from three different steady-state cultures (wild-type, wee1-50 mutant and pom1Δ mutant). We have concluded that in 190 cases (63.8%) the bilinear model was more adequate than either the linear or the exponential ones. These 190 cells were further examined by separately analyzing the linear segments of the best fitted bilinear models. Linear and exponential functions have been fitted to these growth segments to determine whether the previously fitted bilinear functions were really correct. The majority of these growth segments were found to be linear; nonetheless, a significant number of exponential ones were also detected. However, exponential ones occurred mainly in cases of rather short segments (<40 min), where there were not enough data for an accurate model fitting. By contrast, in long enough growth segments (≥40 min), linear patterns highly dominated over exponential ones, verifying that overall growth is probably bilinear.
... During the subsequent division or mitosis phase M, the cell typically divides into two daughter cells. Progression through the cell cycle is tightly controlled by genetic networks Li and Wang, 2014a;Sveiczer et al., 2004;Wang et al., 2010a). From a physics perspective, genetic control of the cell cycle is naturally considered as a limit cycle. ...
... The gene regulatory network controlling the fission yeast cell cycle is complex and involves a few hundred genes (Sveiczer et al., 2004). Even a simplified network based on experimental studies still involves 10 key genes (Davidich and Bornholdt, 2008), Fig. 11(a). ...
Life is characterized by a myriad of complex dynamic processes allowing organisms to grow, reproduce, and evolve. Physical approaches for describing systems out of thermodynamic equilibrium have been increasingly applied to living systems, which often exhibit phenomena unknown from those traditionally studied in physics. Spectacular advances in experimentation during the last decade or two, for example, in microscopy, single cell dynamics, in the reconstruction of sub- and multicellular systems outside of living organisms, or in high throughput data acquisition have yielded an unprecedented wealth of data about cell dynamics, genetic regulation, and organismal development. These data have motivated the development and refinement of concepts and tools to dissect the physical mechanisms underlying biological processes. Notably, the landscape and flux theory as well as active hydrodynamic gel theory have proven very useful in this endeavour. Together with concepts and tools developed in other areas of nonequilibrium physics, significant progresses have been made in unraveling the principles underlying efficient energy transport in photosynthesis, cellular regulatory networks, cellular movements and organization, embryonic development and cancer, neural network dynamics, population dynamics and ecology, as well as ageing, immune responses and evolution. Here, we review recent advances in nonequilibrium physics and survey their application to biological systems. We expect many of these results to be important cornerstones as the field continues to build our understanding of life.
... An effective inhibitory phosphorylation is executed by Wee1 (and Mik1) kinase(s), resulting in a low-activity pre-MPF form in early G2. MPF (M-phase promoting factor, the Cdk/cyclin B or Cdc2/Cdc13 dimer) becomes fully active when Cdc25 (and Pyp3) phosphatases remove the inhibitory phosphate group in late G2 (Hayles, Fisher, Woolard, & Nurse, 1994;Sveiczer, Tyson, & Novak, 2004). In fission yeast, Wee1 also has an upstream regulatory network. ...
During the mitotic cycle, the rod‐shaped fission yeast cells grow only at their tips. The newly born cells grow first unipolarly at their old end, but later in the cycle, the ‘new end take‐off’ event occurs, resulting in bipolar growth. Photographs were taken of several steady‐state and induction synchronous cultures of different cell cycle mutants of fission yeast, generally larger than wild type. Length measurements of many individual cells were performed from birth to division. For all the measured growth patterns, three different functions (linear, bilinear and exponential) were fitted, and the most adequate one was chosen by using specific statistical criteria, considering the altering parameter numbers. Although the growth patterns were heterogeneous in all the cultures studied, we could find some tendencies. In cultures with sufficiently wide size distribution, cells large enough at birth tend to grow linearly, whereas the other cells generally tend to grow bilinearly. We have found that among bilinearly growing cells, the larger they are at birth, the rate change point during their bilinear pattern occurs earlier in the cycle. This shifting near to the beginning of the cycle might finally cause a linear pattern, if the cells are even larger. In all of the steady‐state cultures studied, a size control mechanism operates to maintain homeostasis. By contrast, strongly oversized cells of induction synchronous cultures lack any sizer, and their cycle rather behaves like an adder. We could determine the critical cell size for both the G1 and G2 size controls, where these mechanisms become cryptic.
TAKE AWAY
• Most individual fission yeast cells in steady‐state cultures grow bilinearly.
• In strongly oversized fission yeast cells, linear growth dominates over bilinear.
• Above birth length thresholds, both the G1 and G2 size controls become cryptic.
... APC-Slp1-dependent degradation of cyclin B and Mes1 triggers MI-to-MII transition but is insufficient to promote the exit. This is in contrast to fission yeast mitosis, in which APC-Slp1 is primarily responsible for driving the cells from metaphase back to G1 (31). ...
Upon nitrogen starvation, Schizosaccharomyces pombe exit mitotic cell cycle and become irreversibly committed to the completion of meiosis program. Meiotic cell divisions are coordinated with sporulation events to produce haploid spores. In the last few decades, experiments on fission yeast have revealed different molecular players involved in two meiotic cell divisions, MI and MII. How the MI entry, MI to MII transition, and MII exit occur due to the dynamics of the regulatory network is not well understood. In this work, we developed a comprehensive mathematical model of the network that describes the temporal dynamics of meiotic progression. The model accounts for the phenotypes of several experimental data (single and multiple mutations). We demonstrate the control strategy involving multiple feedback loops to yield two successive division cycles. The differential regulation of APC/C co-activators and its inhibitors is crucial for the dynamics of both MI to MII transition and MII exit. This model generates mechanistic insights that help in further experiments and modeling.
... [43]Stochastic model of cell cycle predicted that removal of any one of these positive feedback loops increases variability in various cell cycle properties such as cycle time, size at birth and division etc. Further similar architecture of PFLs are also known to present in activation of maturation promoting factor (MPF) in cell cycle network of Saccharomyces pombe (fission yeast) [65]. In our models the parameter values are within the realistic range of biological parameters. ...
Cellular differentiations are often regulated by bistable switches resulting from specific arrangements of multiple positive feedback loops (PFL) fused to one another. Although bistability generates digital responses at the cellular level, stochasticity in chemical reactions causes population heterogeneity in terms of its differentiated states. We hypothesized that the specific arrangements of PFLs may have evolved to minimize the cellular heterogeneity in differentiation. In order to test this we investigated variability in cellular differentiation controlled either by parallel or serial arrangements of multiple PFLs having similar average properties under extrinsic and intrinsic noises. We find that motifs with PFLs fused in parallel to one another around a central regulator are less susceptible to noise as compared to the motifs with PFLs arranged serially. Our calculations suggest that the increased resistance to noise in parallel motifs originate from the less sensitivity of bifurcation points to the extrinsic noise. Whereas estimation of mean residence times indicate that stable branches of bifurcations are robust to intrinsic noise in parallel motifs as compared to serial motifs. Model conclusions are consistent both in AND- and OR-gate input signal configurations and also with two different modeling strategies. Our investigations provide some insight into recent findings that differentiation of preadipocyte to mature adipocyte is controlled by network of parallel PFLs.
... That is, if the inference diagram of a system has root SCCs, then one may only need to select state variables from different root SCCs, and the system will be observable through monitoring these state variables. Biological systems are typical nonlinear systems [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Observer design for biological systems has important realworld implications. ...
... Circadian rhythms are widely in existence in various plants and animals [12], which are controlled by biomolecular networks. Circadian rhythms have been extensively investigated during the last decades [18][19][20][21][22][23]. For example, in 1995, Goldbeter established a mathematical model for the circadian rhythms in the Drosophila [11]. ...
... Hereinafter, we numerically verify the effectiveness of the designed observers. Firstly, we assume ( ) = 0; the output The Scientific World Journal (3) and (17) with step input signal ( ) in (19). (b) The error dynamics between systems (3) and (17). ...
The paper investigates the observer design for a core circadian rhythm network in
Drosophila
and
Neurospora
. Based on the constructed highly nonlinear differential equation model and the recently proposed graphical approach, we design a rather simple observer for the circadian rhythm oscillator, which can well track the state of the original system for various input signals. Numerical simulations show the effectiveness of the designed observer. Potential applications of the related investigations include the real-world control and experimental design of the related biological networks.
... Recent models [17,25,26] have begun the difficult task of assembling larger scope models aimed at a regulatory system governing complete cell cycle transit. Coincident with the use of yeast as the primary model organism in cell cycle research, models of yeast cell cycles dominate the field [27][28][29][30][31][32][33][34][35][36]. Other models use the language and information from frog eggs [22], sea urchins [37], drosophila [38], and mammalian cultured cells [14,17,25,39]. ...
Few of >150 published cell cycle modeling efforts use significant levels of data for tuning and validation. This reflects the difficultly to generate correlated quantitative data, and it points out a critical uncertainty in modeling efforts. To develop a data-driven model of cell cycle regulation, we used contiguous, dynamic measurements over two time scales (minutes and hours) calculated from static multiparametric cytometry data. The approach provided expression profiles of cyclin A2, cyclin B1, and phospho-S10-histone H3. The model was built by integrating and modifying two previously published models such that the model outputs for cyclins A and B fit cyclin expression measurements and the activation of B cyclin/Cdk1 coincided with phosphorylation of histone H3. The model depends on Cdh1-regulated cyclin degradation during G1, regulation of B cyclin/Cdk1 activity by cyclin A/Cdk via Wee1, and transcriptional control of the mitotic cyclins that reflects some of the current literature. We introduced autocatalytic transcription of E2F, E2F regulated transcription of cyclin B, Cdc20/Cdh1 mediated E2F degradation, enhanced transcription of mitotic cyclins during late S/early G2 phase, and the sustained synthesis of cyclin B during mitosis. These features produced a model with good correlation between state variable output and real measurements. Since the method of data generation is extensible, this model can be continually modified based on new correlated, quantitative data.
... It is observed that the dimer of CDK/ CDC13 is the one that drives the cell cycle progression where its dynamics triggers the mitosis event. In the absence of this dimer, the model shows that fission yeast experiences endoreplication (Novak and Tyson, 1997;Sveiczer et al., 2004). Mammalian has four CDKs that govern the cell cycle. ...
... Cell Biology and Physiology of the Fission Yeast Cell Cycle The fission yeast Schizosaccharomyces pombe has very frequently been applied since the 1950s as a model organism in cell biology, microbial physiology (▶ Cell Cycle, Physiology), and genetics, and later also in molecular biology, genomics, and systems biology (Mitchison 1990;MacNeill 2002;Sveiczer et al. 2004). As a species, S. pombe belongs to class Schizosaccharomycetes, subphylum Archiascomycotina, and phylum Ascomycota. ...
... Furthermore, deleting the mitotic activator phosphatase gene cdc25 in the temperature sensitive wee1-50 background generated quantized cycles at the restrictive temperature (Sveiczer et al. 1996). By the end of the second millennium, a "wiring diagram" for the fission yeast cell cycle engine was made (Fig. 4), which was based on the above mentioned experiments and could be studied by methods of mathematical modeling (▶ Cell Cycle Modeling, Differential Equation) (Sveiczer et al. 2004). Since sequencing of the whole S. pombe genome has been finished (MacNeill 2002), these models probably contained the major players of the network; however, novelties in the regulatory mechanisms still arise. ...
... In the center of Fig. 4 is the Cdc2/Cdc13 dimer protein complex (Sveiczer et al. 2004). Cdc2 is the regulatory kinase (cyclin-dependent kinase or Cdk) subunit, which phosphorylates its specific substrate proteins at specific Ser or Thr residues (▶ Cyclins and Cyclin-dependent Kinases). ...
