Modeling the fission yeast cell cycle: Quantized cycle times in
 wee1
 −
 cdc25Δ
 mutant cells

Sveiczer, Ákos; Csikász‐Nagy, Attila; Győrffy, Béla; Tyson, John J.; Novák, Béla

doi:10.1073/pnas.97.14.7865

Cited by 112 publications

(109 citation statements)

References 40 publications

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“…38 From a dynamical point of view, the most interesting aspect of the problem are the quantized cycles in wee1 Ϫ cdc25⌬ double-mutant cells, which we have emphasized in this paper. The theory proposed here is slightly different from our proposal in Sveiczer et al 39 In that paper, we assumed that Slp1 could not degrade Cdc13 directly, but only indirectly by activating Ste9. Furthermore, we assumed that Mik1 activity could be downregulated by phosphorylation by MPF, exactly as Wee1.…”

Section: Discussioncontrasting

confidence: 41%

Mathematical model of the cell division cycle of fission yeast

Novák

Pataki

Ciliberto

et al. 2001

Chaos: An Interdisciplinary Journal of Nonlinear Science

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153

187

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Much is known about the genes and proteins controlling the cell cycle of fission yeast. Can these molecular components be spun together into a consistent mechanism that accounts for the observed behavior of growth and division in fission yeast cells? To answer this question, we propose a mechanism for the control system, convert it into a set of 14 differential and algebraic equations, study these equations by numerical simulation and bifurcation theory, and compare our results to the physiology of wild-type and mutant cells. In wild-type cells, progress through the cell cycle ͑G1→S→G2→M͒ is related to cyclic progression around a hysteresis loop, driven by cell growth and chromosome alignment on the metaphase plate. However, the control system operates much differently in double-mutant cells, wee1 Ϫ cdc25⌬, which are defective in progress through the latter half of the cell cycle ͑G2 and M phases͒. These cells exhibit ''quantized'' cycles ͑interdivision times clustering around 90, 160, and 230 min͒. We show that these quantized cycles are associated with a supercritical Hopf bifurcation in the mechanism, when the wee1 and cdc25 genes are disabled. © 2001 American Institute of Physics. ͓DOI: 10.1063/1.1345725͔To reproduce itself, a cell must replicate all of its components and divide into two nearly identical daughter cells. During this cycle, the cell's deoxyribonucleic acid "DNA…, which stores its genetic information, must be replicated precisely, and the two copies of each DNA molecule "called sister chromatids… must be segregated accurately to the daughter cells " Fig. 1…. In eukaryotic cells, these two steps, called DNA replication and mitosis, occur during distinct temporal phases of the cell cycle "S phase and M phase… separated by gaps "G1 and G2…. Maintaining the correct order of events is the responsibility of the cell cycle engine. 1 Over the past 20 years, molecular biologists have uncovered many components of this engine. Cellcycle genes from one species can often replace their counterparts in other species, even between yeast and human cells, indicating that the cell cycle engine is an ancient and highly conserved mechanism among eukaryotes. From such discoveries, we can now construct schematic diagrams of the cell cycle engine in many different species, 2,3 but how can we be sure that a diagram is consistent with the overall physiology of cell division in any particular species? Biochemical reaction kinetics, in combination with the modern theory of nonlinear dynamical systems, provide just the tool we need to derive the physiological consequences of complex molecular regulatory networks. We illustrate this tool by associating some unusual features of the fission yeast cell cycle to bifurcations in the system of equations describing its cell cycle engine.

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Section: Discussioncontrasting

confidence: 41%

Mathematical model of the cell division cycle of fission yeast

Novák

Pataki

Ciliberto

et al. 2001

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

153

187

View full text Add to dashboard Cite

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“…Such polymodality has been reported in mammalian (39), yeast (40), and amphibian (41) cell cycles. Several mechanisms have been proposed to account for this polymodality, including specific gene circuits with complex dynamics (42,43) and intercell communication (44). Our results hint at a simpler mechanism for such quantized cellular transitions.…”

supporting

confidence: 48%

A genetic timer through noise-induced stabilization of an unstable state

Turcotte

García-Ojalvo

Süel

2008

Proc. Natl. Acad. Sci. U.S.A.

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Stochastic fluctuations affect the dynamics of biological systems. Typically, such noise causes perturbations that can permit genetic circuits to escape stable states, triggering, for example, phenotypic switching. In contrast, studies have shown that noise can surprisingly also generate new states, which exist solely in the presence of fluctuations. In those instances noise is supplied externally to the dynamical system. Here, we present a mechanism in which noise intrinsic to a simple genetic circuit effectively stabilizes a deterministically unstable state. Furthermore, this noise-induced stabilization represents a unique mechanism for a genetic timer. Specifically, we analyzed the effect of noise intrinsic to a prototypical two-component gene-circuit architecture composed of interacting positive and negative feedback loops. Genetic circuits with this topology are common in biology and typically regulate cell cycles and circadian clocks. These systems can undergo a variety of bifurcations in response to parameter changes. Simulations show that near one such bifurcation, noise induces oscillations around an unstable spiral point and thus effectively stabilizes this unstable fixed point. Because of the periodicity of these oscillations, the lifetime of the noise-dependent stabilization exhibits a polymodal distribution with multiple, well defined, and regularly spaced peaks. Therefore, the noise-induced stabilization presented here constitutes a minimal mechanism for a genetic circuit to function as a timer that could be used in the engineering of synthetic circuits.bifurcation ͉ dynamics ͉ circuit ͉ stochastic ͉ quantized cycle S tochastic fluctuations in gene expression and protein concentrations are a natural by-product of biochemical reactions in cells. Properties of this biochemical noise within genetic circuits, such as their amplitude, distribution, and propagation, have been extensively characterized (1-9). Additionally, theoretical and experimental studies have established that such noise can induce stochastic switching between distinct and stable phenotypic states (5, 10-23). Noise within genetic circuits is therefore thought to contribute to phenotypic heterogeneity in genetically identical cellular populations. It has also recently been shown experimentally that noise can trigger cellular differentiation in fruit flies and bacteria (14,17,18,24). Together, these studies establish that noise can play an active functional role in cellular processes by effectively destabilizing and thus inducing escape from stable phenotypic states.Besides its common role in destabilizing stable states, noise can also have the more counterintuitive effect of generating new stable states that do not exist in the absence of fluctuations (25). In particular, noise-induced bistability has been reported theoretically (26, 27) and experimentally (2). In those situations, one of the two stable solution branches is usually present irrespective of fluctuations, whereas the second one is purely induced by noise (28). The appeara...

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“…Together, they reveal a number of valuable insights related to regulating the phases of the cell cycle. The first is that many of the motifs involve nodes [5,8,9,10 in budding yeast (16)(17)(18)(19)(20) and 2, 3, 4, 6 in fission (21)(22)(23)(24)(25)] known to be master regulators. This is not surprising, but it is a confirmation that the type of analysis presented here correlates with what is known by biologists.…”

Section: Resultsmentioning

confidence: 99%

Process-based network decomposition reveals backbone motif structure

Wang

Chen

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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A central challenge in systems biology today is to understand the network of interactions among biomolecules and, especially, the organizing principles underlying such networks. Recent analysis of known networks has identified small motifs that occur ubiquitously, suggesting that larger networks might be constructed in the manner of electronic circuits by assembling groups of these smaller modules. Using a unique process-based approach to analyzing such networks, we show for two cell-cycle networks that each of these networks contains a giant backbone motif spanning all the network nodes that provides the main functional response. The backbone is in fact the smallest network capable of providing the desired functionality. Furthermore, the remaining edges in the network form smaller motifs whose role is to confer stability properties rather than provide function. The process-based approach used in the above analysis has additional benefits: It is scalable, analytic (resulting in a single analyzable expression that describes the behavior), and computationally efficient (all possible minimal networks for a biological process can be identified and enumerated). Prior work on network decomposition-understanding a network's components-has focused on two types of analysis. The first, which we will call motif occurrence analysis, examines all possible small motifs with two, three, or four nodes and by searching for these motifs in known networks, identifies those motifs that occur most frequently across all known networks (7-9). The assumption is that frequently occurring motifs then form a useful building block or module that confers some functionality or property. The second type of work, which we will call motif function analysis, focuses more closely on network function or dynamics. This approach starts with a given network and its known dynamic behavior (the function of the network) and, by removing the edges in a small motif, tries to characterize the effect of the motif. The thinking here is if the removal of a motif results in a loss of function, the motif can be said to contribute to the function. Note that, because any subset of connected edges can be a plausible motif, the number of trials needed for a systematic search of all motifs grows exponentially large, a limitation that also afflicts the motif-occurrence approach. These approaches leave open the question: Do networks contain large motifs that are a primary determining factor in achieving a network's function?In this paper, we present a unique approach to decomposition that addresses the above large-motif question in the affirmative. This approach, which we call process-based analysis, starts by characterizing the space of all possible networks that provide the desired function (process) and then identifies, among these, the minimal networks (with the fewest edges). These minimal networks, it turns out, are few in number and capture the primary functionality-the removal of any single edge from a minimal network destroys the network's function. Thus, suc...

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Modeling the fission yeast cell cycle: Quantized cycle times in wee1 ⁻ cdc25Δ mutant cells

Cited by 112 publications

References 40 publications

Mathematical model of the cell division cycle of fission yeast

Mathematical model of the cell division cycle of fission yeast

A genetic timer through noise-induced stabilization of an unstable state

Process-based network decomposition reveals backbone motif structure

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Modeling the fission yeast cell cycle: Quantized cycle times in wee1 − cdc25Δ mutant cells

Cited by 112 publications

References 40 publications

Mathematical model of the cell division cycle of fission yeast

Mathematical model of the cell division cycle of fission yeast

A genetic timer through noise-induced stabilization of an unstable state

Process-based network decomposition reveals backbone motif structure

Contact Info

Product

Resources

About

Modeling the fission yeast cell cycle: Quantized cycle times in wee1 ⁻ cdc25Δ mutant cells