Andrea Ciliberto ¹, Bela Novak ^{2, 3}, and John J. Tyson ¹

 ¹ Department of Biology, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061
² Molecular Network Dynamics Research Group of Hungarian Academy of Sciences, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
³ Department of Agricultural Chemical Technology, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

Address correspondence to John J. Tyson, Dept. of Biology, M.C. 0406, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061. Tel.: (540) 231-4662. Fax: (540) 231-9307. email: tyson@vt.edu

The morphogenesis checkpoint in budding yeast delays progression through the cell cycle in response to stimuli that prevent bud formation. Central to the checkpoint mechanism is Swe1 kinase: normally inactive, its activation halts cell cycle progression in G2. We propose a molecular network for Swe1 control, based on published observations of budding yeast and analogous control signals in fission yeast. The proposed Swe1 network is merged with a model of cyclin-dependent kinase regulation, converted into a set of differential equations and studied by numerical simulation. The simulations accurately reproduce the phenotypes of a dozen checkpoint mutants. Among other predictions, the model attributes a new role to Hsl1, a kinase known to play a role in Swe1 degradation: Hsl1 must also be indirectly responsible for potent inhibition of Swe1 activity. The model supports the idea that the morphogenesis checkpoint, like other checkpoints, raises the cell size threshold for progression from one phase of the cell cycle to the next.

Key Words: molecular networks; dynamical systems; cell cycle; size control; Swe1 kinase
The full online version of this article contains supplemental material.
Abbreviations used in this paper: MPF, M-phase promoting factor; ND, nuclear division.

Tyson and Novak (2001) have proposed a simplified version (Fig. 1) of a model by Chen et al. (2000) of the budding yeast cell cycle. In the Tyson-Novak model, Cln1, Cln2, Clb5, and Clb6 are lumped together as "Cln", and Clb1 and Clb2 are lumped together as "Clb2". Cln synthesis is due to SBF, and therefore is a function of cell size (Dirick et al., 1995). Cln-dependent kinase activity induces degradation of Sic1, and initiates DNA synthesis (via Clb5-6). Moreover, Cln-dependent kinase activity inactivates Cdh1, permitting Clb2 level to rise. Cdc28–Clb2 activity, relieved from Sic1 and Cdh1 inhibition, turns on its own transcription through Mcm1, and turns off Cln transcription by inhibiting SBF. The cell enters into M phase, and Cdc28–Clb2 starts a negative feedback loop by activating a putative intermediate enzyme, and by enhancing Cdc20 transcription. The ultimate effect of the loop is to activate the anaphase promoting complex, which degrades Clb2 and drives the cell out of mitosis.

Figure 1. Molecular mechanism of the cell-cycle engine in budding yeast.

AA, amino acids; APC, anaphase promoting complex; Cdc20 and Cdh1, proteins that target Clb2 to the APC; Cln, G1 cyclins; IE, intermediary enzyme; Mcm1, transcription factor for Clb2; SBF, transcription factor for Cln; SCF, Skp1–Cdc53–F-box protein complex; Sic1, stoichiometric inhibitor of Cdc28–Clb2; five small-circles, degradation ragments.

Notice that Cdc28–Clb2 has two major antagonists, Sic1 and Cdh1. In G1 phase, Sic1 and Cdh1 are active and Cdc28–Clb2 is repressed, and vice versa in S-G2-M. Cln- dependent kinase activity pushes the engine from G1 to S-G2-M by inactivating Sic1 and Cdh1. Cln synthesis turns on when the cell grows to a critical size, because Mass activates SBF.

The transition from S-G2-M back to G1 is driven by Cdc20, which targets Clb2 for degradation and (indirectly) activates Cdh1. For further details, see Tyson and Novak (2001) and Chen et al. (2000). The asterisk identifies the more active form of a protein.

Figure 2. The Swe1 box.

Swe1 can be present in four different forms during the cell cycle: unchanged (Swe1), phosphorylated by Cdc28–Clb2 (PSwe1); or modified by Hsl1 (Swe1M) or both (PSwe1M). The doubly modified form we assume to be less stable than the others. The unphosphorylated, unmodified form of Swe1 is assumed to be most active in
phosphorylating Cdc28–Clb2. Cdc28 is dephosphorylated by Mih1. We assume that Cdc28–Clb2 phosphorylates and activates Mih1, and MAPK (Mpk1) inactivates Mih1. The asterisk identifies the more active form of a
protein.

The morphogenesis checkpoint acts like a "governor" to the cell cycle engine, slowing progression through the cell cycle when a particular danger signal (failure to bud) is perceived. To understand the relationship between the engine and its governor, it is useful to introduce the notion of a bifurcation diagram. In Fig. 10, we plot Cdc28–Clb2 activity (the state of the engine) as a function of cell size (the motive force for cell cycle progression in yeast; see Bifurcation analysis, available at http://www.jcb.org/cgi/content/full/jcb.200306139/DC1; Tyson et al., 2001, 2002).

Under normal conditions (Fig. 10 A), the Cdc28-control system has two characteristic states: a stable steady state (at small size) and a stable oscillatory state (at large size). A small newborn cell is attracted to the stable steady state of low Cdc28–Clb2 activity; kept low by active Cdh1 and Sic1 (Fig. 1). The cell is trapped in G1 because it is too small to warrant a new round of DNA replication and division. When the cell grows to a critical size (Fig. 10 A, mass = 1), the stable steady state is lost, and the cell cycle engine begins an oscillation that drives Cdc28–Clb2 to larger activity. The cell replicates its DNA and enters mitosis. The mitotic state is
intrinsically unstable, because high levels of Cdc28–Clb2 turn on Cdc20, which destroys Cdc28's cyclin partner.

As Cdc28 activity drops, the cell divides and the control system is reset to the domain of the stable steady state. The duration of the budded phase (S-G2-M) is fixed at 60 min, the time it takes to complete one oscillation. The duration of G1 phase is variable, depending on growth rate and asymmetry of division.

Figure 10. Bifurcation diagrams for the cell cycle engine.

We plot Cdc28–Clb2 activity, representative of the state of the cell cycle control system, against cell mass, M, which is the driving force for progression through the cell cycle. That is, for a fixed value of M, we solve the differential equations in Table S1 until the control system reaches a stable, self-maintaining state, which is either a steady state (no further change in activities of the regulatory proteins) or an oscillatory state (perfectly
repeated fluctuations of their activities). Horizontal bars are placed at the Cdc28–Clb2 level characteristic of steady states, and vertical arrows represent the range of fluctuations of Cdc28–Clb2 activity in an oscillatory state. These diagrams are schematic cartoons; for accurately computed bifurcation diagrams, see online
supplemental material (Bifurcation analysis) and Fig. S1. Notice the axes are scaled logarithmically. Because we assume cells grow exponentially, equal distances along the log(mass) axis represent equal intervals of time. Along the log(activity) axis we associate low activity with G1, intermediate activity with S-G2, and high activity with M phase.

(A) Checkpoint silent. The bold dashed line is a cell-cycle trajectory: as the cell grows, the Cdc28 control system is attracted to the stable, self-maintaining state at its current cell mass. A small cell persists in the G1-state until that state disappears at M = 1. Thereafter, the cell executes an oscillation in Cdc28–Clb2 activity, passing through S, G2 and M phases. When Cdc28 activity falls, as the cell exits mitosis, the cell divides and the newborn progeny are attracted to the stable G1-state.

(B) Checkpoint invoked. At the restrictive temperature, a cdc24ts cell continues to grow but fails to make a bud. Consequently, Swe1 is stabilized, and a new self-maintaining steady state, with intermediate activity of Cdc28–Clb2, is created. The cell arrests in S-G2 phase for about one mass-doubling time, until it grows to M = 2, where the G2-arrested state disappears. At this time, the cell adapts to the checkpoint signal, enters mitosis, and becomes dinucleate. Because the cell does not divide, it stays in the oscillatory regime and rereplicates its DNA after a very short G1 phase. The cell reenters mitosis and becomes tetranucleate. The time between NDs is the period of the underlying oscillatory state, 60 min in the model.

Related article in JCB: "Math models morphogenesis and mitosis". Alan W. Dove  JCB 2003 163: 1184. 

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