The Dynamics of Cell Cycle Regulation

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The Dynamics of Cell Cycle Regulation
J. Tyson, A. Csikasz-Nagy B. Novak

• John Ruero
• 8 March 2003

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Agenda

• Cell Cycle Regulation
• Physiology
• Molecular Mechanism
• Wild Type Cells
• Toggle Switches, Amplifiers Oscillators
• Consequences

3
Agenda

• Primer on Dynamical Systems
• Bifurcation Theory Primer
• Checkpoints
• Pheromone
• Unreplicated or Damaged DNA
• Spindle Assembly Chromosome Alignment
• Conclusion

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Cell Cycle

• Cell Cycle is the process by which one cell
  becomes two.
• Chromosome Cycle
• - DNA Replication
• - Physical Separation of two complete
  genomes to daughter nuclei
• Growth Cycle
• - Replication of all other cell components
• - Physical Separation to daughter cells

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Chromosome Cycle

• Physiology
• Two Basic Processes
• DNA Synthesis (S phase)
• During S phase, double-stranded DNA
  molecules are replicated to produce pairs of
  sister chromatids held together by proteins
  called cohesins.
• Mitosis (M phase) with four subphases

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Subphases in M Phase

• Prophase
• Replicated chromosomes condense into compact
  structures
• Metaphase
• Condensed chromosomes are aligned on the
  midplane of the mitotic spindle
• Anaphase
• Cohesins are degraded and sister chromatids are
  partitioned into two separate bundles

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Subphases in M Phase

• Telophase
• When daughter nuclei form and the cell begins
  to divide
• The S and M phases are separated in time by two
  gap called the G1 and G2 phases, the complete
  cycle constituting the cell cycle G1-S-G2-M.
• Note It is crucial that S and M phases
  alternate in time. Why?
• If a haploid cell attempts two mitotic nuclear
  divisions in a row without a complete intervening
  S phase, its progeny will inherit grossly
  incomplete genomes and die.
• Repeated S phases without intervening mitoses is
  not immediately fatal but is unusual.

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G1 Phase

• G1 phase controls entry into the S phase, making
  sure that
• a. cells are large enough to warrant a new
  round of DNA synthesis
• b. any damage suffered by the DNA has been
  repaired
• c. and external conditions favor mitotic cell
  division.

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G2 Phase

• G2 phase guards entry into mitosis, making sure
  that
• a. DNA is fully replicated
• b. any new damage sustained by DNA has been
  repaired
• c. and the cell is large enough to divide.

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The Cell Cycle

• In growing cells, the four phases proceed
  successively, taking from 10-20 hrs.
• Interphase comprises the G1, S, and G2 phases.
  DNA is synthesized in S and other cellular
  macromolecules are synthesized throughout
  interphase, roughly doubling cells mass.
• During G2 the cell is prepared for mitotic (M)
  phase when the genetic material is evenly
  proportioned and the cell divides.
• Non-dividing cells exit the normal cycle,
  entering the quiescent G0 state.

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Molecular Mechanism (1)

• Enzymes called Cyclin-dependent protein kinases
  (CDKs) are the master molecules of the cell
  cycle.
• CDKs trigger major events of the chromosome cycle
  by phosphorylating certain target proteins on
  chromosomes and elsewhere.
• At anaphase, the destruction of mitotic CDK
  activity allows cells to divide and enter G1
  phase of the next cell cycle.

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Molecular Mechanism (2)

• Exit from mitosis is controlled by the
  anaphase-promoting complex (APC) which initiates
  the degradation of cohesins and mitotic cyclins.
  
• Therefore, to understand the molecular
  mechanism of cell reproduction is to understand
  the regulation of CDK and APC activities.

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Molecular Mechanism (3)

• In the mitotic cycle of fission yeast, a single
  CDK (called Cdc2) in combination with a single
  B-type cyclin (called Cdc13) triggers both the S
  phase (modest Cdc2 activity) and M phase (high
  Cdc2 activity). The activity Cdc2Cdc13 is
  regulated in three different ways
• a. Availability of cyclin subunits
• b. Phosphorylation of kinase subunits
• c. Binding to a stoichiometric inhibitor.

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Cell Cycle Molecular Mechanism
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Molecular Mechanism (4)

• Cdc13 concentration is low at G1 and rising
  steadily through S, G2 and early M phases. As
  cells exit mitosis, Cdc13 level rapidly degrades.
  This Cdc13 degradation is mediated by two
  proteins called Slp1 and Ste9 for ubiquitination
  by the APC and destroyed subsequently by
  proteasomes. At G1, cells contain a protein Rum1
  which binds to and inhibits any Cdc2Cdc13 dimers
  that may be present.

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Molecular Mechanism (5)

• To leave G1 and enter S phase, Ste9 and Rum1 must
  be neutralized. This is aided by starter kinases
  Cig1, Cig2 and Puc1 which are not opposed by Ste9
  and Rum1, which phosphorylate Ste9 and Rum1,
  thereby inactivating them and labeling them for
  degradation.
• During G2, Cdc13 is stable and Rum1 is absent,
  Cdc2Cdc13 is inactive.
• To enter M with high Cdc2 activity, kinases Wee1
  and Mik1 must be inactivated, and Cdc25 activated.

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Toggle Switches Oscillators

• The apparent activities of the different proteins
  and kinases (feedback loops that may, under
  appropriate conditions, cannot coexist) work like
  toggle switches.
• Another interaction of proteins mutually amplify
  one another, which generate oscillations.

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Consequences

• Quantitatively, these molecular mechanisms are
  converted into a set of differential equations,
  and numerical simulation is used to study
  solution to these differential equations.
• Qualitatively, these relations between kinetic
  equations and cell physiology are clearly
  revealed through the methods of dynamic systems
  theory.

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Dynamic Systems Primer (1)

• What are dynamic systems?
• A dynamical system is a set of nonlinear
  ordinary differential equations,
• dx1/dt fi(x1,, xn p1,, pm), i 1, n
• where
• xi concentration (or activity) of the i-th
  protein in the reaction network
• pj value of the j-th parameter (rate
  constant, binding constant, etc.)
• fi synthesis degradation activation
  inactivation, where synthesis are nonlinear
  functions of the variable concentrations and
  constant parameters in the model

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Dynamic Systems Primer (2)

• The model has three parts
• a. set of rate equations fi,,fn
• b. set of parameter values p1,,pm
• c. set of initial conditions x1(0),,xn(0)

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Dynamic Systems Primer (3)

• Steady state (SS) solution
• At a steady state x1,,xn, the rates of
  change are all identically zero, fi(x1,, xn
  p1,, pm)0 for all i. Hence, at a steady state,
  protein concentrations are unchanging in time.
• Oscillatory solution
• For an oscillatory solution, protein
  concentrations change or vary in time, repeating
  themselves after a characteristic period Tosc gt 0.

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Dynamic Systems Primer (4)

• A steady state is stable if any small
  perturbation away from a steady state returns to
  the steady state.
• A state is unstable if some perturbations grow
  larger with time, and the control system leaves
  the vicinity of the steady state.
• Stable solutions represent physiologically
  observable states of the control system.
• For example, a stable steady state may lose its
  stability or cease to exist, and an oscillatory
  solution may pop into existence. These changes
  in the solution of dynamical systems are called
  bifurcations.

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Bifurcation Theory Primer

• Bifurcations of a dynamical system can be
  characterized by a one-parameter bifurcation
  diagram.
• A bifurcation diagram is constructed by singling
  out one variable, say x1, as a representative of
  all dynamic variables in the control system and
  one parameter, say p1, as a representative of all
  the rate-determining factors in the model. The
  steady-state value x1 is plotted as a function
  of p1. At these specific values called
  bifurcation points, strange things happen.

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Examples of Dynamical Systems and Bifurcation
Theory

• Seesaw
• Economic applications (dynamic demands,
  advertising, etc.)
• Cell Cycle

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Example of Bifurcation Diagram for the Full Cell
Cycle
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Checkpoints (1)

• Pheromone
• Molecules secreted into the extracellular
  environment to convey to neighboring cells the
  mating-type identity of the pheromone-secreting
  cell, triggering a series of activities that
  causes it to halt in G1 phase, and prepare for
  mating.
• Unreplicated or damaged DNA
• If after entering the S phase, a cell runs into
  trouble completing the DNA replication, it must
  delay entry into the M phase through a series of
  protein activities.

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Checkpoints (2)

• Spindle Assembly and Chromosome Alignment If a
  cell runs into problems assembling the mitotic
  spindle or aligning all its chromosomes on the
  spindle, then a spindle surveillance mechanism
  delays the metaphase-to-anaphase transition.

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Conclusion (1)

• The physiological characteristics of a cell are
  determined by networks of interacting proteins
  that process energy, material and information.
• Computer simulations can be used for careful
  analysis of kinetic properties of small networks
  (say around 10-50 differential equations). This
  simulation compares model behavior with observed
  experiments.
• Bifurcation theory helps uncover the dynamical
  principles of control systems.

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Conclusion (2)

• Bifurcation diagrams give a new and useful
  perspective on the growth and reproduction of the
  fission yeast. From this view, progress through
  the cell cycle is a sequence of bifurcations
  between stable states of regulatory networks
  G1-S-G2 (interphase) and mitotic (M) modules.
• Progress from one stage to the other can be
  restrained by checkpoints mechanisms that check
  and monitor the states of the cells DNA and
  mitotic components.

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Thank You

• Presentation based on the BioEssays article
  The dynamics of cell cycle regulation by J.
  Tyson, A. Csikasz-Nagy B. Novak, 2002.