A simple model for the eukaryotic cell cycle

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A simple model for the eukaryotic cell cycle Powered By Docstoc
					A simple model for the eukaryotic
           cell cycle
        Andrea Ciliberto
        The cell division cycle

                                    G1
                                      St
                            on          ar
                         isi              t
                 ll   div
               ce
                                                   S
                                                   (DNA Replication)
           h
      Finis



   M                                          G2
                             G2/M
(mitosis)
Kohn, Mol. Biol. Cell., 1999
How did we get to this mess??
Murray and Kirschner, Science, 1989
Xenopus and the clock paradigm




Cell mass decreases during early divisions




                              Alberts et a., Molecular Biology of the Cell.2002
In Xenopus oscillations progress independently
    of DNA presence and cell cycle events
                Autonomous oscillations!




                                    Alberts et a., Molecular Biology of the Cell.2002
MPF, the mitosis promoting factor




                        Murray and Kirschner, Science, 1989
                          MPF is a heterodimer


                                      CDK          cyclin dependent kinase
                                      Cyc          cyclin (regulatory subunit)



Only cyclin synthesis and degradation are required for Xenopus early cycles.




                                                 Alberts et a., Molecular Biology of the Cell.2002
CDK is activated by cyclin binding and once
  activated it induces cyclin degradation

                   CDK


                           CDK
             Cyc           Cyc




                                 ‘X’




                   APCa          APCi
But something else must be at work...


                CDK


                         CDK
          Cyc            Cyc




                               ‘X’




                APCa           APCi
Cyclin threshold




                   Solomon et al, Cell, 1990
Yeast and the domino paradigm



                           G1



   Anaphase                          S




      Metaphase                 G2
                             Balanced growth and division



                       Cell cycle                                      Cytoplasmic
                        engine                                           growth
                                        TC                TD
                                             Size control
                   4
Cytoplasmic mass




                   3
                                                          T C > TD


                   2
                                                                 T C = TD       exponential
                                                                                 balanced
                   1
                                                                                  growth

                                               T C < TD
                   0
                         0          1             2          3              4
Cell division cycle (cdc) mutants are temperature sensitive




                                                           Hartwell, Genetics, 1991




                                   Alberts et a., Molecular Biology of the Cell.2002
Wee1 controls a rate limiting step in the cell cycle
        Cell division and cell growth are coupled


          wild type      wee1          cdc25




                unreplicated DNA




                                               Nurse, Noble lecture, 2000
                       Basic cell cycle properties


                                - Cell physiology-
- Coupling of mass growth and cell division.
- Once the cell enters the cycle,it is commited to finish it: irreversibility.
- The cell halts during cell cycle progression if something has gone wrongly.


                               -Molecular network-
-Oscillations of MPF drive cells into and out of mitosis.
- Cdc28 activity is controlled by Wee1 (negative) and Cdc25 (positive).
Dominoes and clocks: Cdc28 is the
budding yeast homologous of MPF’s
         catalytic subunit




         Cdc28   =   Cdc2    =   CDK1
 MPF =
          Clb2       Cdc13       CycB
Phosphorylation as well as cyclin binding controls MPF activity




                    Wee1
                                           Cdc2
              P
                                                    mass
            Cdc2            Cdc2
                                             Cyc
             Cyc            Cyc




                   Cdc25P

                                     ‘X’


                                   APCi            APCa
Phosphorylation as well as cyclin binding controls MPF activity




                    Wee1          Wee1P         Cdc2
             P
                                                         mass
            Cdc2            Cdc2
                                                  Cyc
            Cyc             Cyc




                   Cdc25P         Cdc25

                                          ‘X’


                                    APCi                APCa
Isolation and analysis of a positive feedback: the network...




                            Wee1          Wee1P
                                                  G2
                      P

                    Cdc2           Cdc2
                     Cyc           Cyc
                                                  M




         Notice, here no cyclin synthesis, no cyclin degradation!!
...and the physiology




                        Solomon et al, Cell, 1990
               Part II
Standard laws of biochemical kinetics
   applied to molecular networks
                Law of Mass Action: forward reaction
                                         ka
                              pMPF             MPF



       dMPF                                   Steady State solution (MPFSS)
            = ka ! pMPF
        dt                                         dMPF
       pMPF = MPFtot - MPF                                =0
                                                    dt
       dMPF
            = ka ! (MPFtot - MPF)                  MPF SS = MPFtot
        dt


Notice: no dimer, only MPF. Cdk is supposed to be present in excess throughout
the cycle. Increasing MPF total mimics an increase in cyclin total.
                           dMPF
                                = ka ! (MPFtot -MPF)
                            dt

                                                                        MPFtot
  0.2                                                      1




                                                    MPF
                         dMPF
                              >0                          0.8

  0.1
                          dt
dMPF                                                      0.6

 dt                                                       0.4
   0                                      dMPF
                                               =0
                                           dt             0.2

  -0.1
                                                           0
         0   0.2   0.4    0.6   0.8   1
                                                                0   4    8     12   16   20
                   MPF                                                       time
Law of Mass Action: reversible reaction
                    ka
           pMPF           MPF
                     ki
     dMPF
          = ka ! pMPF - ki ! MPF
      dt


       Steady State solution
          dMPF
                 =0
           dt
                  ka ! MPFtot
          MPF =
              SS

                    ka + ki
                         ka
         pMPF                    MPF
                         ki
 dMPF
      = ka ! (MPFtot " MPF) - ki ! MPF
  dt
                   production            elimination
                       +                      -

                               dMPF
                                    =0
       0.25                     dt
dMPF
                        dMPF    dMPF
 dt    0.2                   >0      <0
                         dt      dt
       0.15


       0.1


       0.05


         0
              0   0.2    0.4     0.6   0.8   1
                               MPF
       1
MPF
      0.8


      0.6


      0.4


      0.2


       0
            0   4   8      12   16   20

                    time




                                          t
                   Law of Mass Action:
               catalyzed reversible reaction
       ka
                              dMPF
pMPF        MPF                    = ka ! (MPFtot " MPF) - ki ! MPF ! Wee1
       ki                      dt
                                                          production      elimination
                                                              +                -
        Wee1

                       rate
                 0.25                         4       3

                 0.2                5                       2
                 0.15


                 0.1                                        1

                 0.05


                   0
                        0     0.2       0.4   0.6     0.8       1   MPF
                                543 2             1
                                                    Nullclines

                      ka
     pMPF                                         dMPF
                                MPF                    = ka ! (MPFtot " MPF) - ki ! MPF ! Wee1
                  ki                               dt
                                                                      production          elimination
                                                                          +                    -
                      Wee1

     rate
0.25                                3                       MPFSS
                            4                                              dMPF
                                                                  1
                                                                                <0
0.2               5                       2                                 dt
                                                                                              dMPF
0.15
                                                                                                   =0
                                                                                               dt
0.1                                       1                      0.5

                                                                           dMPF
0.05                                                                            >0
                                                                            dt
 0                                                MPF
       0    0.2       0.4   0.6     0.8       1                   0
                                                                       0            2.5            5
              543 2             1                                           1   2         3    4
                                                                                    Wee1
           What happens if MPF total increases?




     rate
0.25                                3                   MPFSS
                            4                                       dMPF
                                                           1
                                                                         <0
0.2               5                       2                          dt
                                                                                       dMPF
0.15
                                                                                            =0
                                                                                        dt
0.1                                       1               0.5

                                                                    dMPF
0.05                                                                     >0
                                                                     dt
 0                                                MPF
       0    0.2       0.4   0.6     0.8       1            0
                                                                0            2.5            5
              543 2             1                                    1   2         3    4
                                                                             Wee1
            Michaelis-Menten: forward reaction
                               kwa
                     Wee1P           Wee1




dWee1 kwa ! Wee1P                     Steady State solution
     =                                  dWee1
 dt    J + Wee1P                               =0
dWee1 kwa ! (Wee1tot - Wee1)              dt
     =                                  Wee1SS = Wee1tot
 dt    J + (Wee1tot - Wee1)
    0.2                                                  1
                                                                      Wee1tot
dWee1                                               b
 dt             dWee1                                   0.8

    0.1
                      >0
                 dt                                     0.6


                                                        0.4
        0
                                         dWee1
                                               =0       0.2
                                          dt
    -0.1                                                 0
            0   0.2   0.4    0.6   0.8   1                    0   4   8     12   16   20
                            Wee1                                          time
 Michaelis-Menten: reversible reaction

                         kwa
              Wee1P            Wee1
                         kwi

         k1                           k2
Wee1P               Enzyme1:Wee1P          Wee1
              k1r
       Enzyme1                     Enzyme1



         k3                           k4
Wee1                Enzyme2:Wee1           Wee1P
              k3r
       Enzyme2                     Enzyme2
   if [enzym1TOT], [enzyme2TOT] << [Wee1TOT]

          k wa =[enzyme1TOT ]k 2
          k wi =[enzyme2 TOT ]k 4


dWee1 kwa ! (Wee1tot " Wee1) kwi ! Wee1
     =                      -
  dt    J + Wee1tot -Wee1     J + Wee1
              production            elimination
                  +                      -
              Michaelis-Menten: reversible reaction

        kwa                       dWee1 kwa ! (Wee1tot " Wee1) kwi ! Wee1
Wee1P          Wee1                    =                      -
        kwi                         dt    J + Wee1tot -Wee1     J + Wee1
                                                  production         elimination
                                                      +                   -
                                      dWee1
                                            =0
                      rate             dt
                      0.5
                              dWee1        dWee1
                                    >0           <0
                      0.4      dt           dt

                      0.3


                      0.2


                      0.1


                      0.0
                            0.0     0.2   0.4    0.6   0.8     1.0


                                          Wee1*
                                    Nullclines
             kwa                 dWee1 kwa ! (Wee1tot " Wee1) kwi ! Wee1
Wee1P               Wee1              =                      -
             kwi                   dt    J + Wee1tot -Wee1     J + Wee1
                                               production                  elimination
                                                   +                            -

                dWee1                         Wee1SS
                      =0
 rate            dt                               1
                                                               dWee1
 0.5
         dWee1       dWee1                                           <0
               >0          <0                                   dt
 0.4      dt          dt

 0.3                                             0.5

                                                                dWee1
 0.2
                                                                      >0
                                                                 dt
 0.1


 0.0                                              0
                                                       0             2.5            5
       0.0    0.2   0.4    0.6    0.8   1.0
                                                           1     2         3   4
                    Wee1SS                                           MPF
      Phase plane analysis




     Wee1P           Wee1
               kwi
                        ki
                MPF          pMPF
                        ka


dMPF
     = ka ! (MPFtot " MPF) - ki ! MPF ! Wee1
 dt

dWee1 kwa ! (Wee1tot " Wee1) kwi ! Wee1
     =                      -
  dt    J + Wee1tot -Wee1     J + Wee1
MPFSS                                    MPF
            dMPF
   1
                 <0




                                           5
             dt
                               dMPF
                                    =0               dWee1
                                                           >0
                                                                  dWee1
                                                                        <0
                                dt                    dt           dt
  0.5




                                           2.5
            dMPF
                 >0
             dt
   0




                                           0
        0            2.5            5
             1   2         3    4




                                                            0.5
                                                 0




                                                                      1
                     Wee1                                  Wee1SS
            dMPF
   1
                 <0




                                          5
MPFSS
             dt




                                        MPF
                        dMPF
                             =0                     dWee1
                                                          >0
                                                                    dWee1
                                                                          <0
                         dt                          dt              dt
  0.5




                                          2.5
            dMPF
                 >0
             dt
   0




                                          0
        0         2.5      1        5




                                                            0.5
                                                0




                                                                           1
                 Wee1                                             Wee1SS
                         MPF




                          0.5




                           0
                                0       2.5     Wee1    5
           How does MPF increases with Cyclin total?

                                            ka ! MPFtot
                              MPF   SS
                                         =
                                           ki ! Wee1+ka


                                          MPF
MPF




 0.5




  0
       0         2.5   Wee1    5                    0

                                                          MPFtot
Not quite the same!




                      Solomon et al, Cell, 1990
Wee1P         Wee1
        kwi
                 ki
         MPF          pMPF
                 ka
              Michaelis-Menten:
         catalyzed reversible reaction
                    kwa
            Wee1P          Wee1
                     kwi


                      MPF


dWee1 kwa ! (Wee1tot " Wee1) kwi ! Wee1! MPF
     =                      -
  dt    J + Wee1tot -Wee1         J + Wee1
              production          elimination
                  +                    -
                                             Nullclines


 Wee1P                        Wee1     dWee1 kwa ! (Wee1tot " Wee1) kwi ! Wee1! MPF
                  kwi                       =                      -
                                         dt    J + Wee1tot -Wee1         J + Wee1

                   MPF                                 production             elimination
                                                           +                       -

                                                        Wee1SS           dWee1
rate                                                     1
                                                                               <0
0.5                                                                       dt
                                             5
                                                        0.8
0.4
                                             4                               dWee1
                                                                                   =0
0.3                                          3          0.6                   dt
0.2                                          2          0.4       dWee1
                                                                        >0
0.1
                                             1                     dt
                                                        0.2
                                        .1
0.0
      0.0   0.2         0.4      0.6   0.8       1.0     0
                                                              0      1   2    3    4    5
                        Wee1SS                                           MPF
              Phase plane analysis




                                           dWee1
                                                 =0
MPFSS                         Wee1SS        dt
1                             1

          dMPF       dMPF    0.8
               <0         =0                  dWee1
           dt         dt                            <0
                             0.6
0.5                                            dt
                              0.4 dWee1
          dMPF                          >0
               >0             0.2
                                   dt
           dt
0                              0
      0      2.5      5            0   1     2    3    4   5
              Wee1                               MPF
                Phase plane analysis



                                             dWee1
                                                   =0
Wee1                           Wee1SS         dt
5             dMPF
                   <0           1
               dt
                               0.8
                    dMPF                        dWee1
                         =0    0.6                    <0
2.5                  dt                          dt
                               0.4 dWee1
                                         >0
          dMPF                      dt
               >0              0.2
           dt
0                               0
      0       0.5         1          0   1     2    3    4   5
               MPFSS                               MPF
First solution, MPF wins, Wee1 loses


         1
                               MPFtot=1.5

        0.8
 Wee1
        0.6



        0.4



        0.2



         0
              0   0.4   0.8     1.2    1.6


                              MPF
Second solution, Wee1 wins, MPF loses

           1

                                  MPFtot=0.5
          0.8



   Wee1   0.6



          0.4



          0.2



           0
                0   0.4   0.8     1.2    1.6

                                MPF
Third solution, both can win: hysteresis


        1
                              MPFtot=1

       0.8



       0.6
Wee1
       0.4



       0.2



        0
             0   0.4   0.8   1.2   1.6


                       MPF
How does MPF increases with Cyclin total?
Wee1                Wee1               Wee1




       MPFtot=0.5
                            MPFtot=1          MPFtot=1.5




       MPF                 MPF                 MPF
Hysteresis in the Xenopus early cycles: simulation
             of an experimental result




              From Sha et al, PNAS, 2003
What happens if cyclin total increases with cell mass?
        Wee1          Wee1P         Cdc2
 P
                                             mass
Cdc2            Cdc2
                                      Cyc
Cyc             Cyc




       Cdc25P         Cdc25

                              ‘X’


                        APCi                APCa
                               Conclusion

-Same wiring in different organisms, combination of positive and negative
feedbacks.
- In Xenopus early development, with large mass, the cell cycle is a limit
cycle oscillator, the negative feedback plays the key role.
- Artificially, an additional mechanism of control emerges, based on a
positive feedback loop.
- Both positive and negative feedbacks are at work in yeast. In these
organisms, mass growth drives the cell cycle.
- Positive feedbacks introduce checkpoints and irreversibility in the cycle.
The negative feedback the capability to start a new process.