Mathematical Model for Cell Cycle Regulation and Cancer

1
Mathematical Model for Cell Cycle Regulation and
Cancer

• Mandri Obeyesekere
• UT M.D.Anderson Cancer Center
• Dept. of
• Biostatistics and Applied Mathematics
• Houston

2
The Cell Cycle
3
Concept of ModelingPathways-possible
M/G1
S
G2
M/G1
4
Concept of ModelingPathways-known
M/G1
S
G2
M/G1
5
Concept of ModelingPathways-chosen
M/G1
S
G2
M/G1
6
Concept of ModelingPathways-modeled
M/G1
S
G2
M/G1
7
Models for cell regulationAgur- 2
variable, M-phase,Science-1991Goldbeter-
coupling of multiple cyclesTyson-
6,12,variables YeastThron- Switches,
bistabilityObeyesekere- M,G1,S/M mammalianKohn
- step by step networksAguda-
networks-modules
8
Related Kinetics for Modeling

• Production/degradation
• Activation/deactivation
• Sequestration/release
• Association/disassociation
• promotion/inhibition

9
Intracellular Proteins in Consideration

• G1 phase
• Cyclin D/cdk4
• Cyclin E/cdk2
• Rb
• E2F
• (Growth Factors)

• S-M Phase
• Cyclin A/cdk1
• Cyclin A/cdk2
• Cyclin B/cdk1
• Cdc25c
• P53 (tumor suppressor)
• P21 (kinase inhibitor)
• Mdm2 (oncogene)

10
A Cancer Related Problem

• About 30 of all sarcomas show an amplification
  of the MDM2 gene
• mdm2 causes cancer.
• When mdm2 is over expressed, polyploidy is
  observed.
• Polyploidy is a common sign in many cancers.
• Function of mdm2 causing cancer is not yet known

11
Multi Nucleated cells
(Guillermina Lozano-M.D.Anderson Cancer Center)
Polyploidy of mammary cells when MDM2 is over
expressed.
12
Outline

• Biological Problem The Cell Cycle
• Mathematical Model
• Mathematical/Numerical Studies
• Predictions and Biological Impact

13
P53 involved S-M phase interactions

• p53 activates p21
• p53 promotes mdm2 production
• Mdm2 deactivates p53 by binding to p53
• p21 inhibits the activity of cyclin A and B

14
S-M Phase ModelIntracellular Proteins in
Consideration

• Cyclin A/cdk1
• Cyclin A/cdk2
• Cyclin B/cdk1
• Cdc25c
• P53 (tumor suppressor)
• P21 (kinase inhibitor)
• Mdm2 (oncogene)

15
S-M Pathway
16
The Mathematical Model
Y1
17
Normal S-M cycle
18
Normal S-M Cycle Parameter Values

• Production ratesA10.2
• A20.06 A30.2
  A60.3
  A70.1
  A80.1
• Inhibition ratesH15.0
  H25.0 H35.0
  H60.2
• OthersDM1.5C0.1
  B72.0 B80.8

• Michaelis Menten parametersP34.0
  Q30.1
  P410.0 Q42.0
  P514.0Q51.0P63.5Q62.0
• Degradation rates
• D10.8 D20.7
  D30.15
  D40.3 D60.2
  D70.1
  
• D80.2

19
Other Variables
20
Cell Arrest
Degradation rate of p53(d6) is reduced from 0.2
to 0.01 at time t 75.
21
Important Facts of This Problem

• When mdm2 is over expressed, polyploidy is
  observed.
• Polyploidy is a common sign in many cancers.
• Function of mdm2 causing cancer is not yet known

22
Ploidy and BrdU in Mammary Epithelial Cells
Control, p53 -/- , MDM2 and DNA content
(Genes Dev. 11714-7251997)
23
Comparison of p53 -/- and MDM2/p53 -/-
24
Irregular S-M cycle
25
Mathematical Inferences

• Period doubling mimics polyploidy
• What are the possible pathways for mdm2 action?
• If there exists many, are all possible?
• Design experiments.

26
Dynamics of Cell Cycle Control Bifurcation
Properties
27
Bifurcation Diagram
28
Irregular S-M Cycle
29
More Results
30
Choosing a Pathway
high levels of cyclinA/cdk1 together with a high
MPF signal
31
Conclusion

• Mathematical Modeling allows system analysis of
  a complex problem.
• Qualitative approaches can produce valuable
  results.
• Evaluation of parameter values could be achieved
  by mathematical methods as well as by experiments.

32
Acknowledgments
Dr. Gigi Lozano Dept. of Molecular Genetics UT
M.D. Anderson Cancer Center Dr. Edwin
Tecarro NIH/NIGMS - GM59918
33
Acknowledgements
Dr. Edwin Tecarro Dr. David Goodrich Dr. Shaochun
Bai Dr. Dennis Thron Dr. Gigi Lozano Dr. Jean
Wang NIH/NIGMS - GM59918
34
(No Transcript)
35
(No Transcript)
36
G1 phase Model
37
G1 phase Mathematical Model
38
Normal Cell Cycle- Mathematical Solutions
39
Normal Cell Cycle -Time course
40
Mathematical Analysis-BifurcationSystem Behavior
41
Experimental Results(David Goodrich-Roswell Park)
42
Experiments-Continued
43
Problems?

• Parameter values-model
• (System behavior)
• Experimental evaluation
• (experimental limitations)
• Numerical estimation-
• ( Time dependent variable profiles)
• How crucial is this information?
• Qualitative vs. Quantitative - a balance