Outline

1. Outline • A Biological Perspective • The Cell • The Cell Cycle • Modeling • Mathematicians I have known

2. Molecular Basis of Disease Cancer Heart disease Neurodegenerative illnesses

4. If we can understand disruption of molecular events at the cellular level we can perhaps prevent or stop disease manifestation at the organismal level

5. The Cell

6. A variety of membrane-bounded compartments exist within eucaryotic cells, each specialized to perform a different function.

7. Forms of Biological Information • DNA • Information is contained in the primary structure (the sequence of bases). • Protein • Information is contained at multiple structural levels (primary, secondary, tertiary, quaternary)

12. The Cell Cycle • Two processes must alternate during eukaryotic cell division • Genome must be replicated in S phase • Genome must be halved during M phase

14. Cell cycle events must be highly regulated in a temporal manner

15. Genetic and molecular studies in diverse biological systems have resulted in identification and characterization of the cell cycle machinery

16. Mitotic spindle Chiasmata DNA replication Dynamic instabilty Cell-cycle control Cdc mutants Maturation-promoting factor The restriction point Regulation of Cdc2 Yeast centromeres Cell-cycle conservation Cyclin characterization Replication origins Checkpoint control Retinoblastoma/E2F p53 Body-plan regulation The mitotic checkpoint A new class of cyclins The APC and proteolysis SCF and F-box proteins CDK inhibitors Sister-chromatid cohesion

18. P CDK substrate product cyclin ATP + ADP The cell cycle engines • Cyclin Dependent Kinases (CDKs)

19. Cyclin D-CDK4 Cyclin E-CDK2 Cyclin A-CDK2 Cyclin B-CDC2

20. CDK activity

21. asyn hours 0 4 8 12 14 16 20 24 28 32 cyclin A cyclin E Cdk2 Cyclin and CDK expression as cells re-enter the cell cycle G0 G1 S cell cycle phases

24. Cyclin D-CDK4 Cyclin E-CDK2 CDK inhibitors Cyclin A-CDK2 Cyclin B-CDC2

27. The Cell Cycle • Complex system • Components are identified • Highly regulated • Defined parameters

28. Cell Cycle Characteristics • Temporally ordered events • Irreversibility • Oscillations • Checkpoints • Positive and negative feedback loops

29. Positive Feedback Loop

30. 70kg human ~ 1013 cells

31. Complexity Overall properties not predictable from what is known about constituent parts

32. Reductionist-analytical strategies focus on component properties and actions, but do not necessarily describe dynamic behavior of the larger system.

33. The best test of our understanding of cells will be to make quantitative predictions about their behavior and test them. This will require detailed simulations of the biochemical processes taking place within cells… Hartwell, Hopfield, Leibler, and Murray

34. What’s the problem? • Cartoons are cartoons • They do not quantitatively describe the experimental data they summarize • Used in a loose qualitative manner • Informal, verbal • Not reliable for judging accuracy of mechanistic proposals

35. Can Mathematical Modeling Help? • Notion of mathematical modeling adding value to standard approaches • Help to formalize and predict behavior, suggest experiments • Bioessays 24, 2002.

36. Modeling the Cell Cycle • Start from a grocery list of parts • Break down large scale systems into smaller functional modules • Simulate steady states, oscillations, sharp transitions

37. Formulate interactions as precise molecular mechanisms. • Convert the mechanism into a set of nonlinear ordinary differential equations. • Study the solutions of the differential equations by numerical simulation. • Use bifurcation theory to uncover the dynamical principles of control systems.

38. Cells progressing through the cell cycle must commit irreversibly to mitosis.

39. Questions • What causes cyclin degradation to turn on and off periodically? • Why don’t rates of synthesis and degradation balance each other? • There must be some mechanism for switching irreversibly between phases of net cyclin synthesis and net cyclin degradation.

40. Models, models, everywhere • Many competing models because the degrees of freedom were unbounded. • Could occur by hysteresis (ie toggle-like switching behavior in a dynamical system). • Time delayed negative feedback loops.

41. vs

42. The Hysteresis Model of Novak and Tyson • Describes a network of interlocking positive and negative feedback loops controlling cell cycle progression. • Proposes a bistable switch is created by the positive feedback loops involving cyclin B-cdc2 and its regulatory proteins.

43. Hysteresis • It takes more of something to push a system from state A to B than it does to keep the system in B. • Creates a bistable system with a rachet to prevent slippage backwards. • Irreversibility was proposed to arise on transversing a hysteresis loop

44. Experimental System Need pic of xenopus • Using Xenopus egg extracts to demonstrate the cell cycle exhibits hysteresis • The amount of cyclin required to induce entry into mitosis is larger than the amount of cyclin needed to keep the extract in mitosis.

45. Steady state cdc2 kinase activity as a function of [cyclin] Black dots=experimental Gray dots=proposed Ti=inactivation threshold Ta=activation threshold

46. The hysteresis model made nonintuitive predications that were confirmed experimentally. • [cyclin B] to drive mitosis > [cyclin B] to stay in mitosis. • Unreplicated DNA elevates the cyclin B threshold for cdc2 activation; ie checkpoints enlarge the hysteresis loop. • Cdc2 activation slows down at cyclin B concentrations marginally above the threshold.

47. Mathematicians I have known

48. Cyclin D-CDK4 Cyclin E-CDK2 p27kip1 Cyclin A-CDK2 Cyclin B-CDC2

49. p27kip1 P CDK substrate CDK product cyclin cyclin ATP + ADP p27kip1 Inhibited Model of p27kip1 Function

50. Cyclin E-CDK2 can phosphorylate p27kip1