1. Dynamical Modeling in Biology: a semiotic perspective Junior Barrera BIOINFO-USP

2. Layout Introduction Dynamical Systems System Families System Identification Genetic networks design Cell Cycle Modeling Discussion

3. Introduction

4. To describe feelings, we have poetry, music, painting,... To describe qualitative concepts, we have natural languages To describe quantitative and abstract concepts, we have mathematics To study a phenomena requires an adequate language

5. Dynamical Phenomenon: objects change state in time

6. Physics describes natural phenomena by mathematical laws The laws of Physics are validated by quantitative measures The experimentally validated laws are mathematical models of the phenomena The mathematical modeling of phenomena requires quantitative measures

7. molecule cell tissue organism Population Biological Phenomena are multi-scale, dynamical and, in many cases, measurable animation

8. Ecological System

9. The life cycle of the malaria parasite

10. Digestive System

11. Neuron The key unit of living beings for electric signal processing

12. Nobel Prize in Medicine 1963: Hodgkin - Huxley discoveries concerning the ionic mechanisms involved in excitation and inhibition of nerve cell membrane presented a mathematical model describing the dynamics of the action potential

16. n The equation derived from the circuit is: n Where g l is constant and g Na and g K are time and voltage dependent, represented by: animation

17. Molecular Biology

18. Knowledge evolution in genetics

19. Fundamental laws apply for all kinds of organisms Dynamical phenomena: protein and DNA interaction, gene networks, pathways Measurable variables: expression, protein signal, concentrations in biochemical reactions

20. Dynamical System

21. Graphical Interpretation

22. State Transition Graph x1x1 x2x2 x3x3 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 u1u1 u2u2 u1u1 u3u3  t  {  xi :L mN  L nN }  x1 (u 1 ) = x 2  t,j  {  xi,j :L mN  L }

23. x1= y1x1= y1 x 2 = y 2 t t initial state u u’ Final state Simulation

24. Example - architecture Graph representing the transition function components (  t,j ) states association

25. Example - dynamics

26. Example - simulation

27. System Families

28. Independent Subsystems If the system architecture has more than one connected component, it is composed of independent subsystems

29. Replication Crucial systems may be replicated for safety

30. Example 1: Liquid Level System Input valve control float Output valve Goal: Design the input valve control to maintain a constant height regardless of the setting of the output valve (height) (input flow ) (output flow ) (volume ) (resistance )

31. Feedback Control System Plant Controller  Disturbance Transducer + – Reference Value n(t) y(t) u(t) e(t) b(t) r(t) e(t) = r(t) - b(t)

32. Transient Response Characteristics plant Plant with controller

33. AB-Controlability Let A and B be subsets of possible states A LDS is AB-controlable if, for every a  A and b  B, there is a path in the transition graph from a to b.

34. x1x1 x2x2 x3x3 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 u1u1 u2u2 u1u1 u3u3 A B System AB-Controlable

35. N-Robustness A state r is N-robust if there is an unconditional path in the transition graph from every x such that d(r,x)  N.

36. Robust and no Robust States r x d(r,x)  2

37. System identification

38. S L S( ,  )

39. Stochastic Non Linear problem u and y are random processes S xo ( ,  )(u) is an estimator of y vector of functions each component function has a basis S opt ( ,  ) S( ,  ) S Er[S( ,  )(u), y]

40. Stochastic Linear Problem

42. Genetic Network Design

43. Cell peptide non peptide GENES NETWORK Translat.Transcr. Proteins Pool Pathways Metabolic

44. Cell peptide non peptide GENES NETWORK Translat.Transcr. Proteins Pool microarray Pathways Metabolic

45. Cell peptide non peptide GENES NETWORK Translat.Transcr. Proteins Pool microarray Pathways Metabolic proteomics

46. Hypothesis: the system is fault tolerant, that is, there is more than one system doing the same task.

49. System Sampling each line comes from one gene clustering

50. Designed by exhaustive simulations Controllable Robust Limit circle of size N

51. Proteome Transcriptome Genome Pathways  Wet Lab What genes regulate the pathway A->B->C->D ?

52. Cell Cycle Modeling

53. Tissue Cell-1Cell-2 Cell-3Cell-4 peptide non peptide

54. animation

55. Interphase Mitosis

56. Division Steps Cell Cycle Modeling u1 I u2 u5 v vfp w1 w2 w1fp w2fp w1f w2f x1 x6 y1 y2 z x1f x3f x4f x6f x6fp x1fp y1fp y2fp............ z Forward Signal Feedback to p Feedback to previous layer y1f y2f p

63. Robust Operational States operational state transition states

64. Division Steps Nockout u1 I u2 u5 v vfp w1 w2 w1fp w2fp w1f w2f x1 x6 y1 y2 z x1f x3f x4f x6f x6fp x1fp y1fp y2fp............ z Forward Signal Feedback to p Feedback to previous layer y1f y2f p

67. Discussion

68. Dynamical systems is an adequate language to express biological phenomena To discuss individual gene functionality does not make sense Gene functionality is the action of a set of genes working in concert, the genetic networks Challenge: design dynamical systems that mimic genetic networks In the future, functional data basis will store dynamical models. The research challenge will be to improve and integrate them.