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

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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 Population Biological Phenomena are multi-scale, dynamical and, in many cases, measurable organism tissue molecule cell 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 The equation derived from the circuit is: 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 x 2 u 1 u2 x 3 u 1 u 3 x 4 x 5 φ t {φ xi :L mn L nn } φ x1 (u 1 ) = x 2 φ t,j {φ xi,j :L mn L } x 3 x 1 x 6 x 7 x 8

23 Simulation initial state x 2 = y 2 t t u u Final state Final state x 1 = y 1

24 Example - architecture Graph representing the transition function components (φ 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 flow) q i Input valve control Goal: Design the input valve control to maintain a constant height regardless of the setting of the output valve float (height) H (resistance) V (volume) Output valve (output flow) q o

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

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 System AB-Controlable x 3 B x 2 u 1 u2 u 3 u 1 x 4 x 5 x 3 x 1 x 6 x 7 x 8 A

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 d(r,x) 2 x

37 System identification

38 S L S(ϕ,ψ)

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

40 Stochastic Linear Problem Model Structure y( t) = ay( t 1) + bu( t 1) + e( t) Given: { u( 1), y( 1)},{ u( 2), y( 2)},...,{ u( N), y( N)} To determine: a and b Prediction y$( t) = ay( t 1) + bu( t 1)

41 Prediction Error y( t) y$( t) = y( t) ay( t 1) bu( t 1) Cost Function Results N J( a, b) = { y( t) ay( t 1) bu( t 1)} a$ b$ = t= 2 ( T Φ Φ) 1 Φ T y( 2) y( 3)... y( N) y( 1) u( 1) y( ) u( ) = 2 2 Φ... y( N 1) u( N 1) 2 for y( t) = ay( t 1) + bu( t 1) + e( t)

42 Genetic Network Design

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

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

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

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

47 6 4 time course data C1 C2 C3 2 log2(ratio) time

49 System Sampling each line comes from one gene clustering

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

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

52 Cell Cycle Modeling

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

54 animation

55 Interphase Mitosis

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

63 Robust Operational States transition states operational state

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

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.

69 Objected oriented database P1 P2 Pn Pi : analytical and mining procedures (kernel parallel)

70 GRID Computer - DCC-IME-USP Internet and Intranet E4000 E4000:Databases and web application services (by SEFAZ) 10 processors 16 G-bytes main memory 1 T-bytes disk Processing services E3500 V880 V880?... (by CAGE-FAPESP) 4 processors 8 gigabytes (by Malaria-FAPESP) 16 processors 32 G-bytes (by eucalipto-cnpq???) 16 processors 32 G-bytes

Molecular Biology: from sequence analysis to signal processing. University of Sao Paulo. Junior Barrera

Molecular Biology: from sequence analysis to signal processing Junior Barrera University of Sao Paulo Layout Introduction Knowledge evolution in Genetics Data acquisition Data Analysis A system for genetic