A NEW ANNOTATION TOOL FOR MALARIA BASED ON INFERENCE OF - - PowerPoint PPT Presentation

A NEW ANNOTATION TOOL FOR MALARIA BASED ON INFERENCE OF PROBABILISTIC GENETIC NETWORKS

• J. Barrera1, R. M. Cesar Jr. 1, D. C. Martins Jr.1,
• E. F Merino2 , R. Z. N. Vêncio1 , F. G. Leonardi1,
• M. M. Yamamoto2, C. A. B. Pereira1, H. A. del Portillo2

UNIVERSITY OF SAO PAULO, BRAZIL 1- Institute of Mathematics and Statistics 2- Institute of Biomedical Sciences

Layout

• Introduction
• Probabilistic genetic

network (PGN)

• PGN design
• Data analysis pipeline
• Biological

interpretation

Introduction

Functional Classification

Sinusoidal signal Non Sinusoidal signal

Interaction Graph

glycolysis plastid genome

Probabilistic Genetic Network (PGN )

Network dynamics: State of the regulatory network at time t:

• =

] [ . . ] [ ] [ ] [

2 1

t x t x t x t x

n

} 1 , , 1 { ] [ + − ∈ t xi

]) [ ( ] 1 [ t x t x φ = +

Expression of gene i at time t:

φi

] 1 [ + t xi ] [t x j ] [t xk

• =

n

φ φ φ φ . . .

2 1

]) [ ( ] 1 [ t x t x

i i

φ = +

predictors target

Probabilistic Genetic Network (PGN)

φi

• −

− = + ]) [ ], [ | 1 ( 1 ]) [ ], [ | ( ]) [ ], [ | 1 ( 1 ] 1 [ t x t x p t x t x p t x t x p t x

k j k j k j i

] [t xj ] [t xk

]) [ ], [ | ( ]) [ ], [ | ( ]) [ ], [ | ( : }, 1 , , 1 { , , t x t x w p t x t x z p t x t x y p w z y w z y

k j k j k j

+ >> ≠ ≠ − ∈ ∃

• is characterized by the conditional probabilities

]) [ | ] 1 [ ( t x t x p

i

+

This system

• depends just on the previous time
• is time translation invariant
• is a conditionally independent Markov chain

∏

=

+ = +

n i i

t x t x p t x t x P

1

]) [ | ] 1 [ ( ]) [ | ] 1 [ (

PGN Design

PGN Design.

] 48 [ ],..., 2 [ ], 1 [ x x x

Target genes

Entropy

• −

∈

= → −

} 1 , , 1 {

1 ) ( ] 1 , [ } 1 , , 1 { :

y

y P P

Distribution of Y

• −

∈

− =

} 1 , , 1 {

) ( log ) ( ) (

y

y P y P Y H

Mutual information

) | ( ) ( ) , ( ≥ − = X Y H Y H Y X I

• 1

1 P(Y)

• 1

1 P(Y’)

) ' ( ) ( Y H Y H > ) ' ' ( ) ' ( Y H Y H =

• 1

1 P(Y’’)

Mean mutual information estimation

• ∧

∧ ∧ ∧

− = . )) | ( log( ) | ( ) ( )] | ( [ X Y P X Y P X P X Y H E

Mean conditional entropy

• −

= )) | ( log( ). | ( ) ( )] | ( [ X Y P X Y P X P X Y H E

Mean mutual information

]] | [ [ ) ( )] , ( [ X Y H E Y H Y X I E − = )] | ( [ ) ( )] , ( [ X Y H E Y H Y X I E

∧ ∧ ∧

− =

Estimation of P(Y|X) If #(X=(a,b)) ≥ n, then If #(X=(a,b)) < n, then is uniform

)) , ( | (

^

b a X Y P =

)) , ( ( # )) , ( ) (( # )) , ( | (

^

b a X b a X c Y b a X c Y P = = ∧ = = = =

Y: the taget gene at t+1, that is, X: the predictors at t, that is, ]) [ ], [ ( t x t x X

k j

= ] 1 [ + = t x Y

i

For a fixed parameter n

Estimation of P(X) for a fixed parameter n

X P(X)

If #(X=(a,b)) ≥ n, then If #(X=(a,b)) < n, then

]) [ ], [ ( t x t x X

k j

=

• ∀

< = −

= =

) , ( , )) , ( ( #

)) , ( ( #

b a n b a X

b a X N

• ∀

≥ = +

= =

) , ( , )) , ( ( #

)) , ( ( #

b a n b a X

b a X N | } )) , ( ( :# ) , {( | 3 1 )) , ( (

2 ^

n b a X b a N N N b a X P ≥ = − × + = =

+ − − + + − +

= × + = = N b a X N N N b a X P )) , ( ( # )) , ( (

^

• For each target gene, rank all predictors by their mean

estimated mutual information;

• Choose best predictors;
• Design the interaction graph

Building Interactions Graphs

Target gene Predictor genes

Data analysis pipeline

USP dataset determination USP dataset

Scaling and quantization

Quantized USP dataset

Design

• f

PGN

Target genes Plasmo DB Metabolic Pathways DeRisi´s transcriptome Table

• f

predictors GraphViz Functional groups Overview set Output graph

Biological Interpretation

Data analysis pipeline

GPR

USP-dataset

• directly from original .gpr “raw” data;
• intensity = foreground mean - background median;
• mean for replicated time points;
• different definition of “weak” spots and elimination rules;
• no interpolation used;
• consider ALL accepted oligos as unique entities (including

_almost sinusoidal). USP-dataset: 6532 oligos Overview dataset: 3719 oligos

Weak spots definition

X = (0, 0, ... , 100, 100, ... , 100, 0, 0, ... , 0, 0) <X> = 9 * 100 / 46 = 19.56 R = normalized cy5/cy3 = X/<X> = R = (0, 0, ... , 5.11, 5.11, ... , 5.11, 0, 0, ... , 0, 0) log2(R) = (-∞, -∞, ... , 1.63, 1.63, ..., 1.63, -∞, -∞, ... , -∞) Not amenable to Fourier analysis due to infinities.

Scaling

For each i, estimate the mean and standard desviation

]] [ [

^

t x E

i

]] [ [

^

t xi σ ]] [ [ ]] [ [ ] [

^ ^

t x t x E x t n

i i i i

σ − =

normal transform

Quantization

Let and denote, respectively, the normalized signals greater and lower than zero at t..

] [t ni

+

] [t ni

−

1 then ]], [ [ ] [ If then ]], [ [ ] [ and ]] [ [ ] [ If 1 then ]], [ [ ] [ If

^ ^ ^ ^

− = < = < > + = >

− − + + − − + +

[t] x t n E t n [t] x t n E t n t n E t n [t] x t n E t n

i i i i i i i i i i i

Output example

Plastid genome In Overview Organelar Translation machinery In Overview Unknown group In Overview Unknown group Not in Overview

In Overview Not in Overview

Back

Back

Back

Biological Interpretation

Glycolytic PGN network (single genes)

glycolysis transcription machinery cytoplasmic translation ribonucleotide synthesis deoxynucleotide synthesis DNA replication proteoasome plastid genome kinases actin myosoin motors mitochondrial

isomerase G3PDH 6 PFK mutase hexokinase Pyruvate kinase TP isomerase aldolase Pyruvate kinase PG kinase enolase

No TCA genes

550 apicoplast proteins 124 apicoplast proteins

Apicoplast PGN network (singlets)

glycolysis transcription machinery cytoplasmic translation ribonucleotide synthesis deoxynucleotide synthesis DNA replication proteoasome plastid genome kinases actin myosoin motors mitochondrial

Apicoplast PGN network (doublets)

glycolysis transcription machinery cytoplasmic translation ribonucleotide synthesis deoxynucleotide synthesis DNA replication proteoasome plastid genome kinases actin myosoin motors mitochondrial

466/ bipartite 124/phase PGN 676 Biological validation

• J. Barrera, R.M. Cesar Jr., C. P. Pereira, D. Martins,
• R. Z. Vencio, E. F. Merino, M. M. Yamamoto