Design of PGNs for malaria parasite and cell cycle control systemsjb/lectures/genetic networks... · 2006. 3. 1. · • Cell cycle regulation • Design of PGN from data • Malaria

Design of PGNs for

malaria parasite and cell cycle

control systems

Junior Barrera

DCC-IME-USP / BIOINFO-USP

Layout

• Introduction

• Probabilistic genetic network (PGN)

• Cell cycle regulation

• Design of PGN from data

• Malaria parasite

GENES NETWORK

Translat.Transcr.

Proteins

Pool

Pathways

Metabolic

microarray

Regulatory System

Layout

• Introduction





GENE is aGENE is a

NON LINEAR STOCHASTIC GATENON LINEAR STOCHASTIC GATE

SYSTEM: SYSTEM: built by compiling these gatesbuilt by compiling these gates

Expression of a Gene Expression of a Gene depends ondepends on

Activator and Inhibitory SignalsActivator and Inhibitory Signals

Network dynamics:

State of the regulatory network at time t:

=

][

.

.

][

][

][

2

1

tx

tx

tx

tx

n

}1,0,1{][ +−∈txi

])[(]1[ txtx φ=+

Expression of gene i at time t:

φi ]1[ +txi

][tx j

][txk

=

nφ

φ

φ

φ

.

.

.

2

1

])[(]1[ txtx ii φ=+

target

predictors

Probabilistic Genetic Network (PGN)

φi

−−

=+

])[],[|1( 1

])[],[|0(0

])[],[|1(1

]1[

txtxp

txtxp

txtxp

tx

kj

kj

kj

i

][tx j

][txk

])[],[|(])[],[|(])[],[|(

:},1,0,1{,,

txtxwptxtxzptxtxyp

wzywzy

kjkjkj +>>

≠≠−∈∃

Layout

• Introduction





Phases of the Cell CyclePhases of the Cell Cycle

(*)

Model: architecture and dynamicsModel: architecture and dynamics

Transition Function

aij = ag green arrow from i to j

aij = ar red arrow from i to j

Simulation parameters: ag = -ar = 1

Li, 2004.

Time StepsTime Steps

One single pulse of One single pulse of CSCS = 2 at = 2 at t = t = --11DeterministicDeterministic

START

G1

S

G2

M

Stationary G1

0000--33

0000--22

0000--11

110000

111111

111122

111133

)1( +tS j0)( =tS j 1)( =tS j

∑j

jij Sa )0(

M MM

M M M

00

00

11

22

22

22

22

00

00

00

11

22

22

22

00

00

00

00

11

22

22

--33

--22

--11

00

11

22

33

)1( +ty j

0)( =tS j 1)( =tS j∑

j

jij Sa )0(

M MM

M M M

2)( =tS j

M

M

Binary 3 Levels (0, 1, 2)00

21 →→

00

00

11

22

22

22

22

00

00

00

11

22

22

22

00

00

00

00

11

22

22

--33

--22

--11

00

11

22

33

)1( +ty j

0)( =tS j 1)( =tS j∑

j

jij Sa )0(

M MM

M M M

2)( =tS j

M

M

=

=

=+

=+

005.0 with

005.0 with

99.0 with )1(

)1(

Pb

Pa

Pty

tx

i

i

{ } { })1(2,1,0, where +−∈ tyba i

Stochastic Transition Function

PGN with PGN with P = P = 0.99 0.99 One single pulse of One single pulse of CSCS = 2 at = 2 at t = t = --11


Total input signal driving a generic variable

: memory of the system

Driving functionDriving function forfor

: weight for variable at time

Our gene modelOur gene model

∑∑= =

−=N

j

m

k

j

k

jii ktxatd1 1

)()(

StochasticStochastic

TransitionTransition

FunctionFunction

Our gene modelOur gene model

<

≤≤

≥

=+

1

21

2

)(0

)(1

)(2

)1(

ii

iii

ii

i

thtdif

thtdthif

thtdif

ty

Our network architectureOur network architecture

G1 G1 phasephase S, G2 S, G2 andand M M phasesphases

time

Forward Forward signalsignal

Feedback to P Feedback to P

Feedback to Feedback to previousprevious

layerlayer

Trigger gene

F F : : integrationintegration ofof signalssignals fromfrom layerlayer ss

ss PP wwvv zzyyxxGene Gene LayersLayers

s1

I

s2

s5

ExternalExternal

stimulistimuli

F

P

v

w1

w2

x1

x6

y1

y2

z

.

.

.

.

.

.

One single pulse of One single pulse of FF = 2 at = 2 at t = t = --11


z

F

P

v

w1

x1

y1

PGN with PGN with P = P = 0.990.99

Signal Signal FF = period 50 oscillator= period 50 oscillator


z

F

P

v

w1

x1

y1




z

F

P

v

w1

x1

y1


Layout

• Introduction





Architecture

Identification.][],...,2[],1[ nxxx

target genes

Entropy

∑−∈

=

→−

}1,0,1{

1)(

]1,0[}1,0,1{:

y

yP

P

Distribution of Y

∑−∈

−=}1,0,1{

)(log)()(y

yPyPYH

Mutual information

0)|()(),( ≥−= XYHYHYXI

-1 0 1

P(Y)

-1 0 1

P(Y’)

)'()( YHYH > )''()'( YHYH =

-1 0 1

P(Y’’)

Mean mutual information estimation

∑ ∑∧∧∧∧

−= .))|(log()|()()]|([ XYPXYPXPXYHE

Mean conditional entropy

∑ ∑−= ))|(log().|()()]|([ XYPXYPXPXYHE

Mean mutual information

]]|[[)()],([ XYHEYHYXIE −=

)]|([)()],([ XYHEYHYXIE∧∧∧

−=

Estimation of P(Y|X)

If #(X=(a,b)) ≥ n, then

If #(X=(a,b)) < n, then is uniform)),(|(^

baXYP =

)),((#

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

^

baX

baXcYbaXcYP

=

=∧====

Y: the taget gene at t+1, that is,

X: the predictors at t, that is, ])[],[( txtxX kj=

]1[ += txY 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

])[],[( txtxX kj=

∑∀

- For each target gene, rank the couples of all genes by

_their estimated mutual information and sample size;

- When two mutual information are equal, the one

_estimated from a larger sample comes first;

- Choose the best couples;

- Design the interaction graph

Buiding Interaction Graphes

Layout

• Introduction





The life cycle of the malaria parasite

CAMDA, 2004

Malaria parasite genes with almost

sinusoidal signals

DeRisi, 2003.

Sinousoidal

signals

DeRisi, 2003.

Functional Classification

Malaria parasite genes

Sinousoidal

signals

Non sinousoidal

signals

Functional Classification

Interaction Graph

Glycolisis Apicoplast

System architecture

USP datasetdetermination

USP

dataset

Scaling

and

quantization

Quantized

USPdataset

Design

of

PGN

Target

genes

Plasmo DB

MetabolicPathways

DeRisi´s

transcriptomeTable

of

predictors

GraphViz

Functional

groups

Overview

set

Output

graph

Biological Interpretation

Good spots

Weak spots

Bad spots

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

1

.

.

.

6532

Genes

t

NO INTERPOLATION

System architecture


USP

dataset

Scaling

and

quantization

Quantized

USPdataset

Design

of

PGN

Target

genes

Plasmo DB

MetabolicPathways

DeRisi´s

transcriptomeTable

of

predictors

GraphViz

Functional

groups

Overview

set

Output

graph


Scaling

For each i, estimate the mean

and standard desviation

of the spots

]][[^

txE i

]][[^

txiσ

]][[

]][[][][

^

^

tx

txEtxtn

i

iii

σ

−=

Scale normalization of the spots

Quantization

Let and denote, respectively, the normalized

signals greater and lower than zero at t.

][tni+ ][tni

−

1 then ]],[[][ If

0 then ]],[[][ and ]][[][ If

1 then ]],[[][ If

^

^^

^

−=<

=≤≥

+=>

−−

++−−

++

[t]xtnEtn

[t]xtnEtntnEtn

[t]xtnEtn

iii

iiiii

iii

System architecture


USP

dataset

Scaling

and

quantization

Quantized

USPdataset

Design

of

PGN

Target

genes

Plasmo DB

MetabolicPathways

DeRisi´s

transcriptomeTable

of

predictors

GraphViz

Functional

groups

Overview

set

Output

graph


Architecture

Identification.]48[],...,2[],1[ xxx

target genes

System architecture


USP

dataset

Scaling

and

quantization

Quantized

USPdataset

Design

of

PGN

Target

genes

Plasmo DB

MetabolicPathways

DeRisi´s

transcriptomeTable

of

predictors

GraphViz

Functional

groups

Overview

set

Output

graph


Output example

Plastid genomeIn Overview

Organelar Translation machinery

In Overview

Unknown groupIn Overview

Unknown groupNot in Overview

In Overview

Not in Overview

J. Barrera, R.M. Cesar Jr., C. P. Pereira, D. Martins,

R. Z. Vencio, E. F. Merino, M. M. Yamamoto

www.bioinfo.usp.br

Documents

Design of PGNs for malaria parasite and cell cycle control systemsjb/lectures/genetic networks... · 2006. 3. 1. · • Cell cycle regulation • Design of PGN from data • Malaria