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Modeling & reconstruction of 

genetic networks

Tra Thi Vu, June 2004

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regulatory

system

construct &

revise models

model

comparison

predictions datasimulation experiment

reconstruction

regulatory

networks

biological

knowledge

The scheme

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Signaling network

mRNAs

proximal network

intracellular network

intercellular network

DNA

substrate

proteins protein kinases

and phosphatases

receptor 

proteinssignaling factor 

synthesizing enzymesand peptide hormones

trans

factors

The extended genetic network

Somogyi & Sniegoski 1996 

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Black box concept

?

input output

math. modeling

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 Artificial neural network

t0

t2 = t 1 + ¨2t

t1 = t 0 + ¨1t

...

the state of the network at time ti is defined by its state at time ti-1 and

connection weights wij between elements

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The nonlinear dynamic model

k1i, k2i: accumulation & degradation rate constants of gene product i

bi : external inputs act as reaction delay parameters

wij: level of regulatory influence of particular gene product j on gene i

ii

 j

i jij

ii  zk 

b ywk 

dt dz

21)](exp[1

1

!§

wi,1

7

y1y2

y3

bi

wi,2

wi,3

�

zi

V ohradsky, J. Faseb, 2001

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The inverse problem

 A B C 

 A 0 -10 0

B 15 0 -2

C  0 7 5

 A

B C

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using LMBP_NC algorithm to solve problem

� discretization: conversion of recurrent network into singlelayer network

� training network: training single layer network by LMBP (Levenberg-Marquardt Backpropagation) algorithm

� simulation test: simulation results of reconstructedweights Wre are compared to the original data profile in

actual error Ef , then accept or reject Wre

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� discretization

)(' t  yi

)())(()( 21 t  yk bt  y f  k t o iii j

 j

ijii ! §

),(t  yi )(t oi

)()( 't  yt  z ii !

ii

 j

i jijii  yk b y f  k 

dt 

dy21 )( ! § (1)

(2)

are inputs, outputswhere

(3)are targets

is computed by Lagrange¶s formula using

four of its neighbors _ a)2(),1(),1(),2( t  yt  yt  yt  y iiii

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� training network

o(t) := f(W,y(t)) Err = |z(t)-o(t)|

Wnew = Wold + ¨W

y(t) o(t)

z(t)

initial W0

u JW  I  JW  JW W i

T 

iii*]*[ 1!( Q

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� simulation test

simulation program

http://proteom.biomed.cas.cz/genexp

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Results

cII

cIpre cIprm

cro

N

cI

+

-

-

+

alternative pathways of the phage genetic network

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Conclusions

� the LMBP_NC algorithm can be used to reconstructsmall scale networks if there are enough data pointsavailable

� an advantage of the LMBP_NC algorithm is the ability to

overcome dependent parameter ¨t in comparing to other traditional methods which involve approximation of differential equations by difference equations

� applied interpolation in reasonable intervals for generating more data points is possible

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Further works

� alternative solutions for the inverse problem, then

comparing among algorithms

� evaluate estimated model parameters, thus identify

sensitivity of each parameter and then pruning network� search for experimental data from transcriptomics and

proteomics databases available for the model

reconstruction

� stochastic simulation of the phage model, then develop

the model that could involve both stochasticity and

continuousness (deterministic dynamics)