Modeling and Analysis of Gene Regulatory Networks - Modeling in Computational Biology and Biomedicine - page 73

a b

promotor AlgU mucA mucB mucC mucD

+

+

+ AlgU anti-AlgU

AlgU anti−AlgU

-

+

+

mucus

mucus
production

Fig. 2.13 Mucus production in Pseudomonas aeruginosa ( a ) The main regulatory genes ( b )A
possible interaction graph (identical to the one of Fig. 2.9 )

a

+2

0..2 0..1

anti-AlgU

b

AlgU

+1

(0,1) (1,1) (2,1)

-1

K AlgU ,∅ =0 K anti-AlgU ,∅ =0

(0,0) (1,0) (2,0)

K AlgU ,{ AlgU } =1 K anti-AlgU ,{ AlgU } =1

K AlgU ,{ anti-AlgU } =0
K AlgU ,{ AlgU , anti-AlgU } =2

Fig. 2.14 Modeling the mucus production in Pseudomonas aeruginosa ( a ) The interaction
graph of Fig. 2.13 together bounds, logical thresholds and logical parameters. ( b ) The resulting
asynchronous state graph. It satisfies the formulas ( 2.28 )and( 2.29 ). It has two attractors: a cyclic
attractor { (1 , 0) , (2 , 0) , (2 , 1) , (1 , 1) } in which mucus is regularly produced, and a stable state ( 0 , 0 )
in which mucus is not produced

the concentration level of AlgU is repeatedly equal to b AlgU . Thus this information
can be expressed in CTL as:

( l AlgU = b AlgU ) ⇒ AX ( AF ( l AlgU = b AlgU )) . (2.28)

Moreover we know that the wild bacteria never produces mucus by themselves when
starting from a basal state (second attractor):

( l AlgU =0) ⇒ AG ( l AlgU <b AlgU ) . (2.29)

Using SMB IO N ET , one shows that, among the 73 asynchronous state graphs
that can be built using the logical method, from the interaction graph of Fig. 2.13 ,
there are 17 asynchronous state graphs verifying the two previous formulas (one of
them is display in Fig. 2.14 ). Consequently, because the set of remaining models
is not empty, the epigenetic question receives a positive answer from the modeling
standpoint. This epigenetic question has not only an academic interest because this
prediction has been validated experimentally that could lead to new therapeutic
strategies.