Formal Composition of Signaling Pathways
a Master thesis project proposal in Formal Methods
Eindhoven University of Technology (August 2009)
Signaling pathways or signal transduction cascades are a common type of
dynamics in the living cell. A signal from outside of the cell is caught by a
receptor in the membrane which switches to its active form. in turn, certain
proteins that ﬂoat around in the cytosol can be activated by the inner side
of the receptor. Next, the protein in its activated form may activate yet
another protein, etc. The mechanism allows the cell to properly react to
stimuli from its environment by ﬁltering and ampliﬁcation of the incoming
In the ﬁgure, on the left, a signal L activates the receptor R. The
receptor changes state from R (inactivated) to R∗ (activated). Now, R∗
catalyzes the transformation of protein A to its form A∗ . Then, A∗ catalyzes
the transformation of the protein B to its form B ∗ . From a quantitative
perspective one may want to compute the signal ﬂow for B ∗ . I.e., given
the arrival rate λ for the signal L, the kinetic rate r, ra and rb for the
reaction R → R∗ , A → A∗ and B → B ∗ , respectively, what is the resulting
production of the target protein B ∗ for this cascade?
Figure 1: Cross-talk between two signaling pathways.
Interaction between signaling pathways, so-called cross-talk, is a frequently
occurring phenomenon. The left cascade in the ﬁgure, the one from R to B ∗ ,
inﬂuences the right cascade, the one from S to D∗ . The red inhibition arrow
from A∗ to the arrow for the transformation of C into C ∗ indicates that the
presence of A∗ has a negative eﬀect on the production of C ∗ . The inhibition
arrow constitutes a cross-link between the two pathways. One can imagine
that such is captured by the expression
(R, λ, r); (A, ra ); (B, rb ) [ −,A,C ] (S, µ, s); (C, rc ); (D, rd )
a left cascade of a top layer and two following ones, a similar right cascade
where (the output of) the A-layer on the left inhibits (the reaction of) the
C-layer on the right. The quantitative question becomes, what is the signal
ﬂow for the right pathway given its composition with the left one? In this
concrete example we have single link cross-talk, but multiple link cross-talks
between various cascade are possible too.
The aim of this Master project is to deﬁne a general framework for the
composition of signaling cascades. For this, either an existing process based
modeling language such as SPiM or Bio-PEPA can be used, or an own
special-purpose description language can be developed. Both qualitative
and quantitative properties about cascade composition will be identiﬁed
and proved. Validation of the framework against existing example signaling
pathway from the biological literature using tool support for the framework
completes the project.
Further information can be obtained from Dr. E.P. de Vink, firstname.lastname@example.org,
HG 7.32. The references mentioned are available from the TU/e library or
can be sent on request.
Calder, M., Vyshemirsky, V., Orton, R., Gilbert, D.: Analysis of signalling
pathways using continuous time Markov chains. Transactions on Computa-
tional Systems Biology VI 4220 (2006), 44–67.
Fisher, J., Piterman, N., Hajnal, A., Henzinger, T.A.: Predictive Modeling
of Signaling Crosstalk during C. elegans Vulval Development. PLoS Com-
putational Biology 3(5) (May 2007) e92ﬀ
Heiner, M., Koch, I., Will, J.: Model validation of biological pathways using
Petri nets demonstrated for apoptosis. Journal BioSystems 75 (2004) 15–28
Sreenath, S.N., Soebiyanto, R., Mesarovic, M.D., Wolkenhauer, O.: Coor-
dination of crosstalk between MAPK-Pkc pathways: an exploratory study.
Systems Biology, IET 1 (2007) 33–40