Transcript Hybrid Functional Petri Nets to Model the Canonical Wnt Pathway

Hybrid Functional Petri Net
model of the Canonical Wnt
Pathway
Koh Yeow Nam, Geoffrey
Modeling the Wnt Signaling
Pathway
• The Wnt signaling pathway has been a focus of intense
research as it is one of the main pathways of both cell
growth/development as well as genetically linked diseases
such as human cancer.
• The more understood pathway that involves Wnt proteins
is known as the canonical Wnt pathway, and in this
pathway, the protein β-catenin plays an important part.
• However, in the recent years, other pathways that
involved the Wnt proteins are being discovered, including
those that control the aspects of gastrulation movements
etc. These pathways are collectively known as the noncanonical pathways.
Modeling the Wnt Signaling
Pathway
• Although the canonical pathway has been studied
extensively, quantitative studies are less common.
• Here we will attempt to recreate a model based on “The
roles of APC and Axin Derived from Experimental and
Theoretical Analysis of the Wnt Pathway” by Lee et al.
using a model known as a Hybrid Functional Petri Net,
which is a variant of the Petri Net model, used traditionally
to model computer, telecommunication systems etc.
Canonical Wnt Pathway
• The canonical Wnt pathway has three major components –
the extracellular Wnt protein, intracellular β-catenin and
the Glycogen Synthase Kinase 3β (GSK-3β)
• Although there are variations by different groups on the
exact details on how the components interact, the main
idea, however, remains the same
Canonical Wnt Pathway
• Wnt proteins are a secreted protein which trigger off cell
activities by first binding with a seven-membranespanning superfamily of cell surface receptors – Frizzled
(Fz)
• Recent evidence also suggests that co-receptors LRP5/6
are also required in binding of Wnt proteins
Note that for our model,
some of the other
components such as
the DKK and WIF-1 are
not added in as there is
not enough information
about them. However in
subsequent work, as
more and more
information are
obtained, they will be
added in
Canonical Wnt Pathway
• When the Wnt protein (or ligands in some text) binds to
the Fz receptors, it recruits the intracellular Dishevelled
Protein (Dsh) to the plasma membrane where it is
phosphorylated.
Canonical Wnt Pathway
• The degradation complex consist of the three proteins
GSK-3β, Axin and APC.
• Initially, GSK-3β will phosphorylate Axin and APC within the
complex.
• In this form, the degradation complex can bind to another
protein – β-catenin and phosphorylate it, marking it for
degradation by proteasomes (by ubiquitination).
Canonical Wnt Pathway
• Dsh regulates this degradation negatively by inhibiting the
phosphorylation of Axin and APC in the degradation
complex (Possibly by relocating the Axin from the
cytoplasm to the plasma membrane), preventing β-catenin
from binding to the degradation complex.
• β-catenin is an important component in this pathway as it
is a required co-factor in the expression of certain genes
that is needed in cell growth and development, such as
WISP1 – 3 family and the NOV gene. (Similarly,
uncontrolled action of β-catenin will lead to mass
expression of certain genes, leading to Cancer)
Canonical Wnt Pathway
•
β-catenin exists in the cytoplasm
(attached to cadherin, a protein
involved in cell adhesion) in the
unphosphorylated form
•
In the presence of the degradation
complex, it gets phosphorylated and
subsequently marked for
degradation by proteasomes
•
However, if it remains
unphosphorylated, it will get
translocated into the nucleus, where
it acts as a co-factor (together with
other factors like TCF/LEF) to
trigger off gene expression
Modeling the pathway
• In modeling the pathway, we use the Hybrid Functional
Petri Net, which is a variant of Petri net
• Like the Petri net, it has places and transitions but it has
continuous and discrete versions of it to capture discrete
events such as whether a gene is ‘on’ or ‘off’ as well as
continuous features such as protein concentrations
• Also, it has, in addition to the normal arc, test arcs and
inhibition arcs
Modeling the pathway
• The model that we are adopting from (with slight
modifications) is as below
Modeling the pathway
• The entire pathway
Simulation
• This model is then input into a commercial program – Cell
IllustratorTM by Gene Networks Inc
• Simulation is then conducted using that program
• [Demonstration]
Parameters
• One of the main concerns in any modeling endeavor is the
availability of parameters, such as initial constants,
association constants etc.
• For this modeling, most of the parameters were obtained
from the paper by Lee et al. but some had to be guesses
from the constants that are given or are obtained from the
Internet
Parameters
• The equation equivalent for the HFPN model is based on
the mass action law form of the kinetic model
Results
•
For the results, we are interested in the steady state values of the Wnt
pathway with and without Wnt protein stimulation (Dynamics will be
considered at a later stage)
Results
• Some of the results, (especially the ones with Wnt
stimulation) do not really correspond to the results given in
the paper.
• A possible reason is that the parameters are not
accurately captured (those missing parameters).
• Also the inability of the model to capture constraints can
be another factor in the inaccuracy.
• But still, we can see the potential of using such a model to
simulate bio-pathways such as the Wnt signaling pathway
Conclusions
• For this modeling exercise, we are trying to access the
suitability of using a model such as HFPN as well as to
see if we could generate any interesting results
• In terms of ease of modeling and visual appeal, the HFPN
is definitely superior to equation based modeling but
further work has to be established to handle other factors
such as its relationship with the already established
equation based laws such as the mass-action laws, rate
laws and power laws as well as to handle other factors
such as constraints and also the role genetic switches
play (in this example, the discrete portion the HFPN is not
exploited as we stop short just before gene expression)
Conclusions
• In future works, we will definitely look at some other
models as HFPN is just a starting platform. Possible
candidates include the Hybrid Automata, which is closer to
control theory and can capture constraints in a natural
way
• The long term goal is to develop a modeling framework in
which all pathways associated with Wnt signaling can be
handled in a uniform and integrated manner