PNNL-13501 - Pacific Northwest National Laboratory

determining the combinatorial state and transition
network invariants that characterize both the flow and
conditional regulation of information flow in the signaling
reaction network.
In addition, we will investigate the algebraic symmetries
of these nets in terms of a path algebra representation.
These algebraic representations will be used to identify
the existence of operational signal processing symmetry
group invariants in terms of process semiorder relations.
These symmetry invariants are shown to correspond to the
state and transition invariants and will be used to obtain
sets of optimal paths that indicate observably reachable
states with optimal molecular signaling bandwith. We
will also explore the use of incidence matrix
representations of circuits, and both path and relational
algebraic representations of network path configurations
to computationally establish the existence of hypergraph
isomorphisms between different signaling paths.
Additionally, we will explore the use of reverse Bayesian
inference (abductive inference) methods to identify and
define the characteristics of hidden states. We conjecture
that the multi-dimensionality of molecular
communications in a pathway can be modeled by using a
dimension-matched hierarchy of scale-invariant Petri nets.
Petri nets are stochastically extensible as an application
for modeling the microscopic reactive diffusive transport
kinetics of signal pathways within and between cells. We
will use the discrete (hidden) Markov nature of timed
stochastic Petri networks to discretely represent the
continuous Markov state transition models of diffusive
molecular transport systems. In turn, the associated sets
of state transition probability measures will be used to
define the molecular analogs of classical information
theory (as developed by Shannon and Weaver) that
underly the emerging theory of molecular
communications.
Coupled Rate Equations
Cell signaling is a complex phenomena, yet it is such a
fundamentally important part of cellular behavior that the
basic principles of cell signaling are the same in
essentially all organisms. The response of a cell to its
environment is governed by cell-signaling mechanisms.
Figure 1 illustrates a network of signaling pathways that
activate the mitogen-activated-protein kinase (MAPK) in
response to ligand binding to the epidermal-growth-factor
receptor (EGFR). Co-activation of phospholipase C-γ1
(PLCγ) modifies MAPK signal characteristics by
interaction between modules K and H mediated by protein
kinase C (PKC). A feedback loop connects H and K
through module E (cf. Figure 1). Figure 2 shows a Petri
118 FY 2000 Laboratory Directed Research and Development Annual Report
net representation of component A of the MAPKactivating
network.
F
PLC g
IPS
DAG
PKC
Ca K
E
AA
PLA 2
Ca DAG
EGFR
Figure 1. A network of signaling pathways associated with
MAPK activation
Even though kinetic data are sparse, Iyengar and
coworkers at the Mount Sinai School of Medicine
maintain a database of kinetic parameters for modules
found in well-studied pathways. Signaling networks, like
that shown in Figure 1, assembled from these modules
have emergent properties, like bistatic activation profiles,
that may be biologically significant. We will use Petri net
representations to evaluate the bistability of the network
shown in Figure 1.
Nonhomogeneous Kinetic Models
SHC
+
GRB
+
SOS
RAS
RAF
+
MEK
+
MAPK
1.2
Localization of reactants is an important mechanism by
which cells regulate signaling processes. In collaboration
with Professor Leslie Loew at the University of
Connecticut Health Center (UCHC), we are including
spatial inhomogeneity in kinetic models of signaling
pathways. We will expand the capabilities of the
problem-solving environment being developed in Dr.
Loew’s laboratory through links to NWGrid and
NWPhys, the Laboratory’s grid generation and physics
solver codes, respectively. More efficient computational
methods and extended functionality are required for the
applications of virtual cell technology that we envision.
For example, changes in cell morphology are often a part
of signaling dynamics. We are also applying spatial
inhomogeneous kinetic models in our collaboration with
A
Nucleus
H