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The two faces of network dynamics
Evolving network models describe the dynamics/assembly/evolution
of
networks by the addition/removal of nodes and edges.
It is possible to have network dynamics even if there are no
node/edge additions/removals, i.e. the network is fixed. This can be
called dynamics
on
the network.
In many networks node attributes can change in time or depending on
context. E.g.
•
the abundance of chemicals in a chemical reaction network
•
the health status of individuals in a disease contact network
For these networks it is not enough to specify the nodes and edges,
we also need to define a node
state
( e.g. a continuous variable, or a
discrete category).
Each node’s state is determined by the states of the nodes adjacent to
it (in directed networks the orientation of the edges should be toward
the regulated node).
Understanding the dynamics and function of
molecular/cellular networks
Cells are complex systems
•
functionally diverse elements
•
these elements’ abundances and activities change in time or
based on context
•
diverse interactions that form networks
•
signal transduction, gene regulatory, metabolic
•
have a function that needs to be performed
•
sense and respond to the environment
•
maintain homeostasis
•
need certain dynamical features
•
sensitive to some changes, insensitive/adaptable to others
•
robust to unwanted perturbations
•
What is the relationship between the topological features of
intracellular interaction networks and the dynamic behavior of
cells?
Toward network dynamics
Network topology needs to be complemented by a description of
network dynamics – states of the nodes and changes in the state
First step 
pseudodynamics
: propagation of activation in
interaction space, starting from a source (signal)
This can only be done in directed networks. In effect we use topological
analysis as a proxy for dynamic information on signal propagation.
Q: What topological properties should be studied and what dynamic
properties do they reflect?
Pseudodynamic signal propagation
Act., dist. 2
Act., dist. 4
Inh., dist 2
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Pseudodynamic effects of knockouts
Forward and reverse dynamic modeling
Dynamic modeling of interaction network:
Input:
components; interactions; states of components
Hypotheses:
interaction network; transfer functions; parameters
Output:
behavior of components in time
Validation:
capture known behavior
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 Fall '09
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