Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
Decomposition of biological Decomposition of biological t kt knetworksnetworks
Alice Hubenko and Igor Mezić
Outline of the talk
Network topology and regulation
Giant Strong Component
Parametric sensitivity analysis can be usedParametric sensitivity analysis can be used
to identify dominating forward‐feedback structure of
the Giant Strong Component
Modeling a biological network
Each concentration is a state in the dynamical system
Elementary reaction
i
d
reaction rate constant
HVD decompositionHVD decomposition reveals the crude structure of "influence" in the network
Does not need the exact form of equations!
[1] I. Mezić, Coupled Nonlinear Dynamical Systems: Asymptotic Behavior and Uncertainty Propagation, 43rd IEEE Conference on Decision and Control December 14‐17,(2004).
HVD decomposition for biological networks
1. Identify Strong Components (SCs) of graph G.
2. Make the graph of strong components SC(G). Vertices of SC(G) correspond to strong components.
3. Place vertices of SC(G) with no out‐edges in the top level.
4. To form the next level: cut all the vertices that have been assigned to some level from SC(G) and find the vertices with no out‐edges in the resulting graph.
Problem: giant strong component
The dynamics of each component can only be affected by the ones below it
•Problem: Giant strong component
Cutting hubs reduces the size of the networkCutting hubs reduces the size of the network, but may can alter dynamical properties
[2] H. Ma and A. Zeng, Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms, Bioinformatics, 2003[3] S. Schuster et al., Exploring the pathway structure of metabolism: Decomposition into subnetworks and application to Mycoplasma pneumoniae, Bioinformatics,18, 2002
Decomposition of NFkB network
Identifying Minimal Production Unit
Dynamical system with 15 states and 29 parameters
HVD decomposition obtained by cycle search: a rather complicated procedure
[3] Y. Lan, I. Mezić, On the architecure of cell regulation networks , BMC systems biology
Modeling a biological networkParametric sensitivity analysis
Sensitivity coefficientParameters =reaction rate constants
steady state
Step function perturbationAbsolute value of sensitivity coefficient
ters
paramet
timeNFkB network
Modeling a biological networkParametric sensitivity analysis
Sensitivity metricsy
s
ity m
etrics
vity m
etrics
sensitiv
sensitiv
parametersparameters
Finding the forward structure
Sensitivity metrics
Parameters that affect within short time interval:Parameters that affect within short time interval:
States affected b these parametersStates affected by these parameters:
States in forward part obtained by using sensitivity metrics are identical to reduction obtained by
i f db k i l h i [3]removing feedbacks using cycle search in [3]
Finding the dominating feedbacks
P t th t ff t ithi l ti i t lParameters that affect within long time interval
R lti d i ti f db kResulting dominating feedbacks:
Conclusions
•Based on the idea that the forward part of the complex biological network is activates before the feedbacks take effect, we used parametric sensitivity analysis to identify the forward part of the network
•Parametric sensitivity analysis is a promising tool in finding dominant parts of complex biological networkscomplex biological networks
Thank you!Thank you!