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International Conference on Complex Systems (ICCS2006)

Topological properties of networks and phenotypic stability

Julio Cesar Monte
Medicine Dept, Federal University of Sao Paulo

Min Liu
Physics Dept, University of Houston

     Full text: Not available
     Last modified: January 30, 2006

Abstract
Topological properties of networks and phenotypic stability

Julio Monte1 and Min Liu2
1Federal University of Sao Paulo (UNIFESP), Nephrology Division, Sao Paulo, Brazil
2Physics Department, University of Houston, Houston, USA


Robustness is the ability that biological systems have to maintain phenotypic stability in face of diverse perturbations. Mutation of genes, important in terminal differentiation of the kidney, results in abnormal phenotype. Recent results on the topology of real biological networks indicate that biological network follows a power-law degree distribution (scale free). Under the assumption that living cells can be modeled as non-linear dynamics system, cell types can be idealized as attractors. Here, we investigate how topology changes affect the dynamical properties of the scale-free model. To address why we have less robustness at later differentiation of the kidney when a few cell types must give arise to many, we hypothesized that for a few cell types differentiate in several different cell types, the network must have some freedom of choice among so many possibilities (attractors). The trade-off for that is the decrease of the stability. Less robustness is a consequence of this balance. Using an in-degree scale free network (N= 20) we analyzed the dynamics of the network at different values of scale free exponent γ, γ=2.6 and γ=1.5. Our analysis shows that starting at lower scale free exponent (γ=1.5) two different initial states reach different attractors both after a pretty long transient time. It may indicate that the system stays in the chaotic phase. In contrast, with the same two initial states as above, but at γ=2.6, systems converge to one attractor after a shorter transient time indicating an order phase somehow. The simulation results match well the scale-free Boolean network phase diagram analytically derived by Aldana recently. Furthermore, our analysis suggests that dynamic topological changes at the same network could explain different levels of resilience during biological process.


1.Aldana M, Cluzel P. A natural class of robust networks. Proc Natl Acad Sci U S A. 2003 Jul 22;100(15):8710-4
2.Aladana M. Boolean dynamics of networks with scale-free topology. Physica D 185 (2003) 45-66
3.Sampogna RV, Nigam SK Implications of gene networks for understanding resilience and vulnerability in the kidney branching program. Physiology (Bethesda). 2004 Dec;19:339-47. Review




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