Differential network entropy reveals cancer system hallmarks 01-21-2014d2303

2015-01-13

UCL Cancer Institute University College London
Centre for Mathematics and Physics in the Life Sciences and Experimenal Biology, University College London
Department of Physics, Northeastern University, Boston, Massachusetts
2012

location
"C:\Users\kurtw_000\Box Sync\DocDR\2014\1-21-14\Differential network entropy reveals cancer system hallmarks.pdf"
http://www.nature.com/srep/2012/121113/srep00802/full/srep00802.html

Abstract
The cellular phenotype is described by a complex network of molecular interactions. Elucidating network properties that distinguish disease from the healthy cellular state is therefore of critical importance for gaining systems-level insights into disease mechanisms and ultimately for developing improved therapies. By integrating gene expression data with a protein interaction network we here demonstrate that cancer cells are characterised by an increase in network entropy. In addition, we formally demonstrate that gene expression differences between normal and cancer tissue are anticorrelated with local network entropy changes, thus providing a systemic link between gene expression changes at the nodes and their local correlation patterns. In particular, we find that genes which drive cell-proliferation in cancer cells and which often encode oncogenes are associated with reductions in network entropy. These findings may have potential implications for identifying novel drug targets.

Sentence in dissertation
-In another study, researchers discovered that the entropy of a random walk on the protein interaction network graph was higher in cancer cells than normal cells in all of the 6 different cancer tissue types investigated

Comment
What the authors do here looks interesting and useful, but I don't think it is what I am most interested in because they keep the topology of the network (based on protein interaction data) the same for all samples and just change the weights (based on gene expression data).  Then they measure the entropy of a random walk on these different networks with the same topology but different weights.  I am most interested in what types of changes occur in the topology between healthy and disease systems.  I suppose one could apply a threshold to the weights in the network to obtain changes in topology.  However, what type of network would have the lowest entropy for a random walk?  The answer would be a network that formed a circle.  If you took a random walk with a certain number of steps from any node, you would always land on one of two nodes a certain number of steps from the chosen node resulting in a low entropy.  Since a circle is not a scale-free small-world network, the entropy of a random walk is not the metric I have been searching for. .

placemark (I have not finished looking through this paper)
Differential network entropy and differential expression are anti-correlated.

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By integrating gene expression data with a protein interaction network we here demonstrate that cancer cells
are characterised by an increase in network entropy

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we find that genes which drive cell-proliferation in cancer cells and which
often encode oncogenes are associated with reductions in network entropy

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In this work, we explore the role of network entropy in cancer, with the weights reflecting correlations in gene
expression and normalized to define a random walk on a protein interaction network.

some interesting referenced papers
- Regulation patterns in signaling
networks of cancer
- Statistical analysis of the cancer cell’s
molecular entropy using high-throughput data

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a fluctuation theorem of dynamical systems theory 9 which
asserts that the macroscopic resilience of a system, R, is correlated to the level of uncertainty or entropy
(disorder), S, of the underlying microsopic dynamical processes that take place within that system.

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 demonstrates that network entropy can predict a gene
property, i.e essentiality, which determines the system’s robustness under knock-down of the respective gene

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 the dynamics
we consider refers to the random walk generated by a stochastic matrix on the network

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therefore the dynamics is not entirely specified by the network topo-
logy. In fact, we assume that the network topology is unchanged
between the normal and cancer phenotypes, but allow the dynamics,
defining the weights in the network, to be dependent on the pheno-
type.

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Equivalently, we view the protein interaction network as pro-
viding only a backbone topological structure as to which interactions
are allowed, and use the phenotype-specific gene expression data
(and specifically, the correlations in gene expression over the disease
phenotype) to modulate and approximate the interaction probabil-
ities. Using this perspective, cancer cells differ from normal cells due
to differential weights on the same underlying network.

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cancer is characterized by an increase in
network entropy

entropy-robustness theorem

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 We
previously showed that primary breast cancers that metastasize
exhibit an increased network entropy compared to breast cancers
that do not spread 6 .

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The network entropy of a node i was defined by. . .

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clearly confirmed that cancer is characterised by an increased net-
work entropy

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We also observed that the magnitude of differential entropy
change was strongly anti-correlated to node degree

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 diffusion equation over the
network allowing for paths of maximum length 2

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