1. Subnetwork State Functions Define Dysregulated Subnetworks in Cancer
Salim A. Chowdhury, Rod K. Nibbe, Mark R.Chance,
Mehmet Koyuturk
JCB 2011
Today I will present this paper that describe the CRANE algorithm.
This algorithm finds subnetworks that dysregulate metastatic cancer..

2. Previous Work
The objective of this work is to find out which of the cancer patient will have metastasis (me·tas·ta·sis).
The first work done in this area took the gene expression of patients with and without metastasis and try to predict the metastasis in new patients.
In this example non of the genes can differentiate the case and control.
Then researches notice that the gene that they used in the prediction tend to form “hot spots” in the PPI network.
So instead of using single genes as markers they looked on subnetworks.
And look on the average expression in the subnetwork.
To find these subnetworks they did an heuristic search over the network.
These methods improve the predictions.
You can see for example S1 – the average expression of genes in S1 can differentiate the case and control.
But there are more complicated situations – for example when the genes in the subnetwork affect the phenotype in an opposite direction.
Then the additive methods wouldn’t work.
Notice that the additive method doesn’t differentiate the case and control in S2.
But if we look real closely you can see that there is some pattern that differentiate case and control in S2.
When both g5 and g6 are high but g7 is low.
And when both g5 and g6 are low but g7 is high.
Notice that in this case a simple heuristic search would note yield
since it is hard to decompose the affect of a set to the affect of single genes.

3. Mutual Information Entropy H(X)
Mutual Information I(Y;X) = H(X)-H(X|Y)
high entropy
low entropy
Entropy is a measure of the disorder - uncertainty associated with a random variable.
Mutual Information is the amount of randomness in the random variable X given that you know the value of Y.
low mutual information
high mutual information

4. Dysregulation Measure
Mutual Information –
Dysregulation Measure C 1 1
C is the vector of phenotype 1 indicates metastasis and zero no metastasis.
For a single gene we calculate the mutual information between C and the gene expression.
This is a measure of how the gene dysregualte the phenotype.
For a subnetwork – the additive approach:
We calculate an average gene expression over the subnetwork E(S)
and calculate the mutual information between C and E(S).
And what KRANE dose:
First binarized the expression profile.
Then calculate the mutual information between C and the binarized expression.
This measure could be divided to different state-functions.
Each state function is a combination of binary expression profile.
For S2 we have 4 state functions.

5. Combinatorial Coordinate Dysregulation
State function is considered informative if:
There is no redundancy in the state function
for every

6. Pruning the search space
Where
As we mention before simple search heuristics just wont be good enough in our case.
On the other hand exhaustive search required exponential time.
To solve this problem KRANE prune the search space.
This is done using the following bound.
Notice that Jbound() is not J()
This result will help us decide if we would like to extend subnetwork S. If we will not extend S.

7. KRANE Algorithm S is extensible if1 1
We are give a subnetwork and a state function fs.
1. fs is informative if it has a large J value and there are no redundant genes in S.
Meaning that removing a gene from S will not increase the value of J.
2. S is extensible …
3. We extend S be adding one of the neighbors of the most recent gene we added to S.
4. From the possible extensions …
5. We will stop extending if …
S is extensible if
From the possible extension we choose to further check only b extensions with the top J() value.
Stop extending S if |S|>d.

8. Complexity Complexity is exponential in d.
To make sure we don’t miss subnetworks we should use
Using Jbound() we could prune the search space thus reducing running time without loosing results.
We will now illustrate the search space.

9. CRANE Runtime

10. Neural Network Classification
Rank the subnetwork according to I(FS;C) and take the top K ranked subnetworks that are not overlapping.
Use these Network as input for NN that predicts metastasis.
In this example we have two subnetworks.
Each subnetwork is an input to one neuron in the input layer.
All the neurons in the input layer are connected to one output neuron.

11. They used two data set of colon cancer that had information about liver metastasis.
One data set used for training and the other for testing.
Then they switch - so the second dataset used for training and the first for testing.

12. Effect of parameters
F-measure is an harmonic average of precision and recall.
Lets focus on the effect of parameter d (the maximum size of the subnetwork).
Notice that for d>3 performance decline.
This could be due to the fact that the number of state functions we examine grows exponentially with respect to d.
Therefore we have here a dimensionality problem.

13. Notice there is a very small overlap between the top subnetwork for d=6 d=7 and d=8.
There is almost no overlap.
This result with the results we saw in the previous slide tell us that d should be chosen very carefully.
And that we should be more suspicious with the results for larger d’s.
For d=6 look at the enriched processes – they are all related to the development of metastasis.

14. There are some processes that effect the development of metastasis:
Cell adhesion and motality, degradation of the extracellular matrix and chronic inflammation.
Here we look on a subnetwork that is tightly connected to these process
And could not be found using additive methods since some of its proteins are down-regulate will other are up-regulated in metastatic cancer.
This map was created based of one of the subnetworks that was found for d=6.
Additional curated interactions were added to the basic subnetwork.
Green lines represent activating interaction while red lines represent inhibitory interaction.
Let look on the gene SPP1 marked with orange circle.
Notice that SPP1 interact with a number of the integrin heterodimers to increase their activity.
(marked with orange stars)
Integrin heterodimers play a major role in mediating cell adhesion and cell motility.
SPP1 when binding to one of the Integrin heterodimers promotes the creation of new blood vessels.
Notice that SPP1 is up-regulated in metastasis samples.
Now lets look on MMP1 and MMP2 marked in a purple circle.
MMP proteins are involved in the breaking of extracellular matrix.
Manly collagen (marked with purple stars) that is know as a primary substrate for colon tumors.
MMP1 inhibits Vitronectin.
Therefore when MMP1 is downregulated in metastasis -> Vitronectin is active -> increase the activity of Integrin heterodimer.
MMP2 inhibits another Integrin heterodimers.
Therefore when MMP2 is downregulated in metastasis -> increase the activity of Integrin heterodimer.

15. Conclusion Advantages: Combinatorial dysregulation.
More sophisticated heuristics base on theoretical bound (“almost” exhaustive search).
Shortcomings:
Runtime is exponential in d so we could check only relatively small networks.
Even for small values of d we have dimensionality problems.
No post-processing that tries to merge subnetworks.
Dismissing of overlapping subnetworks.