A new mathematical framework for network analysis.

1. eLife, 2014
Pizza Club
20 April 2016
Gaia Zaffaroni

2. Some terminology
• GRN: gene regulatory network
• A network is composed of:
• Nodes, represent genes
• Edges, represent interactions, e.g. protein-protein
physical interaction, co-expression, transcriptional
regulation, …
• Topology: the structure of the network
• Robustness: is a complex property of the system
that makes it able to tolerate a wide variety of
perturbations (any change in the conditions)
maintaining its function

3. Motifs
Tran, N. H. et al. Counting motifs in the human interactome. Nat. Commun. 4:2241 doi:
10.1038/ncomms3241 (2013).

4. Introduction
• Interaction networks are a fundamental feature of
biological systems
• Biological networks are stable: they can recover their
equilibrium state after perturbation
• Selective pressure causes them to have specific
topologies
• Transcriptional networks:
• Nodes=genes and transcription factors
• Edges=transcriptional regulation
• Assumption: gene expression level corresponds to protein
activity level
•  these networks cannot capture post-transcriptional and
translational regulations

5. Real networks
• Collection of curated transcriptional networks
• Examples: E.coli, M.tuberculosis, P.aeruginosa,
S.cerevisiae, mouse and human

6. Hypothesis
• To be stable, the network should not depend on
the change of any of the individual quantitative
parameters
• protein concentration,
• affinity for a DNA sequence,
• promoter availability,
• rate of transcription
• It should also be stable to the addition of new links
• The robustness then should depend on qualitative
features of the network

7. Qualitative Stability
• The topology is stable even if the edge strength
changes
• Mathematical concept:
• Long feedback loops are negative for stability
• They are in general associated with oscillations, but in a
real system they can cause chaotic behavior

8. Presence of feedback loops

9. Presence of incomplete feedback
loops

10. TF regulation

11. Motifs

12. Illegal feedback loops
E. coli
There are 7 2-node feedback loops:
4 are into potentially instable motifs
3 can act as switches
These genes are related with drug
resistance and/or acid resistance
Similar configuration that can
display chaotic behavior

13. Cancer cells
K562 (Leukemia cell line)
GM12878 (non-cancer cell line)

14. Dynamic networks
Murine dentritic cells after stimulation with pathogens

15. Dynamic networks

16. Conclusions
• BQS allows to do new predictions based on the
robustness “criteria”
• It provides theoretical justification for observed
network features
• It helps in explaining the overall structure of GRNs
at different scales