Post on 19-Dec-2015
A Real-life Application of
Barabasi’s Scale-Free
Power-LawPresentation for ENGS 112
Doug Madory
Wed, 1 JUN 05
Fri, 27 MAY 05
Background
Common property of many large networks is vertex connectivities follow a scale-free power-law distribution.
Consequence of two generic mechanisms:
(i) networks expand continuously by the addition of new vertices, and
(ii) new vertices attach preferentially to sites that are already well connected.
So what?
The objective of network theory is not network diagrams, but insight!
Application of Barabasi’s theory to bioinformatics has produced several significant biological discoveries
Determining Roles of Proteins Within Metabolism
Proteins are traditionally identified on the basis of their individual actions
Modern research is trying to determine contextual or cellular function of proteinsRequires analysis of 1000’s of simultaneous
protein-protein interactions – unworkable!Must analyze as a complex network
Protein-Protein Interaction
Map of protein-protein interactions forms a scale-free power-law network Few highly-connected proteins play central role in
mediating interactions among numerous, less connected proteins
Consequence is tolerance to random errors Removal of highly-connected proteins rapidly increases
network diameter computationally
Highly-Connected Proteins
When highly-connected proteins are removed in order of connectivity, mortality of cell increases Highly-connected proteins paramount to survival 93% of proteins have <5 links, 21% essential 0.7% of proteins have >15 links, 62% essential
Conversely when proteins are removed at random, effect is negligible
More Characteristics of Highly-Connected Proteins
Most hub proteins same across species 4% of all proteins were found in all organisms of
experiment These were also the most highly connected proteins
Species-specific differences expressed in least connected proteins
Small-World in Organisms
Connectivity characterized by network diameter Shortest biochemical pathway averaged over all pairs
of substrates
For all known non-biological networks average node connectivity is fixed Implies increased diameter as new nodes added Therefore more complex organisms should have
greater network diameters – but they don’t!!!
Conservation of Diameter All metabolic networks share
same diameter! As organism complexity
increases individual proteins are increasingly connected to maintain constant metabolic network diameter
Larger diameter would attenuate organism’s ability to respond efficiently to external changes
Conservation of Diameter
Minitab analysis of Barabasi’s data for diameter
3.53.43.33.23.13.0
Median
Mean
3.323.303.283.263.243.223.20
Anderson-Darling Normality Test
Variance 0.0151Skewness 0.104338Kurtosis -0.311452N 43
Minimum 3.0000
A-Squared
1st Quartile 3.2000Median 3.30003rd Quartile 3.4000Maximum 3.5000
95% Confidence I nterval for Mean
3.2528
1.48
3.3286
95% Confidence I nterval for Median
3.2000 3.3000
95% Confidence I nterval for StDev
0.1015 0.1564
P-Value < 0.005
Mean 3.2907StDev 0.1231
95% Confidence I ntervals
Summary for Diameter
Conservation of Gamma All metabolic networks
share power-law a. A. Fulgidus (archae) b. E. coli (bacterium) c. C. Elegans (eukaryote) d. All 43 organisms (avg)
for all life about 2.2
Conservation of
Minitab analysis of Barabasi’s data for
2.42.32.22.12.0
Median
Mean
2.202.192.182.172.16
Anderson-Darling Normality Test
Variance 0.0080Skewness 0.024458Kurtosis 0.234872N 86
Minimum 2.0000
A-Squared
1st Quartile 2.1000Median 2.20003rd Quartile 2.2000Maximum 2.4000
95% Confidence Interval for Mean
2.1646
4.99
2.2029
95% Confidence Interval for Median
2.2000 2.2000
95% Confidence Interval for StDev
0.0776 0.1050
P-Value < 0.005
Mean 2.1837StDev 0.0893
95% Confidence I ntervals
Summary for g
Conclusions Barabasi’s network theory offers insights into
metabolic networks in cellular biology Correlation between connectivity and
indispensability of a protein confirms that robustness against lethal mutations is derived from organization of protein interactions
Metabolic networks within all living things have almost same diameter and