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Connectivity and expression in protein networks :
Proteins in a complex are uniformly expressed
Shai Carmi1, Shlomo Havlin1, Erez Levanon2, Eli Eisenberg3
1 Minerva Center and the Department of Physics, Bar-Ilan University, Ramat-Gan, Israel ; 2 Compugen Ltd., Tel-Aviv, Israel ; 3 School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, Israel
Background
Numerical Results
Protein interaction networks
• The yeast Saccharomyces cerevisiae serves as the model
organism for most analyses of protein-protein interaction networks.
All
Synexpression
Gene
Fusion
HMS
# of proteins
2,617
260
293
670
# of interactions
11,855
372
358
1,958
Correlation
0.167
0.4
-0.079
0.164
P-Value
10-42
10-9
-
10-9
1.7·10-2
• Its complete set of genes and proteins and extensive data on
gene expression are available [1].
• In addition, large datasets of protein-protein interactions based
on a wide range of experimental methods are available [2].
• One can represent this data as a network where proteins are the
vertices, interactions are the edges, and expression levels are the
weights of vertices.
Model
Analysis of correlations between
concentrations of interacting proteins
Definitions
• 3 type of particles involved : A,B,C.
2-Hybrid Synthetic
2Lethality neighborhood
954
TAP
• Can form size-2 complexes AB,AC,BC and size-3 complex ABC (which is
the desired product).
Rules
• Total amount of each type is A0,B0,C0.
678
998
806
907
886
6,378
3,676
0.097
0.285
0.054
0.291
• Look at stationary solutions.
10-9
5·10-4
10-49
• Add conservation of material
equations.
• Can write reaction equations.
• Ignore 3-particle processes.
• Strongest correlation in synexpression (since those interactions are inferred from correlated
mRNA expressions).
• Assume constant ratio
between all association and
dissociation coefficients.
• Strong correlation in HMS (High-throughput Mass Spectroscopy) and TAP (Tandem Affinity
Purification) corresponding to physical interactions, i.e. experimental evidence that the
proteins bind together in-vivo).
• In a different way – A protein interacts on average with 0.49% of proteins with similar
concentrations as opposed to 0.36 ± 0.01% for random proteins.
Explore the solution
• Define the effectiveness of ABC production :
eff ≡ [ABC] / min(A0,B0,C0).
• Work in the regime where A0,B0,C0>> 1.
Hypothesis
The strong correlation is due to protein complexes.
Statistical analysis of protein networks
• The efficiency is maximized when the two more abundant components have
approximately the same concentration. See figure (eff plotted, for fixed C0 = 102)
Proteins in a complex have similar concentrations.
Picture remains the same when –
• Allowing for 2 different
association/dissociation ratios.
• Power-law degree distribution (Protein network is scale-free).
• Small world property (logarithmically small average distance).
Test hypothesis directly
• Robustness to random deletion of proteins.
• Study data set of protein complexes.
• Relation between degree and protein essentiality.
• Study 5-cliques (fully-connected subgraphs of 5 vertices, termed pentagons)
which are believed to be part of
complexes.
• Many more results…[3]
Two classes of interactions
• Transmission of information within the cell : protein A interacts
with protein B and changes it, by a conformational or chemical
transformation. Proteins usually dissociate shortly after the
completion of the transformation.
• Formation of a protein complex. In this mode of operation the
physical attachment of two or more proteins is needed in order to
allow for the biological activity of the combined complex. Typically
stable over longer time scales.
• Define the variance of the protein
concentrations as a measure of their
uniformity.
• Studying 4-components system.
• When fixing two components
(i.e. B0,C0), [ABC] has a maxima for a
finite A0. Adding more A’s will decrease
the number of product complexes.
(In the figure, B0=C0=103)
• Find that concentrations in complexes
are significantly uniform. (Figure =>)
• Easy to explain – When adding more
A’s, all B’s and C’s stick to A to form
many AB’s and AC’s
• Result robust when repeating the above
tests with mRNA expression levels.
• No free B’s and C’s are left, less ABC’s
can be produced. (See figure =>)
Conclusions
Some refs
[1] S. Ghaemmaghami et. al. , Nature 425, 737 (2003).
• Solution of a simple model shows that the efficiency of complex formation is maximized when all concentrations are roughly equal.
[2] C. von-Mering et. al. , Nature 417, 399 (2002).
• Tendency of members in a cellular protein complexes to have uniform concentration can be explained as a selection towards efficiency.
[3] A.L. Barabasi and Z.N. Oltavi, Nat. Rev. Genet. 5, 101 (2004).
• More details in http://arxiv.org/abs/q-bio/?0508021