Propagation of perturbations

in protein binding networks

Sergei MaslovBrookhaven National Laboratory

Experimental interaction data are binary instead of graded it is natural to study topology

Very heterogeneous number of binding partners (degree)

One large cluster containing ~80% proteins

Perturbations were analyzed from purely topological standpoint

Ultimately one want to quantify the equilibrium and dynamics: time to go beyond topology!

Law of Mass Action equilibrium

dDAB/dt = r(on)AB FA FB – r(off)

AB DAB

In equilibrium DAB=FA FB/KAB where the dissociation constant KAB= r(off)

AB/ r(on)AB

has units of concentration Total concentration = free concentration

+ bound concentration CA= FA+FA

FB/KAB FA=CA/(1+FB/KAB) In a network Fi=Ci/(1+neighbors j Fj/Kij) Can be numerically solved by iterations

What is needed to model? A reliable network of reversible (non-catalytic)

protein-protein binding interactions CHECK! e.g. physical interactions between yeast

proteins in the BIOGRID database with 2 or more citations. Most are reversible: e.g. only 5% involve a kinase

Total concentrations Ci and sub-cellular localizations of all proteins CHECK! genome-wide data for yeast in 3 Nature papers

(2003, 2003, 2006) by the group of J. Weissman @ UCSF. VERY BROAD distribution: Ci ranges between 50 and 106

molecules/cell Left us with 1700 yeast proteins and ~5000 interactions

in vivo dissociation constants Kij OOPS! . High throughput experimental techniques are

not there yet

Let’s hope it doesn’t matter

The overall binding strength from the PINT database: <1/Kij>=1/(5nM). In yeast: 1nM ~ 34 molecules/cell

Simple-minded assignment Kij=const=10nM(also tried 1nM, 100nM and 1000nM)

Evolutionary-motivated assignment:Kij=max(Ci,Cj)/20: Kij is only as small as needed to ensure binding given Ci and Cj

All assignments of a given average strength give ROUGHLY THE SAME RESULTS

Robustness with respect to assignment of Kij

Spearman rank correlation: 0.89

Pearson linear correlation: 0.98

Bound concentrations: Dij

Spearman rank correlation: 0.89

Pearson linear correlation: 0.997

Free concentrations: Fi

Numerical study of propagation of perturbations

We simulate a twofold increase of the abundance C0 of just one protein

Proteins with equilibrium free concentrations Fi changing by >20% are significantly perturbed

We refer to such proteins i as concentration-coupled to the protein 0

Look for cascading perturbations

Resistor network analogy Conductivities ij – dimer (bound)

concentrations Dij

Losses to the ground iG – free (unbound)

concentrations Fi

Electric potentials – relative changes in free concentrations (-1)L Fi/Fi

Injected current – initial perturbation C0

SM, K. Sneppen, I. Ispolatov, arxiv.org/abs/q-bio.MN/0611026;

What did we learn from this mapping?

The magnitude of perturbations` exponentially decay with the network distance (current is divided over exponentially many links)

Perturbations tend to propagate along highly abundant heterodimers (large ij )

Fi/Ci has to be low to avoid “losses to the ground”

Perturbations flow down the gradient of Ci

Odd-length loops dampen the perturbations by confusing (-1)L Fi/Fi

Exponential decay of perturbations

O – realS - reshuffledD – best propagation

SM, I. Ispolatov, PNAS in press (2007)

HHT1

What conditionsmake some

long chains good conduits

for propagation of concentration perturbations

while suppressing it along side branches?

Perturbations propagate along dimers with large concentrations

They cascade down the concentration gradient and thus directional

Free concentrations of intermediate proteins are lowSM, I. Ispolatov, PNAS in press (2007)

Implications of our results

Cross-talk via small-world topology is suppressed, but… Good news: on average perturbations via

reversible binding rapidly decay Still, the absolute number of

concentration-coupled proteins is large In response to external stimuli levels of

several proteins could be shifted. Cascading changes from these perturbations could either cancel or magnify each other.

Our results could be used to extend the list of perturbed proteins measured e.g. in microarray experiments

Genetic interactions Propagation of concentration

perturbations is behind many genetic interactions e.g. of the “dosage rescue” type

We found putative “rescued” proteins for 136 out of 772 such pairs (18% of the total, P-value 10-

216)

SM, I. Ispolatov, PNAS in press (2007)

SM, I. Ispolatov, PNAS in press (2007)

Intra-cellular noise Noise is measured for total concentrations

Ci (Newman et al. Nature (2006)) Needs to be converted in biologically

relevant bound (Dij) or free (Fi) concentrations

Different results for intrinsic and extrinsic noise

Intrinsic noise could be amplified (sometimes as much as 30 times!)

Could it be used for regulation and signaling?

3-step chains exist in bacteria: anti-anti-sigma-factors anti-sigma-factors sigma-factors RNA polymerase

Many proteins we find at the receiving end of our long chains are global regulators (protein degradation by ubiquitination, global transcriptional control, RNA degradation, etc.) Other (catalytic) mechanisms spread perturbations

even further Feedback control of the overall protein

abundance?

Future work

KineticsNon-specific vs specific How quickly the equilibrium is

approached and restored? Dynamical aspects of noise

How specific interactions peacefully coexist with many non-specific ones

Kim Sneppen NBI, Denmark

Iaroslav IspolatovResearch scientistAriadne Genomics

THE END

S. cerevisiae curated PPI network used in our study

Genome-wide protein binding networks

Nodes - proteins Edges - protein-

protein bindings Experimental data

are binary while real interactions are graded one deals only with topology

Going beyond topology and modeling the binding

equilibrium and propagation of perturbations

SM, K. Sneppen, I. Ispolatov, arxiv.org/abs/q-bio.MN/0611026; SM, I. Ispolatov, PNAS in press (2007)

100

101

102

103

104

105

10610

0

101

102

103

104

concentration (molecules/cell)

hist

ogra

mKij=max(Ci,Cj)/20

total concentration Ci

bound concentrations Dij

free concentration Fi

Indiscriminate cross-talk is suppressed

What did we learn from topology?

1. Broad distribution of the degree K of individual nodes

2. Degree-degree correlations and high clustering

3. Small-world-property: most proteins are in the same cluster and are separated by a short distance (follows from 1. for <K2>/<K> > 2 )

Protein binding networkshave small-world property

Large-scale Y2H experiment

86% of proteins could be connected

Curated dataset used in our study

83% in this plot

S. cerevisiae

Why small-world matters? Claims of “robustness” of this network

architecture come from studies of the Internet where breaking up the network is undesirable

For PPI networks it is the OPPOSITE: interconnected pathways are prone to undesirable cross-talk

In a small-world network equilibrium concentrations of all proteins in the same component are coupled to each other

2

1

3

mRNA polyadenylation;

protein sumoylation

unfolded protein binding

G2/M transition of cell cycle

mRNA, protein, rRNA export from

nucleus

RNA polymerase I, III

RNA polymeras

e II

35S primary transcript processing

protein phosphatase type 2A

HSP82 SSA1 KAP95 NUP60 : -1.13 SSA2 HSP82 SSA1 KAP95: -1.51 HSC82 CPR6 RPD3 SAP30: -1.20 SSA2 HSP82 SSA1 MTR10: -1.57

CDC55 PPH21 SDF1 PPH3: -2.42 CDC55 PPH21 SDF1 SAP4: -2.42 PPH22 SDF1 PPH21 RTS1: -1.18

Propagation to 3rd neighbors

CDC55| 2155 | 8600 | 1461 | protein biosynthesis* | protein phosphatase type 2A activity | CPR6| 4042 | 18600 | 114 | protein folding | unfolded protein binding* | HSC82| 4635 | 132000 | 4961 | telomere maintenance* | unfolded protein binding* | HSP82| 6014 | 445000 | 115 | response to stress* | unfolded protein binding* | KAP95| 4176 | 51700 | 41 | protein import into nucleus | protein carrier activity | MTR10| 5535 | 6340 | 6 | protein import into nucleus* | nuclear localization sequence binding | NUP60| 102 | 4590 | 1693 | telomere maintenance* | structural constituent of nuclear pore | PPH21| 874 | 5620 | 95 | protein biosynthesis* | protein phosphatase type 2A activity | PPH22| 930 | 4110 | 72 | protein biosynthesis* | protein phosphatase type 2A activity | PPH3| 1069 | 2840 | 200 | protein amino acid dephosphorylation* | protein phosphatase type 2A activity | RPD3| 5114 | 3850 | 269 | chromatin silencing at telomere* | histone deacetylase activity | RTS1| 5389 | 300 | 80 | protein biosynthesis* | protein phosphatase type 2A activity | SAP30| 4714 | 704 | 80 | telomere maintenance* | histone deacetylase activity | SAP4| 2195 | 279 | 20 | G1/S transition of mitotic cell cycle | protein serine/threonine phosphatase activity | SDF1| 6101 | 5710 | 451 | signal transduction | molecular function unknown | SSA1| 33 | 269000 |40441 | translation* | ATPase activity* | SSA2| 3780 | 364000 |83250 | response to stress* | ATPase activity* |

• Only 7 pairs in the DIP core network• But in Krogan et al. dataset there are 84 pairs at d=3, 17 pairs at d=4, and 1 pair at d=5 (sic!). Total=102• Reshuffled concentrationssame network, Total=16

'RPS10A' 'SPC72' [ 1.4732] 'SEC27' 'URA7' [ 1.2557] 'HTB2' 'YBR273C' [ 1.3774] 'HTB2' 'TUP1' [ 1.2796] 'RPS10A' 'AIR2' [ 2.3619] 'HTB2' 'UFD2' [ 1.3717] 'HTB2' 'YDR049W' [ 1.3645] 'HTB2' 'PLO2' [ 1.2640] 'HTB2' 'YDR330W' [ 1.3774] 'RPN1' 'GAT1' [ 1.4277] 'HTB2' 'YFL044C' [ 1.3774] 'SEC27' 'STT3' [-1.2321] 'GIS2' 'STT3' [ 1.3437] 'HTB2' 'YGL108C' [ 1.3774] 'HTB2' 'UFD1' [ 1.3744] 'RPS10A' 'AIR1' [ 2.3833] 'HTB2' 'FBP1' [ 1.3576] 'HTB2' 'YMR067C' [ 1.3510]

AIR1| 2889 | mRNA export from nucleus* | molecular function unknown | nucleus* AIR2| 916 | mRNA export from nucleus* | molecular function unknown | nucleus* FBP1| 4207 | gluconeogenesis | fructose-bisphosphatase activity | cytosol GAT1| 1857 | transcription initiation from RNA polymerase II promoter* | specific RNA polymerase II transcription factor activity* | nucleus* GIS2| 5039 | intracellular signaling cascade | molecular function unknown | cytoplasm HTB2| 136 | chromatin assembly or disassembly | DNA binding | nuclear nucleosome PLO2| 1291 | telomere maintenance* | histone deacetylase activity | nucleus* RPN1| 2608 | ubiquitin-dependent protein catabolism | endopeptidase activity* | cytoplasm* RPS10A| 5667 | translation | structural constituent of ribosome | cytosolic small ribosomal subunit (sensu Eukaryota) SEC27| 2102 | ER to Golgi vesicle-mediated transport* | molecular function unknown | COPI vesicle coat SPC72| 78 | mitotic sister chromatid segregation* | structural constituent of cytoskeleton | outer plaque of spindle pole body STT3| 1987 | protein amino acid N-linked glycosylation | dolichyl-diphosphooligosaccharide-protein glycotransferase activity | oligosaccharyl transferase c. TUP1| 710 | negative regulation of transcription* | general transcriptional repressor activity | nucleus UFD1| 2278 | ubiquitin-dependent protein catabolism* | protein binding | endoplasmic reticulum UFD2| 932 | response to stress* | ubiquitin conjugating enzyme activity | cytoplasm* URA7| 174 | phospholipid biosynthesis* | CTP synthase activity | cytosolYBR273C| 534 | ubiquitin-dependent protein catabolism* | molecular function unknown | endoplasmic reticulum*YDR049W| 1043 | biological process unknown | molecular function unknown | cytoplasm*YDR330W| 1328 | ubiquitin-dependent protein catabolism | molecular function unknown | cytoplasm*YFL044C| 1880 | protein deubiquitination* | ubiquitin-specific protease activity | cytoplasm*YGL108C| 2073 | biological process unknown | molecular function unknown | cellular component unknownYMR067C| 4506 | ubiquitin-dependent protein catabolism* | molecular function unknown | cytoplasm*

Propagation to 4th neighborsin Krogan nc

Weight of links

Perturbations sign-alternate j Dij/Ci=1-Fi /Ci <1

thus perturbations always decay

Resistor network analogy

• j~Fj/Fj – potentials, Dij , Fj , Ci –currents

• Dij – conductivity between interacting nodes

• Fi – shunt conductivity to the ground

<1/Kd>=1/5.2nMclose to our choice of 10nM

Data from PINT database (Kumar and Gromiha, NAR 2006)

How much data is out there?

Species Set nodes edges # of sources

S.cerevisiae HTP-PI 4,500 13,000 5

LC-PI 3,100 20,000 3,100

D.melanogaster HTP-PI 6,800 22,000 2

C.elegans HTP-PI 2,800 4,500 1

H.sapiens LC-PI 6,400 31,000 12,000

HTP-PI 1,800 3,500 2 H. pylori HTP-PI 700 1,500 1

P. falciparum HTP-PI 1,300 2,800 1

Breakup by experimental technique in yeast

BIOGRID database S. cerevisiae

Affinity Capture-Mass Spec 28172

Affinity Capture-RNA 55

Affinity Capture-Western 5710

Co-crystal Structure 107

FRET 43

Far Western 41

Two-hybrid 11935

Total 46063

Sprinzak et al., JMB, 327:919-923, 2003

Christian von Mering*, Roland Krause†, Berend Snel*, Michael Cornell‡, Stephen G. Oliver‡, Stanley Fields§ & Peer Bork*NATURE |VOL 417, 399-403| 23 MAY 2002

TAP-Mass-Spec

Yeast 2-hybrid

HHT1