Propagation of noise and perturbations in protein binding networks Sergei Maslov Brookhaven 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 dD AB /dt = r (on) AB F A F B – r (off) AB D AB In equilibrium D AB =F A F B /K AB where the dissociation constant K AB = r (off) AB / r (on) AB has units of concentration Total concentration = free concentration + bound concentration  C A = F A +F A F B /K AB  F A =C A /(1+F B /K AB ) In a network F i =C i /(1+  neighbors j F j /K ij ) 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 C i of all proteins  CHECK! genome-wide data for yeast in 3 Nature papers (2003, 2006) by the group of J. UCSF. VERY BROAD distribution: C i ranges between 50 and 10 6 molecules/cell Left us with 1700 yeast proteins and ~5000 interactions in vivo dissociation constants K ij 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/(5nM). In yeast: 1nM ~ 34 molecules/cell Simple-minded assignment K ij =const=10nM (also tried 1nM, 100nM and 1000nM) Evolutionary-motivated assignment: K ij =max(C i,C j )/20: K ij is only as small as needed to ensure binding given C i and C j All assignments of a given average strength give ROUGHLY THE SAME RESULTS

Robustness with respect to assignment of K ij Spearman rank correlation: 0.89 Pearson linear correlation: 0.98 Bound concentrations: D ij Spearman rank correlation: 0.89 Pearson linear correlation: Free concentrations: F i

Numerical study of propagation of perturbations We simulate a twofold increase of the abundance C 0 of just one protein Proteins with equilibrium free concentrations F i 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 D ij Losses to the ground  iG – free (unbound) concentrations F i Electric potentials – relative changes in free concentrations (-1) L  F i /F i Injected current – initial perturbation  C 0 SM, K. Sneppen, I. Ispolatov, arxiv.org/abs/q-bio.MN/ ;

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 ) F i /C i has to be low to avoid “losses to the ground” Perturbations flow down the gradient of C i Odd-length loops dampen the perturbations by confusing (-1) L  F i /F i

Exponential decay of perturbations O – real S - reshuffled D – best propagation

SM, I. Ispolatov, PNAS in press (2007) HHT1

What conditions make 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 low SM, 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

Intra-cellular noise Noise is measured for total concentrations C i (Newman et al. Nature (2006)) Needs to be converted in biologically relevant bound (D ij ) or free (F i ) 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

Kinetics Non-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 Ispolatov Research scientist Ariadne Genomics

THE END

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

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

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 / > 2 )

Protein binding networks have 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

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mRNA polyadenylation; protein sumoylation unfolded protein binding G2/M transition of cell cycle mRNA, protein, rRNA export from nucleus RNA polymerase I, III RNA polymerase II 35S primary transcript processing protein phosphatase type 2A

HSP82  SSA1  KAP95  NUP60 : SSA2  HSP82  SSA1  KAP95: HSC82  CPR6  RPD3  SAP30: SSA2  HSP82  SSA1  MTR10: CDC55  PPH21  SDF1  PPH3: CDC55  PPH21  SDF1  SAP4: PPH22  SDF1  PPH21  RTS1: Propagation to 3 rd neighbors CDC55| 2155 | 8600 | 1461 | protein biosynthesis* | protein phosphatase type 2A activity | CPR6| 4042 | | 114 | protein folding | unfolded protein binding* | HSC82| 4635 | | 4961 | telomere maintenance* | unfolded protein binding* | HSP82| 6014 | | 115 | response to stress* | unfolded protein binding* | KAP95| 4176 | | 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 | |40441 | translation* | ATPase activity* | SSA2| 3780 | |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 concentrations same network, Total=16

'RPS10A' 'SPC72' [ ] 'SEC27' 'URA7' [ ] 'HTB2' 'YBR273C' [ ] 'HTB2' 'TUP1' [ ] 'RPS10A' 'AIR2' [ ] 'HTB2' 'UFD2' [ ] 'HTB2' 'YDR049W' [ ] 'HTB2' 'PLO2' [ ] 'HTB2' 'YDR330W' [ ] 'RPN1' 'GAT1' [ ] 'HTB2' 'YFL044C' [ ] 'SEC27' 'STT3' [ ] 'GIS2' 'STT3' [ ] 'HTB2' 'YGL108C' [ ] 'HTB2' 'UFD1' [ ] 'RPS10A' 'AIR1' [ ] 'HTB2' 'FBP1' [ ] 'HTB2' 'YMR067C' [ ] 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 | cytosol YBR273C| 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 unknown YMR067C| 4506 | ubiquitin-dependent protein catabolism* | molecular function unknown | cytoplasm* Propagation to 4 th neighbors in Krogan nc

Weight of links Perturbations sign-alternate  j D ij /C i =1-F i /C i <1 thus perturbations always decay

Resistor network analogy  j ~  F j /F j – potentials,  D ij,  F j,  C i –currents D ij – conductivity between interacting nodes F i – shunt conductivity to the ground

=1/5.2nM close 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 Affinity Capture-RNA 55 Affinity Capture-Western 5710 Co-crystal Structure 107 FRET 43 Far Western 41 Two-hybrid Total 46063

Sprinzak et al., JMB, 327: , 2003

Christian von Mering*, Roland Krause†, Berend Snel*, Michael Cornell‡, Stephen G. Oliver‡, Stanley Fields§ & Peer Bork* NATURE |VOL 417, | 23 MAY 2002 TAP- Mass-Spec Yeast 2-hybrid

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