Propagation of noise and perturbations in protein binding networks

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 • 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 Ciof all proteins • CHECK! genome-wide data for yeast in 3 Nature papers (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

Free concentrations: Fi Bound concentrations: Dij Spearman rank correlation: 0.89 Pearson linear correlation: 0.98 Spearman rank correlation: 0.89 Pearson linear correlation: 0.997 Robustness with respect to assignment of Kij

Numerical study of propagation of perturbations • We simulate a twofold increase of the abundance C0 of just one protein • Proteins with equilibrium free concentrations Fichanging by >20% are significantly perturbed • We refer to such proteins i as concentration-coupled to the protein 0 • Look for cascadingperturbations

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 – real S - reshuffled D – best propagation

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

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 theconcentration 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 Ci (Newman et al. Nature (2006)) • Needs to be converted in biologically relevantbound (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 inbacteria: 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 theequilibrium is approached and restored? • Dynamical aspects ofnoise • How specific interactions peacefully coexistwith many non-specific ones

Iaroslav IspolatovResearch scientistAriadne Genomics Kim Sneppen NBI, Denmark

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 of772 such pairs (18% of the total, P-value 10-216) SM, I. Ispolatov, PNAS in press (2007)

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

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 S. cerevisiae curated PPI network used in our study

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)

Indiscriminate cross-talk is suppressed

What did we learn from topology? • Broad distribution of the degree K of individual nodes • Degree-degree correlations and high clustering • 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 86% of proteins could be connected 83% in this plot S. cerevisiae Large-scale Y2H experiment Curated dataset used in our study

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

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

Propagation to 3rd neighbors 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 • 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 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* |

Weight of links • Perturbations sign-alternate • j Dij/Ci=1-Fi /Ci <1thus 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>=1/5.2nM 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

Propagation of noise and perturbations in protein binding networks

Propagation of noise and perturbations in protein binding networks

Presentation Transcript

Protein Binding Networks: from Topology to Kinetics

Protein Binding Phenomena

Plasma drug protein binding

PROTEIN BINDING

Ligand configurational entropy and protein binding

Identification of protein-protein binding motifs

Back Propagation and Representation in PDP Networks

Ultrasensitivity and noise propagation in a synthetic transcriptional cascade

Drug distribution and protein binding

Drug-Protein Binding

Protein Function –Binding

Creb Binding Protein

Protein networks

Lecture 3 Protein binding networks

Propagation in Networks

Propagation of perturbations in protein binding networks

GTP-binding proteins and protein phosphorylation

Dynamical response networks under perturbations

Protein Binding Site Mapping

E1A binding protein p300

Protein Binding Site Mapping