Propagation of noise and perturbations in protein binding networks

Presentation Transcript

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

robustness with respect to assignment of k ij

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

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)

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

2

1

3

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* |

propagation to 4 th neighbors in krogan nc

'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]

Propagation to 4th neighborsin Krogan nc

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*