# Presentation: 545352

## Propagation of perturbations in protein binding networks

- Sergei Maslov
- Brookhaven National Laboratory

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

-   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

## 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 – real
- S - reshuffled
- D – best
- propagation

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

## What conditionsmake some 
long chains good conduits for propagation of concentration perturbations while suppressing it along side branches?

- long chains good conduits for propagation of concentration perturbations while suppressing it along side branches?

## Slide 13

## Slide 14

## Slide 15

##   Perturbations propagate along dimers with large concentrations

-   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

## 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)

-    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!)

## Slide 22

## 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

- Kim Sneppen NBI, Denmark

- Iaroslav IspolatovResearch scientistAriadne Genomics

## THE END

##  Genome-wide protein binding networks

*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)

## Slide 30

## Indiscriminate cross-talk is suppressed

## Slide 32

## 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 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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## Slide 41

## 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

## Propagation to 3rd neighbors

-      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

## Propagation to 4th neighborsin Krogan nc

-     '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 | 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 4th neighborsin 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/Kd>=1/5.2nM

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

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

## Slide 48

## Slide 49

## 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

## Yeast 2-hybrid

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

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