# Presentation: 777660

## Lecture 3
Protein binding networks

- Protein binding networks

##  Genome-wide protein binding networks

*C. elegans *PPI from Li et al. (Vidal’s lab), Science (2004)

-  Genome-wide protein binding networks

- Nodes - proteins
- Edges - protein-protein binding interactions
- Functions
- Structural (keratin)
- Functional (ribosome)
- regulation/signaling (kinases)
- etc

## 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

## Yeast two-hybrid technique

-     uses two “hybrid proteins”: bait X* (X fused with Gal4p DNA-binding domain) and prey Y* (Y fused with Gal4p activation domain)

-  Cons: wrong (very high) concentrations, localization (unless both proteins are nuclear), and even host organism (unless done in yeast)
-  Pros: direct binding events
-  Main source of noise: self-activating baits

## Affinity capture +Mass Spectrometry

- Affinity capture +Mass Spectrometry

**Ionizer**

**(multi-)protein complex ****pulled out by affinity-tagged protein (bait)**

**+**

**_**

**Mass Filter**

**Detector**

-  Pros: in vivo concentrations and localizations
-  Cons: binding interactions are often indirect
-  Main source of noise: highly abundant and sticky proteins

**Notes:**
Take Home Message: Basic Principles behind Mass Spec

## 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

## What are the common topological features?

- Broad distribution of the number of interaction partners of individual proteins

##  What’s behind this broad distribution? 

-  What’s behind this broad distribution?
-  Three explanations were proposed:
-  EVOLUTIONARY (duplication-divergence models)
-  BIOPHYSICAL (stickiness due to surface hydrophobicity)
-  FUNCTIONAL(tasks of vastly different complexity)

- From YY. Shi, GA. Miller., H. Qian., and K. Bomsztyk, PNAS **103**, 11527 (2006)

## Evolutionary explanation:duplication-divergence models 

- A. Vazquez, A. Flammini, A. Maritan, and A. Vespignani. Modelling of protein interaction networks. cond-mat/0108043, (2001) published in ComPlexUs 1, 38 (2003)
- Followed by R. V. Sole, R. Pastor-Satorras, E. Smith, T. B. Kepler, A model of large-scale proteome evolution, cond-mat/0207311 (2002) published in Advances in Complex Systems 5, 43 (2002)
- Then many others including I.Ispolatov, I., Krapivsky, P.L., Yuryev, A., Duplication-divergence model of protein interaction network, Physical Review, E 71, 061911, 2005.

-  Network has to grow
-  Preferential attachment in disguise: as ki grows so is the probability to duplicate one of the neighbors

## Vazquez-Flammini-Maritan-Vespignani model

- Start with two interacting proteins
- At each step randomly pick a protein i and duplicate it to i’
- With probability p make the interaction i–i’ (duplicated homodimer)
- For every node j — i and i’ select one of the two links and remove it with probability q
- Preferential attachment in disguise: as ki grows so is the probability to duplicate one of the neighbors

##         Tell-tale signs of gene duplication in PPI networks

- Right after duplication

- After some time

## Yeast regulatory network

- SM, K. Sneppen, K. Eriksen, K-K. Yan, BMC Evolutionary Biology (2003)

## 100 million years ago

- 100 million years ago

## Traces of duplication in PPI networks

- SM, K. Sneppen, K. Eriksen, and K-K. Yan,  BMC Evol. Biol. **4**, 9 (2003)
- (a similar but smaller scale-plot vs Ks in A. Wagner MBE 18, 1283 (2001)

## But: how important are duplications for shaping hubs?

- J. Berg, M. Lässig, and A. Wagner,  BMC Evol. Biol. (2004)

-  Duplication-divergence
- models could still be OK if
- sequences diverge relatively fast

## Biophysical explanation:“stickiness” models 

- G. Caldarelli, A. Capocci, P. De Los Rios, M.A. Munoz, Scale-free Networks without Growth or Preferential Attachment: Good get Richer, cond-mat/0207366, (2002) published in PRL (2002)
- Followed by Deeds, E.J. and Ashenberg, O. and Shakhnovich, E.I., A simple physical model for scaling in protein-protein interaction networks, PNAS (2006)
- Then others including Yi Y. Shi, G.A. Miller, H. Qian, and K. Bomsztyk, Free-energy distribution of binary protein–protein binding suggests cross-species interactome differences, PNAS (2006).

## Original Candarelli et al. model

- Stickiness (they called it fitness) is exponentially distributed P(Si>S)=exp(-AS)
- Nodes i—j interact if Si+Si>T (hard threshold)
- <K(S)>=Nexp(-A(T-S))=C exp(AS)  P(Si>S)=C/<K(S)>
- P(Ki>K)=P(Si>S(K))~1/K  P(K)~1/K2
- No preferential attachment: network does not have to grow!

## Recent modifications

- Deeds et al.: Biophysically stickiness should have Gaussian PDF
- It spoils powerlaw somewhat
- Shi et al.: Soft threshold
- Binding i - j is detected with probability pij=F(Si+Sj).
- For Yeast-2-hybrid F(Si+Sj) is given by  exp(Si+Sj-T)/(1+ exp(Si+Sj-T))
- Removes unrealistic properties of the hard threshold model: neighbors(i) are all neighbors(j) if  Si<Sj

## There are just TOO MANY homodimers

-   Null-model: *P**self** ~<k>/N*
*N **(r)*dimer *=N **** P**self**= <k>*
-   Not surprising as
- homodimers have many functional roles

- I. Ispolatov, A. Yuryev, I. Mazo, and SM, **33**, 3629 NAR (2005)

*N **(r)*dimer

## Network properties around homodimers

## I. Ispolatov, A. Yuryev, I. Mazo, and SM, 33, 3629 NAR (2005)

- I. Ispolatov, A. Yuryev, I. Mazo, and SM, **33**, 3629 NAR (2005)

## Our interpretation

- Both the number of interaction partners Ki and the likelihood to self-interact are proportional to the same “stickiness” of the protein Si which could depend on
- the number of hydrophobic residues on the surface
- protein abundance
- its’ popularity (in networks taken from many small-scale experiments)
- etc.
- In random networks pdimer(K)~K2 not ~K like we observe empirically

- I. Ispolatov, A. Yuryev, I. Mazo, and SM, **33**, 3629 NAR (2005)

## Functional explanation:there are as many binding partners as needed for function

- Not an explanation: why difficulty of functions is so heterogeneous?
- Difficult to check: the function of many binding interactions is poorly understood (quite clear in transcriptional regulatory networks e.g. in *E. coli *)
- The 3rd explanation does not exclude the previous two: Evolution by duplications combined with pure Biophysics (stickiness) provide raw materials from which functional interactions are selected

## What are the common topological features?

- Broad distribution of the number of interaction partners (degree K) of individual proteins
- Anti-hierarchical (disassortative) architecture. Hubs avoid other hubs and thus are on a periphery.

## Central vs peripheral network architecture

- A. Trusina, P. Minnhagen, SM, K. Sneppen*, Phys. Rev. Lett. ****92****, 17870, (2004*)

- random

## What is the case for protein interaction network 

- What is the case for protein interaction network

- SM, K. Sneppen*, Science  ****296****, 910 (2002*)

## What are the common topological features?

- Broad distribution of the number of interaction partners (degree K) of individual proteins
- Anti-hierarchical (disassortative) architecture.
- Small-world-property (follows from 1.  for <K2>/<K>>2 )

## Protein binding networkshave small-world property

## Why small-world matters?

- Claims of “robustness” of this network architecture come from studies of the Internet where breaking up the network is a disaster
- For PPI networks it is the OPPOSITE: interconnected networks present a problem
- In a small-world network equilibrium concentrations of all proteins are coupled to each other
- Danger of undesirable cross-talk

## Going beyond topology and modeling the equilibrium and kinetics

- SM, K. Sneppen, I. Ispolatov,* *q-bio/0611026;   SM, I. Ispolatov, PNAS in press (2007)

##  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 41

## Slide 42

## Slide 43

##   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 50

## 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?

## NOW BACK TO TOPOLOGY

## Summary

- There are many kinds of protein networks
- Networks in more complex organisms are more interconnected
- Most have hubs – highly connected proteins and a broad (~scale-free) distribution of degrees
- Hubs often avoid each other (networks are anti-hierarchical or disassortative)
- Networks evolve by gene duplications
- There are many self-interacting proteins. Likelihood to self-interact and the degree K both scale with protein’s “stickiness”

## THE END

## Why so many genes could be deleted without any consequences?

## Possible sources of robustness to gene deletions

- Backup via the network (e.g. metabolic network could have several pathways for the production of the necessary metabolite)
- Not all genes are needed under a given condition (say rich growth medium)
- Affects fitness but not enough to kill
- Protection by closely related homologs in the genome

## Protective effect of duplicates

**Gu, et al 2003**Maslov, Sneppen, Eriksen, Yan 2003

- Yeast

- Worm

- Maslov, Sneppen, Eriksen, Yan  2003

- Z. Gu, ... W.-H. Li, Nature (2003)

- Maslov, Sneppen, Eriksen, Yan  BMC Evol. Biol.(2003)