Nagyméretű, ritka gráfok
moduláris, játékelméleti és
perturbációdinamikai
elemzése biológiai és más
valós hálózati problémák
megoldásában
www.linkgroup.hu
csermely@eok.sote.hu
Prof. Csermely
Péter
Semmelweis Egyetem, LINK-csoport
Advantages of network multi-disciplinarity
Networks have general properties
• small-worldness
• hubs (scale-free degree distribution)
• nested hierarchy
• stabilization by weak links
Karinthy, Watts & Strogatz,
1929
1998
Barabasi & Albert, 1999
Csermely, 2004; 2009
Generality of network properties offers
• judgment of importance
• innovation-transfer across different layers of complexity
Example to break conceptual barriers
Aging is an early warning signal
of a critical transition: death
ecosystem, market, climate
• slower recovery from perturbations
• increased self-similarity of behavior
• increased variance of fluctuation-patterns
Nature 461:53
Prevention: central elements
with less predictable behavior
• omnivores, top-predators
• market gurus
• stem cells
Farkas et al, Science Signaling 4:pt3
Less predictable (creative) elements
have a large dynamic centrality
Creative: few links to
hubs, unexpected re-routing,
flexible, unpredictable
Distributor: hub,
specialized to signal
distribution, predictable
change of roles
Csermely,
Nature 454:5
TiBS 33:569
TiBS 35:539
Problem solver:
specialized to a task,
predictable
Creative elements are central and…
Cyt-P450
(CYP2B4)
Creative amino acids
• centre of residue-network
• in structural holes
Creative proteins
• stress proteins
• signaling switches
drug-binding
Csermely,
Nature 454:5
TiBS 33:569
TiBS 35:539
oxidation
Creative cells
• stem cells
• our brain
Creative persons
• firms
• societies
mobile
Creative elements of social networks
Ron Burt,
Structural holes,
Harvard Univ. Press 1992
Robert: broker – netokrat
James: looser
3 examples of network modelling
• topological centrality is central in network perturbations
(Turbine: www.linkgroup.hu/Turbine.php)
• community centrality: prediction of survival importance
(ModuLand: www.linkgroup.hu/modules.php)
• game-centrality: prediction of biological regulators
(NetworGame: www.linkgroup.hu/NetworGame.php)
Turbine algorithm assessing
network perturbation dynamics
any real networks can be added, modified
normalizes the input network
any perturbation types (multiple, repeated, etc.)
any models of dissipation, teaching and aging
Matlab compatible
Farkas et al, Science Signaling 4:pt3
www.linkgroup.hu/Turbine.php
Hubs + inter-modular nodes are primary
transmitters of network perturbations
Start: module-center hub
Farkas et al., Science Signaling 4:pt3
www.linkgroup.hu/Turbine.php
Starting node: bridge
3 examples of dynamic centrality
• topological centrality is central in network perturbations
(Turbine: www.linkgroup.hu/Turbine.php)
• community centrality: prediction of survival importance
(ModuLand: www.linkgroup.hu/modules.php)
• game-centrality: prediction of biological regulators
(NetworGame: www.linkgroup.hu/NetworGame.php)
Importance of modular overlaps
of protein-protein interaction networks in stress
networks:
• STRING 7
(5329/190018)
• BioGRID
(5329/91749)
• Ekman
(2444/6271)
resting
protein weight
mRNA expression
multiplication
average
resting link-weight
weights:
• equal units
• proteins
(Nature 441:840)
• mRNA-s
continuous
weights
discrete
weights
unique
stress
average
stress
stressed
protein weight
multiplication
average
stressed link-weight
13 stress conditions, 65 experiments
(Gasch et al, Mol. Biol. Cell 11:4241)
6 stress conditions, 32 experiments
(Causton et al, Mol. Biol. Cell 12:323)
(Cell 95:717)
Mihalik & Csermely
PLoS Comput. Biol. 7:e1002187
analysis of overlapping network modules:
ModuLand method
ModuLand method family detects
ovelapping network communities
community
heaps of all
nodes/links
community
landscape
communities
as landscape hills
network
hierachy
Kovacs et al, PLoS ONE 5:e12528
www.linkgroup.hu/modules.php
network of network scientists; Newman PRE 74:036104
Community heaps: NodeLand method
startingzones
node
influence
community-44: 1127 schoolchildren, 5096 friendships; Add-Health
ModuLand method family detects
ovelapping network communities
community
landscape
community
centrality:
a measure
of the influence
of all other nodes
community
heaps of all
nodes/links
communities
as landscape hills
network
hierachy
available as
a Cytoscape
plug-in
Kovacs et al, PLoS ONE 5:e12528
www.linkgroup.hu/modules.php
network of network scientists; Newman PRE 74:036104
Changing community centralities
reflect the importance of survival in stress
protein
synthesis
protein
degradation
survival
processes
energy
distribution
energy
distribution
Mihalik & Csermely
PLoS Comput. Biol. 7:e1002187
• yeast protein-protein interaction
network: 5223 nodes, 44314 links
• stress: 15 min 37°C heat shock
• link-weight changes: mRNA
expression level changes
Changes of yeast interactome in crisis:
a model of systems level adaptation
• BioGrid yeast interactome:
5223 nodes, 44314 links
• stress: 15 min 37°C heat shock
+ Gasch et al. MBC 11:4241
• link-weight changes: mRNA
expression level changes
Stressed yeast cell:
• nodes belong to less modules
• modules have less intensive contacts
smaller overlaps between modules
Mihalik & Csermely
PLoS Comput. Biol. 7:e1002187
1. Stress-induced overlap decrease is general
• proteins: water, stretch
• brain: disease states, such as Alzheimer
• animal compementary coop.: alpha-male
• social dimensions: dissociate in stress, firms
• ecosystems: patch separation in desiccation
2. Topological phase transitions reflect the overlap-decrease at one level higher
network diameter
degrees of freedom
stress
apoptosis
assembly >
disassembly
disassembly >
assembly
Derenyi et al. Physica A 334:583 Csermely: Weak Links (Springer 2009)
Crisis survival: of
creative
elements
Consequences
network
crisis
cell
death
creative
elements*
stress
network
desintegration
increased network flexibility
• spared links
• noise and damage localization
• modular independence: larger
response-space and better conflict
management
*Schumpeterian
destruction
Szalay et al, FEBScreative
Lett. 581:3675;
Palotai et al. IUBMB Life 60:10
Mihalik & Csermely. PLoS Comput. Biol. 7:e1002187
Bridges of Met-tRNA-synthase network
identify signaling amino acids
Ghosh et al. PNAS 104:15711
signaling amino acids
other amino acids
Szalay-Bekő et al. in preparation
Overlaps of signaling
pathways are most
pronounced in humans
growing prevalence of
signaling cross-talks
Korcsmaros et al,
Bioinformatics 26:2042;
PLoS ONE 8:e19240
www.SignaLink.org – 2010 version:
646 proteins, 991 links in humans
3 examples of dynamic centrality
• topological centrality is central in network perturbations
(Turbine: www.linkgroup.hu/Turbine.php)
• community centrality: prediction of survival importance
(ModuLand: www.linkgroup.hu/modules.php)
• game-centrality: prediction of biological regulators
(NetworGame: www.linkgroup.hu/NetworGame.php)
NetworGame program
• any model or real networks can be added (weighted, directed)
• any game types (prisoners’ dilemma, hawk-dove, stag hunt, etc.)
• any strategy update rules
• synchronized, asynchron, semi-synchron update
• starting strategies can be set individually by elements
Farkas et al., Science Signaling 4:pt3
www.linkgroup.hu/NetworGame.php
Q-learning helps cooperation
regular
network
small
world
network
PD-game
best-takes
over
replacing
37 links
from 900
3.5% cooperators
18% cooperators
PD-game
Q-learning
replacing
37 links
from 900
18% cooperators
Wang et al. PLoS ONE 3:e1917
18% cooperators
Q-learning
1. helps cooperation even at high temptation levels
2. stabilizes cooperation at different network topologies
2
1
SAME with
• other short term strategy update rules
• other network topologies
• other games (extended-PD or Hawk-Dove)
Wang, Szalay, Zhang & Csermely
PLoS ONE 3:e1917
Long-term learning
1. helps
2. BUT does not stabilize cooperation
1
2
SAME with
• other short term strategy update rules
• other network topologies
• other games (extended-PD or Hawk-Dove)
Wang, Szalay, Zhang & Csermely
PLoS ONE 3:e1917
Long-term learning + innovation
1. helps cooperation even at high temptation levels
2. stabilizes cooperation at different network topologies
2
SAME with
• other short term strategy update rules
• other network topologies
• other games (extended-PD or Hawk-Dove)
Wang, Szalay, Zhang & Csermely
PLoS ONE 3:e1917
1
Learning + innovation
expand cooperative network topologies
learning + innovation
Q-learning
learning
imitation
(best-takes-over)
SAME with
• other short term strategy update rules
• other network topologies
• other games (extended-PD or hawk-dove)
Wang, Szalay, Zhang & Csermely
PLoS ONE 3:e1917
we are do not depend
(that much…)
on the network around us
Game-centrality: prediction of key
nodes of social regulation I.
hispanic
old
union leaders: strike
BC
BC
sociogram leaders: work
BC
young
Farkas et al., Science Signaling 4:pt3
www.linkgroup.hu/NetworGame.php
Michael’s strike network; Michael, Forest Prod. J. 47:41
Hawk-dove game (PD game: same)
Start: all-cooperation = strike
Strike-breaker: defects
BC-s are the best strike-breakers
Game-centrality: prediction of key
nodes of social regulation II.
doves
BC
BC
instructor
BC
BC
hawks
hawk-dove game:
50-50% random starting D/C
recovers network modules
administrator
prisoners’ dilemma/stag hunt games
most influential single defective elements
BC
Farkas et al., Science Signaling 4:pt3
www.linkgroup.hu/NetworGame.php
Zachary karate club network; J.Anthropol. Res. 33:452
largest betweenness centrality
Game-centrality: prediction of key
nodes of biological regulation
• Met-tRNA-synthase protein structure network
signaling amino acids (Ghosh, PNAS 104:15711)
largest game-centrality
• yeast protein-protein interaction network
amino acids regulating evolution (Levy, PLoS
Biol 6:e264): large game centrality
Farkas et al., Science Signaling 4:pt3
www.linkgroup.hu/NetworGame.php
A könyvek innen
tölthetőek le:
Bemutatkozás
www.csermelyblog.hu
Acknowledgments
Stress Ágoston
Mihalik
Aging
maybe You as a
collaborator
Eszter
Hazai
Shijun Wang
Gábor I. Simkó
Turbine:
perturbation
NetworGame
István A. Kovács
Kristóf Z. Szalay
ModuLand
www.linkgroup.hu
info@linkgroup.hu
Robin Palotai
Máté Szalay-Bekő
half from the BME…
Turbine algorithm: perturbation model
dissipation of perturbations
‘learning’ – ‘aging’: changes of link weights
attenuation of other links, if a link gains weight
Es, free energy of starting node; Ee, free energy of the other node on the link; l, degree;
w, link weight; D0, dissipation constant; Cs, amplification constant; A, aging sensitivity;
Cw, attenuation constant
if perturbation exceeds a limit: links are exchanged to half as many random links
Farkas et al., Science Signaling 4:pt3
www.linkgroup.hu/Turbine.php
Game rules
• canonical Prisoner’s Dilemma game: CC:R(3); CD:S/T(0/3-6); DD:P(1)
extended PD game: CC:R(1); CD:S/T(0/1-2); DD:P(0)
Hawk-Dove game: CC:G/2 (C>G); CD:G; DD:-(G-C)/2
• 2,500 agents are tied to network nodes (no evolution)
• agents can play with their neighbors only
• they can either defect or cooperate
• 50-50% defectors and cooperators start
at a random distribution
• 5,000 plays, % of cooperators on last 10 rounds
• average of 100 games is displayed
Wang, Szalay, Zhang and Csermely
PLoS ONE 3:e1917
Strategy update rules
• short-term strategy update: best takes over (imitation, copy the richest neighbor)
replicator dynamics (pair-wise comparision dynamics; copy randomly selected
neighbor, if richer); proportional updating (spread to all neighbors,
if richer)
• long-term learning, innovative strategy update: Q-learning
(a type of reinforcement learning
optimal strategy to maximize total discounted expected reward;
annealing temp 100, discount factor 0.5)
• long-term learning: accumulated payoff not only last round
• innovation: opposite of agent’s strategy with p (0.0001) probability
• synchronized update, averaged payoffs
Wang, Szalay, Zhang and Csermely
PLoS ONE 3:e1917