Motifs in Complex Networks

Amir Razmjou

Overview

• Introduction

• Biology and Motifs

• Motifs Generalizations

• Software Systems and Motifs

• Motifs Profiles – Characterizing Wikipedia Pages

• Conclusion

Motifs are everywhere!

• Network sub-graphs namely motifs occur repeatedly across different networks. They describe motifs as fundamental building blocks of networks, whose structure can be associated with a particular function

• It has been shown that some motifs seem to be particularly relevant in describing the architecture of complex networks.

Motifs in scale-free networks

Where they come from?

• Motifs are more common than others because their functional relevance?

• An alternative view is that the rules of network growth can by themselves favor some motifs with no special relation to the underlying functionality

• Example: Proteins perform functions, the overall architecture of the protein network is easily reproduced by means of a simple model of node duplication and rewiring

• Chemistry

Each node in the randomized networks has the same number of incoming and outgoing edges as does the corresponding node in the real network

How to detect them?

Frequency of motifs an another property of scale-free networks

Concentration C of the feedforward loop motif in real and randomized subnetworks of the E. coli transcription network

Bi-fan and FFL apear the most in these networks out of 13 possibility for 3 node sub graph and 199 possibility for four-node sub graphs. The occurance of other subgraphs are even less relative to random graphs.

• The concentration of motifs in the subnetworks is about the same as that in the full network.

• In contrast, the concentration of the corresponding subgraphs in the randomized versions of the subnetworks decreases sharply with size.

• The existance of such property can be indication of an evolved or designed system.• They are resilient to disruptions!!!

• Edges directed from a node representing a predator to the node representing its prey

• Suggests: 1. Direct interactions between species at

different levels.2. Two species that are prey of the same

predator both tend to share the same prey.

Food Web

Generalization

• Do the same networks that share certain network motif also share the same structural combination of that motif?

• Computational Difficult Problem. Enumerating all subgraphs of given size is a difficult task but enumerating generalization of given subgraphcan be performed efficiently.

• Motif generalizations: family of motifs that share the same architectural theme.

Roles

The FFL has three roles, whereas the three-loop has only one role.There’s a permutation of these node with corresponding edges that preserves the motif structure.

Strong vs Weak

• In each simple generalization a single node and its connections are duplicated. In the first simple generalization, the X role and its connections are duplicated.

• In strong generalization every X, Y, Z triplet forms a motif. In weak generalization every node participates in at least generalization.

Biology

• DNA –> mRNA –> Protein -> You

• E. Coli

E. Coli

• Network motifs first were founded in these organisms for the first time.

• It eats everything. • We eat Bacon break down proteins. • We eat Cereal it breaks down Carbohydrates.• We drink milk it break down lactose.• It can morph to an organism that half of its weight is protein

enzymes to lactose enzymes in matter of few seconds. • It does that by gene regulation. Regulator gene • Regulator gene is the gene that regulates a gene.• Among all the steps of protein synthesis we can regulate the

process

Regulator Proteins – Transcription Network

• Instead of one gene they have multiple genes but they all break down protein.

• Operator site right between promoter. • As soon as lactose appears it binds to operator and operators

switches on promoter to express genes to produce proteins to break down lactose. It’s positive control since the operator will be turned on only if there’s some lactose molecules out there.

• But in case of tryptophan it works backward.

X

Y

Z

• X role is a global transcription factor which controls many genes

• Y role is usually a local transcription factor which controls specific gene system

• Z nodes are the regulated genes which share a specific function.

• In case of positive regulation and AND logic, the three-node FFL has been shown to function as a persistence detector.

• It filters out short input stimuli to X and responds only to persistent signals

Feed-forward Logic Motif in Gene Regulation

X

Y

Z

On the other hand it responds quickly to off steps in the input to X.

Feed-forward Logic Motif in Gene Regulation

X

Y

Z1Z1 Z1

Feed-forward Logic Motif in Gene Regulation

X

Y

Z

AND

the multi-Z FFL can act as persistence detector for all of its output genes

The turn-off order of the Z genes upon a gradual decay of efficient of the X

Multi-output FFL can encode a temporal order of expression of the Z genes

Cell Generation • In simple regulation, transcription factor Y is

activated by a signal Sy. When active, it binds the promoterof gene X to enhance or inhibit its transcription rate.

• In negative autoregulation (NAR), X is a transcription factor that represses its own promoter.

• In positive autoregulation (PAR), X activates its own promoter

• NAR speeds the response time (the time needed to reach halfway to the steady-state concentration) relative to a simple-regulation system that reaches the same steady-state expression. PAR slows the response time

C1- FFL

I1- FFL

Characterizing Wikipedia Pages Using Edit Network Motif Profiles

• To what extend quality of a Wikipedia article can be determined from looking at the network of edits around an article?

• Wikipedia depends on collaboration and consensus in contrast to traditional encyclopedias where authority determines from expert contributors.

The Objective is to characterize Wikipedia articles in terms of edit network motif profiles and then examine whether or not articles at different quality level have characteristic network motif profiles.

Network definition Two-mode network of articles and contributors. The article nodes are linked by hyperlinks and contributors are linked if they have worked on the same article.

The edit networks for two versions of the 2011 Tohoku earthquake and tsunami Wikipedia article. The network on the left is from two days after the earthquake and the one on the right is after ten days. The blue circles are the editors and the yellow squares are the articles

Different Motifs

• There are 31 unlabeled network motifs with between one and five nodes.

• When we allow that nodes can be either ‘editor’ or ‘article’ these 31 unlabeled network motifs produce 419 two-labeled network motifs.

• When single node network motifs and network motifs with editor-editor or article-article edges are removed the set reduces to the 17 network motifs.

Clustering Results

Results• For the History dataset, there is good

clustering of the B class to the top right and of Start class articles to the bottom left. However, the Featured Articles are more spread out with clusters to the left and right marked L and R

• The Wikipedia quality scale has a further minor dimension which reflects the importance of an article and it transpires that the Featured Articles on the left are inclined to be low or mid importance compared to high or top importance articles on the right.

• Seems that the anomalous position of the article at X5 is due vandalism. It is an article on Antisemitism and much of its edit history can be attributed to vandalism.

• The situation with the article at Y6 is

The Featured Articles are yellow; the B class articles are red; and the Start class articles are blue

Network motifs in computational graphs: Software Architecture

• The main goal of this study is to see if functionality, as opposed to network evolution, is a main constraint to the emergence of network motifs in real software map graphs

• Software Systems offer a unique opportunity of exploring different levels of complexity with well-defined functional behaviors. As opposed to most examples of evolving computational networks,

Software Maps

• Nodes are easily identified because they are proceeded by the C++ keyword class.

• Edges are different type of dependency, composition, inheritance, and association.

• This analysis is centered an the study of topological patterns and does not take into account detailed relationship semantics

Comparison of motifs to domains

Results 1

• The reason for using biological networks with artificial software networks• Both networks are known to perform computational tasks or can be described by

means of an equivalent computational circuit. • Both networks might share some commonalities relating the mechanisms that

shape their evolution.• Cyclical dependences in software maps imply that a module is related to itself,

which may be acceptable, unacceptable, or required. Ambiguity in the functional meaning of cycles suggests that subgraphs in software graphs are not strictly related to well-defined functions. The ubiquity of subgraphs in software networks seems to be a consequence of top-down mechanisms of software organization (functional) and not a consequence of selective pressures (evolutionary). DISCUSSION

• A number of network motifs are obtained the most common being shared with other systems involving computational traits such as genetic and neural networks.

Duplicated Model

Comparison of Real Software Maps with Duplication Model Dimensions concentration of 4 different motifs in share between duplicated model and real one.

Results 2

• Most of our knowledge about motifs comes from bacteria and biology• It seems that regulatory network in E. Coli Bacteria to be so modular even engineered!

Concolusion

• R Milo, S Shen-Orr, S Itzkovitz, N Kashtan, D Chklovskii & U Alon, Network Motifs: Simple Building Blocks of Complex Networks. Science, 298:824-827 (2002).

• Kashtan, Nadav, et al. Topological generalizations of network motifs. Physical Review E 70.3 (2004): 031909.

• Uri Alon. Network motifs: theory and experimental approaches• Nature Reviews Genetics 8, 450-461 (June 2007).• Yang, Kai-Hsiang, et al. Web appearance disambiguation of personal names based on

network motif. Proceedings of the 2006 IEEE/WIC/ACM International Conference on Web Intelligence. IEEE Computer Society, 2006.

• Valverde, Sergi, and Ricard V. Solé. Network motifs in computational graphs: A case study in software architecture. Physical Review E 72.2 (2005): 026107.

• Wu, Guangyu, Martin Harrigan, and Pádraig Cunningham. Characterizing wikipediapages using edit network motif profiles. In Proceedings of the 3rd international workshop on Search and mining user-generated contents, pp. 45-52. ACM, 2011.

References