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Class presentations, Epilogue

CS 249B: Science of NetworksWeek 15: Monday, 05/05/08Daniel BilarWellesley CollegeSpring 2008

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Goals today

� Epilogue of CS249B and review

� (Network science redux: Up one level of scale to Motifs)

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Epilogue: Have we done what we set out to do?

Metrics, models, processes and algorithms of networks

� Graph theory� Probability theory� Power laws � Phenomenological models

� Random graphs (Erdos-Reniy)� Small world (Watts-Strogatz)

� Generative (dynamic) models� Preferential attachment (aka Yule

process , Gibrat principle, Matthew effect)

� Hierarchy generation (fractal, self-similarity)

� [Self-organized criticality, EOC]� HOT systems

� Processes and Consequences� Attack, Error tolerances� Diffusion, Epidemics

Learning to learn� Dealing with unknowns,

confusion, abundance of new material

� Efficient reading of difficult papers

� Mind maps/ Concept maps� Presentation to audience� Culminating project

Scientific paradigm� Witness the unfolding of the

scientific paradigm� Course material� Self

� A first-hand look at the acquisition, discussion, correction and evaluation of scientific models to explain phenomena

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You� You showed consistent progress and development, application of our class concepts, and most of all inquisitive couragein your final project

� You took chances, dared to be bold, staked out a position, then argued scientifically, empirically and logically – this is key

� Imagination as the first step is much more important than knowledge “Think like Einstein”

� Don’t fear being wrong, you cannot grow if you do not take that chance

It was a pleasure and a real treat to work with you this semester ☺

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Have a great summer!� You might forget most material of this course in time -> not so tragic� More important are practice of skills that you learned are universally

applicable� Dealing with unknowns, confusion, abundance of new material� Efficient reading of difficult papers, negotiating unknowns, impasses� Clearly expressing yourself in English

� The Scientific Paradigm: In order of importance� Being bold, Primacy of data, “Consillience of Induction” and logic

looks like a duckquacks like a duckhas duck genome

hangs out with ducksPope tells you it is a duck

lives in waterdoes ducky things“I am your father” Duck Vader ☺

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Comparing Apples with Oranges

� A spectrographic analysis of ground, desiccated samples of a Granny Smith apple and a Sunkist navel orange

Sandford S. Apples and oranges: a comparison. Annals of Improbable Research 1995;1(3)

Read other ground breaking research: “Is Kansas flatter than a pancake?” at

http://www.improbable.com/airchives/paperair/volume9/v9i3/kansas.html

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Addendum

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Motifs

� We discussed some properties of network and some conclusions that researchers drew

� Some processes (which are temporal, i.e. over time) may be driven or influenced by re-occurring structures or subgraphpatterns

� In the network context, these structures are called motifs

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Recurring Patterns are motifsIdea: If a pattern occurs more often in real world

networks than random networks, it is called a motifWhere have we seen this type of approach before?

Technique:1. Construct many random graphs with the same number of

nodes and edges ( and same node degree distribution)

2. Count the number of motifs in those graphs

3. Calculate the Z score: the probability that the given number of motifs in the real world network could have occurred by chance

� Software available:� http://www.weizmann.ac.il/mcb/UriAlon/

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Motif count criteria

� Three concepts are considered for the determination of motif frequency, which have different applications and restrictions on counting overlapping matches (i.e. matches sharing edges or vertices) for motif frequency.

� F1 has no restrictions

� F2 allows the sharing of vertices, but not of edges

� F3 does not allow any sharing of network elements

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Application of F1, F2 and F3

motif matches in the target graph

motif to be foundgraph

one of {M1,M2,M3,M4,M5}

F3

{M1,M4} or {M3,M4}F2

{M1,M2,M3,M4,M5}F1

MatchConcept

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3-node Feed-forward loop

Idea: Processes decision-making based on fluctuating external signals

Shen-Orr, Milo, Mangan, Alon. Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics, 31:64-68 (2002)

“coherent FF loop act as a circuit that rejects transient activation signals from the general transcription factor and responds only to persistent signals, while allowing a rapid system shutdown”

What does this mean in English?

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4-node: Single-Input module

“motif can show a temporal program of expression according to a hierarchy of activation thresholds of the genes”

What does this mean in English?

Shen-Orr, Milo, Mangan, Alon. Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics, 31:64-68 (2002)

Idea: Temporal ordering useful in processes that require several stages to complete

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What is a Z-score?

� A common statistical way of standardizing data on one scale so a ‘normalized’ comparison can take place� “yard stick” for all types of data

� Each z-score corresponds to a point in a normal distribution

� z-score will describe how much a point deviates from a mean or specification point.

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What the Z score meansµ =mean number of times the motifappeared in the random graph

# of times motif

appeared in random graph

zx=x - µµµµx

σσσσx

σ standard deviationthe probability observing a Z

score of 2 is 0.02275

In the context of motifs:

Z > 0, motif occurs more often

than for random graphs

Z < 0, motif occurs less often

than in random graphs

|Z| > 1.65, only a 5% chance of

random occurence

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Z-scores and motif profiling

Milo et al. Superfamilies of designed and evolved networks.Science, 303:1538-42 (2004)

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General motif detection approach

Milo, Shen-Orr, Itzkovitz, Kashtan, Chklovskii & Alon. Network Motifs: Simple Building Blocks of Complex NetworksScience, 298:824-827 (2002)

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Milo (2002) Motif discovery� Discovery of recurring patterns – motifs in broad empirical networks

� Can randomly remove, add, change 20% of edges and set of significant motifs do not change!

� Speculation on classification of network families based on motifs

� “Information processing”, computational circuits?

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Mangan (2003) FFL motif

� Investigation of one motif, the Feed Forward loop� Most significant network motifs in both E. coli and yeast� A three-gene pattern, is composed of two input transcription factors, one of which

regulates the other, both jointly regulating a target gene.� The FFL has eight possible structural types (why?), because each of the three

interactions in the FFL can be activating or repressing� Mathematically modeled the 8 types

� All are sign sensitive� Both coherent and incoherent types delay responses to stimulus steps, but only in one

direction

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Milo (2004) Family classification� Superfamilies can be constructed

based on Triad Significance Profile (TSP) acting as a “Motif signature”� Motif and antimotif

� Examples

Sensory transcription networks� “rate limited networks” by

individual component, faster� FFL over-, 3-chain under-

represented

Signal transduction networks� Not “rate limited”, slower� Triads 7,9,10 (+), 1,2,4,5 (-)

Social networks, languageWWW

Similarities between networks visualized bylooking at the correlation between theTSPs of different networks. Correlationsused to cluster the networks into distinctsuperfamilies

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Finding classes on graphs based on motif signatures

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Papers of interest

� Shen-Orr (2002) “Network motifs in the transcriptional regulation network of Escherichia coli”

� Przulj (2006) “Biological Network Comparison Using Graphlet Degree Distribution”

� Gupta (2007) “Quantifying similarities betweeen motifs”

� Learn more at http://www.weizmann.ac.il/mcb/UriAlon

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Comparing Apples with Oranges

� A spectrographic analysis of ground, desiccated samples of a Granny Smith apple and a Sunkist navel orange

Sandford S. Apples and oranges: a comparison. Annals of Improbable Research 1995;1(3)

Read other ground breaking research: “Is Kansas flatter than a pancake?” at

http://www.improbable.com/airchives/paperair/volume9/v9i3/kansas.html