Network Motifs: simple Building Blocks of Complex Networks R. Milo et. al. Science 298, 824 (2002) Y. Lahini

The cell and the environment Cells need to react to their environment Reaction is by synthesizing task-specific proteins, on demand. The solution – regulated transcription network E. Coli – 1000 protein types at any given moment >4000 genes (or possible protein types) – need regulatory mechanism to select the active set We are interested in the design principles of this network

Proteins are encoded by DNA DNA – the instruction manual, 4-letter chemical alphabet – A,G,T,C DNA RNA Protein transcription translation

Gene Regulation Transcription factor external signal Proteins are encoded by the DNA of the organism. protein promoter region ACCGTTGCAT Coding region DNA Proteins regulate expression of other proteins by interacting with the DNA

INCREASED TRANSCRIPTION X X* Sx X* Y Y X Y Y X binding site gene Y X Y Bound activator Two types of Transcription Factors: 1.Activators No transcription Sub-second Seconds Hours Separation of time scales: TF activation level is in steady state

Bound repressor X Y X X* Sx No transcription X* Bound repressor Two types of Transcription Factors: Repressors Unbound repressor X Y Y Y Y

Equations of gene regulation If X* regulates Y, the net production rate of gene Y is α- Dilution/degradation rate K – activation coefficient [concentration]; related to the affinity β – maximal expression level Step approximation – gene is on (rate β) or off (rate 0) with threshold K

Nodes are proteins (or the genes that encode them) Edges = regulatory relation between two proteins XY The gene regulatory network of E. coli

13 3-node circuits Analyzing networks Find n-node subgraphs in real graph. Find all n-node subgraphs in a set of randomized graphs with the same distribution of incoming and outgoing arrows. ( Newman, 2000, Sneppen, Malsov 2002) Assign Z-score for each subgraph. Subgraphs with high Z-scores are denoted as Network Motifs.

Analyzing networks The idea- patterns that occur in the real network much more then in a randomized network, must have functional significance. The randomized networks share the same number of edges and number of nodes, but edges are assigned at random

The known E. Coli transcription network

A random graph based on the same node statistics

3-node network motif – the feedforward loop Nreal=40 Nrand=7±3

Mangan, Alon, PNAS, JMB, 2003 The feedforward loop : a sign sensitive filter The feedforward loop is a filter for transient signals while allowing fast shutdown

OFF pulse Vs. =lacZYA=araBAD The Feedforward loop : a sign sensitive filter Mangan, Alon, PNAS, JMB, 2003

Temporal and expression level program generator The temporal order is encoded in a hierarchy of thresholds Expression levels hierarchy is encoded in hierarchy of promoter activities Single Input Module Z1Z2Z3Z1Z2Z3 Z1Z2Z3Z1Z2Z3

Single Input Module motif is responsible for exact timing in the flagella assembly

Kalir et. al., science,2001 Single Input Module motif is responsible for exact timing in the flagella assembly

Single Input Module turns on the SOS response in E. coli

Shallow network, few long cascades. Modular The gene regulatory network of E. coli Shen-Orr et. al. Nature Genetics 2002 Single input modules Feed-forward loops

Evolution of transcription networks In 1 day, copies of e-coli, replication of DNA. Mutation rate is –10 mutations per letter in the population per day Even single DNA base change in the promoter can change the activation/repression rate Edges can be lost or gained (i.e. selected) easily.

Links between WebPages – a completely different set of motifs is found WebPages are nodes and Links are directed edges 3 node results:

Head Sensory Ring Motor Ventral Cord Motor [White, Brenner 1986; Durbin, Thesis, 1987] Structure of a nematode neuronal circuitry

Neurons and transcription share similar motifs C. elegans

Summary The production of proteins in cells is regulated using a complex regulation network Network motifs: simple building blocks of complex networks An algorithm to identify network motifs Example: the transcription network of E. coli. The feed forward loop as a sign sensitive filter The single input module: exact temporal ordering of protein expression

Thanks

Equations of gene regulation If X* regulates Y, the net production rate of gene Y is α- Dilution/degradation rate K – activation coefficient [concentration]; related to the affinity Β – maximal expression level n – the Hill parameter (steepness of the response, usually 1-4) Step approximation – gene is on (rate β) or off (rate 0) with threshold K

Actors’ web

Mathematicians & Computer Scientists

Sexual contacts: M. E. J. Newman, The structure and function of complex networks, SIAM Review 45, (2003).

High school dating: Data drawn from Peter S. Bearman, James Moody, and Katherine Stovel visualized by Mark Newman

Internet as measured by Hal Burch and Bill Cheswick's Internet Mapping Project.Internet Mapping Project

KEGG database: Metabolic networks

Transcription regulatory networks Bacterium: E. coli Single-celled eukaryote: S. cerevisiae

C. elegans neuronal net

X1X1 X2X2 … Z1Z1 Z2Z2 … Array of gates for hard-wired decision making Dense Overlapping Regulons (DOR) Buchler, Gerland, Hwa, PNAS 2003 Setty, Mayo, Surette, Alon, PNAS 2003 N real = 203 N rand = 47±12 Z Score = 13 X3X3 XnXn Z3Z3 ZmZm Bi-fan