Network Motifs simple Building Blocks of Complex Networks

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

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

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

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

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

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

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

The Feedforward loop : a sign sensitive filter Vs. =lac. ZYA =ara. BAD OFF pulse Mangan, Alon, PNAS, JMB, 2003

Single Input Module Z 1 Z 1 Z 2 Z 2 Z 3 Z 3 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 motif is responsible for exact timing in the flagella assembly

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

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

Evolution of transcription networks • In 1 day, 1010 copies of e-coli, 1010 replication of DNA. • Mutation rate is 10 -9 – 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 Web. Pages – a completely different set of motifs is found • • Web. Pages are nodes and Links are directed edges 3 node results:

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

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, 167 -256 (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.

Metabolic networks KEGG database: http: //www. genome. ad. jp/kegg 2. html

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

C. elegans neuronal net

Dense Overlapping Regulons (DOR) X 1 X 2 X 3 … Xn Bi-fan Z 1 Z 2 Z 3 … Zm Nreal = 203 Nrand = 47± 12 Z Score = 13 Array of gates for hard-wired decision making Buchler, Gerland, Hwa, PNAS 2003 Setty, Mayo, Surette, Alon, PNAS 2003