The Structure, Function, and Evolution of Biological Systems

Instructor: Van SavageSpring 2010 Quarter

4/15/2010

Alon Book

Other important ways to construct gene networks: Gene regulation and motifs

• Organism must be able to respond to environment and gene expression is one way to do this

• One gene can create a protein that either activates or represses another gene

X Y activation

X Y repression

Y

promoter region (easily evolvable)

X*X

Draw network for these regulations

• Arrows denote direction of regulation and give two types of edges or links for each possible gene pair

• Edges are not color coded in this work, although they could be to denote activation or repression. More on that later.

• Gene regulation and epistatic networks could be combined but has not been done. Regulation may be a type of epistasis.

• New type of self link. Not possible for epistasis. How common are these?

12

3

4 56

E coli network has been measured

• N=424 genes, E=519 total edges, and 40 of those are self edges

• Is this a lot or a little? What do we compare with?

12

3

4 56

Ep=E/N is expected number of self edges

For network below N=6 and E=8 edges, so Ep=4/3

Variance is approximately E/N (Poisson), so standard deviation is 2/Sqrt(3), so for our exampleThe one self edge is expected by random chance

For E Coli Ep=1.2+/-1.1, so many more self edges that expected

Why are there so many self edges?

12

3

4 56

1. Selection for self edges

2. Frozen accident

3. Without faithful regulation for certain genes there can be major problems, and genes are most faithful to themselves

4. Some dynamical advantage

Compare with unregulated

Xst=β/α and T1/2=Xst/2β€

dXdt

= β −αX

€

dXdt

= β 1

1+ XK ⎛ ⎝ ⎜

⎞ ⎠ ⎟n

⎛

⎝

⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟−αX

Hill function

€

X st = (β /αK)1/n+1K →K

Can now adjust speed, β, without affecting asymptote/steady state, which is fixed physiologically. Allows faster response times.

unregulated

regulated

What about activation instead of repression?

€

dXdt

= β XK + X n ⎛ ⎝ ⎜

⎞ ⎠ ⎟−αX

Hill function

Slows down response time and allows for a type of memory

What other types of “motifs” might be possible to look for?

Consider all possible network with 3 nodes.

Only 13 possibilities.

How do we look to see if a give motif is overrepresented inthe data?

All 3-node subgraphs

Overrepresentation

There are N2 possible edges between N genes, so chanceof picking specific edge is 1/N2. If there are E edges in network,you have E chances to pick it, so p~E/N2 chance of picking edge.

For a given subgraph, Nn chance of picking the n correct nodesand pg chance of picking correct g edges in subgraph.

Expected number of subgraphs with n nodes and g edges is

where a is symmetry number and λ=E/N is mean connectivity€

N n pg

a= λ

gN n−g

a

Keep connectivity fixed while increasing network size

For n=3 subgraphs

Two edge patterns become more common

Three edge patterns stay constant proportion

Four and higher edge patterns become vanishingly small

Only one n=3 subgraph is overrepresented: Feed Forward Loop

42 FFLs exist. We would expect on the order of λ3~1.7+/-1.10 FBLs exist. May even be selected against.

FFL FBL

FFLs in E Coli

Possible types of FFLs

Types of FFLs in Yeast and E Coli

What are function of FFLs?Now, can add detail of whether arrows are activating or repressing

One is coherent and one is incoherent

Coherent allows us to integrate two signals with and AND or anOR gate.

AND creates delays in response to make sure signal is really there

OR creates delays in fall to make sure signal is really gone

Incoherent allows integration of two contradictory signals

Other types cause interference or cross signals

Problems with this approach

All subgraphs are taken out of context.

Is that reasonable or appropriate?

How useful is it?

Next class we will move onto papers using networks motifsfor gene regulation

First Homework set is due in two weeks (April 20, 2010).