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The Structure, Function, and Evolution of Biological Systems

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### The Structure, Function, and Evolution of Biological Systems

Instructor: Van Savage

Spring 2010 Quarter

4/22/2010

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

X

Y

X*

promoter region (easily evolvable)

Overrepresentation

There are N2 possible edges between N genes, so chance

of 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, Nnchance of picking the n correct nodes

and 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

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

FBL

FFL

42 FFLs exist. We would expect on the order of λ3~1.7+/-1.1

0 FBLs exist. May even be selected against.

Positive feedback equations with implicit dependence on copy number

x are monomers (unactivated), y are dimers (activated)

d0 are occupied states and d1 are unoccupied

m is mRNA, σ is transcription, γpis degradation

k± is binding/unbinding, κ± is coupling/uncoupling for dimers

N=d/C is copy number

Quasi steady state approximation (QSSA)

Not really used.

They just look at

equilibrium and steady

states without worrying about

relative time scales.

Positive feedback solutions using quasi steady state approximation (QSSA)

Equilibrium concentration with copy number

Transition in copy number occurs at

Vary numbers of whole motifs, not of nodes within motif

Multiple stable states

ratios

Equations for motifs and food webs

mortality to predation

Growth

rate

maintenance

consumption

Density

dependence

Type 2 functional

response

Scaling of terms with mass

Choose time

scale of 1

Mass-specific

metabolic rate

Consumption rate

relative to

metabolic rate

Very particular choice of parameter values. Out to

4 decimal. Likely means there results are extremely sensitive

and not robust. Connectance is low and size is medium.

Persistence of motifs

more

frequent

less

frequent

Different

Results

than given

in Milo.

Omnovory

is FFL.

Persistence

is measured as

fraction of species

That persist after a

specified number

of time steps.

Conclusions and questions

Motif persistence is not tied to web persistence

Most common motifs are tied to web persistence

Are there larger motifs where persistence in isolation

and persistence of whole web do match? If so, those

motifs might be the real building blocks.

Do webs with different patterns of motifs that imply

less persistence have greater short term robustness?

How do prey selection and dynamics of motifs and

motif representation change in time? What does this

mean for our results?

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