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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

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The structure function and evolution of biological systems

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
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
Overrepresentation regulation and motifs

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
Keep connectivity fixed while increasing network size regulation and motifs

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.


Mileyko et al
Mileyko regulation and motifs et al.


Positive feedback equations with implicit dependence on copy number
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


Bistable feedback
Bistable number Feedback





Quasi steady state approximation qssa
Quasi steady state approximation (QSSA) number

Not really used.

They just look at

equilibrium and steady

states without worrying about

relative time scales.



Equilibrium concentration with copy number
Equilibrium concentration with copy number approximation (QSSA)

Transition in copy number occurs at

Vary numbers of whole motifs, not of nodes within motif


Condition for transition
Condition for transition approximation (QSSA)




Multiple stable states
Multiple stable states approximation (QSSA)

ratios


Transition in oscillations as well
Transition in oscillations approximation (QSSA)as well


Physical values o f parameters
Physical values o approximation (QSSA)f parameters


Stouffer and bascompte
Stouffer and approximation (QSSA)Bascompte


Equations for motifs and food webs
Equations for motifs and food webs approximation (QSSA)

mortality to predation

Growth

rate

maintenance

consumption

Density

dependence

Type 2 functional

response


Scaling of terms with mass
Scaling of terms with mass approximation (QSSA)

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
Persistence of motifs approximation (QSSA)

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.


Contribution of motifs to whole web persistence
Contribution of motifs to whole approximation (QSSA)web persistence


Contribution of motifs to whole web persistence1
Contribution of motifs to whole approximation (QSSA)web persistence


Conclusions and questions
Conclusions and questions approximation (QSSA)

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?


Second approximation (QSSA)Homework set is due in two weeks (May 4, 2010).


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