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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Instructor: Van Savage
Spring 2010 Quarter
promoter region (easily evolvable)
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
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+/-1.1
0 FBLs exist. May even be selected against.
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
Not really used.
They just look at
equilibrium and steady
states without worrying about
relative time scales.
Transition in copy number occurs at
Vary numbers of whole motifs, not of nodes within motif
mortality to predation
Type 2 functional
scale of 1
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.
is measured as
fraction of species
That persist after a
of time steps.
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).