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Lecture 6: The Mathematics of Lecture 6: The Mathematics of RecruitmentRecruitment
Rob PhillipsCalifornia Institute of Technology
(Beautiful work of David Goodsell)
All Together Now: The Lac OperonAll Together Now: The Lac Operon
Our goal: mathematize the story told by all of these cartoons.In particular, compute the probability of RNAP binding as a function of concentration of all the other molecular actors.
)(
)0((L) Repression
bound
bound
Lp
Lp
Repression in the Lac Operon: The Repression in the Lac Operon: The
Experimental Backdrop Experimental Backdrop
(Muller et al.)
RepressionRepression
Single operator case
p
eNR
Rp
RpR
rd
NS
bound
bound
11
)(
)0()(Repression
rdeN
R
NS
1
1boundp
Oehler et al. (1994)
We fit the first point of each set
Repression and Looping IRepression and Looping I
This is the only point used to fit the looping energy
Beta-Galactosidase ActivityBeta-Galactosidase Activity
Ian B. Dodd et al. Genes Dev. 2004; 18: 344-354
(Dove et al.)
(Lawrence et al.)
DNA in a Tight Squeeze: Case StudiesDNA in a Tight Squeeze: Case Studies
(Goodsell)(Bustamante et al.)
Gene RegulationEukaryotic DNA PackingViral DNA Packing
DNA-binding proteins such as Lac repressor loop DNA.Ubiquitous in prokaryotes and eukaryotes.
DNA in nucleus wound around protein – histone octamer.Radius of curvature comparable to DNA thickness.
15 microns of data confined to 50nm capsid.Packing forces related to infection mechanism.