Transcript Coarse-Graining of Macromolecules

Lecture 6: The Mathematics of
Recruitment
(Beautiful work of David Goodsell)
Rob Phillips
California Institute of Technology
The Case of Activation
(Nissley et al.)
All 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.
Repression in the Lac Operon: The
Experimental Backdrop
pbound ( L  0)
Repression(L) 
pbound ( L)
(Muller et al.)
Repression
Single operator case
pbound  1
R   rd
e
pbound ( R  0)
N NS
R   rd
Repression( R) 
 1
 1
e
pbound ( R)
1 p
N NS
Oehler et al. (1994)
We fit the
first point of
each set
Lac Repressor: Different Views
(Beautiful work of David Goodsell)
Repression and Looping I
This is the
only point
used to fit
the looping
energy
Operator quality
Vilar and Leibler ‘03
Operator distance
Beta-Galactosidase Activity
(Dove et al.)
(Lawrence et al.)
Ian B. Dodd et al. Genes Dev. 2004; 18: 344-354
The Regulation Factor
Synergistic Activation
Interaction through DNA bending
No interaction
DNA in a Tight Squeeze: Case Studies
(Bustamante et al.)
Viral DNA Packing
15 microns of data
confined to 50nm capsid.
Packing forces related to
infection mechanism.
(Goodsell)
Eukaryotic DNA Packing
DNA in nucleus wound
around protein – histone
octamer.
Radius of curvature
comparable to DNA
thickness.
Gene Regulation
DNA-binding proteins
such as Lac repressor
loop DNA.
Ubiquitous in
prokaryotes and
eukaryotes.
Genes in Eukaryotes
Nucleosomes
Beams and Biology
Kinematics of Beam Bending
Nucleosome Structure Continued
(Richmond and Davey)
Experiments on Nucleosome Accessibility
Accessibility vs Burial Depth