Lecture 6: The Mathematics of Recruitment Rob Phillips California Institute of Technology (Beautiful work of David Goodsell)

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 (Muller et al.)

Repression Single operator case 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 Ian B. Dodd et al. Genes Dev. 2004; 18: (Dove et al.) (Lawrence et al.)

The Regulation Factor

Synergistic Activation No interaction Interaction through DNA bending

DNA in a Tight Squeeze: Case Studies (Goodsell) (Bustamante et al.) Gene Regulation Eukaryotic DNA Packing Viral 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.

Genes in Eukaryotes

Nucleosomes

Beams and Biology Beams and Biology

Kinematics of Beam Bending

Nucleosome Structure Continued (Richmond and Davey)

Experiments on Nucleosome Accessibility

Accessibility vs Burial Depth