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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