Lecture 6: The Mathematics of Lecture 6: The Mathematics of RecruitmentRecruitment

Rob PhillipsCalifornia Institute of Technology

(Beautiful work of David Goodsell)

The Case of ActivationThe Case of Activation

(Nissley et al.)

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

Lac Repressor: Different ViewsLac Repressor: Different Views

(Beautiful work of David Goodsell)

Repression and Looping IRepression and Looping I

This is the only point used to fit the looping energy

Operator qualityOperator quality

Vilar and Leibler ‘03

Operator distanceOperator distance

Beta-Galactosidase ActivityBeta-Galactosidase Activity

Ian B. Dodd et al. Genes Dev. 2004; 18: 344-354

(Dove et al.)

(Lawrence et al.)

The Regulation FactorThe Regulation Factor

Synergistic ActivationSynergistic Activation

No interaction

Interaction through DNA bending

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.

Genes in EukaryotesGenes in Eukaryotes

NucleosomesNucleosomes

Beams and BiologyBeams and Biology

Kinematics of Beam BendingKinematics of Beam Bending

Nucleosome Structure ContinuedNucleosome Structure Continued

(Richmond and Davey)

Experiments on Nucleosome AccessibilityExperiments on Nucleosome Accessibility

Accessibility vs Burial DepthAccessibility vs Burial Depth