Lecture 3: Statistical Mechanics of Lecture 3: Statistical Mechanics of Gene RegulationGene Regulation

Rob PhillipsCalifornia Institute of Technology

(Schulten et al.)(Small et al.)

How Big is a Genome?How Big is a Genome?

““The Great Polymer Languages”The Great Polymer Languages”

A Reminder on DNA: One of the “Great A Reminder on DNA: One of the “Great

Polymer Languages”Polymer Languages”

The Meaning of a TerabyteThe Meaning of a Terabyte

1 gggcggcgac ctcgcgggtt ttcgctattt atgaaaattt tccggtttaa ggcgtttccg 61 ttcttcttcg tcataactta atgtttttat ttaaaatacc ctctgaaaag aaaggaaacg 121 acaggtgctg aaagcgaggc tttttggcct ctgtcgtttc ctttctctgt ttttgtccgt 181 ggaatgaaca atggaagtca acaaaaagca gctggctgac attttcggtg cgagtatccg 241 taccattcag aactggcagg aacagggaat gcccgttctg cgaggcggtg gcaagggtaa 301 tgaggtgctt tatgactctg ccgccgtcat aaaatggtat gccgaaaggg atgctgaaat 361 tgagaacgaa aagctgcgcc gggaggttga agaactgcgg caggccagcg aggcagatct 421 ccagccagga actattgagt acgaacgcca tcgacttacg cgtgcgcagg ccgacgcaca 481 ggaactgaag aatgccagag actccgctga agtggtggaa accgcattct gtactttcgt 541 gctgtcgcgg atcgcaggtg aaattgccag tattctcgac gggctccccc tgtcggtgca 601 gcggcgtttt ccggaactgg aaaaccgaca tgttgatttc ctgaaacggg atatcatcaa

………………….

48301 catgaggttg ccccgtattc agtgtcgctg atttgtattg tctgaagttg tttttacgtt 48361 aagttgatgc agatcaatta atacgatacc tgcgtcataa ttgattattt gacgtggttt 48421 gatggcctcc acgcacgttg tgatatgtag atgataatca ttatcacttt acgggtcctt 48481 tccggtgatc cgacaggtta cg

(Thanks to Farid Abraham)

Sizing up Sizing up E. ColiE. Coli

A Reminder on the Central DogmaA Reminder on the Central Dogma

Lifestyles of BacteriophageLifestyles of Bacteriophage

Gene Regulatory Decisions: The Gene Regulatory Decisions: The

Case of Phage LambdaCase of Phage Lambda

Phage lambda can either lay in wait or immediately reproduce.Viral life cycle dictated by regulatory decisions – the lambda switch.

Gene Regulation and Gene Regulation and

Development: Case of Development: Case of DrosophilaDrosophila

(Berman et al.)

Spatial patterns of gene expression lead to anterior-posterior polarity.Gradients in regulatory proteins.

The Great Idea of Jacob and The Great Idea of Jacob and

Monod: Genes that Control GenesMonod: Genes that Control Genes

Observations on phage life cycle and bacterial growth in presence of different sugars led to picture of gene regulation.Use of sugars other than glucose (such as lactose) seemed to be tightly controlled.

(Muller-Hill)

How Are Genes Regulated?How Are Genes Regulated?

Genes can be regulated at many stages along the path from DNA to protein.Transcriptional control is one of the most important mechanisms and will be the focus of our discussion.

RNA Polymerase: Bound or Not?RNA Polymerase: Bound or Not?

(Cramer ‘02)(Ptashne and Gann)

For us, the whole question of transcriptional regulation will come down to the question of whether or not RNAP is bound to the promoter or not!There are an array of molecules (transcription factors) that participate in recruiting RNAP to its promoter.

Repressors: The CartoonRepressors: The Cartoon

Repressor molecules inhibit action of RNA polymerase.Repressors can be under the control of other molecules (i.e. inducers) that dictate when repressor is bound and not.

Activators: The CartoonActivators: The Cartoon

Activator molecules enhance the action of RNA polymerase.Activators can be under the control of other molecules (i.e. inducers) that dictate when activator is bound and not.Activators “RECRUIT” the polymerase.

Adhesive interaction between RNAPand activator

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.

Structures of the Molecular Actors Structures of the Molecular Actors

in the Lac Dramain the Lac Drama

(Beautiful work of David Goodsell)

RNAP+DNA+mRNA

Lac Repressor

CRP and DNA

Products of the Lac Operon

)(

)0((L) Repression

bound

bound

Lp

Lp

Repression level depends upon the spacing of the operators.Once again, we assert that the dynamical definition can be replaced by an equilibrium description.

Repression in the Lac Operon: the Repression in the Lac Operon: the

Role of Looping Role of Looping