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7.81J/8.591J/9.531J

Systems Biology‘modeling biological networks’

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Introducing ...

Lectures: Recitations:

TR 1:00 -2:30 PM W 4:00 - 5:00 PMRm. 6-120 Rm. 26-204

Alexander van Oudenaarden Rui Zhen TanRm. 68-371B ruizhentan@gmail.comavano@mit.edu Rm. 68-359

Shankar Mukherjimukherji@mit.eduRm. 68-359

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Take-home Exams:

Exam 1 due 10/02/07 15 %Exam 2 due 10/18/07 15 %Exam 3 due 11/01/07 15 %Exam 4 due 11/13/07 15 %Exam 5 due 11/27/07 15 %Final due 12/11/07 25 %

Final Problem Set will be a take-home PSbroadly covering the course material

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Text books: none

Handouts will be available on-line

Good reference (biology textbook):Molecular biology of the cellAlberts et al.

Matlab will be used intensively during thecourse, make sure you known (or learn) howto use it (necessary for problem sets)

Web-page: web.mit.edu/biophysics/sbio(contains all course materials)

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Intrinsic challenge of this class:

mixed audience with wildly different backgrounds

⇒ read up on your biology or math if needed

⇒ recitations (W 4PM, Rm. 26-204) are intended to close the gaps and prepare for homework

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Systems Biology ?

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Systems Biology ≈ Network Biology

GOAL: develop a quantitative (mathematical) understanding of thebiological function of genetic and biochemical networks

gene A

gene C

gene E

gene B

gene D

gene F

INPUT

OUTPUT

- function of gene product A-F can be known in detail but this is notsufficient to reveal the biological function of the INPUT-OUTPUT relation

- a system approach (looking beyond one gene/protein) is necessary toreveal the biological function of this whole network

- what is the function of the individual interactions (feedbacks andfeedforwards) in the context of the entire network ? 8

Three levels of complexity

I Systems Microbiology (~14 Lectures)

‘The cell as a well-stirred biochemical reactor’

II Systems Cell Biology (~8 Lectures)

‘The cell as a compartmentalized system withconcentration gradients’

III Systems Developmental Biology (~3 Lectures)

‘The cell in a social context communicating withneighboring cells’

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I Systems Microbiology (14 Lectures)

‘The cell as a well-stirred biochemical reactor’

L1 IntroductionL2 Chemical kinetics, Equilibrium binding, cooperativityL3 Lambda phageL4 Stability analysisL5-6 Genetic switchesL7 E. coli chemotaxisL8 Fine-tuned versus robust modelsL9 Receptor clusteringL10-11 Stochastic chemical kineticsL12-13 Genetic oscillatorsL14 Circadian rhythms

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I Systems Microbiology (14 Lectures)

‘The cell as a well-stirred biochemical reactor’

L1 IntroductionL2 Chemical kinetics, Equilibrium binding, cooperativityL3 Lambda phageL4 Stability analysisL5-6 Genetic switchesL7 E. coli chemotaxisL8 Fine-tuned versus robust modelsL9 Receptor clusteringL10-11 Stochastic chemical kineticsL12-13 Genetic oscillatorsL14 Circadian rhythms

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Introduction phage biology

Excellent book:

A genetic switch by Mark Ptashne

Phage genome:48512 base pairs ~ 12 kB‘phage.jpg’ ~ 10 kB

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The central dogma defines three major groups of biomolecules (biopolymers):

1. DNA (passive library, 6×109 bp, 2 m/cell,75×1012 cells/human, total length150×1012 m/human ~ 1000 rsun-earth)

2. RNA (‘passive’ intermediate)3. Proteins (active work horses)

The fourth (and final) group consists ofso-called ‘small molecules’.

4. Small molecules (sugars, hormones,vitamines, ‘substrates’ etc.)

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The lysis-lysogeny decision:

As the phage genome is injectedphage genes are transcribed andtranslated by using the host’smachinery.

Which set of phage proteins areexpressed determines the fate of thephage: lysis or lysogeny

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The lysis-lysogeny decision is a genetic switch

RNAp RNAp

only ‘space’ for one RNA polymerase (mutual exclusion)16

Single repressor dimer bound - three cases:

I Negative control, dimer binding to OR2 inhibitsRNAp binding to right PR promoter.

Positive control, dimer binding to OR2 enhancesRNAp binding to left PRM promoter.

cI transcript

more repressor monomers

more repressor dimers

inhibition

activation

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II Negative control, dimer binding to OR1 inhibitsRNAp binding to right PR promoter.

Negative control, dimer binding to OR1 inhibitsRNAp binding to left PRM promoter (too distant).

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III Negative control, dimer binding to OR3 inhibitsRNAp binding to left PRM promoter.

Positive control, dimer binding to OR3 allowsRNAp binding to right PR promoter.

Cro transcript

more Cro monomers

more Cro dimers

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Repressor-DNA binding is highly cooperative

intrinsic association constants:KOR1 ~ 10 KOR2 ~ 10 KOR3

However KOR2* >> KOR2 (positive cooperativity)

cI OFF Cro OFF

cI ON

cI OFF

Cro OFF

Cro OFF20

Flipping the switch by UV:

In lysogenic state, [repressor]is maintained at constant levelby negative feedback(“chemo-stat”)

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UV radiation induces SOS response (DNA damage)protein RecA becomes specific protease for λ repressor

after cleavage monomers cannot dimerize anymore,[repressor dimers] decreases,when all repressors vacate DNA, Cro gene switches on.

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other lytic genes

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Cooperative effects make sharp switch(‘well defined’ decision)

Note: several layers of cooperativity:dimerization, cooperative repressor binding

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I Systems Microbiology (14 Lectures)

‘The cell as a well-stirred biochemical reactor’

L1 IntroductionL2 Chemical kinetics, Equilibrium binding, cooperativityL3 Lambda phageL4 Stability analysisL5-6 Genetic switchesL7 E. coli chemotaxisL8 Fine-tuned versus robust modelsL9 Receptor clusteringL10-11 Stochastic chemical kineticsL12-13 Genetic oscillatorsL14 Circadian rhythms

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The Flagellum

> 40 genes involved

1000 H+ / rotation

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Absence of chemical attractant

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Presence of chemical attractant

chemical gradient sensed in a temporal manner30

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Chemotaxis of Escherichia coli

CW rotation: ‘tumbles’CCW rotation: ‘runs’

absence aspartate gradient random walk (diffusion)presence aspartate gradient biased random walk towards

aspartate source

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Chemotactic pathway in E. coli.

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Correlation of receptor methylation with behavioral response.

Adaptation:

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fast

slowinterm

ediate

What is the simplest mathematical modelthat is consistent with the biology andreproduces the experiments ?

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I Systems Microbiology (14 Lectures)

‘The cell as a well-stirred biochemical reactor’

L1 IntroductionL2 Chemical kinetics, Equilibrium binding, cooperativityL3 Lambda phageL4 Stability analysisL5-6 Genetic switchesL7 E. coli chemotaxisL8 Fine-tuned versus robust modelsL9 Receptor clusteringL10-11 Stochastic chemical kineticsL12-13 Genetic oscillatorsL14 Circadian rhythms

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37Kondo et al. PNAS (1994) 38

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The circadian clock consists of only 3 proteins:KaiA, KaiB and KaiC

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Circadian Oscillations inSingle Cells

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The circadian clock consists of only 3 proteins and can bereconstituted in vitro

Kondo et al. (2005) 42

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Modeling the cell cycle

45http://www.mpf.biol.vt.edu/research/budding_yeast_model 46

II Systems Cell Biology (8 Lectures)

‘The cell as a compartmentalized system withconcentration gradients’

L15 Diffusion, Fick’s equations, boundary and initial conditionsL16 Local excitation, global inhibition theoryL17-18 Models for eukaryotic gradient sensingL19-20 Center finding algorithmsL21-22 Modeling cytoskeleton dynamics

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II Systems Cell Biology (8 Lectures)

‘The cell as a compartmentalized system withconcentration gradients’

L15 Diffusion, Fick’s equations, boundary and initial conditionsL16 Local excitation, global inhibition theoryL17-18 Models for eukaryotic gradient sensingL19-20 Center finding algorithmsL21-22 Modeling cytoskeleton dynamics

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Eukaryotic Chemotaxis

How is this different from E. coli chemotaxis ?

temporal versus spatial sensing

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cyclic AMP (cAMP) is an attractantfor Dictyostelium (social amoeba)

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cyclic AMP (cAMP) is an attractantfor Dictyostelium (social amoeba)

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uniform step in cAMP

cAMP gradient

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Response of Dictyostelium to cAMP

initialdistributiont ~ 3 s

steady-statedistributiont ∞

uniform stepin cAMP

uniform and transient polarized and persistent

cAMP gradient

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Response of Dictyostelium to pulsed cAMP

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geometry of cell: circularinside cytoplasm: well-stirredinside membrane: diffusion-limited

GFP-PH binds special lipids in membrane:PIP2 and PIP3

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The molecules in the model:

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II Systems Cell Biology (8 Lectures)

‘The cell as a compartmentalized system withconcentration gradients’

L15 Diffusion, Fick’s equations, boundary and initial conditionsL16 Local excitation, global inhibition theoryL17-18 Models for eukaryotic gradient sensingL19-20 Center finding algorithmsL21-22 Modeling cytoskeleton dynamics

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how to find the middle ofa cell ?

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Most of MinE accumulates at the rim of this tube, in the shapeof a ring (the E ring). The rim of the MinC/D tube andassociated E ring move from a central position to the cellpole until both the tube and ring vanish. Meanwhile, a newMinC/D tube and associated E ring form in the opposite cellhalf, and the process repeats, resulting in a pole-to-poleoscillation cycle of the division inhibitor.A full cycle takes about 50 s.

minEminC/D

59gfp-minC

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GFP-minD

61gfp-minE is localizedin a ring

minEminD

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gfp-minE

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Recent results demonstratethat the min proteins assemble in

helices

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II Systems Cell Biology (8 Lectures)

‘The cell as a compartmentalized system withconcentration gradients’

L15 Diffusion, Fick’s equations, boundary and initial conditionsL16 Local excitation, global inhibition theoryL17-18 Models for eukaryotic gradient sensingL19-20 Center finding algorithmsL21-22 Modeling cytoskeleton dynamics

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Center finding in an eukaryotic cell: fission yeastThe importance of the cytoskeleton

67 68Chang et al.

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Microtubules

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Microtubules

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kinesin is a molecular motor that runs to the plus end of a MT72

dynein is a molecular motor that runs to the minus end of a MT

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Black tetra

Movies !74

III Systems Developmental Biology (3 Lectures)

‘The cell in a social context communicating withneighboring cells’

L23 Quorum sensingL24-25 Drosophila development

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III Systems Developmental Biology (3 Lectures)

‘The cell in a social context communicating withneighboring cells’

L23 Quorum sensingL24-25 Drosophila development

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major advantage ofDrosphila:

each stripe in theembryo correspondsto certain body partsin adult fly

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egg (contains maternal components,maternal effects, onlydetermined by mother)

zygote (contains DNAfrom father and mother,zygotic effects)

80early development

nuclei formplasma membrane

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radioactive labeled RNA reveals localizationat pole

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interpreting the bicoid gradient (createdby maternal effects) by zygotic effect(gene expression by embryo itself)

hunchback is a zygotic effect !

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hunchback readsthe bicoid gradient

84Houchmandzadeh et al.

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Center finding in the Drosophila embryo

bicoid

hunchback86

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I Systems Microbiology (14 Lectures)

‘The cell as a well-stirred biochemical reactor’

L1 IntroductionL2 Chemical kinetics, Equilibrium binding, cooperativityL3 Lambda phageL4 Stability analysisL5-6 Genetic switchesL7 E. coli chemotaxisL8 Fine-tuned versus robust modelsL9 Receptor clusteringL10-11 Stochastic chemical kineticsL12-13 Genetic oscillatorsL14 Circadian rhythms