Introduction to Physical Biology: Models and Numbers

Transcription

1 Introduction to Physical Biology: Models and Numbers Boulder Lectures on Soft Matter Physics July 2012 Yitzhak Rabin R. Phillips, J. Kondev, J. Theriot, Physical Biology of the Cell (Garland, 2009) A.D. Bates and A. Maxwell, DNA Topology (Oxford, 2005)

2 Building blocks of cells 4 types of macromolecules made of simple repeat units: proteins DNA Polysaccharides lipids

3 Distribution of macromolecules in E. coli bacterium

4 Language of DNA and proteins:

5 Nucleotides: purines pyrimidines

6 Chemical structure of DNA Conclusions at a glance: 1. Each strand has a direction (3 to 5 ) 2. GC bp more stable than AT bp 3 h-bonds instead of 2! 3. Bases turn inwards how do proteins recognize sequence?

7 Standard B form of DNA The grooves allow access to proteins

8 Rosetta stone - translating bp code to aa sequence

9 Models of DNA what is the question?

10 Models of proteins:

11 Models of membranes:

12 Models of Bacteria

13 Pictures are nice - but quantitative data requires quantitative models! The toolbox of physics and chemistry: Simple tools (we understand them well): Harmonic oscillator Ideal gas Two level systems (Ising model) Diffusion and random walks Polymer physics DH and PB models of charges in solution Elasticity of rods and plates Low Reynolds number hydrodynamics Rate equations Newton s equations (MD simulations)

14 Complex tools (we do not understand them well enough): Non-linear dynamics (attractors) Reaction-diffusion equations Many body systems of complex elements Quantum chemistry of large molecules Topology

15 Example simple applications of harmonic oscillator:

16 Choice of model requires knowing the order of magnitude of some characteristic numbers! Examples: 1. Is inertia important for bacterial propulsion? Estimate the Reynolds number of E. coli s motion in water Inertia is irrelevant velocity is proportional to the force and responds instantaneously to it! (Aristotle beats Newton for bacteria)

17 2. Confinement of DNA: Estimate the radius of gyration of the lambda phage DNA: Kuhn segment length of DNA: a=100nm; Length of DNA: L= bp 0.3nm = nm

18 What is the volume fraction occupied by DNA? Virus ( lambda phage) bacteria sperm cell somatic cell

19 How is the highly confined state of DNA maintained? Viruses: crystal-like density and arrangement need motors for packing No proteins inside to balance electrostatic repulsion Wigner crystal type stabilization by walls

20 Bacteria: single DNA is packed without confining wallsin < 10% of bacterial volume need attractions! 1. DNA is packaged by about a dozen of nucleoid-associated proteins that bend and twist it HU, high concentration H-NS HU, low conc. IHF Dps FIS

21 2. Topology: bacterial DNA is circular conserved linking number Lk = # of turns of double helix Topology-changing enzymes (gyrases, topoisomerases) can cut one DNA strand, overwind (Lk > Lk 0 ) or unwind (Lk < Lk 0 ) it, and glue it together again. (this destabilizes the double helix promotes recognition and reactivity of exposed bases?)

22 Linking number can be decomposed into twist and writhe: L k = Tw +Wr

23 Plasmids form right-handed (-) supercoils E.coli genome Supercoiling of bacterial DNA helps with its packing?

24 Eukaryotic (human) cells: 46 DNA molecules inside nucleus Chromosomes are segregated during mitosis what about interphase chromatin?

25 Spaghetti soup model of chromatin? Problem numerous inter-chain entanglements for N > Ne (Ne=200) -like a polymer melt! Even a single DNA molecule confined in a nucleus (R G /R nucleus > 10) will be strongly self-entangled! Lua et al, 2004

26 Solution I: entanglements and knots can be removed by topo II Sikorav and Janninck, C. R. Acad. Sci. Paris t. 316, serie II, p. 751, 1993 Solution II: DNA molecules are organized in crumpled globules and segregated in space Grosberg et al, Europhys. Lett. 23, 373, 1993 Crumpled (unknotted) globule: d f =3 Equilibrium (knotted) globule: d f =2 HiC experiments agree with crumpled/fractal globule: R(s)=const s 1/3 Lieberman et al, Science 326, 289 (2009)

27 Chromatin territories: Segregation vs interpenetration?

28 Small scale organization of chromatin 30 nm fiber nucleosomes Nucleosome chain 147bp DNA wrapped around histone octamer with 50 bp linker Histone octamer: cylinder of r=3.5nm and h=6nm Very dilute!

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