DNA/RNA structure and packing

Transcription

1 DNA/RNA structure and packing

2 Reminder: Nucleic acids one oxygen atom distinguishes RNA from DNA, increases reactivity (so DNA is more stable) base attaches at 1, phosphate at 5 purines pyrimidines Replace methyl group with H to get RNA base uracil

3 polymerization and base pairing -anti-parallel strands (one runs 3 to 5, the other 5 to 3 ) -bases pair through hydrogen bonds: 3 for C-G and 2 for A-T -bases also stack with each other for added stability of helix

4 DNA melting DNA helix is a competition between energy (base pairing) and entropy (unwinding) Poland-Scheraga model 1D random walk for each strand Energy of base-pair breaking is only a few kt (2-3 hydrogen bonds) What is the free energy of formation for a bubble of length n bases? The most probable bubble length?

5 DNA melting E(N,n) =E init + ne bp G = E TS starting points n right S = k ln W = k ln (N n + 1) (2n)! (n!)(n!) k [ln(n n + 1) + 2n ln 2] = E bp kt N 1 n +1 +2ln2 =0 E bp /kt 2ln2= 1/(N n + 1) < 0 always E bp > 2kT ln 2 no bubble! E bp < 2kT ln 2 finite size

6 DNA melting Note that it is temperature dependent!

7 Polymerase chain reaction (PCR) -Used in practically every application involving DNA (genetic testing, sequencing, gene expression, etc.) Nobel Prize in Chemistry 1) high temperature melts the DNA 2) annealing so that primers (10-20 bp) can bind to the individual strands 3) (heat-stable) polymerase comes in and completes each strand 4) temperature is raised and cycle repeated

8 DNA/RNA looping Looping of DNA/RNA is relevant for a variety of processes -DNA transcription -RNA structure and activity -DNA organization -translational regulation -genetic recombination PBoC 8.2.4

9 DNA/RNA looping (entropy) loop formation relies on two ends coming together spontaneously What is the probability of this happening? P (R; N) = 1 /2Na 2 2πNa 2 e R2 1D random walk P 2 πn δ a 1 (1D) P Ltot 6 πn 3 ( δ a )3 1 L 3/2 tot (3D) PBoC 8.2.4

10 DNA/RNA looping (entropy) 1D (L -1/2 ) Probability 3D (L -3/2 ) N

11 DNA/RNA looping (energy) -bending DNA costs energy E bend = EIL 2R 2 E loop =2π 2 kt( L p L ) Lp ~ 50 nm, L = 0.34*Nbp nm Eloop = 3000kT/Nbp bending energy decreases as DNA length increases PBoC

12 DNA/RNA looping (free energy) G = E bend T S G = kt[ 3000 N bp ln(p )] P 6 πn 3 ( δ a )3 1 N 3/2 bp G = kt[ 3000 N bp ln N bp + const.] PBoC minimum around 2000 bp

13 DNA/RNA looping (free energy) J-factor: proportional to exp(-βδg) More accurate calculations (using WLC) show minimum is around 500 bp; agrees with experiments PBoC

14 DNA/RNA looping (free energy) J-factor: proportional to exp(-βδg) new experiments confirmed deviation from WLC at short lengths Work in Kim lab (GT) show that a kinkable WLC (KWLC) model can explain the new data Le, Kim. (2014) Probing the elastic limit of DNA bending. Nucleic Acids Res., 42, Maher (2006) Structure, 14, x + in plot from Vafabakhsh, Ha. (2012) Extreme bendability of DNA less than 100 base pairs long revealed by single-molecule cyclization. Science, 337,

15 DNA/RNA looping proteins can bind and force DNA to loop

16 Lac repressor -regulates expression of genes in E. coli for lactose metabolism -no lactose in environment LacI binds DNA, bending it into a loop so genes can t be expressed -binding of lactose to LacI frees it and the genes are transcribed -simulations revealed that the headgroups of LacI absorb most of the strain, keeping DNA looped Structural dynamics of the Lac repressor-dna complex revealed by a multiscale simulation. Elizabeth Villa, Alexander Balaeff, and Klaus Schulten. Proceedings of the National Academy of Sciences, USA, 102: , 2005.

17 DNA packaging ϕ29 model Petrov & Harvey (2008) Biophys J 95: DNA is typically very compact compared to its extended length -bacteriophage (virus) has, e.g., 10 μm of DNA packed into a 50-nm capsid -electrostatics, bending energy both resist compaction packing ratio ( Vext. / Vpack. ) illustrates that significant forces are required to package DNA

18 DNA packaging ϕ29 virus packing optical tweezers (peak force ~ 60 pn) fit to theoretical model for ϕ29, extrapolation to other viruses

19 DNA ejection in real time DNA is ejected at up to 60 kbp/s! LamB protein initiates ejection; flow causes DNA to be stretched out Real-time observations of single bacteriophage λ DNA ejections in vitro. Paul Grayson, Lin Han, Tabita Winther, Rob Phillips, PNAS. 5 Sep 2007; 104(37):