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DNA/RNA structure and packing
Replace methyl group with H to
get RNA base uracil
Reminder: Nucleic acidsone oxygen atom distinguishes RNA from DNA, increases reactivity (so DNA is more stable)
base attaches at 1’, phosphate at 5’
pyrimidinespurines
-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
polymerization and base pairing
DNA melting
DNA helix is a competition between energy (base pairing) and entropy (unwinding)
Energy of base-pair breaking is only a few kT (2-3 hydrogen bonds)
1D random walk for each strand
What is the free energy of formation for a bubble of length n bases?
The most probable bubble length?
Poland-Scheraga model
DNA meltingE(N,n) = Einit + nEbp G = E � TS
S = k lnW = k ln
✓(N � n+ 1) · (2n)!
(n!)(n!)
◆starting points n right
n left⇡ k [ln(N � n+ 1) + 2n ln 2]
@G
@n= Ebp � kT
✓�1
N � n+ 1+ 2 ln 2
◆= 0
Ebp/kT � 2 ln 2 = �1/(N � n+ 1) < 0 always
Ebp > 2kT ln 2 Ebp < 2kT ln 2no bubble! finite size
DNA melting
Note that it is temperature dependent!
Polymerase chain reaction (PCR)
1) high temperature melts the DNA 2) annealing so that primers (10-20 bp) can bind to the individual strands
-Used in practically every application involving DNA (genetic testing, sequencing, gene expression, etc.)
-1993 Nobel Prize in Chemistry (Kary Mullis)
3) (heat-stable) polymerase comes in and completes each strand 4) temperature is raised and cycle repeated
typically 100 - 10,000 bps
PoLS Survey Course
Automated PCR with three temperature baths!
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
DNA/RNA looping (entropy)
loop formation relies on two ends coming together spontaneously
P (R;N) =1
√
2πNa2e−R2/2Na2
What is the probability of this happening?
1D random walk
P◦ ≈
!
2
πN
δ
a∝
1√
Ltot
(1D) P◦ ≈
!
6
πN3(δ
a)3 ∝
1
L3/2
tot
(3D)PBoC 8.2.4
1D (L-1/2) 3D (L-3/2)
N
Pro
babi
lity
DNA/RNA looping (entropy)
DNA/RNA looping (energy)
-bending DNA costs energy Ebend =EIL
2R2
Lp ~ 50 nm, L = 0.34*Nbp nm → Eloop = 3000kT/Nbp
bending energy decreases as DNA length increases
PBoC 10.3.2
Eloop =⇡EI
R=
⇡kTLp
R<latexit sha1_base64="PUH0PnunhGECX8aNPD75LwrH568=">AAACIHicbVDLSgMxFM34rPU16tJNsAiuykwV6kYoSkHBRZW+oFOGTJq2oZlJSDJCGfopbvwVNy4U0Z1+jWk7FG09EDiccw839wSCUaUd58taWl5ZXVvPbGQ3t7Z3du29/briscSkhjnjshkgRRiNSE1TzUhTSILCgJFGMLga+40HIhXlUVUPBWmHqBfRLsVIG8m3i2U/8WQIGediBC9g4gkKy/AGetzE4P1MG1ThrS9msm/nnLwzAVwkbkpyIEXFtz+9DsdxSCKNGVKq5TpCtxMkNcWMjLJerIhAeIB6pGVohEKi2snkwBE8NkoHdrk0L9Jwov5OJChUahgGZjJEuq/mvbH4n9eKdfe8ndBIxJpEeLqoGzOoORy3BTtUEqzZ0BCEJTV/hbiPJMLadJo1JbjzJy+SeiHvnuYLd2e50mVaRwYcgiNwAlxQBCVwDSqgBjB4BM/gFbxZT9aL9W59TEeXrDRzAP7A+v4BHyWhFg==</latexit>
Eloop = 2π2kT (
Lp
L)
R = L/2⇡<latexit sha1_base64="CQJDX2tLR97YavEO+hWxjQImgME=">AAAB8XicbVA9SwNBEJ2LXzF+RS1tFoNgFe+ioI0QtLGwiGI+MDnC3mYvWbK3e+zuCeHIv7CxUMTWf2Pnv3GTXKGJDwYe780wMy+IOdPGdb+d3NLyyupafr2wsbm1vVPc3WtomShC60RyqVoB1pQzQeuGGU5bsaI4CjhtBsPrid98okozKR7MKKZ+hPuChYxgY6XHe3SJbk8qnZh1iyW37E6BFomXkRJkqHWLX52eJElEhSEca9323Nj4KVaGEU7HhU6iaYzJEPdp21KBI6r9dHrxGB1ZpYdCqWwJg6bq74kUR1qPosB2RtgM9Lw3Ef/z2okJL/yUiTgxVJDZojDhyEg0eR/1mKLE8JElmChmb0VkgBUmxoZUsCF48y8vkkal7J2WK3dnpepVFkceDuAQjsGDc6jCDdSgDgQEPMMrvDnaeXHenY9Za87JZvbhD5zPH5zFj5M=</latexit>
*NOTE: Lp is depends on kT, so Eloop is actually temperature independent!
DNA/RNA looping (free energy)
P◦ ≈
!
6
πN3(δ
a)3 ∝
1
L3/2
tot
∆G = kT [3000
Nbp
− ln(P◦)]
∆G = kT [3000
Nbp
+3
2lnNbp + const.]
minimum around 2000 bpPBoC 10.3.3
�G = �Ebend � T�S
1
N3/2bp
*assumes T ≈ 300 K
J-factor: proportional to exp(-βΔG)
More accurate calculations (using WLC) show minimum is around 500 bp; agrees with experiments PBoC 10.3.3
DNA/RNA looping (free energy)
J-factor: proportional to exp(-βΔG)new experiments confirmed deviation from WLC at short lengths
x + in plot from Vafabakhsh, Ha. (2012) Extreme bendability of DNA less than 100
base pairs long revealed by single-molecule cyclization. Science, 337, 1097–1101.
Work in Kim lab (GT) show that a “kinkable WLC” (KWLC) model can explain the new dataLe, Kim. (2014) Probing the elastic limit of DNA bending. Nucleic Acids Res., 42, 10786–94.
Maher (2006) Structure, 14, 1479-80.
DNA/RNA looping (free energy)
DNA/RNA looping
proteins can bind and force DNA to loop
200 nm
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, 102:6783-6788, 2005.
DNA packaging
packing ratio (Vext. / Vpack.) illustrates that significant forces are required to package DNA
-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 ϕ29 model
Petrov & Harvey (2008) Biophys J 95:497-502
DNA packaging
optical tweezers (peak force ~ 60 pN)
fit to theoretical model for ϕ29, extrapolation to other viruses
ϕ29 virus packing
DNA “scrunchworm” hypothesis
B-DNA
SC Harvey. (2015) The scrunchworm hypothesis: Transitions between A-DNA and B-DNA provide the driving force for genome packaging in double-stranded DNA bacteriophages. J. Struct. Biol, 118, 1-8.
Waters, Kim, Gumbart, Lu, Harvey. (2016) DNA scrunching in the packaging of viral genomes. J. Phys. Chem. B 120, 6200-7.
A-DNA
B-DNA
The packing motor clamps DNA at the top while it dehydrates in the middle, shrinking to its A-DNA form, then clamps at the bottom while
it expands into the virus capsid
clamp
clamp
DNA ejection in real time
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):14652-14657.
DNA is ejected at up to 60 kbp/s!
LamB protein initiates ejection; flow causes DNA to be stretched out