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