Single Supercoiled DNAs

DNA Supercoiling in vivo In most organisms, DNA is negatively supercoiled (  ~ -0.06) Actively regulated by topoisomerases, ubiquitous and essential family of proteins Supercoiling is involved in DNA packaging around histones, and the initiation of transcription, replication, repair & recombination Known to induce structural changes in DNA Traditional means of study (gel electrophoresis, sedimentation analysis, cryo-EM…) do not provide for time-resolved, reversible studies of DNA supercoiling

Topological formalism for torsionally constrained DNA Tw (Twist, the number of helical turns of the DNA) + Wr (Writhe, the number of loops along the DNA) _____ Lk (Total number of crossings between the 2 strands) Linking number for torsionally relaxed DNA Lk o = Tw o (Tw o = 1 per 10.5 bp of B-DNA, Wr o = 0) Linking number for torsionally strained DNA  Lk = Lk-Lk o =  Tw + Wr Normalized linking number difference  =  Lk /Lk o

How to torsionally constrain DNA? DNA must be 1) unnicked and 2) unable to rotate at its ends

Magnetic Trap

Depth Imaging

One molecule or two molecules?

Extension vs. Supercoiling

Supercoiling and the buckling transition

Is DNA stretched and supercoiled in vivo or in solution? Relationship between plasmid and extended DNA. Circular  -DNA with  ~ experiences an internal (entropic) tension ~ 0.3 pN

Temperature-dependence of DNA helicity As the temperature increases the DNA helicity progressively increases (i.e. the angle between base pairs increases). Raising the temperature by 15 o C causes -DNA to unwind by ~ 25 turns  DNA unwinds by ~ o / o C/bp

Force-extension curves for SC-DNA

Effect of ionic conditions

Evidence for DNA unwinding: hybridization experiments 3

Hybridization : force and hat curve detection

Sequence/Supercoiling dependence of hybridization

Measuring DNA Unwinding Energetics using low-force data -scDNA +scDNA

Paths to Stretched & Overwound DNA A  A +  B + = A  B  B + twiststretch twist T A+ + W A+B+ = W AB + T B+ T A+ +  W AB+ = T B+ = (2  n) k B T C lolo

Paths to Stretched, Unwound DNA A  A -  B - = A  B  B - twiststretch twist T A- +  W AB- = T B- A - = A +  W AB-

Denaturing DNA before the buckling transition (2  n c ) 2 + E d 1 2 k B T C lolo T B- =  = k B T C lolo (2  n) E d = 2  (n-n c )  c -

Measuring the Work Deficit to Stretch Unwound DNA A - = A +  W AB- Symmetry of plectoneme formation: T A- = T A+  =  W AB+ -  W AB- = T B+ - T B- = 2  2 k B T C lolo (n-n c ) 2

Determination of DNA twist persistence length, critical torque for unwinding, and energy of denaturation c=c= k B T C lolo (2  n c ) -~ 9 pN nm 1/2 (in nm )

High-force properties of supercoiled DNA Leger et al., PRL (1999) 83: Negative Supercoiling Positive Supercoiling S-DNA S-DNA+P-DNA

DNA: the compliant polymorph B-DNA: 10.4 bp/turn 3.3 nm pitch P-DNA: ~2.5 bp/turn 1.5nm/bp S-DNA: 38 bp/turn 22 nm pitch Images: R. Lavery using JUMNA

Effect of torque on transition rates  =  o exp(2  n native  /k B T)  =  o exp(-2  n unwound  /k B T)