1. Single Supercoiled DNAs

2. 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

3. 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

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

5. Magnetic Trap

6. Depth Imaging

7. One molecule or two molecules?

8. Extension vs. Supercoiling

10. Supercoiling and the buckling transition

11. Is DNA stretched and supercoiled in vivo or in solution? Relationship between plasmid and extended DNA. Circular  -DNA with  ~ -0.05 experiences an internal (entropic) tension ~ 0.3 pN

12. 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 ~ 0.012 o / o C/bp

13. Force-extension curves for SC-DNA

14. Effect of ionic conditions

15. Evidence for DNA unwinding: hybridization experiments 3

16. Hybridization : force and hat curve detection

17. Sequence/Supercoiling dependence of hybridization

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

19. 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) 2 1 2 k B T C lolo

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

21. 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 -

22. 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

23. 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 )

24. High-force properties of supercoiled DNA Leger et al., PRL (1999) 83: 1066-1069 Negative Supercoiling Positive Supercoiling S-DNA S-DNA+P-DNA

25. 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

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