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Single Supercoiled DNAs. DNA Supercoiling in vivo. In most organisms, DNA is negatively supercoiled ( s ~ -0.06) Actively regulated by topoisomerases , ubiquitous and essential family of proteins
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DNA Supercoiling in vivo • In most organisms, DNA is negatively supercoiled (s ~ -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 Lko = Two (Two = 1 per 10.5 bp of B-DNA, Wro= 0) Linking number for torsionally strained DNA DLk = Lk-Lko = DTw + Wr Normalized linking number difference s = DLk /Lko
How to torsionally constrain DNA? DNA must be 1) unnicked and 2) unable to rotate at its ends
Is DNA stretched and supercoiled in vivo or in solution? • Relationship between plasmid and extended DNA. Circular l-DNA with s ~ -0.05 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 15oC causes l-DNA to unwind by ~ 25 turns DNA unwinds by ~ 0.012o/oC/bp
Measuring DNA Unwinding Energeticsusing low-force data +scDNA -scDNA
twist stretch stretch twist A A+ B+ = A B B+ 1 kBT C (2pn)2 lo 2 Paths to Stretched & Overwound DNA TA+ + WA+B+ = WAB + TB+ TA+ + DWAB+ = TB+ =
twist stretch stretch twist A A- B- = A B B- Paths to Stretched, Unwound DNA A- = A+ DWAB- TA- + DWAB- = TB-
kBT C (2pn) G = lo 1 kBT C - Ed= 2p(n-nc)Gc lo 2 Denaturing DNA before the buckling transition (2pnc)2 + Ed TB- =
2p2 kBT C (n-nc)2 lo Measuring the Work Deficit to Stretch Unwound DNA A- = A+ DWAB- Symmetry of plectoneme formation: TA- = TA+ D = DWAB+ - DWAB- = TB+ - TB- =
1/2 (in nm ) Determination of DNA twist persistence length,critical torque for unwinding, and energy of denaturation kBT C - (2pnc) ~ 9 pN nm Gc= lo
High-force properties of supercoiled DNA Negative Supercoiling Positive Supercoiling S-DNA+P-DNA S-DNA Leger et al., PRL (1999) 83: 1066-1069
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 a = aoexp(2pDnnativeG/kBT) b = boexp(-2pDnunwoundG/kBT)