Question

Twisting DNA For small torques exerted on a beam of elastic material, there is a linear relationship between the torque and the torsional strain, r- C de/dz, where C is the twist modulus. This is analogous to the bend elasticity worked out in class. Single-molecule experiments using magnetic or optical tweezers allow measurements of the twist elasticity of DNA molecules by systematically winding up the tethered DNA molecule and examining the build up of torque. bead 1 fixed small bead nick a) Use the data shown in Figure 10.38

Problem 3: Twisting DNA For small torques exerted on a beam of elastic material, there is a linear relationship between the torque and the torsional strain, r- C de/dz, where C is the twist modulus. This is analogous to the bend elasticity worked out in class. Single-molecule experiments using magnetic or optical tweezers allow measurements of the twist elasticity of DNA molecules by systematically winding up the tethered DNA molecule and examining the build up of torque. bead 1 fixed small bead nick a) Use the data shown in Figure 10.38(A) to estimate the twist bead 2 fixed modulus C. (b) Estimate the torque needed to wind a 14.8 kb DNA molecule by 10 rotations and by 100 rotations (c) Write an expression for the energy stored in the twisted DNA molecule by virtue of its twist deformation. Using this expression and the data given in Figure 10.38(A), estimate the energy per base pair stored in the DNA molecule of 14.8 kb in length after the molecule has been subjected to 50 complete revolutions (d) An alternative way to measure the twist modulus (as with the bending modulus) is to probe the thermal fluctuations of the molecule. Figure 10.38(B) shows the angular excursion of the molecule (as reported by the motion of a bead stuck to the DNA in the middle of the molecule as shown in Figure 10.37) due to thermal fluctuations Find the probability distribution p(6) by computing the partition function. Show that (Αθ)-)-kBTL/C and use this result and the data to find C. 40 30 20 G/ -10 0 250 500 750 1000 time (s) -0.1 -0.05 0 0.05 0. Atwist (rad bp-1) Figure 10.38: Experimental data from DNA twisting experiment. (A) Experimental results for the relation between the torque and the angular deflection of the DNA molecule. (B) Distribution of angular fluctuations in the bead position. (Adapted from Z. Bryant et al Nature 424:338, 2003.)

Answer 1

Twisting DNA a) 45pNnm Nnmbp 3177 rad rad 9.00.03 C is equal to the slope in figure 10.40A One basepair equals roughly 0.34nm b) T 3177 rad 14800 bp t(10turns)-4, 610-21Nm and τ (100turns)-4, 610-20 Nm c) → W(0) = 21 750-2T) 2.14800 W(0) 3177 pNbp 10593pNbp = 3601-10-12N. 10-9,n = 869kBT for T-300K 1,e-BE(0) with β 1 and Z RBT kBT T 2L kBTL kBTL 1.38.3 14800bp pNnmbp4.14 14800bp pNbp2 0.34(2T)2 rad rad

I hope you understood the problem and got your answers, If yes rate me!! or else comment for a better solutions