WLC with a uniform persistence length L eff p , we use the well-known relation [18] 〈 R 2 $_{ee}$〉 = 2 L eff p L − 2( L eff p ) $^{2}$[1 − e − L/L eff p ] . (8) Comparing this with simulation data, we evaluate L eff p of our duplex for various values of the contour length L . The result shown in Fig. 5 indicates that L eff p decreases from the value 50 nm to 40 nm as the L decreases to 10 nm. It reflects the enhanced flexibility of the duplex, which we attribute to the presence of thermal bubbles. Along the DNA length shorter than 50 nm, if any, a single bubble is most likely to exist, as shown in N$_{b}$ ( m ), Fig. 4. If the single bubble survives as the contour length decreases, its mean size does not change as discussed earlier, consequently yielding larger flexibility. To support this argument quantitatively, we note that the mean end-to-end distance is given by 〈 R 2 $_{ee}$〉 = ∫ L 0 ∫ L 0 dsds $^{′}$〈 t ( s ) · t ( s $^{′}$) 〉 [18], where t ( s ) is the unit tangent vector at the arclength s from an end of the duplex. The tangent correlation function is given by 〈 t ( s ) · t ( s $^{′}$) 〉 = exp {−| s ′ − s | / L$_{ds}$ } if they are the positions within ds region and 〈 t ( s ) · t ( s $^{′}$) 〉 = exp {−| s ′ − s | / 2 L$_{ss}$ } if s and s ′ are the points within the bubble region. Integrating the correlation function along the contour with a bubble of the mean size, 1.7 bp, we evaluate the 〈 R 2 $_{ee}$〉 . Since a bubble occurs with equal probability along the contour we further average the mean square end-to-end distance over all possible position of the bubble, and relate it with the effective persistence length, which is shown by the curve in Fig. 5. For the length larger than 10 nm, this analytical theory agrees with simulation result remarkably, suggesting that the persistence length reduction is indeed due to a single bubble. As the length decreases below that, this curve departs much from the simulation result for the length shorter than that. It is because even a single bubble is unlikely to occur within such a short length so that the persistence length sharply rises to the double strand value. For a long DNA fragment, on the other hand, only a bubble is found in most cases with its average size fixed independently of DNA length, which results in no significant perturbations on the persistence length. For the short duplex with free ends , we also have investigated the mean end-to-end dis- tances of DNA fragments length shorter than 50 nm (147 bp) at 310 K. The persistence length calculated in a similar way from these data is shown by triangles in Fig. 6. It clearly shows that L eff p , in this range of the contour length, are shorter than L$_{ds}$ = 50 nm but converges to the value as the contour length increases. The persistence length in this case 8