FIG. 4: The relative probability of finding m bubbles within three DNA lengths at 310 K. FIG. 5: Effective persistence length of the DNA fragments of the length L taken from inside a 300 bp long DNA (empty circles) This is compared with theoretical curve (line) obtained assuming a single bubble of the size given by the mean, 1.7 bp. elsewhere. Within the short DNAs of our interest, the number of bubbles, if they exist at all, can be regarded to be unity in a good approximation. To focus on the effects of bubble (excluding the end fork effect) on the overall duplex persistence length, we consider an ensemble of fragments with given contour length L ran- domly taken from inside a 300-bp long ( ∼ 100 nm) dsDNA at a physiological temperature. The square of duplex end-to-end distance, R 2 $_{ee}$, is defined as arithmetical average of the end-to-end distances of the two single strands. The thermal average of its square 〈 R 2 $_{ee}$〉 is taken over the ensemble of the duplex with a given L . Suppose that the duplex to be a 7