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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 

