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DNA would randomly occupy a much larger volume than when it is orderly packed. Mathematically, for a non-interacting flexible chain randomly diffusing in 3D, the end-to-end distance would scale as a square root of the polymer length. For real polymers such as DNA, this gives only a very rough estimate; what is important, is that the space available for the DNA in vivo is much smaller than the space that it would occupy in the case of a free diffusion in the solution. To cope with volume constraints, DNA can pack itself in the appropriate solution

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