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When a polymer is modeled by a long elastic rod of homogeneous and isotropic material, we find that its persistence length is proportional to the cube of the critical length for Euler buckling caused by the root-mean-square contraction force. The proportionality constant involves the radius of the circular cross section of the rod. For paramyosin, the persistence length is larger than the critical buckling length by a factor of about 3.
Gerald S. Manning (Sat,) studied this question.