Biofilaments, such as actin and DNA, have for long been modeled as thermally fluctuating elastic rods with homogeneous material properties. Such models are adequate if the length scale of the filaments being studied is much larger than the scale of the heterogeneity. However, advanced single molecule experimental techniques have now made it possible to probe the properties of biomolecules at the scale of a few nanometers. The data emerging from these experiments ought to be greeted with appropriately detailed models. In this paper we study the mechanics of a thermally fluctuating elastic rod whose moduli are a function of position. Such a rod can be used as a model for DNA whose sequence specific properties are known or for a protein oligomer in an AFM where some of the monomers might be unfolded. The mechanics of these rods is understood by first evaluating a partition function through path integral techniques. We develop a computational technique to efficiently evaluate the partition function and use it to obtain the force-extension relation of a fluctuating rod with two different bending moduli as would be the case for a partially unfolded protein oligomer stretched in an AFM. The variance of the transverse fluctuations of the protein oligomer is also evaluated and are found to agree with the results of a Monte Carlo simulation.

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