Supplementary Materials for: Mechanism of DNA compaction by yeast mitochondrial protein Abf2p Raymond W. Friddle, ∗† Jennifer E. Klare, ∗ Shelley S. Martin, † Michelle Corzett, § Rod Balhorn, § Enoch P. Baldwin, † Ronald J. Baskin, † and Aleksandr Noy ∗ ∗ Biosecurity and Nanoscience Laboratory, Chemistry and Materials Science Directorate, Lawrence Livermore Na- tional Laboratory, 7000 East Ave, Livemore, CA 94550 † Department of Molecular and Cellular Biology, University of California at Davis, Davis, CA 95616 § Biology and Biotechnology Program, Lawrence Livermore National Lab- oratory, 7000 East Ave, Livermore, CA 94550 The mean-squared end-to-end distance for a Worm-Like Chain with Bends Consider a polymer chain of n segments of length a. This chain contains an arbitrary number of identical pieces of p segments each. Each of the pieces is a freely rotating polymer chain (FRC)(Flory, 1969; Yamakawa, 1971). These pieces are joined by the angle φ, while all other joint angles within the piece are equal to θ, and all the dihedral angles set unrestricted. The mean squared end-to-end distance of the overall chain is given by, 〈R 2 〉 = n  i=1 n  j=1 〈r i · r j 〉 = n  i=1 〈r 2 i 〉 +2 n−1  i=1 n  j>i 〈r i · r j 〉 (1) The first sum in Eq. 1 is simply the sum over a 2 . The second sum is more involved. The factor of 2 ensures that we account for all terms in the first part of Eq. 1. Consider the case of i = 1, as we look at one piece from segments j =2,...,p. p  j=2 〈r 1 · r j 〉 = p  j=2 α j−1 Summing over the next piece should include the fixed angle φ in place of a θ. Let β = − cos φ, then for the next piece (j = p +1,..., 2p) we have: 2p  j=p+2 β α α j−1 = α p β α p  j=2 α j−1 Likewise, the sum over the third piece of the chain must include two factors of β and remove two factors of α, 3p  j=2p+2 β 2 α 2 α j−1 = α 2p  β α  2 p  j=2 α j−1 Correspondence and requests for materials should be addressed to A.N.: noy1@llnl.gov 1