The Elastic Rod Model for DNA and Its Application to the Tertiary Structure of DNA Minicircles in Mononucleosomes

Abstract

Explicit solutions to the equations of equilibrium in the theory of the elastic rod model for DNA are employed to develop a procedure for finding the configuration that minimizes the elastic energy of a minicircle in a mononucleosome with specified values of the minicircle size N in base pairs, the extent w of wrapping of DNA about the histone core particle, the helical repeat h(0)b of the bound DNA, and the linking number Lk of the minicircle. The procedure permits a determination of the set Y(N, w, h(0)b) of integral values of Lk for which the minimum energy configuration does not involve self-contact, and graphs of writhe versus w are presented for such values of Lk. For the range of N of interest here, 330 < N < 370, the set Y(N, w, h(0)b) is of primary importance: when Lk is not in Y(N, w, h(0)b), the configurations compatible with Lk have elastic energies high enough to preclude the occurrence of an observable concentration of topoisomer Lk in an equilibrium distribution of topoisomers. Equilibrium distributions of Lk, calculated by setting differences in the free energy of the extranucleosomal loop equal to differences in equilibrium elastic energy, are found to be very close to Gaussian when computed under the assumption that w is fixed, but far from Gaussian when it is assumed that w fluctuates between two values. The theoretical results given suggest a method by which one may calculate DNA-histone binding energies from measured equilibrium distributions of Lk.

Writhe formulas and antipodal points in plectonemic DNA configurations

“…The double integral being time consuming to evaluate, one can in a first step discretize it [37] with a reduced number of elements so that it produces an approximate result that only has to be accurate up to ±1 (one still has to estimate how many elements are needed to obtain such an accuracy [4]). Then in a second step, Fuller integral is used to refine the result.…”

Tops and Writhing DNA

“…The writhe of a DNA polymer configuration, viewed as a space curve, is a nonlocal quantity which has subtle geometric and topological properties. The nonlocality of the writhe makes it cumbersome to use in analytical or computational work [17,33,22,21,32,1,4]. This paper is devoted to understanding the writhe for configurations which dominate the partition function: those close to the minima of the energy functional.…”

Conformational analysis of stiff chiral polymers with end-constraints

“…In this context we use the notation (1) If one defines the following inner product on the vector space formed by all 3 × 3 skewsymmetric matrices, (2) where tr(·) denotes the trace of a matrix, then it is clear that (E i ,E j ) = δ ij and Similarly, one can define the matrix commutator as (3) Whereas large rotations are elements of SO (3), small rotations can be associated with the set of 3 × 3 skew symmetric matrices. When endowed with the above inner product and commutator, this set of matrices is called so (3).…”