DNA cyclization and looping in the wormlike limit: Normal modes and the validity of the harmonic approximation

Abstract

For much of the last three decades Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, J, or J factor, for DNA models having sequencedependent bends or inhomogeneous bending flexibility. Within the last ten years, however, approaches based on harmonic analysis of semi-flexible polymer models have been introduced, which offer much greater computational efficiency than Monte Carlo techniques. These methods consider the ensemble of molecular conformations in terms of harmonic fluctuations about a well-defined elastic-energy minimum.However, the harmonic approximation is only applicable for small systems, because the accessible conformation space of larger systems is increasingly dominated by anharmonic contributions. In the case of computed values of the J factor, deviations of the harmonic approximation from the exact value of J as a function of DNA length have not been characterized. Using a recent, numerically exact method that accounts for both anharmonic and harmonic contributions to J for wormlike chains of arbitrary size, we report here the apparent error that results from neglecting anharmonic behavior. For wormlike chains having contour lengths less than four times the persistence length the error in J arising from the harmonic approximation is generally small, amounting to free energies less than the thermal energy, k B T. For larger systems, however, the deviations between harmonic and exact J values increase approximately linearly with size.

Determinants of cyclization–decyclization kinetics of short DNA with sticky ends

“…In the same figure, we also plot the theoretical J factor of a worm-like chain [46] using a range of persistence lengths from 40 to 50 nm (dashed lines). This theoretical J factor should be taken as a lower limit as it approximates the fluctuations about the minimum-energy loop only up to the quadratic terms [51]. As shown in this plot, the J factors of DNA set 1 correspond to persistence lengths between 44 and 49 nm.…”

Loop-closure Kinetics Reveal a Stable, Right-handed DNA Intermediate in Cre Recombination

“…For DNA molecules on the length scale considered here (≈ 10 200 bp) the deviation of the free energy computed by NMA alone from exact values amounts to less than the thermal energy, B k T (where B k is the Boltzmann constant and 300 K T is the temperature); in terms of J this error is approximately within a factor of two. 46 We account here for this theoretical deviation as well as potential uncertainties in the exact value of Kb by introducing an adjustable multiplicative constant α relating computed J-factor curves to those obtained by applying NMA to our structural model, atomic-force and electron microscopy. 30,50 It is difficult to conceive of a mechanism whereby product chirality arises from solely non-productive conformational preferences.…”

“…where n is the number of base pairs in the Cre-loxP mediated DNA loop. NMA allows one to calculate the free energy and to identify the principal modes of vibration of macromolecular structures fluctuating about a mechanical-energy minimum and is mathematically equivalent to the harmonic approximation 45,46. The present structural model of the Cre-loxP synaptosome regards the looped nucleoprotein complex as a Cre half-tetramer anchoring the base of a DNA loop n base pairs in size.…”