Static curvature and flexibility measurements of DNA with microscopy. A simple renormalization method, its assessment by experiment and simulation.

We present the derivation of equations based on statistical polymer chain analysis and a method to quantify the average angle value of intrinsic bends and the local flexibility at a given locus on DNA fragments imaged by electron microscopy. DNA fragments of n base-pairs are considered as stiff chains of n jointed unit rigid rods. If the DNA fragments are composed of two branches A0Am and A0Bn, with, respectively, m and n base-pairs, where the standard deviations of the angle formed by two consecutive base-pairs are uniform over each branch, respectively, sigmathetaA and sigmathetaB, we show that the standard deviation of the angle AmA0Bn is: [formula: see text] where sigmatheta0 is the standard deviation of the angle at locus A0. This equation is established for small angular deviations by analysis of DNA at different scales and the validity of the methodology is controlled with the computation of the reduced chi2 statistical test. The length of the DNA fragments must be of the order of, or below, the persistence length, as determined by sets of statistics from computer simulations of DNA fragments. This is verified experimentally by a detailed analysis of the digitized contours of homogeneous linear 139 base-pair DNA fragments observed by electron microscopy. The images are compared to the reconstruction of DNA fragments from the measurements. The value found, sigma0=4.6 degrees/bp, is consistent with the well-accepted value for DNA in a plane. We discuss the relationship between the standard deviation of the measured angles and the flexibility at the base-pair level. This method is useful to quantify directly from microscopy techniques, such as electron or scanning force microscopy, the true bending angle, either intrinsic or induced by a ligand, and its associated flexibility at a given locus in any small DNA fragment.