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 a nalysis 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 elec tron microscopy. DNA fragments of n base-pairs are considered as stiff chai ns of n jointed unit rigid rods. Lf the DNA fragments are composed of two b ranches A(0)A(m) and A(0)B(n), with, respectively, m and n base-pairs, wher e the standard deviations of the angle formed by two consecutive base-pairs are uniform over each branch, respectively, sigma theta(A) and sigma theta (B), we show that the standard deviation of the angle A(m)A(0)B(n), is: sigma(AmAoBn)(2) = (m-1)(2m-1)/6m sigma(theta A)(2) + (n-1)(2n-1)/6n sigma( theta B)(2) + sigma(theta 0)(2) where sigma theta(0) is the standard deviation of the angle at locus A,. Th is 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 chi(2) statistical test. The length of the D NA 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 c ontours of homogeneous linear 139 base-pair DNA fragments observed by elect ron microscopy. The images are compared to the reconstruction of DNA fragme nts from the measurements. The value found, sigma(0) = 4.6/bp, is consisten t with the well-accepted value for DNA in a plane. We discuss the relations hip between the standard deviation of the measured angles and the flexibili ty at the base-pair level. This method is useful to quantify directly from microscopy techniques, such as electron or scanning force microscopy, the t rue bending angle, either intrinsic or induced by a Ligand, and its associa ted flexibility at a given locus in any small DNA fragment. (C) 1999 Academ ic Press.