DNA is a long polymer with the form of a double helix of about two nanometers diameter (2.10-9 meters). It is composed of nucleotides whose sequence carries the information of heredity. The four possible nucleotides have slightly different geometries, and their sequence along the DNA molecule are thought to influence the shape and the stiffness of the double helix on a scale of few tens to a few hundred base pairs, and thereby its biological activity. DNA minicircles (or miniplasmids) are closed loops with lengths of the order of a few tens or hundreds of base pairs in which the double helix bends around to close on its own tail with some number of twists. Its minimal energy shape and its energy of formation depend on the sequence of base pairs, and can be efficiently computed by polymer and rod models, if shape and stiffness parameters of DNA are provided as inputs. This structure is therefore an interesting experimental motif to test sequence-dependent mechanical properties of the DNA molecule. The purpose of this thesis is to explore the experimental methods to determine the shape and free energy of formation of DNA minicircles. The shapes have been be determined from cryo-electron micrographs. Efficiency of formation has been investigated by a novel method called annealing-cyclization. Cryo-electron microscopy allows observation of very small molecules (here 17 or 11 nm diameter) in vitrified water, in order to keep the 3D shape of the molecules as close as possible to the shape they had in solution. In Chapter 1, I used stereo cryo-electron micrographs to determine and compare the three-dimensional shape of 95 individual DNA minicircles of 158 base pairs, which were identical in sequence except within a 18 bp block which contained either a TATA box sequence or a CAP site. I defined the notion of shape-distance which I used to estimate the error of reconstruction, and I detected clusters of shapes using an appropriate sorting algorithm. However the cluster did not seem to be associated with the variable sequence (TATA or CAP). I then analyzed (in Chapter 2) two-dimensional shapes of shorter DNA minicircles (94 bp) determined by negative staining electron microscopy, designed with either two nicks (breaks in one of the strands) or two gaps (missing nucleotides) at diametrically opposite sites of the minicircles. I observed that the gapped minicircles have an elongated shape with respect to the nicked minicircles, and I used this result together with the results of atomic level molecular dynamics simulations to conclude that the gap flexibility, perhaps together with base unpairing at the gap site, is responsible for this elongated minicircle shape. Finally, I proposed a ligase-free assay to measure the minicircle formation efficiency, which can give a high yield of nicked minicircles. The method avoids the use of ligase and the associated concerns about the effect of ligase concentration on the measurements. I determined an equation from a chemical model of the reaction that fits the experimental data, and I defined the Ja factor which gives a measure of the cyclization yield independent of DNA initial concentration. This method seems to confirm that minicircles with two gaps cyclize more efficiently that minicircles with two nicks, probably because of the gap flexibility. As a perspective, the conclusions of this thesis could be used for the design of minicircle constructs whose shape would be sensitive enough to sequence mutation in order to be detected by electron microscopy. Such shapes could be then compared, thanks to the shape-distance tool defined herein, to shapes computed with known or putative DNA models.