Résumé
We describe the new type of liquid-crystalline state which is stabilized in condensed solutions of DNA fragments in a biologically relevant range of densities. The analysis of strong correlations which take place between DNA at rather short interaxial distances is performed. It is shown that in a system of finite-size helical DNA molecules the rotational and positional fluctuations are coupled and lead to the appearance of the macroscopic helical order. We present a model which accounts for the helical structure of the molecules and for the correlation between the helices. Starting from a (liquid-crystalline) state in which the long (helical) axes of the molecules are already correlated (nematic phase; columnar hexatic phase; columnar 2D hexagonal phase) we study the transition to a correlated helical phase. In this phase, molecules cannot freely rotate in the plane perpendicular to the director and cannot freely shift in the director axis direction, but they can freely perform screw-like helical fluctuations. The model permits to explain a whole series of unusual experimental facts revealed by X-ray diffraction experiments performed both on DNA solutions and on hydrated DNA fibers. It contributes also to the understanding of the mechanisms of chiral recognition of biomolecules during crucial biological processes. The thermodynamics of the phase transition shows the effect of the macroscopic chirality on the correlated helical order. The elastic distortion induced by the chirality of the medium does not induce the macroscopic twisting of the director (as it is the case in the media of rod-like molecules) but induces a variation in the helical repeat unit of individual molecules themselves. The overwinding of the molecule which is due to the macroscopic chirality, is rather small. X-ray diffraction experiments performed on the condensed DNA solutions and in hydrated DNA fibers have shown no director twist but a gradual decrease of the helical repeat unit when increasing the DNA density in the solution. The measured decrease was up to ten percent in the solutions and of the order of few percent in hydrated fibers. The proposed model gives also a natural explanation of the specific crystallographic structure of the hexagonal phase in high-density DNA solutions and to the peculiarities of its X-ray diffraction spectra. To relate our results to the single-molecule experiments, namely to DNA elastic behavior in optical tweezers, we estimate the elastic energy transmitted to, and the elastic torque acting on an individual in the overwinding process. We compare the results with typical energies and torques involved in basic biological processes and discuss the probability of this scenario to take place in the crowded cell environment.