Theo Odijk

Scaling theory of DNA confined in nanochannels and nanoslits.

A scaling analysis is presented of the statistics of long DNA confined in nanochannels and nanoslits. It is argued that there are several regimes in between the de Gennes and Odijk limits introduced long ago. The DNA chain folds back on itself giving rise to a global persistence length that may be very large owing to entropic deflection. Moreover, there is an orientational excluded-volume effect between the DNA segments imposed solely by the nanoconfinement. These two effects cause the chain statistics to be intricate leading to nontrivial power laws for the chain extension in the intermediate regimes. It is stressed that DNA confinement within nanochannels differs from that in nanoslits because the respective orientational excluded-volume effects are not the same.

Osmotic compaction of supercoiled DNA into a bacterial nucleoid

A theory is presented of the phase separation of supercoiled DNA into a nucleoid in a bacterial cell. The suspension consists of DNA interacting with globular proteins in excess salt. A cross virial between DNA and a protein is computed as well as the DNA self-energy arising from excluded volume. The cellular parameters of Escherichia coli would appear to be compatible with the thermodynamic equilibrium derived theoretically. The state of superhelical DNA in the nucleoid could be liquid crystalline and rippled.

Hexagonally packed DNA within bacteriophage T7 stabilized by curvature stress

A continuum computation is proposed for the bending stress stabilizing DNA that is hexagonally packed within bacteriophage T7. Because the inner radius of the DNA spool is rather small, the stress of the curved DNA genome is strong enough to balance its electrostatic self-repulsion so as to form a stable hexagonal phase. The theory is in accord with the microscopically determined structure of bacteriophage T7 filled with DNA within the experimental margin of error.

Polymer- and salt-induced toroids of hexagonal DNA

A model is proposed for polymer- and salt-induced toroidal condensates of DNA, based on a recent theory of the undulation enhancement of the electrostatic interaction in the bulk hexagonal phase of semiflexible polyions. In a continuum approximation, the thermodynamic potential of a monomolecular toroid may be split up in bulk, surface, and curvature contributions. With the help of an approximate analytical minimization procedure, the optimal torus dimensions are calculated as a function of the concentrations of inert polymer and added salt. The stability of the torus is analyzed in terms of its surface tension and a bulk melting criterion. The theory should be applicable to psi-toroids that are not too thick.

DNA confined in nanochannels : Hairpin tightening by entropic depletion

A theory is presented of the elongation of double-stranded DNA confined in a nanochannel based on a study of the formation of hairpins. A hairpin becomes constrained as it approaches the wall of a channel which leads to an entropic force causing the hairpin to tighten. The DNA in the hairpin remains double-stranded. The free energy of the hairpin is significantly larger than what one would expect if this entropic effect were unimportant. As a result, the distance between hairpins or the global persistence length is often tens of micrometer long and may even reach millimeter sizes for 10 nm thin channels. The hairpin shape and size and the DNA elongation are computed for nanoslits and circular and square nanochannels. A comparison with experiment is given.

Electrostatic-Undulatory Theory of Plectonemically Supercoiled DNA

We present an analytical calculation of the electrostatic interaction in a plectonemic supercoil within the Poisson-Boltzmann approximation. Undulations of the supercoil strands arising from thermal motion couple nonlinearly with the electrostatic interaction, giving rise to a strong enhancement of the bare interaction. In the limit of fairly tight winding, the free energy of a plectonemic supercoil may be split into an elastic contribution containing the bending and torsional energies and an electrostatic-undulatory free energy. The total free energy of the supercoil is minimized according to an iterative scheme, which utilizes the special symmetry inherent in the usual elastic free energy of the plectoneme. The superhelical radius, opening angle, and undulation amplitudes in the radius and pitch are obtained as a function of the specific linking difference and the concentration of monovalent salt. Our results compare favorably with the experimental values for these parameters of Boles et al. (1990. J. Mol. Biol. 213:931-951). In particular, we confirm the experimental observation that the writhe is a virtually constant fraction of the excess linking number over a wide range of superhelical densities. Another important prediction is the ionic strength dependence of the plectonemic parameters, which is in reasonable agreement with the results from computer simulations.

Statics and dynamics of condensed DNA within phages and globules.

Several controversial issues concerning the packing of linear DNA in bacteriophages and globules are discussed. Exact relations for the osmotic pressure, capsid pressure and loading force are derived in terms of the hole size inside phages under the assumption that the DNA globule has a uniform density. A new electrostatic model is introduced for computing the osmotic pressure of rod–like polyelectrolytes at very high concentrations. At intermediate packing, a reptation model is considered for DNA diffusing within a toroidal globule. Under tight–packing conditions a model of Coulomb sliding friction is proposed. A general discussion is given of our current understanding of the statics and dynamics of confined DNA in the context of the following experiments: characterization of the liquid crystalline phases, X–ray scattering by phages, osmotic–stress measurements, cyclization within globules and single–molecule determination of the loading forces.

Elastic constants of nematic solutions of rod-like and semi-flexible polymers

Abstract Analytical expressions for the elastic constants of nematic polymer solutions are derived when the macromolecules are monodisperse rod-like, bidisperse rodlike or semi-flexible. These expressions are derived in the gaussian approximation so that they constitute exact leading terms of a general asymptotic expansion for high degree of nematic ordering although the results are justifiable only within the range of validity of the second virial approximation. The limiting forms are in complete agreement with recent numerical work for monodisperse rods.

DNA in a liquid-crystalline environment: Tight bends, rings, supercoils

The entropy of tightly bent DNA is investigated in a variety of problems: closure probabilities, hairpin formation, nicked coils, plectonemic supercoiling, all in states with liquid‐crystalline order. A new semiclassical method is presented for deriving the Green function of a tightly curved wormlike chain. Precise estimates for the entropy arising from undulations are given for tightly bent DNA in weak, intermediate, and strong nematic fields. A formal statistical mechanical analysis is outlined for hairpins and supercoils. The elongation of closed DNA without twist is computed in strong nematic fields. A scaling theory is given for a liquid crystal of untwisted DNA rings in which nematic order and ring elongation are self‐consistently coupled. The elongation of plectonemic supercoils is evaluated for weak and strong nematic fields. The pitch of a cholesteric phase of plectonemic or loose supercoils is shown to be directly related to their writhe.

Statistical theory and structure factor of a semidilute solution of rodlike macromolecules interacting by Van der Waals forces

The second and third virial coefficients are estimated for a semidilute suspension of macromolecular rods interacting by van der Waals forces. Whenever the attractive interaction becomes strong enough to be noticeable, it is no longer quantitatively correct to adopt a second virial approximation. Nevertheless, the statistical properties of the second virial fluid are investigated because it is a very convenient idealization of strongly interacting molecular fluids. Sufficient conditions for the local thermodynamic stability of the isotropic phase are set up. The coupling of orientational with translational degrees of freedom which arises from the anisotropic van der Waals interaction between two rods is particularly manifest in the structure factor. This is calculated analytically with the help of a variational theorem.