Counterion condensation theory for finite polyelectrolyte and salt concentrations

In the present work we analyze the physical fundamentals of Manning's counterion condensation using his charged line model in a simple salt solution. We extend the theory for the cases of finite saline concentration and polymeric concentration tending to zero and the case of both finite concentrations. To find the equilibrium between the phases of free and condensed counterions, besides minimizing the free energy, we deduce an auxiliary equation to determine the two characteristic parameters of the theory, the fraction of condensed counterions and the volume of condensation. We compare the obtained results in the present work for only one infinite charged line with the ones of counterion condensation theory by Schurr and Fujimoto. We find that the linear density of critical charge depends on the concentration of added salt and takes values higher than one, instead of the unitary value predicted by Manning. We obtain the equations by the activity and osmotic coefficients in function of the critical charge density. We compare them with the corresponding equations by Manning for these parameters. We extend the counterion condensation theory to solutions of linear polyelectrolytes for finite saline and polymeric concentrations using a cell model. We modify the electrostatic contribution to the Gibbs energy adding, to the traditional one calculated by Manning, the energy excess due to the macroion present in a cylindrical cell. We apply the theory to obtain the osmotic coefficient and we compare our results with experimental data of DNA osmotic coefficient and with theoretical adjustment using the Poisson-Boltzmann equation.

Electric dichroism transients of aqueous solutions of DNA

In this work we develop a theory of reduced electric linear dichroism transients of DNA fragments in aqueous solution. The DNA fragments are modelled as rigid 'bent-rod molecules' (BRM) with the following physical parameters: electric charge, electric polarizability tensors and hydrodynamical ones, and the average transition probability tensor per molecule. In order to study the growth and decay of electric dichroism transients, the orientational distribution function of the molecules is needed. This function is obtained by solving the time-dependent Fokker-Planck equation in the presence of a low electric field E, using a perturbation method and the Fourier method with time-dependent coefficients. In our calculations the origin of the coordinate system is the mass centre of the BRM. With respect to this centre, the electric dipole moment of the molecule is zero. The developed theory adequately explains the experimental results. We show that the theoretical approach used in this work is equivalent to the one applied in the Brownian dynamics simulation work performed by Porschke and co-workers. We also analyse the effect of a possible electric dipole moment on the transients of the reduced electric linear dichroism in DNA bent fragments.

Optical properties of DNA in aqueous solution

In the study of DNA electric birefringence, it is usual to use theories that consider that molecules in solution are small in relation to the light wavelength. In this work, we study the DNA electric birefringence using a broken-rod macroion (BRM) model composed of two cylindrical arms which does not restrict the size of the molecules. To achieve this, we include the inhomogeneity effect of the light electric field through the molecule and the interaction between its different parts. To analyze the interaction between a molecule and the incident beam of light, we apply the discrete dipole approximation (DDA), according to which each molecule is described as a finite array of electronic coupled oscillators. The electric birefringence is calculated from the oscillator polarizability. This is obtained from experimental data of electric birefringence saturation and from the increment of the solution refraction index in relation to that of the solvent. Furthermore, the oscillator polarizability is also estimated from DNA absorption spectrum using the Kronig-Kramers relations. This allows us to analyze the contributions of the different absorption bands of DNA to the electric birefringence. We analyze the influence of the inhomogeneity of the light electric field and of the intramolecular interactions in the characterization of DNA optical properties using electric birefringence measurements.