My research at the APCTP focuses on the modelisation and the interpretation of counterions distribution at the surface of macromolecules immersed in aqueous solution. When an object is dipped in a solution, its surface acquires a net charge. This surface charge induces an electrical potential, which in turn produces a cloud of counterions in the vicinity of the submerged object in order to neutralize the surfacic charges and to ensure the electroneutrality of the system.
When the surface is weakly charged, the distribution of ions can be calculated theoretically by mean field theory (resolution of the Poisson-Boltzmann equation), figure.1.
However, for systems involving strong surfacic charges, and where strong dielectric contrasts take place, mean field theory is not sufficient to explain behaviors such as the formation of a bidimensional Wigner crystal of counterions in the vicinity of the surface which results from strong correlations, or by the apparition of attractive forces between biomolecules with the same electric charge.
In many biological systems, electrostatic interaction is typically much larger than the thermal energy, and the attractive forces between objects with the same electrical charge can then be induced by repulsive interactions between counterions and image charges induced by the dielectric contrast between the macromolecules and the solvent.
Furthermore, although the litterature does reports this phenomenon in specific cases of two dimensional systems of strongly charged objects with an homogeneous dielectric constant, it is nevertheless insufficient for comparison with real biological systems, and experimental measurements, where strong dielectric contrasts have to be taken into account. For example, in an aqueous solution have a dielectric constant of 80 a protein have a dielectric constant of 2. This type of problem is poorly documented [3,4,5].
Approach used to the study of such systems consist in the Hamiltonian formulation from the field theory proposed by Netz and Orland [1,2]. This Hamiltonian is then inserted into the Langevin equation and integrated by finite element.
This approach ultimately allows us to account in the combined effects of strong coupling regime (crystallization of charges on the surface of the bio-molecule) and strong dielectric contrast (repulsion of couterions from the surface of the macromolecule). These two phenomena are at the origin of a poor screening and induce attractive forces between biomolecules.
[1] R.R. Netz, Eur. Phys. J. E, 5, 557 (2001)
[2] R.R. Netz, H. Orland, Eur. Phys. J. E, 1, 203 (2000)
[3] G.R. Pack et al. Bio. Phys. Jour, 65, 1363, (1993)
[4] A.P. dos Santos, Y. Levin et al. J. Chem. Phys. 135, 044124 (2011)
[5] R. Messina, J. Chem. Phys. 117, 11062 (2002).