John Palmeri

Variational approach for electrolyte solutions: from dielectric interfaces to charged nanopores

A variational theory is developed to study electrolyte solutions, composed of interacting pointlike ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and nonlinear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image-charge repulsion. Our variational equations thus go beyond the mean-field theory, or weak coupling limit, where thermal fluctuations overcome electrostatic correlations, and allows one to reach the opposite strong coupling limit, where electrostatic interactions induced by interfaces dominate. The influence of salt concentration, ion valency, dielectric jumps, and surface charge is studied in two geometries. (i) A single neutral dielectric interface (e.g., air-water or electrolyte-membrane) with an asymmetric electrolyte. A charge separation and thus an electrostatic field get established due to the different image-charge repulsions for coions and counterions. Both charge distributions and surface tension are computed and compared to previous approximate calculations. For symmetric electrolyte solutions close to a charged surface, two zones are characterized. In the first one, in contact with the surface and with size proportional to the logarithm of the coupling parameter, strong image forces and strong coupling impose a total ion exclusion, while in the second zone the mean-field approach applies. (ii) A symmetric electrolyte confined between two dielectric interfaces as a simple model of ion rejection from nanopores in membranes. The competition between image-charge repulsion and attraction of counterions by the membrane charge is studied. For small surface charge, the counterion partition coefficient decreases with increasing pore size up to a critical pore size, contrary to neutral membranes. For larger pore sizes, the whole system behaves like a neutral pore. For strong coupling and small pore size, coion exclusion is total and the counterion partition coefficient is solely determined by global electroneutrality. A quantitative comparison is made with a previous approach, where image and surface charge effects were smeared out in the pore. It is shown that the variational method allows one to go beyond the constant Donnan potential approximation, with deviations stronger at high ion concentrations or small pore sizes. The prediction of the variational method is also compared with MC simulations and good agreement is observed.

The vapor-liquid interface potential of (multi)polar fluids and its influence on ion solvation

The interface between the vapor and liquid phase of quadrupolar-dipolar fluids is the seat of an electric interfacial potential whose influence on ion solvation and distribution is not yet fully understood. To obtain further microscopic insight into water specificity we first present extensive classical molecular dynamics simulations of a series of model liquids with variable molecular quadrupole moments that interpolates between SPC/E water and a purely dipolar liquid. We then pinpoint the essential role played by the competing multipolar contributions to the vapor-liquid and the solute-liquid interface potentials in determining an important ion-specific direct electrostatic contribution to the ionic solvation free energy for SPC/E water-dominated by the quadrupolar and dipolar parts-beyond the dominant polarization one. Our results show that the influence of the vapor-liquid interfacial potential on ion solvation is strongly reduced due to the strong partial cancellation brought about by the competing solute-liquid interface potential.

Ionic Capillary Evaporation in Weakly Charged Nanopores

Using a variational field theory, we show that an electrolyte confined to a neutral cylindrical nanopore traversing a low dielectric membrane exhibits a first-order ionic liquid-vapor pseudo-phase-transition from an ionic-penetration liquid phase to an ionic-exclusion vapor phase, controlled by nanopore-modified ionic correlations and dielectric repulsion. For weakly charged nanopores, this pseudotransition survives and may shed light on the mechanism behind the rapid switching of nanopore conductivity observed in experiments.

Thermal denaturation of fluctuating DNA driven by bending entropy.

A statistical model of homopolymer DNA, coupling internal base-pair states (unbroken or broken) and external thermal chain fluctuations, is exactly solved using transfer kernel techniques. The dependence on temperature and DNA length of the fraction of denaturation bubbles and their correlation length is deduced. The thermal denaturation transition emerges naturally when the chain fluctuations are integrated out and is driven by the difference in bending (entropy dominated) free energy between broken and unbroken segments. Conformational properties of DNA, such as persistence length and mean-square-radius, are also explicitly calculated, leading, e.g., to a coherent explanation for the experimentally observed thermal viscosity transition.

Ionic transport through sub-10 nm diameter hydrophobic high-aspect ratio nanopores: experiment, theory and simulation

Fundamental understanding of ionic transport at the nanoscale is essential for developing biosensors based on nanopore technology and new generation high-performance nanofiltration membranes for separation and purification applications. We study here ionic transport through single putatively neutral hydrophobic nanopores with high aspect ratio (of length Lu2009=u20096u2009μm with diameters ranging from 1 to 10u2009nm) and with a well controlled cylindrical geometry. We develop a detailed hybrid mesoscopic theoretical approach for the electrolyte conductivity inside nanopores, which considers explicitly ion advection by electro-osmotic flow and possible flow slip at the pore surface. By fitting the experimental conductance data we show that for nanopore diameters greater than 4u2009nm a constant weak surface charge density of about 10−2u2009C m−2 needs to be incorporated in the model to account for conductance plateaus of a few pico-siemens at low salt concentrations. For tighter nanopores, our analysis leads to a higher surface charge density, which can be attributed to a modification of ion solvation structure close to the pore surface, as observed in the molecular dynamics simulations we performed.

Thermal denaturation of fluctuating finite DNA chains: the role of bending rigidity in bubble nucleation.

Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a one-dimensional Ising model, which describes the internal base-pair states, coupled to a discrete wormlike chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of poly(dA)-poly(dT) and, by inserting the experimentally known bending rigidities, leads to physically reasonable values for the bare Ising model parameters. Among the thermodynamical quantities explicitly calculated within this model are the internal, structural, and mechanical features of the DNA molecule, such as bubble correlation length and two distinct chain persistence lengths. The predicted variation of the mean-square radius as a function of temperature leads to a coherent explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs. Simple limiting formulas, useful for analyzing experiments, are given for the fraction of broken base pairs, Ising and chain correlation functions, effective persistence lengths, and chain mean-square radius, all as a function of temperature and DNA length.

Microscopic Mechanism for Experimentally Observed Anomalous Elasticity of DNA in Two Dimensions

By exploring a recent model in which DNA bending elasticity, described by the wormlike chain model, is coupled to basepair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic-force microscopy experiments. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally. Although such anomalies exist when DNA fluctuates freely in three dimensions (3D), they are too weak to be detected. Interactions between bases in the helical double-stranded DNA are modified by electrostatic adsorption on a 2D substrate, which facilitates local denaturation. This work reconciles the apparent discrepancy between observed 2D and 3D DNA elastic properties and points out that conclusions about the 3D properties of DNA (and its companion proteins and enzymes) do not directly follow from 2D experiments by atomic-force microscopy.

Ionic exclusion phase transition in neutral and weakly charged cylindrical nanopores

A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir [S. Buyukdagli, M. Manghi, and J. Palmeri, Phys. Rev. Lett. 105, 158103 (2010)]. It is shown that an ion located in a neutral pore undergoes two opposing mechanisms: (i) a deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions from the pore, and (ii) an attractive contribution to the ion self-energy due to the increased screening with ion penetration of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall. For pore radii around 1 nm and bulk concentrations lower than 0.2 mol/l, this mechanism leads to a first-order phase transition, similar to capillary evaporation, from an ionic-penetration state to an ionic-exclusion state. The discontinuous phase transition exists within the biological concentration range (∼0.15 mol/l) for small enough membrane dielectric constants (ε(m) < 5). In the case of a weakly charged pore, counterion penetration exhibits a nonmonotonic behavior and is characterized by two regimes: at low reservoir concentrations or small pore radii, coions are excluded and counterions enter the pore to enforce electroneutrality; dielectric repulsion (image forces) remain strong and the counterion partition coefficient decreases with increasing reservoir concentration up to a characteristic value. For larger reservoir concentrations, image forces are screened and the partition coefficient of counterions increases with the reservoir concentration, as in the neutral pore case. Large surface charge densities (>2 × 10(-3) e/nm(2)) suppress the discontinuous transition by reducing the energy barrier for ion penetration and shifting the critical point toward very small pore sizes and reservoir concentrations. Our variational method is also compared to a previous self-consistent approach and yields important quantitative corrections. The role of the curvature of dielectric interfaces is highlighted by comparing ionic penetration into slit and cylindrical pores. Finally, a charge regulation model is introduced in order to explain the key effect of pH on ionic exclusion and explain the origin of observed time-dependent nanopore electric conductivity fluctuations and their correlation with those of the pore surface charge.

Slow closure of denaturation bubbles in DNA: twist matters.

The closure of long equilibrated denaturation bubbles in DNA is studied using Brownian dynamics simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring freely rotating strands, with a nonzero torsional modulus in the duplex state, κ(φ)=200 to 300k(B)T. For DNAs of lengths N=40 to 100 base pairs (bps) with a large initial bubble in their middle, long closure times of 0.1 to 100μs are found. The bubble starts winding from both ends until it reaches a ≈10 bp metastable state due to the large elastic energy stored in the bubble. The final closure is limited by three competing mechanisms depending on κ(φ) and N: arms diffusion until their alignment, bubble diffusion along the DNA until one end is reached, or local Kramers process (crossing over a torsional energy barrier). For clamped ends or long DNAs, the closure occurs via this last temperature-activated mechanism, yielding a good quantitative agreement with the experiments.

Coupling between denaturation and chain conformations in DNA: stretching, bending, torsion and finite size effects

We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri et al 2007xa0Phys. Rev. Lett.xa099xa0088103). Our discrete helical wormlike chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in dsDNA and ssDNA, these effects are important. Moreover, we explore in this context the role of an additional loop entropy and analyze finite size effects in an experimental context, where polydA-polydT is clamped by two G-Cxa0strands, as well as for free polymers.