Far-Field Electrostatic Signatures of Macromolecular 3D Conformation.

In solution as in vacuum, the electrostatic field distribution in the vicinity of a charged object carries information on its three-dimensional geometry. We report on an experimental study exploring the effect of molecular shape on long-range electrostatic interactions in solution. Working with DNA nanostructures carrying approximately equal amounts of total charge but each in a different three-dimensional conformation, we demonstrate that the geometry of the distribution of charge in a molecule has substantial impact on its electrical interactions. For instance, a tetrahedral structure, which is the most compact distribution of charge we tested, can create a far-field effect that is effectively identical to that of a rod-shaped molecule carrying half the amount of total structural charge. Our experiments demonstrate that escape-time electrometry (ETe) furnishes a rapid and facile method to screen and identify 3D conformations of charged biomolecules or molecular complexes in solution.

Opto-Electrostatic Determination of Nucleic Acid Double-Helix Dimensions and the Structure of the Molecule-Solvent Interface.

A DNA molecule is highly electrically charged in solution. The electrical potential at the molecular surface is known to vary strongly with the local geometry of the double helix and plays a pivotal role in DNA-protein interactions. Further out from the molecular surface, the electrical field propagating into the surrounding electrolyte bears fingerprints of the three-dimensional arrangement of the charged atoms in the molecule. However, precise extraction of the structural information encoded in the electrostatic "far field" has remained experimentally challenging. Here, we report an optical microscopy-based approach that detects the field distribution surrounding a charged molecule in solution, revealing geometric features such as the radius and the average rise per basepair of the double helix with up to sub-Angstrom precision, comparable with traditional molecular structure determination techniques like X-ray crystallography and nuclear magnetic resonance. Moreover, measurement of the helical radius furnishes an unprecedented view of both hydration and the arrangement of cations at the molecule-solvent interface. We demonstrate that a probe in the electrostatic far field delivers structural and chemical information on macromolecules, opening up a new dimension in the study of charged molecules and interfaces in solution.

Electrostatic free energies carry structural information on nucleic acid molecules in solution.

Over the last several decades, a range of experimental techniques from x-ray crystallography and atomic force microscopy to nuclear magnetic resonance and small angle x-ray scattering have probed nucleic acid structure and conformation with high resolution both in the condensed state and in solution. We present a computational study that examines the prospect of using electrostatic free energy measurements to detect 3D conformational properties of nucleic acid molecules in solution. As an example, we consider the conformational difference between A- and B-form double helices whose structures differ in the values of two key parameters-the helical radius and rise per basepair. Mapping the double helix onto a smooth charged cylinder reveals that electrostatic free energies for molecular helices can, indeed, be described by two parameters: the axial charge spacing and the radius of a corresponding equivalent cylinder. We show that electrostatic free energies are also sensitive to the local structure of the molecular interface with the surrounding electrolyte. A free energy measurement accuracy of 1%, achievable using the escape time electrometry (ETe) technique, could be expected to offer a measurement precision on the radius of the double helix of approximately 1 Å. Electrostatic free energy measurements may, therefore, not only provide information on the structure and conformation of biomolecules but could also shed light on the interfacial hydration layer and the size and arrangement of counterions at the molecular interface in solution.

Nonmonotonic Pair Potentials in the Interaction of Like-Charged Objects in Solution.

We consider the long-standing like-charge attraction problem, wherein under certain conditions, similarly charged spheres suspended in aqueous electrolyte have been observed to display a minimum in their interaction potential, contrary to the intuitively expected monotonically varying repulsion. Recently, we described an interfacial mechanism invoking the molecular nature of the solvent that explains this anomalous experimental observation. In our model for the interaction of negatively charged particles in water, the minimum in the pair potential results from the superposition of competing contributions to the total free energy. One of these contributions is the canonical repulsive electrostatic term, whereas the other is a solvation-induced attractive contribution. We find that whereas both contributions grow approximately exponentially with decreasing interparticle separation, the occurrence of a stable, long-ranged minimum in the pair potential arises from differences in the precise interparticle separation dependence of the two terms. Specifically, the interfacial solvation term exhibits a more gradual decay with distance than the electrostatic repulsion, permitting the attractive contribution to dominate the interaction at large distances. Importantly, these disparities become evident in quantities calculated from exact numerical solutions to the governing nonlinear Poisson-Boltzmann (PB) equation for the spatial electrical potential distribution in the system. In marked contrast, we find that the linearized PB equation, applicable in the regime of low surface electrical potentials, does not support nonmonotonic trends in the total interaction free energy within the present model. Our results point to the importance of exact descriptions of electrostatic interactions in real systems that most often do not subscribe to particular mathematical limits where analytical approximations may provide a sufficiently accurate description of the problem.

Electroviscous effect for a confined nanosphere in solution.

A charged colloidal particle suspended in an electrolyte experiences electroviscous stresses arising from motion-driven electrohydrodynamic phenomena. Under certain conditions, the additional contribution from electroviscous drag forces to the total drag experienced by the moving particle can lead to measurable deviations of particle diffusion coefficients from values predicted by the well known Stokes-Einstein relation that describes diffusive behavior of small particles in an unbounded charge-free fluid. In this study, we investigate the role of electroviscous stresses on nanoparticle diffusion in confined geometries using both simulations and experiment. We compare our experimental measurements with the results of a numerically solved continuum model based on the Poisson-Nernst-Planck-Stokes system of equations and find good agreement between experiment and theory. Depending on the radius of the counterion species in solution and the degree of confinement, we find that the viscous drag on polystyrene nanoparticles can be augmented by approximately 10-25% compared to the values predicted by pure hydrodynamic models in the absence of free charge in the fluid. This enhancement corresponds approximately to a 5-10% increase compared to the electroviscous contribution for a charged particle in an unbounded fluid. Contrary to recent reports in the experimental literature, we find neither experimental nor theoretical evidence of an anomalously large enhancement of electroviscous forces on a confined charged nanoparticle in solution.

Electrohydrodynamics of a compound drop.

The behavior of a compound drop, comprising two concentric fluid spheres, in a uniform electric field is studied analytically. The governing electrohydrodynamic equations are solved for Newtonian and immiscible fluids in the framework of leaky-dielectric theory and in the limit of small electric field strength and fluid inertia. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the globule, in terms of the direction of the external flow (pole-to-equator vs equator-to-pole) and the number of vortices (single-vortex vs double vortices) in the shell, and that the senses of the net electric shear stresses at the surfaces of the inner and the outer drops and their relative importance are the key parameters in setting these patterns. A circulation map is constructed, which is used to infer about the likelihood of the flow patterns and transition from one pattern to another for representative fluid systems. For small distortion from the spherical shape, the deformations of the inner and the outer drops are found using normal stress balances at the corresponding surfaces. It is shown that there will be four possible modes for the deformation of the compound drop, which are determined by the net normal electric and hydrodynamic stresses at the pertinent surfaces. The dynamic responses of the inner and the outer drops for representative fluid systems are studied using a deformation map, which characterizes the possibilities of the deformation modes and transition from one mode to another as a function of the fluid properties.

Flow patterns and deformation modes of coaxial liquid columns in transverse electric fields.

Steady-state flow patterns and deformation modes of coaxial liquid columns in transverse electric fields are studied analytically. The governing creeping flow equations are solved for Newtonian and (mutually) immiscible fluids in the framework of leaky dielectric theory. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the columns, in terms of the direction of the external flow (top-to-sides/bottom-to-sides vs. sides-to-top/sides-to-bottom) and the number of vortices (single vortex vs. double vortices) in the shell, and that the senses of the net electric shear stresses at the inner and the outer interfaces and their relative importance are the key parameters in setting these patterns. Equilibrium shapes of the interfaces are also found and it is shown that there are four distinct modes of deformation, depending on the governing nondimensional parameters of the problem. The instability of the jet is also examined qualitatively using the observations pertaining the instability of single-phase drops and jets and the scaling arguments based on the present solution.

Electrohydrodynamics of a liquid drop in confined domains.

The steady-state electrohydrodynamics of a leaky dielectric drop in confined domains is investigated analytically. The governing electrohydrodynamic equations are solved for Newtonian and immiscible fluids in the framework of leaky dielectric theory and for the creeping flow regime. The domain confinement strengthens or weakens the electric field, depending on R>1 or R<1, respectively, where R=σi/σo is the ratio of electric conductivity of the drop to that of the surrounding fluid. Similarly, the flow intensity decreases for R<1, but it remains unchanged or increases for R>1, depending on the interplay of electric and hydrodynamic effects. An expression for the drop deformation for small distortion from the spherical shape is found using the domain perturbation technique. It is shown that below a threshold domain size the confinement effect will lead to the reversal of the tendency of the net normal hydrodynamic stress in deforming the drop to an oblate or a prolate shape, and that below a critical domain size the necessary condition for having an oblate drop will be opposite to the classical one for an unbounded domain.