Test of the Gouy-Chapman theory for a charged lipid membrane against explicit-solvent molecular dynamics simulations

Orientation of Antibody Modified and Reacted on Carboxy-Functionalized Polystyrene Particle Revealed by Zeta Potential Measurement

The comprehensive understanding of the orientation of antibodies on a solid surface is crucial for affinity-based sensing mechanisms. In this study, we demonstrated that the orientation of primary antibodies modified on carboxy-functionalized polystyrene (PS) particles can be analyzed using zeta potential behavior at different pH based on the combined Gouy-Chapman-Stern model and the acid dissociation of carboxy groups and antibodies. We observed that at low surface concentrations of the primary antibody, a side-on orientation was predominant. However, at higher concentrations (approximately 30000 antibodies per PS particle), the orientation shifted to an end-on type due to steric hindrance. Furthermore, the reaction mechanism of the secondary antibody exhibited pH-dependent behavior. At pH > 7, the zeta potential changes were attributed to the antibody-antibody reaction, whereas at pH < 7, adsorption of secondary antibody onto the PS particle was observed, leading to a change in the orientation of the primary antibody modified on the PS particle to an end-on type. The change in zeta potential due to secondary antibody binding indicated a detection limit of 37000 antibodies per PS particle. As a result, we revealed that the analysis of zeta potential behavior enables the evaluation of antibody orientation and the detection of zeptomole order antibodies. This study represents the first demonstration of this capability. We anticipate that the present concept and results will broaden the quantitative application of zeta potential measurements and have significant implications for research areas, including physical chemistry and analytical chemistry.

Surface-dependent quenching of Qdot emission can be a new tool for high resolution measurements

Single quantum dots (Qdots) are often used in the field of single-molecule imaging. Qdots are sensitive to changes in the physical interactions between the Qdots and the surrounding materials. However, the spectral changes in a single Qdot emission have not been studied in detail. Low-temperature plasma treatment of glass surfaces reduced the intensity of the 655 nm emission peak of Qdot655 on glass surfaces, but did not significantly change the intensity of the 580 nm emission. Silanization of the glass surface increases the thickness of the silane layer, and the 655 nm emission peak increased. When single Qdots on the untreated glass were imaged, plasma treatment decreased the intensity of red emission and increased yellow emission. When Qdots were brought close to the glass surface in the range of 28-0 nm, the red emission intensity decreased and the yellow emission intensity increased slightly. When single actin filaments were labeled with Qdots, fluctuations of the yellow and red emission of the Qdot were detected, which reflected the very small distance changes. Our results indicate that the local interaction of Qdots with the glass surface improves the spatial and temporal resolution of optical measurements of biomolecules labeled with Qdots.

Probing and Visualizing Interfacial Charge at Surfaces in Aqueous Solution

Surface charge density and distribution play an important role in almost all interfacial processes, influencing, for example, adsorption, colloidal stability, functional material activity, electrochemical processes, corrosion, nanoparticle toxicity, and cellular processes such as signaling, absorption, and adhesion. Understanding the heterogeneity in, and distribution of, surface and interfacial charge is key to elucidating the mechanisms underlying reactivity, the stability of materials, and biophysical processes. Atomic force microscopy (AFM) and scanning ion conductance microscopy (SICM) are highly suitable for probing the material/electrolyte interface at the nanoscale through recent advances in probe design, significant instrumental (hardware and software) developments, and the evolution of multifunctional imaging protocols. Here, we assess the capability of AFM and SICM for surface charge mapping, covering the basic underpinning principles alongside experimental considerations. We illustrate and compare the use of AFM and SICM for visualizing surface and interfacial charge with examples from materials science, geochemistry, and the life sciences.

Influence of Charge Lipid Head Group Structures on Electric Double Layer Properties

In this study we derived a model for a multicomponent lipid monolayer in contact with an aqueous solution by means of a generalized classical density functional theory and Monte Carlo simulations. Some of the important biological lipid systems were studied as monolayers composed of head groups with different shapes and charge distributions. Starting from the free energy of the system, which includes the electrostatic interactions, additional internal degrees of freedom are included as positional and orientational entropic contributions to the free energy functional. The calculus of variation was used to derive Euler–Lagrange equations, which were solved numerically by the finite element method. The theory and Monte Carlo simulations predict that there are mainly two distinct regions of the electric double layer: (1) the interfacial region, with thickness less than or equal to the length of the fully stretched conformation of the lipid head group, and (2) the outside region, which follows the usual screening of the interface. In the interfacial region, the electric double layer is strongly perturbed, and electrostatic profiles and ion distributions have functionality distinct to classical mean-field theories. Based purely on Coulomb interactions, the theory suggests that the dominant effect on the lipid head group conformation is from the charge density of the interface and the structured lipid mole fraction in the monolayer, rather than the salt concentration in the system.

On the Coupling between Mechanical Properties and Electrostatics in Biological Membranes

Cell membrane structure is proposed as a lipid matrix with embedded proteins, and thus, their emerging mechanical and electrostatic properties are commanded by lipid behavior and their interconnection with the included and absorbed proteins, cytoskeleton, extracellular matrix and ionic media. Structures formed by lipids are soft, dynamic and viscoelastic, and their properties depend on the lipid composition and on the general conditions, such as temperature, pH, ionic strength and electrostatic potentials. The dielectric constant of the apolar region of the lipid bilayer contrasts with that of the polar region, which also differs from the aqueous milieu, and these changes happen in the nanometer scale. Besides, an important percentage of the lipids are anionic, and the rest are dipoles or higher multipoles, and the polar regions are highly hydrated, with these water molecules forming an active part of the membrane. Therefore, electric fields (both, internal and external) affects membrane thickness, density, tension and curvature, and conversely, mechanical deformations modify membrane electrostatics. As a consequence, interfacial electrostatics appears as a highly important parameter, affecting the membrane properties in general and mechanical features in particular. In this review we focus on the electromechanical behavior of lipid and cell membranes, the physicochemical origin and the biological implications, with emphasis in signal propagation in nerve cells.

Inhomogeneity of polylysine adsorption layers on lipid membranes revealed by theoretical analysis of electrokinetic data and molecular dynamics simulations

The adsorption of large polycations on a charged lipid membrane is qualitatively different from the small inorganic cations, which almost uniformly populate the membrane surface. We assume that the polycationic adsorption layer might be laterally inhomogeneous starting from a certain polymer length, and this effect can be more visible for membranes with low anionic lipid content. To study systems with inhomogeneous adsorption layers, we carried out electrokinetic measurements of mobility of liposomes containing anionic and neutral phospholipids in the presence of polylysine molecules. Some of these systems were simulated by all-atom molecular dynamics. Here we proposed a theoretical approach accounting for the formation of separated regions at the membrane surface, which differ in charge density and surface potential. Our model allowed us to determine the adsorption layer's geometric parameters such as surface coverage and surface-bound monomer fraction of polymer, which correlate with the molecular dynamics (MD) simulations. We demonstrated that the configuration polylysine adopts on the membrane surface (tall or planar) depends on the polymer/membrane charge ratio. Both theory and MD indicate a decrease in the anionic lipid content, alongside with a decrease in the bound monomer fraction and corresponding increase in the extension length of the adsorbed polymers.

Anomalous behavior of membrane fluidity caused by copper-copper bond coupled phospholipids

Membrane fluidity, essential for cell functions, is obviously affected by copper, but the molecular mechanism is poorly understood. Here, we unexpectedly observed that a decrease in phospholipid (PL) bilayer fluidity caused by Cu²⁺ was more significant than those by Zn²⁺ and Ca²⁺, while a comparable reduction occurred in the last two ions. This finding disagrees with the placement in the periodic table of Cu just next to Zn and far from Ca. The physical nature was revealed to be an anomalous attraction between Cu⁺ cations, as well as the induced motif of two phospholipids coupled by Cu-Cu bond (PL-diCu-PL). Namely, upon Cu²⁺ ion binding to a negatively charged phosphate group of lipid, Cu²⁺ was reduced to Cu⁺. The attraction of the cations then caused one Cu⁺ ion simultaneously binding to two lipids and another Cu⁺, resulting in the formation of PL-diCu-PL structure. In contrast, this attraction cannot occur in the cases of Zn and Ca ions. Remarkably, besides lipids, the phosphate group also widely exists in other biological molecules, including DNA, RNA, ADP and ATP. Our findings thus provide a new view for understanding the biological functions of copper and the mechanism underlying copper-related diseases, as well as lipid assembly.

Characterization of the interface of binary mixed DOPC:DOPS liposomes in water: The impact of charge condensation

Solutions of liposomes composed of binary mixtures of anionic dioleoylphosphatidylserine (DOPS) and zwitterionic dioleoylphosphatidylcholine (DOPC) are investigated with label-free angle-resolved (AR) second harmonic scattering (SHS) and electrophoretic mobility measurements. The membrane surface potential is extracted from the AR-SHS response. The surface potential changes from -10 to -145 mV with varying DOPS content ( from 0% to 100%) and levels off already at ∼ 10 % DOPS content. The ζ-potential shows the same trend but with a drastically lower saturation value (-44 mV). This difference is explained by the formation of a condensed layer of Na⁺ counterions around the outer leaflet of the liposome as predicted by charge condensation theories for polyelectrolyte systems.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

Validating a Coarse-Grained Voltage Activation Model by Comparing Its Performance to the Results of Monte Carlo Simulations

Simulating the nature of voltage-activated systems is a problem of major current interest, ranging from the action of voltage-gated ion channels to energy storage batteries. However, fully microscopic converging molecular simulations of external voltage effects present a major challenge, and macroscopic models are associated with major uncertainties about the dielectric treatment and the underlying physical basis. Recently we developed a coarse-grained (CG) model that represents explicitly the electrodes, the electrolytes, and the membrane/protein system. The CG model provides a semimacroscopic way of capturing the microscopic physics of voltage-activated systems. Our method was originally validated by reproducing macroscopic and analytical results for key test cases and then used in modeling voltage-activated ion channels and related problems. In this work, we further establish the reliability of the CG voltage model by comparing it to the results of Monte Carlo (MC) simulations with a microscopic electrolyte model. The comparison explores different aspects of membrane, electrolyte, and electrode systems ranging from the Gouy-Chapman model to the determination of the electrolyte charge distribution in the solution between two electrodes (without and with a separating membrane), as well as the evaluation of gating charges. Overall the agreement is very impressive. This provides confidence in the CG model and also shows that the MC model can be used in realistic simulation of voltage activation of membrane proteins with sufficient computer time.

Energetics of the Mixing of Phospholipids in Bilayers Determined Using Vesicle Solubilization

Here, we report an experimental approach for determining the change in the free energy and the enthalpy that accompanies the mixing of the anionic phosphatidylglycerol and the zwitterionic phosphatidylcholine. The enthalpy change originates in the thermal changes of disrupting lipid bilayer vesicles titrated into a surfactant micelle solution and is monitored using isothermal titration calorimetry. The difference in the solubilization enthalpies between pure and mixed lipid vesicles yields the lipid mixing enthalpy. The Gibbs free energy changes are estimated by determining the thermodynamic equilibrium constants of forming a molecular complex between phospholipids and methyl-β-cyclodextrin. We provide direct experimental evidence that mixing of the anionic lipid and the zwitterionic lipid is explained well by the entropic term of the electrostatic free energy of a charged surface in the Gouy-Chapman model. The present strategy enables us to determine the precise energetics of lipid-lipid interactions in near-native environments such as liposomes without any chemical modification to lipid molecules.

Charge reversal at a planar boundary between two dielectrics

Despite the ubiquitous character and relevance of the electric double layer in the entire realm of interface and colloid science, very little is known of the effect that surface heterogeneity exerts on the underlying mechanisms of ion adsorption. Herein, computer simulations offer a perspective that, in sharp contrast to the homogeneously charged surface, discrete groups promote multivalent counterion binding, leading to charge reversal but possibly having not a sign change of the electrophoretic mobility. Counterintuitively, the introduction of dielectric images yields a significantly greater accumulation of counterions, which further facilitates the magnitude of charge reversal. The reported results are very sensitive to both the degree of ion hydration and the representation of surface charges. Our findings shed light on the mechanism for charge reversal over a broad range of coupling regimes operating the adsorption of counterions through surface group bridging attraction with their own images and provide opportunities for experimental studies and theoretical development.

Surface Electrostatic Potential and Water Orientation in the presence of Sodium Octanoate Dilute Monolayers Studied by Means of Molecular Dynamics Simulations

A series of atomistic molecular dynamics simulations were performed in the present investigation to assess the spontaneous formation of surfactant monolayers of sodium octanoate at the water-vacuum interface. The surfactant surface coverage increased until a saturation threshold was achieved, after which any further surfactant addition led to the formation of micellar aggregates within the solution. The saturated films were not densely packed, as might be expected for short-chained surfactants, and all films regardless of the surface coverage presented surfactant molecules with the same ordering pattern, namely, with the ionic heads toward the aqueous solution and the tails lying nearly parallel to the interface. The major contributions to the electrostatic surface potential came from the charged heads and the counterion distribution, which nearly canceled out each other. The balance between the oppositely charged ions rendered the electrostatic contributions from water meaningful, amounting to ca. 10% of the contributions arising from the ionic species. And even the aliphatic tails, whose atoms bear relatively small partial atomic charges as compared to the polar molecules and molecular fragments, contributed with ca. 20% of the total electrostatic surface potential of the systems under investigation. Although the aliphatic tails were not so orderly arranged as in a compact film, the C-H bonds assumed a preferential orientation, leading to an increased contribution to the electrostatic properties of the interface. The most prominent feature arising from the partitioning of the electrostatic potential into individual contributions was the long-range ordering of the water molecules. This ordering of the water molecules produced a repulsive dipole-dipole interaction between the two interfaces, which increased with the surface coverage. Only for a water layer wider than 10 nm was true bulk behavior observed, and the repulsive dipole-dipole interaction faded away.

Lipid charge regulation of non-specific biological ion channels

Lipid charge regulation effects in different protein–lipid conformations highlight the role of electrostatic interactions in conductance and selectivity of non-specific biological ion channels.

Force spectroscopy reveals the effect of different ions in the nanomechanical behavior of phospholipid model membranes: the case of potassium cation

How do metal cations affect the stability and structure of phospholipid bilayers? What role does ion binding play in the insertion of proteins and the overall mechanical stability of biological membranes? Investigators have used different theoretical and microscopic approaches to study the mechanical properties of lipid bilayers. Although they are crucial for such studies, molecular-dynamics simulations cannot yet span the complexity of biological membranes. In addition, there are still some experimental difficulties when it comes to testing the ion binding to lipid bilayers in an accurate way. Hence, there is a need to establish a new approach from the perspective of the nanometric scale, where most of the specific molecular phenomena take place. Atomic force microscopy has become an essential tool for examining the structure and behavior of lipid bilayers. In this work, we used force spectroscopy to quantitatively characterize nanomechanical resistance as a function of the electrolyte composition by means of a reliable molecular fingerprint that reveals itself as a repetitive jump in the approaching force curve. By systematically probing a set of bilayers of different composition immersed in electrolytes composed of a variety of monovalent and divalent metal cations, we were able to obtain a wealth of information showing that each ion makes an independent and important contribution to the gross mechanical resistance and its plastic properties. This work addresses the need to assess the effects of different ions on the structure of phospholipid membranes, and opens new avenues for characterizing the (nano)mechanical stability of membranes.

Concentration dependence of NaCl ion distributions around DPPC lipid bilayers

We study the coordination of excess NaCl to zwitterionic DPPC lipid bilayers using molecular dynamics simulations. We find that Na ions directly coordinate with the DPPC lipid carbonyl groups. As the number of excess ions increases, the number of coordinated ions increases, until it reaches a plateau at a ratio near 1 ion per every four lipids at 310 K, and 1 ion per every six lipids at 323 K. The area per lipid decreases as the number of excess ions is increased. For low number of ions per lipids (1:16 and 1:8), most Na ions are bound to the lipid carbonyls, while the Cl form an ionic cloud around the lipid choline groups. As a result of the Na binding, the lipid has an effective positive charge density. The residence time of Na ions bound to the lipid is longer than 40 ns, while Cl ions exchange faster than the nanoseconds timescale. We find that the bound Na ions replace ordered water around the carbonyls. The net linear charge density near the carbonyl groups stays positive, regardless of the presence of excess salt in the solution.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: theory versus experiment

Aqueous dispersions of phosphatidylglycerol (PG) lipids may present an anomalous chain-melting transition at low ionic strengths, as seen by different experimental techniques such as calorimetry or light scattering. The anomaly disappears at high ionic strengths or for longer acyl-chain lengths. In this article, we use a statistical model for the bilayer that distinguishes both lipid chain and headgroup states in order to compare model and experimental thermotropic and electrical properties. The effective van der Waals interactions among hydrophobic chains compete with the electrostatic repulsions between polar headgroups, which may be ionized (counterion dissociated) or electrically neutral (associated with counterions). Electric degrees of freedom introduce new thermotropic charge-ordered phases in which headgroup charges may be spatially ordered, depending on the electrolyte ionic strength, introducing a new rationale for experimental data on PGs. The thermal phases presented by the model for different chain lengths, at fixed ionic strength, compare well with an experimental phase diagram constructed on the basis of differential scanning calorimetry profiles. In the case of dispersions of DMPG (dimyristoyl phosphatidylglycerol) with added monovalent salt, the model properties reproduce the main features displayed by data from differential scanning calorimetry as well as the characteristic profile for the degree of ionization of the bilayer surface across the anomalous transition region, obtained from the theoretical interpretation of electrokinetic (conductivity and electrophoretic mobility) measurements.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: a statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types--each one associated, respectively, with the polar-headgroup and the acyl-chain states--which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Coarse grained model for exploring voltage dependent ion channels

The relationship between the membrane voltage and the gating of voltage activated ion channels and other systems have been a problem of great current interest. Unfortunately, reliable molecular simulations of external voltage effects present a major challenge, since meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties in terms of the dielectric used and other key features. This work extends our coarse grained (CG) model to simulations of membrane/protein systems under external potential. Special attention is devoted to a consistent modeling of the effect of external potential due to the electrodes, emphasizing semimacroscopic description of the electrolytes in the solution regions between the membranes and the electrodes, as well as the coupling between the combined potential from the electrodes plus the electrolytes and the protein ionized groups. We also provide a clear connection to microscopic treatment of the electrolytes and thus can explore possible conceptual problems that are hard to resolve by other current approaches. For example, we obtain a clear description of the charge distribution in the entire electrolyte system, including near the electrodes in membrane/electrodes systems (where continuum models do not seem to provide the relevant results). Furthermore, the present treatment provides an insight on the distribution of the electrolyte charges before and after equilibration across the membrane, and thus on the nature of the gating charge. The different aspects of the model have been carefully validated by considering problems ranging for the simple Debye-Huckel, and the Gouy-Chapman models to the evaluation of the electrolyte distribution between two electrodes, as well as the effect of extending the simulation system by periodic replicas. Overall the clear connection to microscopic descriptions combined with the power of the CG modeling seems to offer a powerful tool for exploring the balance between the protein conformational energy and the interaction with the external potential in voltage activated channels. To illustrate these features we present a preliminary study of the gating charge in the voltage activated Kv1.2 channel, using the actual change in the electrolyte charge distribution rather than the conventional macroscopic estimate. We also discuss other special features of the model, which include the ability to capture the effect of changes in the protonation states of the protein residues during the close to open voltage induced transition. This article is part of a Special Issue entitled: Membrane protein structure and function.

Dilution technique to determine the hydrodynamic volume fraction of a vesicle suspension

A simple dilution method to determine the hydrodynamic volume fraction of vesicle suspensions is presented. The vesicle suspension is diluted with a solution containing a tracer Y, which is similar to a component X already present in the suspending fluid and which does not bind to or permeate through the vesicles. The concentrations of X and Y in the suspending fluid measured after dilution are used to determine the volume fraction. Using this technique, the volume fractions of vesicle suspensions comprising cationic vesicles prepared in solutions of CaCl(2) (X) were measured by dilution with MgCl(2) (Y) solutions. Various experimental parameters such as the concentration of the MgCl(2) diluents and the dilution volume ratio were studied and their effects optimized to arrive at a robust recipe for measuring the volume fraction. It is demonstrated that the technique can be applied to concentrated suspensions containing multilamellar and polydisperse vesicles.

Influence of solubilizing environments on membrane protein structures

Membrane protein structures are stabilized by weak interactions and are influenced by additional interactions with the solubilizing environment. Structures of influenza virus A M2 protein, a proven drug target, have been determined in three different environments, thus providing a unique opportunity to assess environmental influences. Structures determined in detergents and detergent micelles can have notable differences from those determined in lipid bilayers. These differences make it imperative to validate membrane protein structures.

Electrochemical properties of phospholipid monolayers at liquid-liquid interfaces

Biomembrane models built at the interface between two immiscible electrolytes (ITIES) are useful systems to study phenomena of biological relevance by means of their electrochemical processes. The unique properties of ITIES allow one either to control or measure the potential difference across the biomimetic membranes. Herein we focus on phospholipid monolayers adsorbed at liquid-liquid interfaces, and besides discussing recent developments on the subject, we describe electrochemical techniques that can be used to get insight on the interfacial processes and electrostatic properties of phospholipid membranes at the ITIES. In particular, we examine the electrochemical and physicochemical properties of (modified) phospholipid monolayers and their interaction with other biologically relevant compounds. The use of liquid-liquid electrochemistry as a powerful tool to characterize drug properties is outlined. Although this review is not a survey of all the work in the field, it provides a comprehensive referencing to current research.

Simulations of RNA interactions with monovalent ions

RNA folding and binding reactions are mediated by interactions with ions that make up the surrounding aqueous electrolytic milieu. Although Mg(2+) ions are often implicated as being crucial for RNA folding, it is known that folding is feasible in high concentrations of monovalent alkali-halide salts. Experiments have yielded important information regarding the salt dependence of RNA stability. Recent work has shown that molecular simulations based on explicit representations of solvent molecules and monovalent ions can also provide useful insights regarding the ionic atmospheres around model RNA systems. These insights can help rationalize intriguing observations regarding the dependence of RNA stability on cation type providing one pays attention to important considerations that go into the proper design of molecular simulations. These issues are discussed in detail and the methods are applied to an A-form RNA and B-form DNA sequence. The results of these simulations are compared to previous work on a kissing-loop system with analogous sequence. In particular, ionic atmospheres obtained from molecular simulations are compared to those obtained using the nonlinear Poisson Boltzmann model for continuum electrostatics for these three different nucleic acid systems. The comparisons indicate reasonable agreement in terms of coarse-grained observables such as the numbers of counterions accumulated around the solutes. However, details of the ionic atmospheres, captured in terms of spatial free energy density profiles, are quite different between the two approaches. These comparisons suggest the need for improvements in continuum models to capture sequence-specific effects, ion-ion correlation, and the effects of partial dehydration of ions.