Counterion Release Research Articles

Direct Coagulation Casting of Positively Charged Alumina Suspension by Controlled Release of High Valence Counter Ions from Calcium Phosphate

The idea of controlled release of high valence counter ions was used in direct coagulation casting of ceramics. Calcium phosphate was used as the high valence counter ions source. Influence of the content of calcium phosphate on the viscosity of the suspension with positive charge on particles and the properties of green body were investigated. The results show that the content of calcium phosphate which leads to coagulation of suspension is 0.15–0.2 wt%. The pH changes from acidic regime to basic regime after calcium phosphate addition. Hydrochloric acid is consumed and CaHPO4, Ca(H2PO4)2, and CaCl2 are generated. The electrical double layer of alumina particles is strongly compressed by Ca2+ ions, leading to rapid increase of viscosity. Also, the pH value at high temperature approaches to isoelectric point of alumina and contributes to the instability of suspension. The optimum coagulated temperature is 60°C with coagulation time of 135 min. The compressive strength of green body is up to 2.8 MPa.

Free Energy Difference in Indolicidin Attraction to Eukaryotic and Prokaryotic Model Cell Membranes

We analyzed the thermodynamic and structural determinants of indolicidin interactions with eukaryotic and prokaryotic cell membranes using a series of atomistically detailed molecular dynamics simulations. We used quartz-supported bilayers with two different compositions of zwitterionic and anionic phospholipids as model eukaryotic and prokaryotic cell membranes. Indolicidin was preferentially attracted to the model prokaryotic cell membrane in contrast to the weak adsorption on the eukaryotic membrane. The nature of the indolicidin surface adsorption depended on an electrostatic guiding component, an attractive enthalpic component derived from van der Waals interactions, and a balance between entropic factors related to peptide confinement at the interface and counterion release from the bilayer surface. Thus, whereas we attributed the specificity of the indolicidin/membrane interaction to electrostatics, these interactions were not the sole contributors to the free energy of adsorption. Instead, a balance between an attractive van der Waals enthalpic component and a repulsive entropic component determined the overall strength of indolicidin adsorption.

Structuration mechanism of β-lactoglobulin – acacia gum assemblies in presence of quercetin

The interactions of β-lactoglobulin (BLG) with total Acacia gum (TAG) in presence of quercetin have been investigated in aqueous solutions at pH 4.2 and 25 °C. Isothermal titration calorimetry (ITC) has been used to determine the type and magnitude of the energies involved in the complexation process. Dynamic light scattering (DLS), electrophoretic mobility (μE), turbidity measurements (τ), optical microscopy and Fourier transform infrared spectroscopy in total attenuated reflection mode (ATR-FTIR) were used as complementary methods to better understand the sum of complicated phenomena at the origin of thermodynamic behaviour.The first structuring stage was characterized by an exothermic signal and was mainly controlled by favourable enthalpy changes due to electrostatic interactions between biopolymers. The second structuring stage was largely endothermic and more entropy driven, probably due to the release of small counterions from the electrical double layer and hydrophobic contribution to the binding process, implying the release of water molecules. The population distribution of the different species in solution and their size were determined through DLS. Dispersion turbidity of particles markedly increased and reached a maximum at 0.013 TAGQ:BLG molar ratio corresponding to the appearance of coacervates. Above TAGQ:BLG molar ratio of 0.015, dispersions turbidity decreased, which might be due to an excess of negative charges onto particles as revealed by electrophoretic mobility measurements. FTIR experiments indicated that BLG–TAG interactions, in presence or in absence of quercetin, induced a change in the α-helical structure of BLG. The results also showed significant loss in β-sheets indicating a change in the environment of BLG hydrophobic amino acids and the formation of protein–flavonoid complexes stabilized by hydrophobic associations.The results presented in this study should provide information about thermodynamic mechanisms of TAG–BLG binding processes in presence of an antioxidant, quercetin and will facilitate the application of the formed supramolecular assemblies as functional ingredients in food and non food systems.

Counter-ion effect on surfactant–DNA gel particles as controlled DNA delivery systems

The ability to entrap drugs within vehicles and subsequently release them has led to new treatments for a number of diseases. Based on an associative phase separation and interfacial diffusion approach, we developed a way to prepare DNA gel particles without adding any kind of cross-linker or organic solvent. Among the various agents studied, cationic surfactants offered particularly efficient control for encapsulation and DNA release from these DNA gel particles. The driving force for this strong association is the electrostatic interaction between the two components, as induced by the entropic increase due to the release of the respective counter-ions. However, little is known about the influence of the respective counter-ions on this surfactant–DNA interaction. Here we examined the effect of different counter-ions on the formation and properties of the DNA gel particles by mixing DNA (either single- (ssDNA) or double-stranded (dsDNA)) with the single chain surfactant dodecyltrimethylammonium (DTA). In particular, we used as counter-ions of this surfactant the hydrogen sulfate and trifluoromethane sulfonate anions and the two halides, chloride and bromide. Effects on the morphology of the particles obtained, the encapsulation of DNA and its release, as well as the haemocompatibility of these particles are presented, using counter-ion structure and DNA conformation as controlling parameters. Analysis of the data indicates that the degree of counter-ion dissociation from the surfactant micelles and the polar/hydrophobic character of the counter-ion are important parameters in the final properties of the particles. The stronger interaction with amphiphiles for ssDNA than for dsDNA suggests the important role of hydrophobic interactions in DNA.

Theory of DNA–cationic micelle complexation

We present a theory of spherical micelle formation from cationic amphiphiles in the absence and in the presence of DNA. The distribution of micelle sizes as well as the critical micelle and aggregation concentrations (cmc and cac) are calculated. Micelle formation is favored by the hydrophobic tails but disfavored by the entropic cost associated with counterion condensation. Counterion release drives the complexation between DNA and amphiphiles and causes micellation at a much smaller concentration than in the absence of DNA. The stiffness of double-stranded DNA favors the formation of large micelles leading to a bimodal distribution of micelle sizes.

Slow complexation dynamics between linear short polyphosphates and polyallylamines: analogies with “layer-by-layer” deposits

Polyelectrolyte "complexes" have been studied for almost a century and find more and more applications in cosmetics and DNA transfection. Most of the available studies focused on the thermodynamic aspects of the "complex" formation, mainly to determine phase diagrams and the influence of diverse physicochemical aspects on the formation of "complexes", but conversely less effort has been given to the kinetics of such processes. We describe herein the "complexation" kinetics of a short linear sodium polyphosphate (PSP) with poly(allylamine hydrochloride) (PAH) in the presence of 10 mM, 0.15 M and 1 M NaCl. We find, by using a combination of physicochemical techniques, that mixtures containing a 1 to 1 molar ratio of phosphate and amino groups allow the formation of "complexes" having a few 100 nm in diameter which progressively grow to particles up to 1.5 microns in hydrodynamic diameter, the growth process being accompanied by some progressive sedimentation. During this slow aggregation kinetics, the polyelectrolytes undergo a release of counterions and the zeta potential changes from a positive value to a negative one of -20 mV which is close to the zeta potential of (PSP-PAH)(n) films deposited under identical physicochemical conditions. Even though the complexes have a negative electrophoretic mobility, they contain an equimolar amount of amino and phosphate groups. This allows us to make some assumption about the structure of such "complexes" and to compare them with other published structures. We will also compare them with the aggregates found during the "layer-by-layer" deposition of the same species under the same conditions.

Adsorption of RNase A on Cationic Polyelectrolyte Brushes: A Study by Isothermal Titration Calorimetry

We present a study of the adsorption of a positively charged protein to a positively charged spherical polyelectrolyte brush (SPB) by isothermal titration calorimetry (ITC). ITC is used to determine the adsorption isotherm as a function of temperature and of salt concentration (at physiological pH 7.2). At low ionic strength, RNase A is strongly adsorbed by the SPB particles despite the fact that both the SPB particles and the protein are positively charged. Virtually no adsorption takes place when the ionic strength is raised through added salt. This is strong evidence for counterion release as the primary driving force for protein adsorption. We calculated that ~2 counterions were released upon RNase A binding. The adsorption of RNase A into like-charged SPB particles is entropy-driven, and protein protonation was not significant. Temperature-dependent measurements showed a disagreement between the enthalpy derived via the van't Hoff equation and the calorimetric enthalpy. Further analysis shows that van't Hoff analysis leads to the correct enthalpy of adsorption. The additional contributions to the measured enthalpy are potentially sourced from unlinked equilibria such as conformational changes that do not contribute to the binding equilibrium.

Competing interactions for antimicrobial selectivity based on charge complementarity

Antimicrobial peptides (AMPs) are an evolutionary conserved component of the innate immune system and possible templates for the development of new antibiotics. An important property of antimicrobial peptides is their ability to discriminate bacterial from eucaryotic cells which is attributed to the difference in lipid composition of the outer leaflet of the plasma membrane between the two types of cells. Whereas eucaryotic cells usually expose zwitterionic lipids, procaryotic cells expose also anionic lipids which bind the cationic antimicrobial peptides electrostatically. An example is the antimicrobial peptide NK-2 which is highly cationic and favors binding to anionic membranes. In the present study, the difference in binding affinity of NK-2 for palmitoyl-oleoyl-phosphatidyl-glycerol (POPG) and palmitoyl-oleoyl-phosphatidyl-choline (POPC) is studied using molecular dynamics simulations in conjunction with a coarse grained model and thermodynamic integration, by computing the change in free energy and its components upon the transfer of NK-2 from POPC to POPG. The transfer is indeed found to be highly favorable. Interestingly, the favorable contribution from the electrostatic interaction between the peptide and the anionic lipids is overcompensated by an unfavorable contribution from the change in lipid–cation interactions due to the release of counterions from the lipids. The increase in entropy due to the release of the cations is compensated by other entropic components. The largest favorable contribution arises from the solvation of the counterions. Overall the interaction between NK-2 and POPG is not determined by a single driving force but a subtle balance of competing interactions.

Adsorption of Polyelectrolytes on Calcium Carbonate – Which Thermodynamic Parameters are Driving This Process?

Polyelectrolytes such as dispersants are frequently used to modify the properties of wet preparations applied in the ceramic industry. The working mechanism of those admixtures relies on adsorption on mineral surfaces. Here, an analysis of the thermodynamic parameters which influence adsorption and effectiveness of two cement and clay dispersants was performed. As polyelectrolytes, linear ß‐naphthalenesulfonate formaldehyde (BNS) polycondensate, and comb‐shaped α‐allyl‐ω‐methoxy poly(ethylene glycol)‐maleic anhydride polycarboxylate copolymer (PC) were selected. The standard free energy, enthalpy, and entropy of adsorption on CaCO3 as model substrate were determined at pH 9 and in alkaline CaCl2 solution (pH 12.6 plus 1 g/L Ca2+). From temperature dependent adsorption isotherms the thermodynamic parameters ΔH0 and ΔS0 were established. Additionally, the Gibbs free energy of adsorption was calculated. For PC, the gain in entropy resulting from adsorption is consistently higher than for BNS which exhibits a higher release of enthalpy. Thus, adsorption of comb‐shaped PC occurs as a result of entropy gain owed to the release of counterions and water molecules whereas linear BNS adsorbs because of strong electrostatic attraction to the CaCO3 surface. Obviously, the specific molecular architecture and anionic charge amount of the polyelectrolytes strongly impact the portion of enthalpic and entropic contribution to adsorption.

Synthesis of double hydrophilic block copolymers and induced assembly with oligochitosan for the preparation of polyion complex micelles

This paper reports on the polyion complex micelles (PIC micelles) formed between neutral-ionizable double hydrophilic block copolymers (DHBC), poly(ethylene oxide)-block-poly(acrylic acid) (PEO-b-PAA), and oligochitosan, a natural polyamine. The controlled synthesis of PEO-b-PAA polymers was achieved by atom transfer radical polymerization (ATRP) of tert-butyl acrylate with ω-bromide-functionalized PEO macroinitiators (Mw = 2000 and 5000 g mol−1) and the subsequent deprotection reaction under acidic conditions. A series of copolymers with a narrow molecular weight distribution (Mw/Mn ≤ 1.2) and varied PAA block lengths was synthesized. Capillary electrophoresis (CE) was shown to unambiguously prove the blocky structure of the copolymers. It also showed that about 60% of the sodium counter ions were condensed onto the polyacrylate block in the pure diblock copolymer solution, which is consistent with the formation of polyion complex micelles triggered by counter-ion release in the presence of oligochitosan. The formation of oligochitosan/PAA–PEOcore–corona micelles has been investigated by dynamic light scattering (DLS), small angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). A minimum length of the PAA block is necessary to ensure micelle formation. The range of pH, where PIC micelles form, critically depends on the PAA block length, which also determines the size of the micelles. Micelles can be dissociated at ionic strength above 0.4 mol L−1. Since these PIC micelles have been used as recyclable structuring agents for the formation of ordered mesoporous materials, the reversibilty of the assembling process was studied upon pH and ionic strength cyclic variations. A hysteresis of stability was observed at low pH, probably due to hydrogen bonding.

Phase phenomena in supported lipid films under varying electric potential

We model cyclic voltammetry experiments on supported lipid films where a non-trivial dependence of the capacitance on the applied voltage is observed. Previously, based on a mean-field treatment of the Flory–Huggins type, under the assumption of strongly screened electrostatic interactions, it has been hypothesized that peaks in the capacitance-vs.-voltage profiles correspond to a sequence of structural or phase transitions within the adsorbed film. To examine this hypothesis, in this study we use both mean-field calculations and Monte Carlo simulations where the electrostatic effects due to the varying electric potential and the presence of salt are accounted for explicitly. Our main focus is on the structure of the film and the desorption–readsorption phenomena. These are found to be driven by a strong competition for the progressively charged-up (hydrophobic) surface between lipid hydrocarbon tails and the electrode counterions (cations). As the surface charge density is raised, the following phenomena within the interface are clearly observed: (i) a gradual displacement of the monolayer from the surface by the counterions, leading to complete monolayer desorption and formation of an electric double layer by the surface, (ii) a transformation of the monolayer into a bilayer upon its desorption, (iii) in the case of zwitterionic (or strongly polar) lipid head groups, the desorption is followed by the bilayer readsorption to the electrodevia interaction with the electric double layer and release of the excess counterions into the bulk solution. We argue then that the voltammetry peaks are associated with a stepwise process of formation of layers of alternating charge: electric double layer – upon film desorption, triple or multi-layer – upon film readsoption.

Many Facets of the Polyelectrolyte and Oppositely Charged Colloidal Particle Complexation: Counterion Release and Electrical Conductivity Behavior

The lateral correlated adsorption of polyions onto oppositely charged vesicles, leading to the formation of stable equilibrium clusters of mesoscopic size, is associated to the release of a fraction of counterions, initially condensed on the polyion chains. This ulterior release of counterions provokes an increase of the number of free ions, besides the ones due to the partial ionization of both charged particles and polyions, that can be appropriately monitored by means of electrical conductivity measurements of the whole system. We have investigated this behavior in a suspension of cationic vesicles made up by dioleoyl trimethyl ammonium propane (DOTAP) liposomial vesicles interacting with an anionic polyelectrolyte composed by polyacrylate sodium salt. This system has been in the past extensively studied by us by means of different experimental techniques, and its behavior has been sufficiently characterized, as far as hydrodynamic and electrical properties are concerned. In this note, we report on the dc electrical conductivity behavior during the whole aggregation process, from the single polyion-coated liposomal particles, to polyion-induced liposome clusters, to finally polyion-fully covered liposomes, in polyion excess conditions. We have evaluated the excess of released counterions on the basis of the standard theory of the electrical properties of aqueous charged solutions and compared this quantity with the one predicted by the lateral correlation adsorption model. The agreement is quite good, offering strong experimental evidence of the role played by the release of counterions in the aggregation process. Finally, we have considered a similar liposomial system, where the lateral correlation adsorption was inhibited by structural reasons, having replaced the polyion by a simple electrolyte, whose dissociated ions will adsorb randomly at the particle surface, rather than in a correlated manner. In this case, no counterion release upon complexation occurs, and the electrical conductivity of the suspension approaches the one theoretically expected.

DNA Compaction by a Dendrimer

At physiological pH, a PAMAM dendrimer is positively charged and can effectively bind negatively charged DNA. Currently, there has been great interest in understanding this complexation reaction both for fundamental (as a model for complex biological reactions) as well as for practical (as a gene delivery material and probe for sensing DNA sequence) reasons. Here, we have studied the complexation between double-stranded DNA (dsDNA) and various generations of PAMAM dendrimers (G3-G5) through atomistic molecular dynamics simulations in the presence of water and ions. We report the compaction of DNA on a nanosecond time scale. This is remarkable, given the fact that such a short DNA duplex with a length close to 13 nm is otherwise thought to be a rigid rod. Using several nanoseconds long MD simulations, we have observed various binding modes of dsDNA and dendrimers for various generations of PAMAM dendrimers at varying charge ratios, and it confirms some of the binding modes proposed earlier. The binding is driven by the electrostatic interaction, and the larger the dendrimer charge, the stronger the binding affinity. As DNA wraps/binds to the dendrimer, counterions originally condensed onto DNA (Na+) and the dendrimer (Cl(-)) get released. We calculate the entropy of counterions and show that there is gain in entropy due to counterion release during the complexation. MD simulations demonstrate that, when the charge ratio is greater than 1 (as in the case of the G5 dendrimer), the optimal wrapping of DNA is observed. Calculated binding energies of the complexation follow the trend G5 > G4 > G3, in accordance with the experimental data. For a lower-generation dendrimer, such as G3, and, to some extent, for G4 also, we see considerable deformation in the dendrimer structure due to their flexible nature. We have also calculated the various helicoidal parameters of DNA to study the effect of dendrimer binding on the structure of DNA. The B form of the DNA is well preserved in the complex, as is evident from various helical parameters, justifying the use of the PAMAM dendrimer as a suitable delivery vehicle.

Effect of the molecular structure on the adsorption of conditioning polyelectrolytes on solid substrates

The adsorption of polyelectrolytes onto negatively charged substrates has been studied using dissipative quartz crystal microbalance (D-QCM) and ellipsometry. The polymers studied belong to two families of cationic polymers frequently used as hair conditioners. One of the families is formed by four polymers derived from the poly(diallyl-dimethylammonium chloride), and the other one is formed by two polysaccharide polymers. The control parameters in the study of both families of polymers were the charge density and the rigidity of the chains. The adsorption kinetics of the polymers showed a complex behavior with several processes involved. The total adsorbed amount depends on the nature of the polymer chains, on the ionic strength, and on polymer concentration of the solutions. The comparison of the mass of the adsorbed layers obtained from D-QCM and from ellipsometry allowed us to calculate the water content of the layers. This variable takes high values for all the polymers studied, which is related to the non-homogeneous character of the adsorbed layer, as confirmed by AFM. The analysis of D-QCM results also provides information about the shear modulus of the layers, whose values have been found to be in the MPa range as for rubber-like polymer system. The adsorptions of the polyelectrolytes are not driven exclusively by the electrostatic interactions, entropic contributions being of fundamental importance, and arise mainly from the release of counterions during the adsorption process, and/or the number of loops and tails of the adsorbed chains protruding into the solution.

Overall Charge and Local Charge Density of Pectin Determines the Enthalpic and Entropic Contributions to Complexation with β-Lactoglobulin

The complex formation between β-lactoglobulin and pectins of varying overall charge and local charge density were investigated. Isothermal titration calorimetry experiments were carried out to determine the enthalpic contribution to the complex formation at pH 4.25 and various ionic strengths. Complex formation was found to be an exothermic process for all conditions. Combination with previously published binding constants by Sperber et al. (Sperber, B. L. H. M.; Cohen Stuart, M. A.; Schols, H. A.; Voragen, A. G. J.; Norde, W. Biomacromolecules 2009, 10, 3246-3252) allows for the determination of the changes in the Gibbs energy and the change in entropy of the system upon complex formation between β-lactoglobulin and pectin. The local charge density of pectin is found to determine the balance between enthalpic and entropic contributions. For a high local charge density pectin, the main contribution to the Gibbs energy is of an enthalpic nature, supported by a favorable entropy effect due to the release of small counterions. A pectin with a low local charge density has a more even distribution of the enthalpic and entropic part to the change of the Gibbs energy. The enthalpic part is reduced due to the lower charge density, while the relative increase of the entropic contribution is thought to be caused by a change in the location of the binding place for pectin on the β-lactoglobulin molecule. The association of the hydrophobic methyl esters on pectin with an exposed hydrophobic region on β-lg results in the release of water molecules from the hydrophobic region and surrounding the methyl esters of the pectin molecule. An increase in the ionic strength decreases the enthalpic contribution due to the shielding of electrostatic attraction in favor of the entropic contribution, supporting the idea that the release of water molecules from hydrophobic areas plays a part in the complex formation.

Interpreting protein/DNA interactions: distinguishing specific from non-specific and electrostatic from non-electrostatic components

We discuss the effectiveness of existing methods for understanding the forces driving the formation of specific protein–DNA complexes. Theoretical approaches using the Poisson–Boltzmann (PB) equation to analyse interactions between these highly charged macromolecules to form known structures are contrasted with an empirical approach that analyses the effects of salt on the stability of these complexes and assumes that release of counter-ions associated with the free DNA plays the dominant role in their formation. According to this counter-ion condensation (CC) concept, the salt-dependent part of the Gibbs energy of binding, which is defined as the electrostatic component, is fully entropic and its dependence on the salt concentration represents the number of ionic contacts present in the complex. It is shown that although this electrostatic component provides the majority of the Gibbs energy of complex formation and does not depend on the DNA sequence, the salt-independent part of the Gibbs energy—usually regarded as non-electrostatic—is sequence specific. The CC approach thus has considerable practical value for studying protein/DNA complexes, while practical applications of PB analysis have yet to demonstrate their merit.

Fusion-Relevant Changes in Lipid Shape of Hydrated Cholesterol Hemisuccinate Induced by pH and Counterion Species

Cholesterol hemisuccinate (CHEMS) is a protonable lipid that is frequently used for the construction of pH-responsive delivery systems. Such systems have a stable, lamellar phase at pH 7, but can form a fusogenic, hexagonal phase at pH 5. This behavior can be explained by binding or release of counterions from the solvent and the related variations of the effective size of the polar lipid part. Here, we use MD simulations to study the ion recruitment to neutral or anionic bilayers of CHEMS in water. For deprotonated (anionic) CHEMS, we observed an almost complete decoration of the bilayer with sodium, potassium, or argininium cations, which challenges the previous hypothesis that the stability of bilayers from anionic CHEMS results from the electrostatic repulsion between the charged head groups. Protonated (neutral) bilayers of CHEMS did not bind sodium or potassium, but did adsorb argininium cations. Whereas the headgroup of protonated CHEMS is bent and strongly tilted away from the bilayer normal, the headgroup of the deprotonated CHEMS is found to become outstretched and significantly less tilted arising from the adsorption of the counterions. The tilt reduction is most pronounced upon adsorption of arginine which also leads to an increase in the otherwise constant area per lipid. In general, the cation binding to the deprotonated CHEMS acts to increase the effective headgroup volume. This change in the lipid shape may be one possible fact explaining the hexagonal-lamellar phase transitions for CHEMS known from experiments.

Interactions between Cationic Lipid Bilayers and Model Chromatin

Complexes formed in mixtures of cationic liposomes of varying charge density and nucleosome core particles (NCPs) or nucleosome arrays have been characterized. Under most of the conditions studied, the lipids and NCPs or arrays formed lamellar structures similar to those obtained with the liposomes and pure DNA. Thus, the dissociation of DNA from the NCP or nucleosome array and the formation of a DNA-lipid complex is thermodynamically favored, which can likely be ascribed mainly to the gain in entropy on release of the small counterions. Only at very low liposome charge densities are there indications that the NCPs/arrays do not dissociate upon interaction with the lipid bilayers. The reported results can serve as a valuable reference point in investigations of biologically more relevant systems.

LineardsDNA Partitions Spontaneously into the Inverse Hexagonal Lyotropic Liquid Crystalline Phases of Phospholipids

Recently, we reported that DNA associated with inverse hexagonal (H(II)) lyotropic liquid crystal phases of the lipid 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) was actively transcribed by T7 RNA polymerase. Our findings suggested that key components of the transcription process, probably the T7 RNA polymerase and the DNA, remained associated with the monolithic H(II) phase throughout transcription. Here, we investigate the partitioning of DNA between an H(II) lyotropic liquid crystal phase and an isotropic supernatant phase in order to develop insights into the localization of DNA in liquid crystalline environments. Our results show that linear double stranded DNA (dsDNA) molecules partition spontaneously into monolithic preformed H(II) liquid crystal phases of DOPE. We propose that this process is driven by the increase in entropy due to the release of counterions from the DNA when it inserts into the aqueous pores of the H(II) phase.

Multishell Structures of Virus Coat Proteins

Under conditions of low ionic strength and a pH ranging between about 3.7 and 5.0, solutions of purified coat proteins of cowpea chlorotic mottle virus (CCMV) form spherical multishell structures in the absence of viral RNA. The outer surfaces of the shells in these structures are negatively charged, whereas the inner surfaces are positively charged due to a disordered cationic N-terminal domain of the capsid protein, the arginine-rich RNA-binding motif that protrudes into the interior. We show that the main forces stabilizing these multishells are counterion release combined with a lower charge density in the RNA-binding motif region of the outer shells due to their larger radii of curvature, arguing that these compensate for the outer shells not being able to adopt the smaller, optimal, radius of curvature of the inner shell. This explains why the structures are only stable at low ionic strengths at pHs for which the outer surface is negatively charged and why the larger outer shells are not observed separately in solution. We show how to calculate the free energy of shells of nonoptimal radius of curvature from the elastic properties of the native shell. The spacing between shells is determined mainly by the entropic elasticity of the RNA-binding motifs. Although we focus on CCMV multishells, we also predict the solution conditions under which multishells formed by CCMV coat protein mutants with a lower RNA-binding motif charge are stable, and we examine other viruses as well. We conclude that at a given surface charge density, the boundaries separating regions of stable multishells with different numbers of shells shift to lower ionic strengths upon either increasing the length of the RNA-binding motif, increasing the stiffness of the shells, or decreasing the charge per RNA-binding motif.