The Donnan equilibrium: I. On the thermodynamic foundation of the Donnan equation of state

Porous Microneedles Through Direct Ink Drawing with Nanocomposite Inks for Transdermal Collection of Interstitial Fluid

Interstitial fluid (ISF) is an attractive alternative to regular blood sampling for health checks and disease diagnosis. Porous microneedles (MNs) are well suited for collecting ISF in a minimally invasive manner. However, traditional methods of molding MNs from microfabricated templates involve prohibitive fabrication costs and fixed designs. To overcome these limitations, this study presents a facile and economical additive manufacturing approach to create porous MNs. Compared to traditional layerwise build sequences, direct ink drawing with nanocomposite inks can define sharp MNs with tailored shapes and achieve vastly improved fabrication efficiency. The key to this fabrication strategy is the yield-stress fluid ink that is easily formulated by dispersing silica nanoparticles into the cellulose acetate polymer solution. As-printed MNs are solidified into interconnected porous microstructure inside a coagulation bath of deionized water. The resulting MNs exhibit high mechanical strength and high porosity. This approach also allows porous MNs to be easily integrated on various substrates. In particular, MNs on filter paper substrates are highly flexible to rapidly collect ISF on non-flat skin sites. The extracted ISF is used for quantitative analysis of biomarkers, including glucose, = calcium ions, and calcium ions. Overall, the developments allow facile fabrication of porous MNs for transdermal diagnosis and therapy.

Electrostatic Theory of the Acidity of the Solution in the Lumina of Viruses and Virus-Like Particles

Recently, Maassen et al. measured an appreciable pH difference between the bulk solution and the solution in the lumen of virus-like particles, self-assembled in an aqueous buffer solution containing the coat proteins of a simple plant virus and polyanions (Maassen, S. J.; et al. Small 2018, 14, 1802081). They attribute this to the Donnan effect, caused by an imbalance between the number of negative charges on the encapsulated polyelectrolyte molecules and the number of positive charges on the RNA binding domains of the coat proteins that make up the virus shell or capsid. By applying Poisson-Boltzmann theory, we confirm this conclusion and show that simple Donnan theory is accurate even for the smallest of viruses and virus-like particles. This, in part, is due to the additional screening caused by the presence of a large number of immobile charges in the cavity of the shell. The presence of a net charge on the outer surface of the capsid we find in practice to not have a large effect on the pH shift. Hence, Donnan theory can indeed be applied to connect the local pH and the amount of encapsulated material. The large shifts up to a full pH unit that we predict must have consequences for applications of virus capsids as nanocontainers in bionanotechnology and artificial cell organelles.

Do Aqueous Suspensions of Smectite Clays Form a Smectic Liquid-Crystalline Phase?

Bottom-up strategies for the production of well-defined nanostructures often rely on the self-assembly of anisotropic colloidal particles (nanowires and nanosheets). These building blocks can be obtained by delamination in a solvent of low-dimensionality crystallites. To optimize particle availability, determination of the delamination mechanism and the different organization stages of anisotropic particles in dispersion is essential. We address this fundamental issue by exploiting a recently developed system of fluorohectorite smectite clay mineral that delaminates in water, leading to colloidal dispersions of single-layer, very large (≈20 μm) clay sheets at high dilution. We show that when the clay crystallites are dispersed in water, they swell to form periodic one-dimensional stacks of fluorohectorite sheets with very low volume fraction (<1%) and therefore huge (≈100 nm) periods. Using optical microscopy and synchrotron X-ray scattering, we establish that these colloidal stacks bear strong similarities, yet subtle differences, with a smectic liquid-crystalline phase. Despite the high dilution, the colloidal stacks of sheets, called colloidal accordions, are extremely robust mechanically and can persist for years. Moreover, when subjected to AC electric fields, they rotate as solid bodies, which demonstrates their outstanding internal cohesion. Furthermore, our theoretical model captures the dependence of the stacking period on the dispersion concentration and ionic strength and explains, invoking the Donnan effect, why the colloidal accordions are kinetically stable over years and impervious to shear and Brownian motion. Because our model is not system specific, we expect that similar colloidal accordions frequently appear as an intermediate state during the delamination process of two-dimensional crystals in polar solvents.

Hydrophilic Versus Hydrophobic Coupling in the Pressure Dependence of the Chemical Potential of Alkali Metal and Halide Ions in Water

We computed the chemical potential for some alkali metal ions (K⁺, Rb⁺, and Cs⁺) and two halide ions (Br^- and I^-) in aqueous solution at ambient T and various pressures in the range 1-8000 atm. Results were obtained from classic Monte Carlo simulations in the NPT ensemble by means of the free energy perturbation method. Here, the chemical potential is computed as the sum of a term relative to a Lennard-Jones solute and a term relative to the process in which this solute is transformed into the ion. Hydrophobic and hydrophilic features of these two components of the chemical potential show opposite behaviors under isothermal compression. The increase in pressure determines an increase in the hydrophobic component, which becomes more positive with a stronger effect for larger ions. Correspondingly, the values of the hydrophilic component become more negative for alkali ions, whereas they are only slightly affected by compression for halide ions. Hydrophobic-hydrophilic quasi-compensation in the slopes is observed for Rb⁺. For a smaller ion, such as K⁺, the dependence on pressure of the hydrophilic component is slightly dominant. For a larger ion, as observed in the cases of Cs⁺, Br^-, and I^-, the hydrophobic component assumes the determinant role. Pressure dependence of the chemical potential is little affected by corrections introduced for molecular potential truncation. This view can change for possible boundary artifacts that could have affected the static electrostatic potential. Some inference is obtained from comparison with experimental data at 1 atm on the free energy of hydration. Discrepancies show the characteristic asymmetry between cations and anions. The further addition of a correction based on the static potential significantly reduces these discrepancies with important error cancellation on the sum of chemical potentials of ions of opposite charge. The correction is applied also at higher pressures, and results are compared with those obtained by adding an alternative correction that is based on the water number density. Regardless of the ion, changes of the chemical potential induced by an increase in pressure appear to be dominated by the hydrophobic component, in particular when using the alternative correction. For bromide and iodide electrolytes, the two corrections give chemical potentials in good agreement.

Quantification of Idua Enzymatic Activity Combined with Observation of Phenotypic Change in Zebrafish Embryos Provide a Preliminary Assessment of Mutated idua Correlated with Mucopolysaccharidosis Type I

Mucopolysaccharidosis type I (MPS I) is an inherited autosomal recessive disease resulting from mutation of the α-l-Iduronidase (IDUA) gene. New unknown mutated nucleotides of idua have increasingly been discovered in newborn screening, and remain to be elucidated. In this study, we found that the z-Idua enzymatic activity of zebrafish idua-knockdown embryos was reduced, resulting in the accumulation of undegradable metabolite of heparin sulfate, as well as increased mortality and defective phenotypes similar to some symptoms of human MPS I. After microinjecting mutated z-idua-L346R, -T364M, -E398-deleted, and -E540-frameshifted mRNAs, corresponding to mutated human IDUA associated with MPS I, into zebrafish embryos, no increase in z-Idua enzymatic activity, except of z-idua-E540-frameshift-injected embryos, was noted compared with endogenous z-Idua of untreated embryos. Defective phenotypes were observed in the z-idua-L346R-injected embryos, suggesting that failed enzymatic activity of mutated z-Idua-L346R might have a dominant negative effect on endogenous z-Idua function. However, defective phenotypes were not observed in the z-idua-E540-frameshifted-mRNA-injected embryos, which provided partial enzymatic activity. Based on these results, we suggest that the z-Idua enzyme activity assay combined with phenotypic observation of mutated-idua-injected zebrafish embryos could serve as an alternative platform for a preliminary assessment of mutated idua not yet characterized for their role in MPS I.

Balance of osmotic pressures determines the nuclear-to-cytoplasmic volume ratio of the cell

The volume of the cell nucleus varies across cell types and species and is commonly thought to be determined by the size of the genome and degree of chromatin compaction. However, this notion has been challenged over the years by much experimental evidence. Here, we consider the physical condition of mechanical force balance as a determining condition of the nuclear volume and use quantitative, order-of-magnitude analysis to estimate the forces from different sources of nuclear and cytoplasmic pressure. Our estimates suggest that the dominant pressure within the nucleus and cytoplasm of nonstriated muscle cells originates from the osmotic pressure of proteins and RNA molecules that are localized to the nucleus or cytoplasm by out-of-equilibrium, active nucleocytoplasmic transport rather than from chromatin or its associated ions. This motivates us to formulate a physical model for the ratio of the cell and nuclear volumes in which osmotic pressures of localized proteins determine the relative volumes. In accordance with unexplained observations that are a century old, our model predicts that the ratio of the cell and nuclear volumes is a constant, robust to a wide variety of biochemical and biophysical manipulations, and is changed only if gene expression or nucleocytoplasmic transport is modulated.

Glycosaminoglycans modulate long-range mechanical communication between cells in collagen networks

Glycosaminoglycans (GAGs) are carbohydrates that are expressed ubiquitously in the human body and are among the key macromolecules that influence the development, homeostasis, and pathology of native tissues. Abnormal accumulation of GAGs has been observed in metabolic disorders, solid tumors, and fibrotic tissues. Here we theoretically and experimentally show that tissue swelling caused by the highly polar nature of GAGs significantly affects the mechanical interactions between resident cells by altering the organization and alignment of the collagenous extracellular matrix. The role of GAGs in modulating cellular force transmission revealed here can guide the design of biomaterial scaffolds in regenerative medicine and provides insights on the role of cell–cell communication in tumor progression and fibrosis.

Cells can sense and respond to mechanical forces in fibrous extracellular matrices (ECMs) over distances much greater than their size. This phenomenon, termed long-range force transmission, is enabled by the realignment (buckling) of collagen fibers along directions where the forces are tensile (compressive). However, whether other key structural components of the ECM, in particular glycosaminoglycans (GAGs), can affect the efficiency of cellular force transmission remains unclear. Here we developed a theoretical model of force transmission in collagen networks with interpenetrating GAGs, capturing the competition between tension-driven collagen fiber alignment and the swelling pressure induced by GAGs. Using this model, we show that the swelling pressure provided by GAGs increases the stiffness of the collagen network by stretching the fibers in an isotropic manner. We found that the GAG-induced swelling pressure can help collagen fibers resist buckling as the cells exert contractile forces. This mechanism impedes the alignment of collagen fibers and decreases long-range cellular mechanical communication. We experimentally validated the theoretical predictions by comparing the intensity of collagen fiber alignment between cellular spheroids cultured on collagen gels versus collagen–GAG cogels. We found significantly lower intensities of aligned collagen in collagen–GAG cogels, consistent with the prediction that GAGs can prevent collagen fiber alignment. The role of GAGs in modulating force transmission uncovered in this work can be extended to understand pathological processes such as the formation of fibrotic scars and cancer metastasis, where cells communicate in the presence of abnormally high concentrations of GAGs.

Three-dimensional structural interrelations between cells, extracellular matrix, and mineral in normally mineralizing avian leg tendon

The spatial-temporal relationship between cells, extracellular matrices, and mineral deposits is fundamental for an improved understanding of mineralization mechanisms in vertebrate tissues. By utilizing focused ion beam-scanning electron microscopy with serial surface imaging, normally mineralizing avian tendons have been studied with nanometer resolution in three dimensions with volumes exceeding tens of micrometers in range. These parameters are necessary to yield sufficiently fine ultrastructural details while providing a comprehensive overview of the interrelationships between the tissue structural constituents. Investigation reveals a complex lacuno-canalicular network in highly mineralized tendon regions, where ∼100 nm diameter canaliculi emanating from cell (tenocyte) lacunae surround extracellular collagen fibril bundles. Canaliculi are linked to smaller channels of ∼40 nm diameter, occupying spaces between fibrils. Close to the tendon mineralization front, calcium-rich deposits appear between the fibrils and, with time, mineral propagates along and within them. These close associations between tenocytes, tenocyte lacunae, canaliculi, small channels, collagen, and mineral suggest a concept for the mineralization process, where ions and/or mineral precursors may be transported through spaces between fibrils before they crystallize along the surface of and within the fibrils.

Active volume regulation in adhered cells

Recent experiments reveal that the volume of adhered cells is reduced as their basal area is increased. During spreading, the cell volume decreases by several thousand cubic micrometers, corresponding to large pressure changes of the order of megapascals. We show theoretically that the volume regulation of adhered cells is determined by two concurrent conditions: mechanical equilibrium with the extracellular environment and a generalization of Donnan (electrostatic) equilibrium that accounts for active ion transport. Spreading affects the structure and hence activity of ion channels and pumps, and indirectly changes the ionic content in the cell. We predict that more ions are released from the cell with increasing basal area, resulting in the observed volume-area dependence. Our theory is based on a minimal model and describes the experimental findings in terms of measurable, mesoscale quantities. We demonstrate that two independent experiments on adhered cells of different types fall on the same master volume-area curve. Our theory also captures the measured osmotic pressure of adhered cells, which is shown to depend on the number of proteins confined to the cell, their charge, and their volume, as well as the ionic content. This result can be used to predict the osmotic pressure of cells in suspension.

Kinetics simulation of transmembrane transport of ions and molecules through a semipermeable membrane

We have developed a model to study the kinetics of the redistribution of ions and molecules through a semipermeable membrane in complex mixtures of substances penetrating and nonpenetrating through a membrane. It takes into account the degree of dissociation of these substances, their initial concentrations in solutions separated by a membrane, and volumes of these solutions. The model is based on the assumption that only uncharged particles (molecules or ion pairs) diffuse through a membrane (and not ions as in the Donnan model). The developed model makes it possible to calculate the temporal dependencies of concentrations for all processing ions and molecules at system transition from the initial state to equilibrium. Under equilibrium conditions, the ratio of ion concentrations in solutions separated by a membrane obeys the Donnan distribution. The Donnan effect is the result of three factors: equality of equilibrium concentrations of penetrating molecules on each side of a membrane, dissociation of molecules into ions, and Le Chatelier's principle. It is shown that the Donnan distribution (irregularity of ion distribution) and accordingly absolute value of the Donnan membrane potential increases if: (i) the nonpenetrating salt concentration (in one of the solutions) and its dissociation constant increases, (ii) the total penetrating salt concentration and its dissociation constant decreases, and (iii) the volumes ratio increases (between solutions with and without a nonpenetrating substance). It is shown also that only a slight difference between the degrees of dissociation of two substances can be used for their membrane separation.

Experimental Evidence for Algebraic Double-Layer Forces

According to conventional wisdom, electric double-layer forces normally decay exponentially with separation distance. Here, we present experimental evidence of algebraically decaying double-layer interactions. We show that algebraic interactions arise in both strongly overlapping as well as counterion-only regimes, albeit the evidence is less clear for the former regime. In both of these cases, the disjoining pressure profile assumes an inverse square distance dependence. At small separation distances, another algebraic regime is recovered. In this regime, the pressure decays as the inverse of separation distance.

Influences of sodium and glycosaminoglycans on skin oedema and the potential for ulceration: a finite-element approach

Venous ulcers are chronic transcutaneous wounds common in the lower legs. They are resistant to healing and have a 78% chance of recurrence within 2 years. It is commonly accepted that venous ulcers are caused by the insufficiency of the calf muscle pump, leading to blood pooling in the lower legs, resulting in inflammation, skin oedema, tissue necrosis and eventually skin ulceration. However, the detailed physiological events by which inflammation contributes to wound formation are poorly understood. We therefore sought to develop a model that simulated the inflammation, using it to determine the internal stresses and pressure on the skin that contribute to venous ulcer formation. A three-layer finite-element skin model (epidermis, dermis and hypodermis) was developed to explore the roles in wound formation of two inflammation identifiers: glycosaminoglycans (GAG) and sodium. A series of parametric studies showed that increased GAG and sodium content led to oedema and increased tissue stresses of 1.5 MPa, which was within the reported range of skin tissue ultimate tensile stress (0.1-40 MPa). These results suggested that both the oedema and increased fluid pressure could reach a threshold for tissue damage and eventual ulcer formation. The models presented here provide insights to the pathological events associated with venous insufficiency, including inflammation, oedema and skin ulceration.

Concentration-dependent and configuration-dependent interactions of monovalent ions with an RNA tetraloop

Monovalent salt solutions have strongly coupled interactions with biopolymers, from large polyelectrolytes to small RNA oligomers. High salt concentrations have been known to induce transitions in the structure of RNA, producing non-canonical configurations and even driving RNA to precipitate out of solution. Using all-atom molecular dynamics simulations, we model a monovalent salt species (KCL) at high concentrations (0.1-3m) and calculate the equilibrium distributions of water and ions around a small tetraloop-forming RNA oligomer in a variety of structural arrangements: folded A-RNA (canonical) and Z-RNA (non-canonical) tetraloops and unfolded configurations. From these data, we calculate the ion preferential binding coefficients and Donnan coefficients for the RNA oligomer as a function of concentration and structure. We find that cation accumulation is highest around non-canonical Z-RNA configurations at concentrations below 0.5m, while unfolded configurations accumulate the most co-ions in all concentrations. By contrast, canonical A-RNA structures consistently show the lowest accumulations for all ion species. Water distributions vary markedly with RNA configuration but show little dependency on KCL concentration. Based on Donnan coefficient calculations, the net charge of the solution at the surface of the RNA decreases linearly as a function of salt concentration and becomes net-neutral near 2.5-3m KCL for folded configurations, while unfolded configurations still show a positive solution charge. Our findings show that all-atom molecular dynamics can describe the equilibrium distributions of monovalent salt in the presence of small RNA oligomers at KCL concentrations where ion correlation effects become important. Furthermore, these results provide valuable insights into the distributions of water and ions near the RNA oligomer surface as a function of structural configuration.

Screened Coulomb interactions with non-uniform surface charge

The screened Coulomb interaction between a pair of infinite parallel planes with spatially varying surface charge is considered in the limit of small electrical potentials for arbitrary Debye lengths. A simple expression for the disjoining pressure is derived in terms of a two-dimensional integral in Fourier space. The integral is evaluated for periodic and random charge distributions and the disjoining pressure is expressed as a sum over Fourier–Bloch reciprocal lattice vectors or in terms of an integral involving the autocorrelation function, respectively. The force between planes with a finite area of uniform charge, a model for the DLVO interaction between finite surfaces, is also calculated. It is shown that the overspill of the charge cloud beyond the region immediately between the charged areas results in a reduction of the disjoining pressure, as reported by us recently in the long Debye length limit for planes of finite width.

Collagen intrafibrillar mineralization as a result of the balance between osmotic equilibrium and electroneutrality

Mineralization of fibrillar collagen with biomimetic process-directing agents has enabled scientists to gain insight into the potential mechanisms involved in intrafibrillar mineralization. Here, by using polycation- and polyanion-directed intrafibrillar mineralization, we challenge the popular paradigm that electrostatic attraction is solely responsible for polyelectrolyte-directed intrafibrillar mineralization. As there is no difference when a polycationic or a polyanionic electrolyte is used to direct collagen mineralization, we argue that additional types of long-range non-electrostatic interaction are responsible for intrafibrillar mineralization. Molecular dynamics simulations of collagen structures in the presence of extrafibrillar polyelectrolytes show that the outward movement of ions and intrafibrillar water through the collagen surface occurs irrespective of the charges of polyelectrolytes, resulting in the experimentally verifiable contraction of the collagen structures. The need to balance electroneutrality and osmotic equilibrium simultaneously to establish Gibbs-Donnan equilibrium in a polyelectrolyte-directed mineralization system establishes a new model for collagen intrafibrillar mineralization that supplements existing collagen mineralization mechanisms.

Interaction of Charged Patchy Protein Models with Like-Charged Polyelectrolyte Brushes

We study the adsorption of charged patchy particle models (CPPMs) on a thin film of a like-charged and dense polyelectrolyte (PE) brush (of 50 monomers per chain) by means of implicit-solvent, explicit-salt Langevin dynamics computer simulations. Our previously introduced set of CPPMs embraces well-defined one- and two-patched spherical globules, each of the same net charge and (nanometer) size, with mono- and multipole moments comparable to those of small globular proteins. We focus on electrostatic effects on the adsorption far away from the isoelectric point of typical proteins, i.e., where charge regulation plays no role. Despite the same net charge of the brush and globule, we observe large binding affinities up to tens of the thermal energy, k_BT, which are enhanced by decreasing salt concentration and increasing charge of the patch(es). Our analysis of the distance-resolved potentials of mean force together with a phenomenological description of all leading interaction contributions shows that the attraction is strongest at the brush surface, driven by multipolar, Born (self-energy), and counterion-release contributions, dominating locally over the monopolar and steric repulsions.

Additives for vaccine storage to improve thermal stability of adenoviruses from hours to months

Up to 80% of the cost of vaccination programmes is due to the cold chain problem (that is, keeping vaccines cold). Inexpensive, biocompatible additives to slow down the degradation of virus particles would address the problem. Here we propose and characterize additives that, already at very low concentrations, improve the storage time of adenovirus type 5. Anionic gold nanoparticles (10⁻⁸–10⁻⁶ M) or polyethylene glycol (PEG, molecular weight ∼8,000 Da, 10⁻⁷–10⁻⁴ M) increase the half-life of a green fluorescent protein expressing adenovirus from ∼48 h to 21 days at 37 °C (from 7 to >30 days at room temperature). They replicate the known stabilizing effect of sucrose, but at several orders of magnitude lower concentrations. PEG and sucrose maintained immunogenicity in vivo for viruses stored for 10 days at 37 °C. To achieve rational design of viral-vaccine stabilizers, our approach is aided by simplified quantitative models based on a single rate-limiting step.

Keeping viral vaccines cold from the manufacturers to patients is problematic and costly. Here, Krol and others show additives that can significantly improve at very low concentrations the storage of adenovirus type 5 at ambient and elevated temperature.

Decreased Interfacial Tension of Demixed Aqueous Polymer Solutions due to Charge

Electric charge at the water-water interface of demixed solutions of neutral polymer and polyelectrolyte decreases the already ultralow interfacial tension. This is demonstrated in experiments on aqueous mixtures of dextran (neutral) and nongelling fish gelatin (charged). Upon phase separation, electric charge and a potential difference develop spontaneously at the interface, decreasing the interfacial tension purely electrostatically in a way that can be accounted for quantitatively by Poisson-Boltzmann theory. Interfacial tension is a key property when it comes to manipulating the water-water interface, for instance to create novel water-in-water emulsions.

Settled and unsettled issues in particle settling

Colloid sedimentation has played a seminal role in the development of statistical physics thanks to the celebrated experiments by Perrin, which provided a concrete demonstration of molecular reality and gave strong support to Einstein's theory of Brownian motion. This review, which mostly focuses on settling at low Peclét number, where Brownian fluctuations are dominant, aims to show that a lot more can be learnt both from the sedimentation equilibrium and from the particle settling dynamics of a wide class of systems, ranging from simple colloids to mesogenic suspensions, from soft solids to active particles and living organisms. At the same time, the occurrence of unexpected and surprising effects brings about challenging questions in statistical and fluid mechanics that make sedimentation an exciting field of research.