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

Strong electrostatic attraction drives milk heteroprotein complex coacervation

Coacervates of oppositely charged milk proteins are used in functional food development, mainly to encapsulate bioactives. To uncover the driving forces behind coacervates formation, we study the association of lactoferrin and β-lactoglobulin at amino-acid level detail, using molecular simulations. Our findings show that inter-protein electrostatic interactions dominate and are, surprisingly, equally divided between an isotropic part, due to monopole-monopole attraction of the oppositely charged proteins, and an anisotropic part due to uneven surface charge distributions. In good agreement with recent experimental association constants, the calculated protein-protein interaction free energy is strongly dependent on pH and salt concentration. In addition to thermodynamics, we also investigate amino acid contacts in microstates of trimeric and pentameric protein complexes, and identify interaction hot-spots that drive heteroprotein complex coacervation process.

Nanoparticles insertion and dimerization in polymer brushes

Molecular dynamics simulations are conducted to systematically investigate the insertion of spherical nanoparticles (NPs) in polymer brushes as a function of their size, strength of their interaction with the polymers, polymer grafting density, and polymer chain length. For attractive interactions between the NPs and the polymers, the depth of NPs' penetration in the brush results from a competition between the enthalpic gain due to the favorable polymer-NP interaction and the effect of osmotic pressure resulting from displaced polymers by the NP's volume. A large number of simulations show that the average depth of the NPs increases by increasing the strength of the interaction strength. However, it decreases by increasing the NPs' diameter or increasing the polymer grafting density. While the NPs' effect on the polymer density is local, their effect on their conformations is long-ranged and extends laterally over length scales larger than the NP's size. This effect is manifested by the emergence of laterally damped oscillations in the normal component of the chains' radius of gyration. Interestingly, we found that for high enough interaction strength, two NPs dimerize in the polymer brush. The dimer is parallel to the substrate if the NPs' depth in the brush is shallow. However, the dimer is perpendicular to the substrate if the NPs' are deep in the brush. These results imply that polymer brushes can be used as a tool to localize and self-assemble NPs in polymer brushes.

Unusual Aspects of Charge Regulation in Flexible Weak Polyelectrolytes

This article reviews the state of the art of the studies on charge regulation (CR) effects in flexible weak polyelectrolytes (FWPE). The characteristic of FWPE is the strong coupling of ionization and conformational degrees of freedom. After introducing the necessary fundamental concepts, some unconventional aspects of the the physical chemistry of FWPE are discussed. These aspects are: (i) the extension of statistical mechanics techniques to include ionization equilibria and, in particular, the use of the recently proposed Site Binding-Rotational Isomeric State (SBRIS) model, which allows the calculation of ionization and conformational properties on the same foot; (ii) the recent progresses in the inclusion of proton equilibria in computer simulations; (iii) the possibility of mechanically induced CR in the stretching of FWPE; (iv) the non-trivial adsorption of FWPE on ionized surfaces with the same charge sign as the PE (the so-called "wrong side" of the isoelectric point); (v) the influence of macromolecular crowding on CR.

Switchable Polyacrylic Acid Polyelectrolyte Brushes for Surface Plasmon Resonance Applications

Imaging wide-field surface plasmon resonance (SPR) microscopy sensors based on polyacrylic acid polyelectrolyte brushes (PAA PEBs) were designed to enhance the sensitivity of nano-object detection. The switching behavior of the PAA PEBs against changes in the pH values was investigated by analyzing the chemical, morphological, optical, and electrical properties. At pH ~1, the brushes collapse on the surface with the dominance of carboxylic groups (COOH). Upon the increase in the pH to nine, the switching process completes, and the brushes swell from dissociating most of the COOH groups and converting them into COO- groups. The domination of the negatively charged COO- groups increases the electrostatic repulsion in the polymer chains and stretches the brushes. The sensitivity of the SPR sensing device was investigated using a theoretical approach, as well as experimental measurements. The signal-to-noise ratio for a Au layer increases from six to eighteen after coating with PAA PEBs. In addition, the linewidth of the recorded image decreases from six pixels to five pixels by using the Au-PAA layers, which results from the enhanced spatial resolution of the recorded images. Coating a Au-layer with PAA PEBs enhances the sensitivity of the SPR sensing device, and improves the spatial resolution of the recorded image.

Proteins Adsorbing onto Surface-Modified Nanoparticles: Effect of Surface Curvature, pH, and the Interplay of Polymers and Proteins Acid-Base Equilibrium

Protein adsorption onto nanomaterials is a process of vital significance and it is commonly controlled by functionalizing their surface with polymers. The efficiency of this strategy depends on the design parameters of the nanoconstruct. Although significant amount of work has been carried out on planar surfaces modified with different types of polymers, studies investigating the role of surface curvature are not as abundant. Here, we present a comprehensive and systematic study of the protein adsorption process, analyzing the effect of curvature and morphology, the grafting of polymer mixtures, the type of monomer (neutral, acidic, basic), the proteins in solution, and the conditions of the solution. The theoretical approach we employed is based on a molecular theory that allows to explicitly consider the acid-base reactions of the amino acids in the proteins and the monomers on the surface. The calculations showed that surface curvature modulates the molecular organization in space, but key variables are the bulk pH and salt concentration (in the millimolar range). When grafting the NP with acidic or basic polymers, the surface coating could disfavor or promote adsorption, depending on the solution's conditions. When NPs are in contact with protein mixtures in solution, a nontrivial competitive adsorption process is observed. The calculations reflect the balance between molecular organization and chemical state of polymers and proteins, and how it is modulated by the curvature of the underlying surface.

Proteins and Polyampholytes Interacting with Polyelectrolyte Brushes and Microgels: The Charge Reversal Concept Revised

Weak polyampholytes and globular proteins among them can be efficiently absorbed from solutions by polyelectrolyte brushes or microgels even if the net charge of the polyampholyte is of the same sign as that of the brush/microgel. We use a mean-field approach for calculating the free energy of insertion of a probe polyampholyte molecule into a polyelectrolyte brush/microgel. We anticipate that the insertion of the polyampholyte into similarly charged brush/microgel may be thermodynamically favorable due to the gain in the cumulative re-ionization free energy of the pH-sensitive acidic and basic residues. Importantly, we demonstrate that the polyampholyte (protein) charge sign inversion upon transfer from the bulk of the solution to the brush/microgel does not provide sufficient conditions to assure negative re-ionization free energy balance. Thus (in the absence of other driving or stopping mechanisms), charge sign inversion does not necessarily provoke spontaneous absorption of the polyampholyte into the brush/microgel.

Influence of macromolecular crowding on the charge regulation of intrinsically disordered proteins

In this work we study the coupling between ionization and conformational properties of two IDPs, histatin-5 and β-amyloid 42, in the presence of neutral and charged crowders. The latter is modeled to resemble bovine serum albumin (BSA). With this aim, semi-grand canonical Monte Carlo simulations are performed, so that the IDP charge is a dynamic property, undergoing protonation/deprotonation processes. Both ionization properties (global and specific amino acid charge and binding capacitance) and radius of gyration are analyzed in a large range of pH values and salt concentrations. Without crowder agents, the titration curve of histatin-5, a polycation, is salt-dependent while that of β-amyloid 42, a polyampholyte, is almost unaffected. The salt concentration is found to be particularly relevant at pH values where the protein binding capacitance (directly linked with charge fluctuation) is larger. Upon addition of neutral crowders, charge regulation is observed in histatin-5, while for β-amyloid 42 this effect is very small. The main mechanism for charge regulation is found to be the effective increase in the ionic strength due to the excluded volume. In the presence of charged crowders, a significant increase in the charge of both IDPs is observed in almost all the pH range. In this case, the IDP charge is altered not only by the increase in the effective ionic strength but also by its direct electrostatic interaction with the charged crowders.

Pearl-necklace assembly of human serum albumin with the poly(acrylic acid) polyelectrolyte investigated using small angle X-ray scattering (SAXS)

In this comprehensive study, the interaction of human serum albumin (HSA) with poly(acrylic acid) (PAA) was explored using small angle X-ray scattering (SAXS) combined with chromatography. The results revealed the formation of a complex between HSA macromolecules and PAA chains but solely under some specific conditions of the ionic strength and pH of the medium. In fact, this binding was found to take place only at pH close to 5 and at low ionic strength (0.15 M). Otherwise, for a higher pH and a salt concentration of 0.75 M the HSA-PAA complex tends to dissociate completely showing the reversibility of the complexation. The assessment of the influence of the HSA/PAA molar ratio on the radius of gyration of the complex suggests that 4 HSA molecules could bind to each 100 kDa PAA chain. In addition, the Porod volume evaluation for the same range of the HSA/PAA ratio confirms this assumption. Finally, an all-atom SAXS modelling study using the BUNCH program was conducted to find a compatible model that fits the HSA-PAA complex scattering data. This model allows us to portray the HSA/PAA complex as a pearl-necklace assembly with 4 HSA molecules on the 100 kDa PAA chain.

Large Changes in Protonation of Weak Polyelectrolyte Brushes with Salt Concentration-Implications for Protein Immobilization

We report for the first time that the protonation behavior of weak polyelectrolyte brushes depends very strongly on ionic strength. The pKa changes by one pH step per order of magnitude in salt concentration. For low salt concentrations (∼1 mM), a very high pH is required to deprotonate a polyacidic brush and a very low pH is required to protonate a polybasic brush. This has major consequences for interactions with other macromolecules, as the brushes are actually almost fully neutral when believed to be charged. We propose that many previous studies on electrostatic interactions between polyelectrolytes and proteins have, in fact, looked at other types of intermolecular forces, in particular, hydrophobic interactions and hydrogen bonds.

Probing the protein corona around charged macromolecules: interpretation of isothermal titration calorimetry by binding models and computer simulations

Isothermal titration calorimetry (ITC) is a widely used tool to experimentally probe the heat signal of the formation of the protein corona around macromolecules or nanoparticles. If an appropriate binding model is applied to the ITC data, the heat of binding and the binding stoichiometry as well as the binding affinity per protein can be quantified and interpreted. However, the binding of the protein to the macromolecule is governed by complex microscopic interactions. In particular, due to the steric and electrostatic protein–protein interactions within the corona as well as cooperative, charge renormalization effects of the total complex, the application of standard (e.g., Langmuir) binding models is questionable and the development of more appropriate binding models is very challenging. Here, we discuss recent developments in the interpretation of the Langmuir model applied to ITC data of protein corona formation, exemplified for the well-defined case of lysozyme coating highly charged dendritic polyglycerol sulfate (dPGS), and demonstrate that meaningful data can be extracted from the fits if properly analyzed. As we show, this is particular useful for the interpretation of ITC data by molecular computer simulations where binding affinities can be calculated but it is often not clear how to consistently compare them with the ITC data. Moreover, we discuss the connection of Langmuir models to continuum binding models (where no discrete binding sites have to be assumed) and their possible extensions toward the inclusion of leading order cooperative electrostatic effects.

High-pressure study of magnetic nanoparticles with a polyelectrolyte brush as carrier particles for enzymes

The recovery of enzymes from a reaction medium can be achieved in a convenient way by using magnetic nanoparticles (MNP) as carriers. Here, we present MNP with a polyelectrolyte brush composed of poly(ethylene imine) (PEI) to provide a benign environment for the immobilized enzyme molecules. Yeast alcohol dehydrogenase (ADH) has been tested for enzymatic activity when it is free in solution or adsorbed on the PEI brush-MNP. Furthermore, the effect of pressure on the enzymatic activity has been studied to reveal activation volumes, which are a sensitive probe of the transition state geometry. The results of this study indicate that the secondary structure of ADH is pressure-stable up to 9 kbar. The enzymatic activity of ADH can be analyzed using Michaelis-Menten kinetics free in solution and adsorbed on the PEI brush-MNP. Remarkably, no significant changes of the Michaelis constant and the activation volume are observed upon adsorption. Thus, it can be assumed that the turnover number of ADH is also the same in the free and adsorbed state. However, the maximum enzymatic rate is reduced when ADH is adsorbed, which must be explained by a lower effective enzyme concentration due to steric hindrance of the enzyme inside the PEI brush of the MNP. In this way, the pressure experiments carried out in this study enable a distinction between steric and kinetic effects on the enzymatic rate of adsorbed ADH.

Analyzing protein-ligand and protein-interface interactions using high pressure

All protein function is based on interactions with the environment. Proteins can bind molecules for their transport, their catalytic conversion, or for signal transduction. They can bind to each other, and they adsorb at interfaces, such as lipid membranes or material surfaces. An experimental characterization is needed to understand the underlying mechanisms, but also to make use of proteins in biotechnology or biomedicine. When protein interactions are studied under high pressure, volume changes are revealed that directly describe spatial contributions to these interactions. Moreover, the strength of protein interactions with ligands or interfaces can be tuned in a smooth way by pressure modulation, which can be utilized in the design of drugs and bio-responsive interfaces. In this short review, selected studies of protein-ligand and protein-interface interactions are presented that were carried out under high pressure. Furthermore, a perspective on bio-responsive interfaces is given where protein-ligand binding is applied to create functional interfacial structures.

Interaction of Proteins with Polyelectrolytes: Comparison of Theory to Experiment

We discuss recent investigations of the interaction of polyelectrolytes with proteins. In particular, we review our recent studies on the interaction of simple proteins such as human serum albumin (HSA) and lysozyme with linear polyelectrolytes, charged dendrimers, charged networks, and polyelectrolyte brushes. In all cases discussed here, we combined experimental work with molecular dynamics (MD) simulations and mean-field theories. In particular, isothermal titration calorimetry (ITC) has been employed to obtain the respective binding constants K_b and the Gibbs free energy of binding. MD simulations with explicit counterions but implicit water demonstrate that counterion release is the main driving force for the binding of proteins to strongly charged polyelectrolytes: patches of positive charges located on the surface of the protein become multivalent counterions of the polyelectrolyte, thereby releasing a number of counterions condensed on the polyelectrolyte. The binding Gibbs free energy due to counterion release is predicted to scale with the logarithm of the salt concentration in the system, which is verified by both simulations and experiment. In several cases, namely, for the interaction of proteins with linear polyelectrolytes and highly charged hydrophilic dendrimers, the binding constant could be calculated from simulations to very good approximation. This finding demonstrated that in these cases explicit hydration effects do not contribute to the Gibbs free energy of binding. The Gibbs free energy can also be used to predict the kinetics of protein uptake by microgels for a given system by applying dynamic density functional theory. The entire discussion demonstrates that the direct comparison of theory with experiments can lead to a full understanding of the interaction of proteins with charged polymers. Possible implications for applications, such as drug design, are discussed.

Enzyme Immobilization in Polyelectrolyte Brushes: High Loading and Enhanced Activity Compared to Monolayers

Catalysis by enzymes on surfaces has many applications. However, strategies for efficient enzyme immobilization with preserved activity are still in need of further development. In this work, we investigate polyelectrolyte brushes prepared by both grafting-to and grafting-from with the aim to achieve high catalytic activity. For comparison, self-assembled monolayers that bind enzymes with the same chemical interactions are included. We use the model enzyme glucose oxidase and two kinds of polymers: anionic poly(acrylic acid) and cationic poly(diethylamino)methyl methacrylate. Surface plasmon resonance and spectroscopic ellipsometry are used for accurate quantification of surface coverage. Besides binding more enzymes, the "3D-like" brush environment enhances the specific activity compared to immobilization on self-assembled monolayers. For grafting-from brushes, multilayers of enzymes were spontaneously and irreversibly immobilized without conjugation chemistry. When the pH was between the pI of the enzyme and the p K_a of the polymer, binding was considerable (thousands of ng/cm² or up to 50% of the polymer mass), even at physiological ionic strength. However, binding was observed also when the brushes were neutrally charged. For acidic brushes (both grafting-to and grafting-from), the activity was higher for covalent immobilization compared to noncovalent. For grafting-from brushes, a fully preserved specific activity compared to enzymes in the liquid bulk was achieved, both with covalent (acidic brush) and noncovalent (basic brush) immobilization. Catalytic activity of hundreds of pmol cm^-2 s^-1 was easily obtained for polybasic brushes only tens of nanometers in dry thickness. This study provides new insights for designing functional interfaces based on enzymatic catalysis.

Nonequilibrium Uptake Kinetics of Molecular Cargo into Hollow Hydrogels Tuned by Electrosteric Interactions

Hollow hydrogels represent excellent nano- and microcarriers due to their ability to encapsulate and release large amounts of cargo molecules (cosolutes) such as reactants, drugs, and proteins. In this work, we use a combination of a phenomenological effective cosolute-hydrogel interaction potential and dynamic density functional theory to investigate the full nonequilibrium encapsulation kinetics of charged and dipolar cosolutes by an isolated charged hollow hydrogel immersed in a 1:1 electrolyte aqueous solution. Our analysis covers a broad spectrum of cosolute valences ( z_c) and electric dipole moments (μ_c), as well as hydrogel swelling states and hydrogel charge densities. Our calculations show that, close to the collapsed state, the polar cosolutes are predominantly precluded and the encapsulation process is strongly hindered by the excluded-volume interaction exerted by the polymer network. Different equilibrium and kinetic sorption regimes (interface versus interior) are found depending on the value and sign of z_c and the value of μ_c. For cosolutes of the same sign of charge as the gel, the superposition of steric and electrostatic repulsion leads to an "interaction-controlled" encapsulation process, in which the characteristic time to fill the empty core of the hydrogel grows exponentially with z_c. On the other hand, for cosolutes oppositely charged to the gel, we find a "diffusion-controlled" kinetic regime, where cosolutes tend to rapidly absorb into the hydrogel membrane and the encapsulation rate depends only on the cosolute diffusion time across the membrane. Finally, we find that increasing μ_c promotes the appearance of metastable and stable surface adsorption states. For large enough μ_c, the kinetics enters an "adsorption-hindered diffusion", where the enhanced surface adsorption imposes a barrier and slows down the uptake. Our study represents the first attempt to systematically describe how the swelling state of the hydrogel and other leading physical interaction parameters determine the encapsulation kinetics and the final equilibrium distribution of polar molecular cargo.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Electrostatically Driven Protein Adsorption: Charge Patches versus Charge Regulation

The mechanisms of electrostatically driven adsorption of proteins on charged surfaces are studied with a new theoretical framework. The acid-base behavior, charge distribution, and electrostatic contributions to the thermodynamic properties of the proteins are modeled in the presence of a charged surface. The method is validated against experimental titration curves and apparent p K_as. The theory predicts that electrostatic interactions favor the adsorption of proteins at their isoelectric points on charged surfaces despite the fact that the protein has no net charge in solution. Two known mechanisms explain adsorption under these conditions: (i) charge regulation (the charge of the protein changes due to the presence of the surface) and (ii) charge patches (the protein orients to place charged amino acids near opposite surface charges). This work shows that both mechanisms contribute to adsorption at low ionic strengths, whereas only the charge-patch mechanism operates at high ionic strength. Interestingly, the contribution of charge regulation is insensitive to protein orientation under all conditions, which validates the use of constant-charge simulations to determine the most stable orientation of adsorbed proteins. The present study also shows that the charged surface can induce large shifts in the apparent p K_as of individual amino acids in adsorbed proteins. Our conclusions are valid for all proteins studied in this work (lysozyme, α-amylase, ribonuclease A, and β-lactoglobulin), as well as for proteins that are not isoelectric but have instead a net charge in solution of the same sign as the surface charge, i.e. the problem of protein adsorption on the "wrong side" of the isoelectric point.

End Point Versus Backbone Specificity Governs Characteristics of Antibody Binding to Poly(ethylene glycol) Brushes

End-grafted poly(ethylene glycol) (PEG) brushes are widely used in order to suppress undesired protein adsorption to surfaces exposed to blood or other biological fluids. The specific adsorption of antibodies (Abs) to PEG brushes associated with PEG's antigenicity is drawing increasing attention because it can affect clinical applications. Here, the adsorption to PEG brushes of two Ab types, specifically binding the polymer backbone and the polymer endpoints, is structurally characterized by neutron reflectometry. The measurements yield volume fraction profiles of PEG and of the adsorbed Abs with sub-nanometer resolution perpendicular to the surface. For all brush parameters in terms of grafting density and polymerization degree, the Ab profiles clearly differ between backbone binders and endpoint binders. The adsorbed Ab amount per unit area is substantial for both Ab types and for all brush parameters investigated, even for dense brushes, which impose a considerable osmotic barrier to Ab insertion. The results therefore indicate that variation of brush parameters alone is insufficient to prevent undesired Ab adsorption. Instead, our work motivates further efforts in the search for nonantigenic brush chemistry.

Overcharging and reentrant condensation of thermoresponsive ionic microgels

We investigated the complexation of thermoresponsive anionic poly(N-isopropylacrylamide) (PNiPAM) microgels and cationic ε-polylysine (ε-PLL) chains. By combining electrophoresis, light scattering, transmission electron microscopy (TEM) and dielectric spectroscopy (DS) we studied the adsorption of ε-PLL onto microgel networks and its effect on the stability of suspensions. We show that the volume phase transition (VPT) of microgels triggers a large polyion adsorption. Two interesting phenomena with unique features occur: a temperature-dependent microgel overcharging and a complex reentrant condensation. The latter may occur at fixed polyion concentration, when temperature is raised above the VPT of microgels, or by increasing the number density of polycations at fixed temperature. TEM and DS measurements unambiguously show that short PLL chains adsorb onto microgels and act as electrostatic glue above the VPT. By performing thermal cycles, we further show that polyion-induced clustering is a quasi-reversible process: within the time of our experiments large clusters form above the VPT and partially re-dissolve as the mixtures are cooled down. Finally we give a proof that the observed phenomenology is purely electrostatic in nature: an increase of the ionic strength gives rise to polyion desorption from the microgel outer shell.

Reversible Protein Adsorption on Mixed PEO/PAA Polymer Brushes: Role of Ionic Strength and PEO Content

Proteins at interfaces are a key for many applications in the biomedical field, in biotechnologies, in biocatalysis, in food industry, etc. The development of surface layers that allow to control and manipulate proteins is thus highly desired. In previous works, we have shown that mixed polymer brushes combining the protein-repellent properties of poly(ethylene oxide) (PEO) and the stimuli-responsive adsorption behavior of poly(acrylic acid) (PAA) could be synthesized and used to achieve switchable protein adsorption. With the present work, we bring more insight into the rational design of such smart thin films by unravelling the role of PEO on the adsorption/desorption of proteins. The PEO content of the mixed PEO/PAA brushes was regulated, on the one hand, by using PEO with different molar masses and, on the other hand, by varying the ratio of PEO and PAA in the solutions used to synthesize the brushes. The influence of ionic strength on the protein adsorption behavior was also further examined. The behavior of three proteins-human serum albumin, lysozyme, and human fibrinogen, which have very different size, shape, and isoelectric point-was investigated. X-ray photoelectron spectroscopy, quartz crystal microbalance, atomic force microscopy, and streaming potential measurements were used to characterize the mixed polymer brushes and, in particular, to estimate the fraction of each polymer within the brushes. Protein adsorption and desorption conditions were selected based on previous studies. While brushes with a lower PEO content allowed the higher protein adsorption to occur, fully reversible adsorption could only be achieved when the PEO surface density was at least 25 PEO units per nm². Taken together, the results increase the ability to finely tune protein adsorption, especially with temporal control. This opens up possibilities of applications in biosensor design, separation technologies, nanotransport, etc.

Maximizing the absorption of small cosolutes inside neutral hydrogels: steric exclusion versus hydrophobic adhesion

In this work the equilibrium absorption of nanometric cosolutes (which could represent drugs, reactants, small globular proteins and other kind of biomacromolecules) inside neutral hydrogels is studied. We specially focus on exploring, for different swelling states, the competition between the steric exclusion induced by the cross-linked polymer network constituting the hydrogel, and the solvent-induced short-range hydrophobic attraction between the polymer chains and the cosolute particle. For this purpose, the cosolute partition coefficient is calculated by means of coarse-grained grand canonical Monte Carlo simulations, and the results are compared to theoretical predictions based on the calculation of the excluded and binding volume around the polymer chains. For small hydrophobic attractions or large cosolute sizes, the steric repulsion dominates, and the partition coefficient decreases monotonically with the polymer volume fraction, ϕ_m. However, for large enough hydrophobic attraction strength, the interplay between hydrophobic adhesion and the steric exclusion leads to a maximum in the partition coefficient at certain intermediate polymer density. Good qualitative and quantitative agreement is achieved between simulation results and theoretical predictions in the limit of small ϕ_m, pointing out the importance of geometrical aspects of the cross-linked polymer network, even for hydrogels in the swollen state. In addition, the theory is able to predict analytically the onset of the maximum formation in terms of the details of the cosolute-monomer pair interaction, in good agreement with simulations too. Finally, the effect of the many-body attractions between the cosolute and multiple polymer chains is quantified. The results clearly show that these many-body attractions play a very relevant role determining the cosolute binding, enhancing its absorption in more than one order of magnitude.

From discrete to continuous description of spherical surface charge distributions

The importance of electrostatic interactions in soft matter and biological systems can often be traced to non-uniform charge effects, which are commonly described using a multipole expansion of the corresponding charge distribution. The standard approach when extracting the charge distribution of a given system is to treat the constituent charges as points. This can, however, lead to an overestimation of multipole moments of high order, such as dipole, quadrupole, and higher moments. Focusing on distributions of charges located on a spherical surface - characteristic of numerous biological macromolecules, such as globular proteins and viral capsids, as well as of inverse patchy colloids - we develop a novel way of representing spherical surface charge distributions based on the von Mises-Fisher distribution. This approach takes into account the finite spatial extension of individual charges, and leads to a simple yet powerful way of describing surface charge distributions and their multipole expansions. In this manner, we analyze charge distributions and the derived multipole moments of a number of different spherical configurations of identical charges with various degrees of symmetry. We show how the number of charges, their size, and the geometry of their configuration influence the behavior and relative importance of multipole magnitudes of different order. Importantly, we clearly demonstrate how neglecting the effect of charge size leads to an overestimation of high-order multipoles. The results of our work can be applied to construct analytical models of electrostatic interactions and multipole expansion of charged particles in diverse soft matter and biological systems.

Binding of Lysozyme to Spherical Poly(styrenesulfonate) Gels

Polyelectrolyte gels are useful as carriers of proteins and other biomacromolecules in, e.g., drug delivery. The rational design of such systems requires knowledge about how the binding and release are affected by electrostatic and hydrophobic interactions between the components. To this end we have investigated the uptake of lysozyme by weakly crosslinked spherical poly(styrenesulfonate) (PSS) microgels and macrogels by means of micromanipulator assisted light microscopy and small angle X-ray scattering (SAXS) in an aqueous environment. The results show that the binding process is an order of magnitude slower than for cytochrome c and for lysozyme binding to sodium polyacrylate gels under the same conditions. This is attributed to the formation of very dense protein-rich shells in the outer layers of the microgels with low permeability to the protein. The shells in macrogels contain 60 wt % water and nearly charge stoichiometric amounts of lysozyme and PSS in the form of dense complexes of radius 8 nm comprising 30⁻60 lysozyme molecules. With support from kinetic modelling results we propose that the rate of protein binding and the relaxation rate of the microgel are controlled by the protein mass transport through the shell, which is strongly affected by hydrophobic and electrostatic interactions. The mechanism explains, in turn, an observed dependence of the diffusion rate on the apparent degree of crosslinking of the networks.

Counterion-Release Entropy Governs the Inhibition of Serum Proteins by Polyelectrolyte Drugs

Dendritic polyelectrolytes constitute high potential drugs and carrier systems for biomedical purposes. Still, their biomolecular interaction modes, in particular those determining the binding affinity to proteins, have not been rationalized. We study the interaction of the drug candidate dendritic polyglycerol sulfate (dPGS) with serum proteins using isothermal titration calorimetry (ITC) interpreted and complemented with molecular computer simulations. Lysozyme is first studied as a well-defined model protein to verify theoretical concepts, which are then applied to the important cell adhesion protein family of selectins. We demonstrate that the driving force of the strong complexation, leading to a distinct protein corona, originates mainly from the release of only a few condensed counterions from the dPGS upon binding. The binding constant shows a surprisingly weak dependence on dPGS size (and bare charge) which can be understood by colloidal charge-renormalization effects and by the fact that the magnitude of the dominating counterion-release mechanism almost exclusively depends on the interfacial charge structure of the protein-specific binding patch. Our findings explain the high selectivity of P- and L-selectins over E-selectin for dPGS to act as a highly anti-inflammatory drug. The entire analysis demonstrates that the interaction of proteins with charged polymeric drugs can be predicted by simulations with unprecedented accuracy. Thus, our results open new perspectives for the rational design of charged polymeric drugs and carrier systems.

pH Dependence of Charge Multipole Moments in Proteins

Electrostatic interactions play a fundamental role in the structure and function of proteins. Due to ionizable amino acid residues present on the solvent-exposed surfaces of proteins, the protein charge is not constant but varies with the changes in the environment-most notably, the pH of the surrounding solution. We study the effects of pH on the charge of four globular proteins by expanding their surface charge distributions in terms of multipoles. The detailed representation of the charges on the proteins is in this way replaced by the magnitudes and orientations of the multipole moments of varying order. Focusing on the three lowest-order multipoles-the total charge, dipole, and quadrupole moment-we show that the value of pH influences not only their magnitudes, but more notably and importantly also the spatial orientation of their principal axes. Our findings imply important consequences for the study of protein-protein interactions and the assembly of both proteinaceous shells and patchy colloids with dissociable charge groups.

Sorption and Spatial Distribution of Protein Globules in Charged Hydrogel Particles

We have theoretically studied the uptake of a nonuniformly charged biomolecule suitable for representing a globular protein or a drug by a charged hydrogel carrier in the presence of a 1:1 electrolyte. On the basis of the analysis of a physical interaction Hamiltonian including monopolar, dipolar, and Born (self-energy) contributions derived from linear electrostatic theory of the unperturbed homogeneous hydrogel, we have identified five different sorption states of the system, from complete repulsion of the molecule to its full sorption deep inside the hydrogel, passing through metastable and stable surface adsorption states. The results are summarized in state diagrams that also explore the effects of varying the electrolyte concentration, the sign of the net electric charge of the biomolecule, and the role of including excluded-volume (steric) or hydrophobic biomolecule-hydrogel interactions. We show that the dipole moment of the biomolecule is a key parameter controlling the spatial distribution of the globules. In particular, biomolecules with a large dipole moment tend to be adsorbed at the external surface of the hydrogel, even if like-charged, whereas uniformly charged biomolecules tend to partition toward the internal core of an oppositely charged hydrogel. Hydrophobic attraction shifts the states toward the internal sorption of the biomolecule, whereas steric repulsion promotes surface adsorption for oppositely charged biomolecules or for the total exclusion of likely charged ones. Our results establish a guideline for the spatial partitioning of proteins and drugs in hydrogel carriers, tunable by the hydrogel charge, pH, and salt concentration.

Protein Immobilization onto Cationic Spherical Polyelectrolyte Brushes Studied by Small Angle X-ray Scattering

The immobilization of bovine serum albumins (BSA) onto cationic spherical polyelectrolyte brushes (SPB) consisting of a solid polystyrene (PS) core and a densely grafted poly(2-aminoethyl methacrylate hydrochloride) (PAEMH) shell was studied by small-angle X-ray scattering (SAXS). The observed dynamics of adsorption of BSA onto SPB by time-resolved SAXS can be divided into two stages. In the first stage (tens of milliseconds), the added proteins as in-between bridge instantaneously caused the aggregation of SPB. Then BSA penetrated into the brush layer driven by electrostatic attractions, and reached equilibrium in the second stage (tens of seconds). The amount of BSA immobilized onto brush layer reached the maximum when pH was increased to about 6.1 and BSA concentration to 10 g/L. The cationic SPB were confirmed to provide stronger adsorption capacity for BSA compared to anionic ones.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

Artistic representation of limited valance units consisting of a soft core (in blue) and a small number of flexible bonding patches (in orange).