Effective interactions in lysozyme aqueous solutions: A small-angle neutron scattering and computer simulation study

Biophysical Principles Emerging from Experiments on Protein-Protein Association and Aggregation

Protein-protein association and aggregation are fundamental processes that play critical roles in various biological phenomena, from cellular signaling to disease progression. Understanding the underlying biophysical principles governing these processes is crucial for elucidating their mechanisms and developing strategies for therapeutic intervention. In this review, we provide an overview of recent experimental studies focused on protein-protein association and aggregation. We explore the key biophysical factors that influence these processes, including protein structure, conformational dynamics, and intermolecular interactions. We discuss the effects of environmental conditions such as temperature, pH and related buffer-specific effects, and ionic strength and related ion-specific effects on protein aggregation. The effects of polymer crowders and sugars are also addressed. We list the techniques used to study aggregation. We analyze emerging trends and challenges in the field, including the development of computational models and the integration of multidisciplinary approaches for a comprehensive understanding of protein-protein association and aggregation.

Interactions and pattern formation in a macroscopic magnetocapillary SALR system of mermaid cereal

When particles are deposited at a fluid interface they tend to aggregate by capillary attraction to minimize the overall potential energy of the system. In this work, we embed floating millimetric disks with permanent magnets to introduce a competing repulsion effect and study their pattern formation in equilibrium. The pairwise energy landscape of two disks is described by a short-range attraction and long-range repulsion (SALR) interaction potential, previously documented in a number of microscopic condensed matter systems. Such competing interactions enable a variety of pairwise equilibrium states, including the possibility of a local minimum energy corresponding to a finite disk spacing. Two-dimensional (2D) experiments and simulations in confined geometries demonstrate that as the areal packing fraction is increased, the dilute repulsion-dominated lattice state becomes unstable to the spontaneous formation of localized clusters, which eventually merge into a system-spanning striped pattern. Finally, we demonstrate that the equilibrium pattern can be externally manipulated by the application of a supplemental vertical magnetic force that remotely enhances the effective capillary attraction.

Thermodynamic Signatures of Structural Transitions and Dissociation of Charged Colloidal Clusters: A Parallel Tempering Monte Carlo Study

Computational simulation of colloidal systems make use of empirical interaction potentials that are founded in well-established theory. In this work, we have performed parallel tempering Monte Carlo (PTMC) simulations to calculate heat capacity and to assess structural transitions, which may occur in charged colloidal clusters whose effective interactions are described by a sum of pair potentials with attractive short-range and repulsive long-range components. Previous studies on these systems have shown that the global minimum structure varies from spherical-type shapes for small-size clusters to Bernal spiral and “beaded-necklace” shapes at intermediate and larger sizes, respectively. In order to study both structural transitions and dissociation, we have organized the structures appearing in the PTMC calculations by three sets according to their energy: (i) low-energy structures, including the global minimum; (ii) intermediate-energy “beaded-necklace” motifs; (iii) high-energy linear and branched structures that characterize the dissociative clusters. We observe that, depending on the cluster, either peaks or shoulders on the heat–capacity curve constitute thermodynamics signatures of dissociation and structural transitions. The dissociation occurs at T=0.20 for all studied clusters and it is characterized by the appearance of a significant number of linear structures, while the structural transitions corresponding to unrolling the Bernal spiral are quite dependent on the size of the colloidal system.

Unusual stability of protein molecules in the presence of multivalent counterions

Proteins are known to undergo denaturation and form different phases with varying physicochemical parameters. We report unusual stability of bovine serum albumin protein against commonly used denaturants (temperature and surfactant) in the charged reversal reentrant phase, caused by the multivalent counterions. Unlike monovalent counterions, which promote the denaturants' induced protein unfolding, the unfolding is restricted in the presence of multivalent ions. The observations are beyond the scope of general understanding of protein unfolding and are believed to be governed by ion-ion correlations driven strong condensation of the multivalent ions.

High-Throughput Screening for Colloidal Stability of Peptide Formulations Using Dynamic and Static Light Scattering

Selection of an appropriate formulation to stabilize therapeutic proteins against aggregation is one of the most challenging tasks in early-stage drug product development. The amount of aggregates is more difficult to quantify in the case of peptides due to their small molecular size. Here, we investigated the suitability of diffusion self-interaction parameters (k_D) and osmotic second virial coefficients (B₂₂) for high-throughput (HT) screening of peptide formulations regarding their aggregation risk. These parameters were compared to the effect of thermal stress on colloidal stability. The formulation matrix comprised six buffering systems at two selected pH values, four tonicity agents, and a common preservative. The results revealed that electrostatic interactions are the main driver to control colloidal stability. Preferred formulations consisted of acetate and succinate buffer at pH 4.5 combined with glycerol or mannitol and optional m-cresol. k_D proved to be a suitable surrogate for B₂₂ as an indicator of high colloidal stability in the case of peptides as was previously described for globular proteins and antibodies. Formulation assessment solely based on k_D obtained by HT methods offers important insights into the optimization of colloidal stability during the early development of peptide-based liquid formulations and can be performed with a limited amount of peptide (∼360 mg).

Decoupling copolymer, lipid and carbon nanotube interactions in hybrid, biomimetic vesicles

Bilayer vesicles that mimic a real biological cell can be tailored to carry out a specific function by manipulating the molecular composition of the amphiphiles. These bio-inspired and bio-mimetic structures are increasingly being employed for a number of applications from drug delivery to water purification and beyond. Complex hybrid bilayers are the key building blocks for fully synthetic vesicles that can mimic biological cell membranes, which often contain a wide variety of molecular species. While the assembly and morpholgy of pure phospholid bilayer vesicles is well understood, the functionality and structure dramaticlly changes when copolymer and/or carbon nanotube porins (CNTP) are added. The aim of this study is to understand how the collective molecular interactions within hybrid vesicles affect their nanoscale structure and properties. In situ small and wide angle X-ray scattering (SAXS/WAXS) and molecular dynamics simulations (MD) are used to investigate the morphological effect of molecular interactions between polybutadiene polyethylene oxide, lipids and carbon nanotubes (CNT) within the hybrid vesicle bilayer. Within the lipid/copolymer system, the hybrid bilayer morphology transitions from phase separated lipid and compressed copolymer at low copolymer loadings to a mixed bilayer where opposing lipids are mostly separated from the inner region. This transition begins between 60 wt% and 70 wt%, with full homogenization observed by 80 wt% copolymer. The incorporation of CNT into the hybrid vesicles increases the bilayer thickness and enhances the bilayer symmetry. Analysis of the WAXS and MD indicate that the CNT-dioleoyl interactions are much stronger than the CNT-polybutadiene.

Nanomedical Relevance of the Intermolecular Interaction Dynamics-Examples from Lysozymes and Insulins

Insulin and lysozyme share the common features of being prone to aggregate and having biomedical importance. Encapsulating lysozyme and insulin in micellar nanoparticles probably would prevent aggregation and facilitate oral drug delivery. Despite the vivid structural knowledge of lysozyme and insulin, the environment-dependent oligomerization (dimer, trimer, and multimer) and associated structural dynamics remain elusive. The knowledge of the intra- and intermolecular interaction profiles has cardinal importance for the design of encapsulation protocols. We have employed various biophysical methods such as NMR spectroscopy, X-ray crystallography, Thioflavin T fluorescence, and atomic force microscopy in conjugation with molecular modeling to improve the understanding of interaction dynamics during homo-oligomerization of lysozyme (human and hen egg) and insulin (porcine, human, and glargine). The results obtained depict the atomistic intra- and intermolecular interaction details of the homo-oligomerization and confirm the propensity to form fibrils. Taken together, the data accumulated and knowledge gained will further facilitate nanoparticle design and production with insulin or lysozyme-related protein encapsulation.

Colloidal systems with a short-range attraction and long-range repulsion: Phase diagrams, structures, and dynamics

Colloidal systems with both a short-range attraction and long-range repulsion (SALR) have rich phases compared with the traditional hard sphere systems or sticky hard sphere systems. The competition between the short-range attraction and long-range repulsion results in the frustrated phase separation, which leads to the formation of intermediate range order (IRO) structures and introduces new phases to both equilibrium and nonequilibrium phase diagrams, such as clustered fluid, cluster percolated fluid, Wigner glass, and cluster glass. One hallmark feature of many SALR systems is the appearance of the IRO peak in the interparticle structure factor, which is associated with different types of IRO structures. The relationship between the IRO peak and the clustered fluid state has been careful investigated. Not surprisingly, the morphology of clusters in solutions can be affected and controlled by the SALR potential. And the effect of the SALR potential on the dynamic properties is also reviewed here. Even though much progress has been made in understanding SALR systems, many future works are still needed to have quantitative comparisons between experiments and simulations/theories and understand the differences from different experimental systems. Owing to the large parameter space available for SALR systems, many exciting features of SALR systems are not fully explored yet. Because proteins in low-salinity solutions have SALR interactions, the understanding of SALR systems can greatly help understand protein behavior in concentrated solutions or crowded conditions.

A methodology to calculate small-angle scattering profiles of macromolecular solutions from molecular simulations in the grand-canonical ensemble

The theoretical framework to evaluate small-angle scattering (SAS) profiles for multi-component macromolecular solutions is re-examined from the standpoint of molecular simulations in the grand-canonical ensemble, where the chemical potentials of all species in solution are fixed. This statistical mechanical ensemble resembles more closely scattering experiments, capturing concentration fluctuations that arise from the exchange of molecules between the scattering volume and the bulk solution. The resulting grand-canonical expression relates scattering intensities to the different intra- and intermolecular pair distribution functions, as well as to the distribution of molecular concentrations on the scattering volume. This formulation represents a generalized expression that encompasses most of the existing methods to evaluate SAS profiles from molecular simulations. The grand-canonical SAS methodology is probed for a series of different implicit-solvent, homogeneous systems at conditions ranging from dilute to concentrated. These systems consist of spherical colloids, dumbbell particles, and highly flexible polymer chains. Comparison of the resulting SAS curves against classical methodologies based on either theoretical approaches or canonical simulations (i.e., at a fixed number of molecules) shows equivalence between the different scattering intensities so long as interactions between molecules are net repulsive or weakly attractive. On the other hand, for strongly attractive interactions, grand-canonical SAS profiles deviate in the low- and intermediate-q range from those calculated in a canonical ensemble. Such differences are due to the distribution of molecules becoming asymmetric, which yields a higher contribution from configurations with molecular concentrations larger than the nominal value. Additionally, for flexible systems, explicit discrimination between intra- and inter-molecular SAS contributions permits the implementation of model-free, structural analysis such as Guinier's plots at high molecular concentrations, beyond what the traditional limits are for such analysis.

Soft nanoparticles charge expression within lipid membranes: The case of amino terminated dendrimers in bilayers vesicles

Interactions of charged nanoparticles with model bio-membranes provide important insights about the soft interaction involved and the physico-chemical parameters that influence lipid bilayers stability, thus providing key features of their cytotoxicity effects onto cellular membranes. With this aim, the self-assembly processes between polyamidoamine dendrimers (generation G = 2.0 and G = 4.0) and dipalmitoylphosphatidylcholine (DPPC) lipids were investigated by means of Zeta potential analysis, x-rays, Raman and quasielastic light scattering experiments. Raman scattering data evidenced that dendrimers penetration produce a perturbation of the DPPC vesicles alkyl chains. A linear increase of liposome zeta-potential with increasing PAMAM concentration evidenced that only a fraction of the dendrimers effective charge contributes to the expression of the charge at the surface of the DPPC liposome. The linear region of the zeta-potential extends toward higher PAMAM concentrations as the dendrimer generation decreases from G = 4.0 to G = 2.0. Further increase in PAMAM concentration, outside of the linear region, causes a perturbation of the bilayer characterized by the loss in multilamellar correlation and the increase of DPPC liposome hydrodynamic radius. The findings of our investigation help to rationalize the effect of nanoparticles electrostatic interaction within lipid vesicles as well as to provide important insights about the perturbation of lipid bilayers membrane induced by nanoparticles inclusion.

Self-assembly in a model colloidal mixture of dimers and spherical particles

We investigate the structure of a dilute mixture of amphiphilic dimers and spherical particles, a model relevant to the problem of encapsulating globular "guest" molecules in a dispersion. Dimers and spheres are taken to be hard particles, with an additional attraction between spheres and the smaller monomers in a dimer. Using the Monte Carlo simulation, we document the low-temperature formation of aggregates of guests (clusters) held together by dimers, whose typical size and shape depend on the guest concentration χ. For low χ (less than 10%), most guests are isolated and coated with a layer of dimers. As χ progressively increases, clusters grow in size becoming more and more elongated and polydisperse; after reaching a shallow maximum for χ≈50%, the size of clusters again reduces upon increasing χ further. In one case only (χ=50% and moderately low temperature) the mixture relaxed to a fluid of lamellae, suggesting that in this case clusters are metastable with respect to crystal-vapor separation. On heating, clusters shrink until eventually the system becomes homogeneous on all scales. On the other hand, as the mixture is made denser and denser at low temperature, clusters get increasingly larger until a percolating network is formed.

Aggregation kinetics of irreversible patches coupled with reversible isotropic interaction leading to chains, bundles and globules

In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern–Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined three different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effect of patch size on self-assembly under different solvent qualities for various volume fractions. We will show that at low volume fractions during aggregation process, we end up in a chain conformation for smaller patch size while in a globular conformation for bigger patch size. We also observed a chain to bundle transformation depending on the attractive interaction strength between the chains or in other words depending on the quality of the solvent. We will also show that bundling process is very similar to nucleation and growth phenomena observed in colloidal system with short range attraction. We have also studied the bond angle distribution for this system, where for small patches only two angles are more probable indicating chain formation, while for bundling at very low volume fraction a tail is developed in the distribution. While for the case of higher patch angle this distribution is broad compared to the case of low patch angles showing we have a more globular conformation. We are also proposing a model for the formation of bundles which are similar to amyloid fibers using two patch colloidal particles.

Theory and computer simulation of hard-core Yukawa mixtures: thermodynamical, structural and phase coexistence properties

We report extensive calculations, based on the modified hypernetted chain (MHNC) theory, on the hierarchical reference theory (HRT), and on Monte Carlo simulations, of thermodynamical, structural and phase coexistence properties of symmetric binary hard-core Yukawa mixtures (HCYM) with attractive interactions at equal species concentration. The obtained results are throughout compared with those available in the literature for the same systems. It turns out that the MHNC predictions for thermodynamic and structural quantities are quite accurate in comparison with the MC data. The HRT is equally accurate for thermodynamics, and slightly less accurate for structure. Liquid-vapor (LV) and liquid-liquid (LL) consolute coexistence conditions as emerging from simulations, are also highly satisfactorily reproduced by both the MHNC and HRT for relatively long ranged potentials. When the potential range reduces, the MHNC faces problems in determining the LV binodal line; however, the LL consolute line and the critical end point (CEP) temperature and density turn out to be still satisfactorily predicted within this theory. The HRT also predicts with good accuracy the CEP position. The possibility of employing liquid state theories HCYM for the purpose of reliably determining phase equilibria in multicomponent colloidal fluids of current technological interest, is discussed.

Explicit-water theory for the salt-specific effects and Hofmeister series in protein solutions

Effects of addition of salts on stability of aqueous protein solutions are studied theoretically and the results are compared with experimental data. In our approach, all the interacting species, proteins, ions, and water molecules, are accounted for explicitly. Water molecules are modeled as hard spheres with four off-center attractive square-well sites. These sites serve to bind either another water or to solvate the ions or protein charges. The ions are represented as charged hard spheres, and decorated by attractive sites to allow solvation. Spherical proteins simultaneously possess positive and negative groups, represented by charged hard spheres, attached to the surface of the protein. The attractive square-well sites, mimicking the protein-protein van der Waals interaction, are located on the surface of the protein. To obtain numerical results, we utilized the energy route of Wertheim's associative mean spherical approximation. From measurable properties, we choose to calculate the second virial coefficient B2, which is closely related to the tendency of proteins to aggregate and eventually crystalize. Calculations are in agreement with experimental trends: (i) For low concentration of added salt, the alkali halide salts follow the inverse Hofmeister series. (ii) At higher concentration of added salt, the trend is reversed. (iii) When cations are varied, the salts follow the direct Hofmeister series. (iv) In contrast to the colloidal theories, our approach correctly predicts the non-monotonic behavior of B2 upon addition of salts. (v) With respect to anions, the theory predicts for the B2 values to follow different sequences below and above the iso-ionic point, as also confirmed experimentally. (vi) A semi-quantitative agreement between measured and calculated values for the second virial coefficient, as functions of pH of solution and added salt type and concentration, is obtained.

Softness and non-spherical shape define the phase behavior and the structural properties of lysozyme in aqueous solutions

In this study, Boltzmann inversion is applied in conjunction with molecular dynamics simulations to derive inter-molecular potential for protein lysozyme in aqueous solution directly from experimental static structure factor. The potential has a soft repulsion at short distances and an attraction well at intermediate distances that give rise to the liquid-liquid phase separation. Moreover, Gibbs ensemble Monte Carlo simulations demonstrate that a non-spherical description of lysozyme is better suited to correctly reproduce the experimentally observed properties of such a phase separation. Our findings shed new light on the common problem in molecular and cell biology: "How to model proteins in their natural aqueous environments?"

Effect of anionic and cationic polyamidoamine (PAMAM) dendrimers on a model lipid membrane

In spite of the growing variety of biological applications of dendrimer-based nanocarriers, a major problem of their potential applications in bio-medicine is related to the disruption of lipid bilayers and the cytotoxicity caused by the aggregation processes involved onto cellular membranes. With the aim to study model dendrimer-biomembrane interaction, the self-assembly processes of a mixture of charged polyamidoamine (PAMAM) dendrimers and dipalmitoylphosphatidylcholine (DPPC) lipids were investigated by means of Zeta potential analysis, Raman and x-ray scattering. Zwitterionic DPPC liposomes showed substantially different behaviors during their interaction with negatively charged (generation G=2.5) sodium carboxylate terminated (COO^- Na⁺) dendrimers or positively charged (generation G=3.0) amino terminated (-NH₂) dendrimers. More specifically the obtained results evidence the sensitive interactions between dendrimer terminals and lipid molecules at the surface of the liposome, with an enhancement of the liposome surface zeta potential, as well as in the hydrophobic region of the bilayers, where dendrimer penetration produce a perturbation of the hydrophobic alkyl chains of the bilayers. Analysis of the SAXS structure factor with a suitable model for the inter-dendrimers electrostatic potential allows an estimation of an effective charge of 15 ǀeǀ for G=2.5 and 7.6 ǀeǀ for G=3.0 PAMAM dendrimers. Only a fraction (about 1/7) of this charge contributes to the linear increase of liposome zeta-potential with increasing PAMAM/DPPC molar fraction. The findings of our investigation may be applied to rationalize the effect of the nanoparticles electrostatic interaction in solution environments for the design of new drug carriers combining dendrimeric and liposomal technology.

Soft Interaction in Liposome Nanocarriers for Therapeutic Drug Delivery

The development of smart nanocarriers for the delivery of therapeutic drugs has experienced considerable expansion in recent decades, with the development of new medicines devoted to cancer treatment. In this respect a wide range of strategies can be developed by employing liposome nanocarriers with desired physico-chemical properties that, by exploiting a combination of a number of suitable soft interactions, can facilitate the transit through the biological barriers from the point of administration up to the site of drug action. As a result, the materials engineer has generated through the bottom up approach a variety of supramolecular nanocarriers for the encapsulation and controlled delivery of therapeutics which have revealed beneficial developments for stabilizing drug compounds, overcoming impediments to cellular and tissue uptake, and improving biodistribution of therapeutic compounds to target sites. Herein we present recent advances in liposome drug delivery by analyzing the main structural features of liposome nanocarriers which strongly influence their interaction in solution. More specifically, we will focus on the analysis of the relevant soft interactions involved in drug delivery processes which are responsible of main behaviour of soft nanocarriers in complex physiological fluids. Investigation of the interaction between liposomes at the molecular level can be considered an important platform for the modeling of the molecular recognition processes occurring between cells. Some relevant strategies to overcome the biological barriers during the drug delivery of the nanocarriers are presented which outline the main structure-properties relationships as well as their advantages (and drawbacks) in therapeutic and biomedical applications.

Structural characterization in mixed lipid membrane systems by neutron and X-ray scattering

Lipids membranes, the primary component of the living cell, involve collective behaviour of numerous interacting molecules. The rich morphology and complex phase diagram of the lipid systems require different strategies in describing bio-membranes in order to capture the essential properties of self-assembly processes as well as the underling molecular collective phenomena involved in biological functions. Among the experimental methods used, the scattering techniques such as small angle neutrons and X-rays scattering (SANS and SAXS) are probably the most important experimental approaches for the structural investigation of bio-membranes and mixed lipids complex systems. In this tutorial review we describe the main approaches employed in the investigation of lipid bio-membranes by means of the neutron and x-ray scattering techniques. While introducing the main structural properties of lipid bio-membranes we highlight the important role of lipid components in different biological functions of living organisms. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo.

Coupling of isotropic and directional interactions and its effect on phase separation and self-assembly

The interactions of molecules and particles in solution often involve an interplay between isotropic and highly directional interactions that lead to a mutual coupling of phase separation and self-assembly. This situation arises, for example, in proteins interacting through hydrophobic and charged patch regions on their surface and in nanoparticles with grafted polymer chains, such as DNA. As a minimal model of complex fluids exhibiting this interaction coupling, we investigate spherical particles having an isotropic interaction and a constellation of five attractive patches on the particle's surface. Monte Carlo simulations and mean-field calculations of the phase boundaries of this model depend strongly on the relative strength of the isotropic and patch potentials, where we surprisingly find that analytic mean-field predictions become increasingly accurate as the directional interactions become increasingly predominant. We quantitatively account for this effect by noting that the effective interaction range increases with increasing relative directional to isotropic interaction strength. We also identify thermodynamic transition lines associated with self-assembly, extract the entropy and energy of association, and characterize the resulting cluster properties obtained from simulations using percolation scaling theory and Flory-Stockmayer mean-field theory. We find that the fractal dimension and cluster size distribution are consistent with those of lattice animals, i.e., randomly branched polymers swollen by excluded volume interactions. We also identify a universal functional form for the average molecular weight and a nearly universal functional form for a scaling parameter characterizing the cluster size distribution. Since the formation of branched clusters at equilibrium is a common phenomenon in nature, we detail how our analysis can be used in experimental characterization of such associating fluids.

Protein aggregation in salt solutions

Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein-protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim's thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid-liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer-salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

Weak self-interactions of globular proteins studied by small-angle X-ray scattering and structure-based modeling

We investigate protein-protein interactions in solution by small-angle X-ray scattering (SAXS) and theoretical modeling. The structure factor for solutions of bovine pancreatic trypsin inhibitor (BPTI), myoglobin (Mb), and intestinal fatty acid-binding protein (IFABP) is determined from SAXS measurements at multiple concentrations, from Monte Carlo simulations with a coarse-grained structure-based interaction model, and from analytic approximate solutions of two idealized colloidal interaction models without adjustable parameters. By combining these approaches, we find that the structure factor is essentially determined by hard-core and screened electrostatic interactions. Other soft short-ranged interactions (van der Waals and solvation-related) are either individually insignificant or tend to cancel out. The structure factor is also not significantly affected by charge fluctuations. For Mb and IFABP, with a small net charge and relatively symmetric charge distribution, the structure factor is well described by a hard-sphere model. For BPTI, with a larger net charge, screened electrostatic repulsion is also important, but the asymmetry of the charge distribution reduces the repulsion from that predicted by a charged hard-sphere model with the same net charge. Such charge asymmetry may also amplify the effect of shape asymmetry on the protein-protein potential of mean force.

Generalized phase behavior of cluster formation in colloidal dispersions with competing interactions

Colloidal liquids interacting with short range attraction and long range repulsion, such as proposed for some protein solutions, have been found to exhibit novel states consisting of equilibrium particle clusters. Monte Carlo simulations are performed for two physically meaningful inter-particle potentials across a broad range of interaction parameters, temperatures and volume fractions to locate the conditions where clustered states are found. A corresponding states phase behavior is identified when normalized by the critical point of an appropriately selected reference attractive fluid. Clustered fluid states and cluster percolated states are found exclusively within the two phase region of the state diagram for a reference attractive fluid, confirming the underlying intrinsic relation between clustered states and bulk phase separation. Clustered and cluster percolated states consistently exhibit an intermediate range order peak in their structure factors with a magnitude above 2.7, leading to a semi-empirical rule for identifying clustered fluids in scattering experiments.

Model for a mixture of macroions, counterions, and co-ions in a waterlike fluid

We propose an integral equation theory for a mixture of macroions, counterions, and co-ions in a waterlike fluid in which all the components are accounted for explicitly. The macroions can carry positive and negative surface charges simultaneously, mimicking in this way the situation occurring in protein solutions. To solve this complex model numerically, we utilize the associative mean spherical approximation, developed earlier for low-molecular-mass charge-symmetric electrolyte solutions. To illustrate the potential of this approach, we present numerical results for various experimental conditions. Among the measurable properties we choose to calculate the osmotic coefficient, a quantity that reflects the stability of the solution. We show that the osmotic coefficient depends not only on the magnitude of the net charge on the macroion but also on its sign, as well as on the nature of the low-molecular-mass electrolyte present. These specific ion effects are the consequence of differences in hydration between the ions in solution and charged groups on the macroion.

The role of electrostatics in protein-protein interactions of a monoclonal antibody

Understanding how protein-protein interactions depend on the choice of buffer, salt, ionic strength, and pH is needed to have better control over protein solution behavior. Here, we have characterized the pH and ionic strength dependence of protein-protein interactions in terms of an interaction parameter kD obtained from dynamic light scattering and the osmotic second virial coefficient B22 measured by static light scattering. A simplified protein-protein interaction model based on a Baxter adhesive potential and an electric double layer force is used to separate out the contributions of longer-ranged electrostatic interactions from short-ranged attractive forces. The ionic strength dependence of protein-protein interactions for solutions at pH 6.5 and below can be accurately captured using a Deryaguin-Landau-Verwey-Overbeek (DLVO) potential to describe the double layer forces. In solutions at pH 9, attractive electrostatics occur over the ionic strength range of 5-275 mM. At intermediate pH values (7.25 to 8.5), there is a crossover effect characterized by a nonmonotonic ionic strength dependence of protein-protein interactions, which can be rationalized by the competing effects of long-ranged repulsive double layer forces at low ionic strength and a shorter ranged electrostatic attraction, which dominates above a critical ionic strength. The change of interactions from repulsive to attractive indicates a concomitant change in the angular dependence of protein-protein interaction from isotropic to anisotropic. In the second part of the paper, we show how the Baxter adhesive potential can be used to predict values of kD from fitting to B22 measurements, thus providing a molecular basis for the linear correlation between the two protein-protein interaction parameters.

Reaching new levels of realism in modeling biological macromolecules in cellular environments

An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.