Coarse-Grained Molecular Dynamics Simulations for Understanding the Impact of Short-Range Anisotropic Attractions on Structure and Viscosity of Concentrated Monoclonal Antibody Solutions.

Understanding protein-protein interactions in concentrated therapeutic monoclonal antibody (mAb) solutions is desirable for improved drug discovery, processing, and administration. Here, we deduce both the net protein charge and the magnitude and geometry of short-ranged, anisotropic attractions of a mAb across multiple concentrations and cosolute conditions by comparing structure factors S(q) obtained from small-angle X-ray scattering experiments with those from molecular dynamics (MD) simulations. The simulations, which utilize coarse-grained 12-bead models exhibiting a uniform van der Waals attraction, uniform electrostatic repulsion, and short-range attractions between specific beads, are versatile enough to fit S(q) of a wide range of protein concentrations and ionic strength with the same charge on each bead and a single anisotropic short-range attraction strength. Cluster size distributions (CSDs) obtained from best fit simulations reveal that the experimental structure is consistent with small reversible oligomers in even low viscosity systems and help quantify the impact of these clusters on viscosity. The ability to systematically use experimental S(q) data together with MD simulations to discriminate between different possible protein-protein interactions, as well as to predict viscosities from protein CSDs, is beneficial for designing mAbs and developing formulation strategies that avoid high viscosities and aggregation at high concentration.

Diverse balances of tubulin interactions and shape change drive and interrupt microtubule depolymerization.

Microtubules are stiff biopolymers that self-assemble via the addition of GTP-tubulin (αß-dimer bound to GTP), but hydrolysis of GTP- to GDP-tubulin within the tubules destabilizes them toward catastrophically-fast depolymerization. The molecular mechanisms and features of the individual tubulin proteins that drive such behavior are still not well-understood. Using molecular dynamics simulations of whole microtubules built from a coarse-grained model of tubulin, we demonstrate how conformational shape changes (i.e., deformations) in subunits that frustrate tubulin-tubulin binding within microtubules drive depolymerization of stiff tubules via unpeeling "ram's horns" consistent with experiments. We calculate the sensitivity of these behaviors to the length scales and strengths of binding attractions and varying degrees of binding frustration driven by subunit shape change, and demonstrate that the dynamic instability and mechanical properties of microtubules can be produced based on either balanced or imbalanced strengths of lateral and vertical binding attractions. Finally, we show how catastrophic depolymerization can be interrupted by small regions of the microtubule containing undeformed dimers, corresponding to incomplete lattice hydrolysis. The results demonstrate a mechanism by which microtubule rescue can occur.

Catastrophic depolymerization of microtubules driven by subunit shape change.

Microtubules exhibit a dynamic instability between growth and catastrophic depolymerization. GTP-tubulin (αß-dimer bound to GTP) self-assembles, but dephosphorylation of GTP- to GDP-tubulin within the tubule results in destabilization. While the mechanical basis for destabilization is not fully understood, one hypothesis is that dephosphorylation causes tubulin to change shape, frustrating bonds and generating stress. To test this idea, we perform molecular dynamics simulations of microtubules built from coarse-grained models of tubulin, incorporating a small compression of α-subunits associated with dephosphorylation in experiments. We find that this shape change induces depolymerization of otherwise stable systems via unpeeling "ram's horns" characteristic of microtubules. Depolymerization can be averted by caps with uncompressed α-subunits, i.e., GTP-rich end regions. Thus, the shape change is sufficient to yield microtubule behavior.

Reversible Self-Assembly of Glutathione-Coated Gold Nanoparticle Clusters via pH-Tunable Interactions.

Nanoparticle (NP) clusters with diameters ranging from 20 to 100 nm are reversibly assembled from 5 nm gold (Au) primary particles coated with glutathione (GSH) in aqueous solution as a function of pH in the range of 5.4 to 3.8. As the pH is lowered, the GSH surface ligands become partially zwitterionic and form interparticle hydrogen bonds that drive the self-limited assembly of metastable clusters in <1 min. Whereas clusters up to 20 nm in size are stable against cluster-cluster aggregation for up to 1 day, clusters up to 80 nm in size can be stabilized over this period via the addition of citrate to the solution in equal molarity with GSH molecules. The cluster diameter may be cycled reversibly by tuning pH to manipulate the colloidal interactions; however, modest background cluster-cluster aggregation occurs during cycling. Cluster sizes can be stabilized for at least 1 month via the addition of PEG-thiol as a grafted steric stabilizer, where PEG-grafted clusters dissociate back to starting primary NPs at pH 7 in fewer than 3 days. Whereas the presence of excess citrate has little effect on the initial size of the metastable clusters, it is necessary for both the cycling and dissociation to mediate the GSH-GSH hydrogen bonds. In summary, these metastable clusters exhibit significant characteristics of equilibrium self-limited assembly between primary particles and clusters on time scales where cluster-cluster aggregation is not present.

Impact of solvent granularity and layering on tracer hydrodynamics in confinement.

Classic hydrodynamic arguments establish that when a spherical tracer particle is suspended between parallel walls, tracer-wall coupling mediated by the solvent will cause the tracer to exhibit position-dependent diffusivity. We investigate how the diffusivity profiles of confined tracers are impacted by the diameter size-ratio of the tracer to solvent: starting from the classic limit of infinite size-ratio (i.e., continuum solvent), we consider size-ratios of four or less to examine how hydrodynamic predictions are disrupted for systems where the tracer and solvent are of similar scale. We use computer simulations and techniques based on the Fokker-Planck formalism to calculate the diffusivity profiles of hard-sphere tracer particles in hard-sphere solvents, focusing on the dynamics perpendicular to the walls. Given wall separations of several tracer diameters, we first consider confinement between hard walls, where anisotropic structuring at the solvent lengthscale generates inhomogeneity in the tracer free-energy landscape and undermines hydrodynamic predictions locally. We then introduce confining planes that we term transparent walls, which restrict tracer and solvent center-accessibilities while completely eliminating static anisotropy, and reveal position-dependent signatures in tracer diffusivity solely attributable to confinement. With or without suppressing static heterogeneity, we find that tracer diffusivity increasingly deviates on a local basis from hydrodynamic predictions at smaller size-ratios. However, hydrodynamic theory still approximately captures spatially-averaged dynamics across the pores even for very small tracer-solvent size-ratios over a wide range of solvent densities and wall separations.

Communication: Local structure-mobility relationships of confined fluids reverse upon supercooling.

We examine the structural and dynamic properties of confined binary hard-sphere mixtures designed to mimic realizable colloidal thin films. Using computer simulations, governed by either Newtonian or overdamped Langevin dynamics, together with other techniques including a Fokker-Planck equation-based method, we measure the position-dependent and average diffusivities of particles along structurally isotropic and inhomogeneous dimensions of the fluids. At moderate packing fractions, local single-particle diffusivities normal to the direction of confinement are higher in regions of high total packing fraction; however, these trends are reversed as the film is supercooled at denser average packings. Auxiliary short-time measurements of particle displacements mirror data obtained for experimental supercooled colloidal systems. We find that average dynamics can be approximately predicted based on the distribution of available space for particle insertion across orders of magnitude in diffusivity regardless of the governing microscopic dynamics.

Tuning structure and mobility of solvation shells surrounding tracer additives.

Molecular dynamics simulations and a stochastic Fokker-Planck equation based approach are used to illuminate how position-dependent solvent mobility near one or more tracer particle(s) is affected when tracer-solvent interactions are rationally modified to affect corresponding solvation structure. For tracers in a dense hard-sphere fluid, we compare two types of tracer-solvent interactions: (1) a hard-sphere-like interaction, and (2) a soft repulsion extending beyond the hard core designed via statistical mechanical theory to enhance tracer mobility at infinite dilution by suppressing coordination-shell structure [Carmer et al., Soft Matter 8, 4083-4089 (2012)]. For the latter case, we show that the mobility of surrounding solvent particles is also increased by addition of the soft repulsive interaction, which helps to rationalize the mechanism underlying the tracer's enhanced diffusivity. However, if multiple tracer surfaces are in closer proximity (as at higher tracer concentrations), similar interactions that disrupt local solvation structure instead suppress the position-dependent solvent dynamics.

Structure, thermodynamics, and position-dependent diffusivity in fluids with sinusoidal density variations.

Molecular dynamics simulations and a stochastic method based on the Fokker-Planck equation are used to explore the consequences of inhomogeneous density profiles on the thermodynamic and dynamic properties of the hard-sphere fluid and supercooled liquid water. Effects of the inhomogeneity length scale are systematically considered via the imposition of sinusoidal density profiles of various wavelengths. For long-wavelength density profiles, bulk-like relationships between local structure, thermodynamics, and diffusivity are observed as expected. However, for both systems, a crossover in behavior occurs as a function of wavelength, with qualitatively different correlations between the local static and dynamic quantities emerging as density variations approach the scale of a particle diameter. Irrespective of the density variation wavelength, average diffusivities of hard-sphere fluids in the inhomogeneous and homogeneous directions are coupled and approximately correlate with the volume available for insertion of another particle. Unfortunately, a quantitatively reliable static predictor of position-dependent dynamics has yet to be identified for even the simplest of inhomogeneous fluids.

Synergistic formation and stabilization of oil-in-water emulsions by a weakly interacting mixture of zwitterionic surfactant and silica nanoparticles.

Oil-in-water emulsions were formed and stabilized at low amphiphile concentrations by combining hydrophilic nanoparticles (NPs) (i.e., bare colloidal silica) with a weakly interacting zwitterionic surfactant, caprylamidopropyl betaine, to generate a high hydrophilic-lipophilic balance. The weak interaction of the NPs with surfactant was quantified with contact angle measurements. Emulsions were characterized by static light scattering to determine the droplet size distributions, optical photography to quantify phase separation due to creaming, and both optical and electron microscopy to determine emulsion microstructure. The NPs and surfactant acted synergistically to produce finer emulsions with a greater stability to coalescence relative to the behavior with either NPs or surfactant alone. As a consequence of the weak adsorption of the highly hydrophilic surfactant on the anionic NPs along with the high critical micelle concentration, an unusually large surfactant concentration was available to adsorb at the oil-water interface and lower the interfacial tension. The synergy for emulsion formation and stabilization for the two amphiphiles was even greater in the case of a high-salinity synthetic seawater aqueous phase. Here, higher NP adsorption at the oil-water interface was caused by electrostatic screening of interactions between (1) NPs and the anionic oil-water interface and (2) between the NPs. This greater adsorption as well as partial flocculation of the NPs provided a more efficient barrier to droplet coalescence.

High interfacial activity of polymers "grafted through" functionalized iron oxide nanoparticle clusters.

The mechanism by which polymers, when grafted to inorganic nanoparticles, lower the interfacial tension at the oil-water interface is not well understood, despite the great interest in particle stabilized emulsions and foams. A simple and highly versatile free radical "grafting through" technique was used to bond high organic fractions (by weight) of poly(oligo(ethylene oxide) monomethyl ether methacrylate) onto iron oxide clusters, without the need for catalysts. In the resulting ∼1 µm hybrid particles, the inorganic cores and grafting architecture contribute to the high local concentration of grafted polymer chains to the dodecane/water interface to produce low interfacial tensions of only 0.003 w/v % (polymer and particle core). This "critical particle concentration" (CPC) for these hybrid inorganic/polymer amphiphilic particles to lower the interfacial tension by 36 mN/m was over 30-fold lower than the critical micelle concentration of the free polymer (without inorganic cores) to produce nearly the same interfacial tension. The low CPC is favored by the high adsorption energy (∼10(6) kBT) for the large ∼1 µm hybrid particles, the high local polymer concentration on the particles surfaces, and the ability of the deformable hybrid nanocluster cores as well as the polymer chains to conform to the interface. The nanocluster cores also increased the entanglement of the polymer chains in bulk DI water or synthetic seawater, producing a viscosity up to 35,000 cP at 0.01 s(-1), in contrast with only 600 cP for the free polymer. As a consequence of these interfacial and rheological properties, the hybrid particles stabilized oil-in-water emulsions at concentrations as low as 0.01 w/v %, with average drop sizes down to 30 µm. In contrast, the bulk viscosity was low for the free polymer, and it did not stabilize the emulsions. The ability to influence the interfacial activity and rheology of polymers upon grafting them to inorganic particles, including clusters, may be expected to be broadly applicable to stabilization of emulsions and foams.

Quantifying Single-Ion Transport in Percolated Ionic Aggregates of Polymer Melts.

Single-ion conducting polymers such as ionomers are promising battery electrolyte materials, but it is critical to understand how rates and mechanisms of free cation transport depend on the nanoscale aggregation of cations and polymer-bound anions. We perform coarse-grained molecular dynamics simulations of ionomer melts to understand cation mobility as a function of polymer architecture, background relative permittivity, and corresponding ionic aggregate morphology. In systems exhibiting percolated ionic aggregates, cations diffuse via stepping motions along the ionic aggregates. These diffusivities can be quantitatively predicted by calculating the lifetimes of continuous association between oppositely charged ions, which equal the time scales of the stepping (diffusive) motions. In contrast, predicting cation diffusivity for systems with isolated ionic aggregates requires another time scale. Our results suggest that to improve conductivity the Coulombic interaction strength should be strong enough to favor percolated aggregates but weak enough to facilitate ion dissociation.

Tubulin islands containing slowly hydrolyzable GTP analogs regulate the mechanism and kinetics of microtubule depolymerization.

Dynamic instability of microtubules is characterized by stochastically alternating phases of growth and shrinkage and is hypothesized to be controlled by the conformation and nucleotide state of tubulin dimers within the microtubule lattice. Specifically, conformation changes (compression) in the tubulin dimer following the hydrolysis of GTP have been suggested to generate stress and drive depolymerization. In the present study, molecular dynamics simulations were used in tandem with in vitro experiments to investigate changes in depolymerization based on the presence of islands of uncompressed (GMPCPP) dimers in the microtubule lattice. Both methods revealed an exponential decay in the kinetic rate of depolymerization corresponding to the relative level of uncompressed (GMPCPP) dimers, beginning at approximately 20% incorporation. This slowdown was accompanied by a distinct morphological change from unpeeling "ram's horns" to blunt-ended dissociation at the microtubule end. Collectively these data demonstrated that islands of uncompressed dimers can alter the mechanism and kinetics of depolymerization in a manner consistent with promoting rescue events.

X-ray Scattering and Coarse-Grained Simulations for Clustering and Interactions of Monoclonal Antibodies at High Concentrations.

Attractive protein?protein interactions (PPI) in concentrated monoclonal antibody (mAb) solutions may lead to reversible oligomers (clusters) that impact colloidal stability and viscosity. Herein, the PPI are tuned for two mAbs via the addition of arginine (Arg), NaCl, or ZnSO4 as characterized by the structure factor ( Seff( q)) with small-angle X-ray scattering (SAXS). The SAXS data are fit with molecular dynamics simulations by placing a physically relevant short-range attractive interaction on selected beads in coarse-grained 12-bead models of the mAb shape. The optimized 12-bead models are then used to differentiate key microstructural properties, including center of mass radial distribution functions ( gCOM( r)), coordination numbers, and cluster size distributions (CSD). The addition of cosolutes results in more attractive Seff( q) relative to the no cosolute control for all systems tested, with the most attractive systems showing an upturn at low q. Only the All1 model with an attractive site in each Fab and Fc region (possessing Fab?Fab, Fab?Fc, and Fc?Fc interactions) can reproduce this upturn, and the corresponding CSDs show the presence of larger clusters compared to the control. In general, for models with similar net attractions, i.e., second osmotic virial coefficients, the size of the clusters increases as the attraction is concentrated on a smaller number of evenly distributed beads. The cluster size distributions from simulations are used to improve the understanding and prediction of experimental viscosities. The ability to discriminate between models with bead interactions at particular Fab and Fc bead sites from SAXS simulations, and to provide real-space properties (CSD and gCOM( r)), will be of interest in engineering protein sequence and formulating protein solutions for weak PPI to minimize aggregation and viscosities.

Protein-Protein Interactions of Highly Concentrated Monoclonal Antibody Solutions via Static Light Scattering and Influence on the Viscosity.

The ability to design and formulate mAbs to minimize attractive interactions at high concentrations is important for protein processing, stability, and administration, particularly in subcutaneous delivery, where high viscosities are often challenging. The strength of protein-protein interactions (PPIs) of an IgG1 and IgG4 monoclonal antibody (mAb) from low to high concentration was determined by static light scattering (SLS) and used to understand viscosity data. The PPI were tuned using NaCl and five organic ionic co-solutes. The PPI strength was quantified by the normalized structure factor S(0)/ S(0)HS and Kirkwood-Buff integral G22/ G22,HS (HS = hard sphere) determined from the SLS data and also by fits with (1) a spherical Yukawa potential and (2) an interacting hard sphere (IHS) model, which describes attraction in terms of hypothetical oligomers. The IHS model was better able to capture the scattering behavior of the more strongly interacting systems (mAb and/or co-solute) than the spherical Yukawa potential. For each descriptor of PPI, linear correlations were obtained between the viscosity at high concentration (200 mg/mL) and the interaction strengths evaluated both at low (20 mg/mL) and high concentrations (200 mg/mL) for a given mAb. However, the only parameter that provided a correlation across both mAbs was the oligomer mass ratio ( moligomer/ mmonomer+dimer) from the IHS model, indicating the importance of self-association (in addition to the direct influence of the attractive PPI) on the viscosity.

How Local and Average Particle Diffusivities of Inhomogeneous Fluids Depend on Microscopic Dynamics.

Computer simulations and a stochastic Fokker-Planck equation based approach are used to compare the single-particle diffusion coefficients of equilibrium hard-sphere fluids exhibiting identical inhomogeneous static structure and governed by either Brownian (i.e., overdamped Langevin) or Newtonian microscopic dynamics. The physics of inhomogeneity is explored via the imposition of one-dimensional sinusoidal density profiles of different wavelengths and amplitudes. When imposed density variations are small in magnitude for distances on the scale of a particle diameter, bulk-like average correlations between local structure and mobility are observed. In contrast, when density variations are significant on that length scale, qualitatively different structure-mobility correlations emerge that are sensitive to the governing microscopic dynamics. Correspondingly, a previously proposed scaling between long-time diffusivities for bulk isotropic fluids of particles exhibiting Brownian versus Newtonian dynamics [Pond et al. Soft Matter 2011, 7, 9859-9862] cannot be generalized to describe the position-dependent behaviors of strongly inhomogeneous fluids. While average diffusivities in the inhomogeneous and homogeneous directions are coupled, their qualitative dependencies on inhomogeneity wavelength are sensitive to the details of the microscopic dynamics. Nonetheless, average diffusivities of the inhomogeneous fluids can be approximately predicted for either type of dynamics based on knowledge of bulk isotropic fluid behavior and how inhomogeneity modifies the distribution of available volume. Analogous predictions for average diffusivities of experimental, inhomogeneous colloidal dispersions (based on known bulk behavior) suggest that they will exhibit qualitatively different trends than those predicted by models governed by overdamped Langevin dynamics that do not account for hydrodynamic interactions.

Origin and detection of microstructural clustering in fluids with spatial-range competitive interactions.

Fluids with competing short-range attractions and long-range repulsions mimic dispersions of charge-stabilized colloids that can display equilibrium structures with intermediate-range order (IRO), including particle clusters. Using simulations and analytical theory, we demonstrate how to detect cluster formation in such systems from the static structure factor and elucidate links to macrophase separation in purely attractive reference fluids. We find that clusters emerge when the thermal correlation length encoded in the IRO peak of the structure factor exceeds the characteristic length scale of interparticle repulsions. We also identify qualitative differences between the dynamics of systems that form amorphous versus microcrystalline clusters.