Lipid shape and packing are key for optimal design of pH-sensitive mRNA lipid nanoparticles.

The ionizable-lipid component of RNA-containing nanoparticles controls the pH-dependent behavior necessary for an efficient delivery of the cargo-the so-called endosomal escape. However, it is still an empirical exercise to identify optimally performing lipids. Here, we study two well-known ionizable lipids, DLin-MC3-DMA and DLin-DMA using a combination of experiments, multiscale computer simulations, and electrostatic theory. All-atom molecular dynamics simulations, and experimentally measured polar headgroup pKa values, are used to develop a coarse-grained representation of the lipids, which enables the investigation of the pH-dependent behavior of lipid nanoparticles (LNPs) through Monte Carlo simulations, in the absence and presence of RNA molecules. Our results show that the charge state of the lipids is determined by the interplay between lipid shape and headgroup chemistry, providing an explanation for the similar pH-dependent ionization state observed for lipids with headgroup pKa values about one-pH-unit apart. The pH dependence of lipid ionization is significantly influenced by the presence of RNA, whereby charge neutrality is achieved by imparting a finite and constant charge per lipid at intermediate pH values. The simulation results are experimentally supported by measurements of α-carbon 13C-NMR chemical shifts for eGFP mRNA LNPs of both DLin-MC3-DMA and DLin-DMA at various pH conditions. Further, we evaluate the applicability of a mean-field Poisson-Boltzmann theory to capture these phenomena.

Electrostatic interactions control the adsorption of extracellular vesicles onto supported lipid bilayers.

Communication between cells located in different parts of an organism is often mediated by membrane-enveloped nanoparticles, such as extracellular vesicles (EVs). EV binding and cell uptake mechanisms depend on the heterogeneous composition of the EV membrane. From a colloidal perspective, the EV membrane interacts with other biological interfaces via both specific and non-specific interactions, where the latter include long-ranged electrostatic and van der Waals forces, and short-ranged repulsive "steric-hydration" forces. While electrostatic forces are generally exploited in most EV immobilization protocols, the roles played by various colloidal forces in controlling EV adsorption on surfaces have not yet been thoroughly addressed. In the present work, we study the adsorption of EVs onto supported lipid bilayers (SLBs) carrying different surface charge densities using a combination of quartz crystal microbalance with dissipation monitoring (QCM-D) and confocal laser scanning microscopy (CLSM). We demonstrate that EV adsorption onto lipid membranes can be controlled by varying the strength of electrostatic forces and we theoretically describe the observed phenomena within the framework of nonlinear Poisson-Boltzmann theory. Our modelling results confirm the experimental observations and highlight the crucial role played by attractive electrostatics in EV adsorption onto lipid membranes. They furthermore show that simplified theories developed for model lipid systems can be successfully applied to the study of their biological analogues and provide new fundamental insights into EV-membrane interactions with potential use in developing novel EV separation and immobilization strategies.

Ion and Site Correlations of Charge Regulating Surfaces: A Simple and Accurate Theory.

Charge regulation is fundamental in most chemical, geochemical, and biochemical systems. Various mineral surfaces and proteins are well-known to change their charge state as a function of the activity of the hydronium ions, that is, the pH. Besides being modulated by the pH, the charge state is sensitive to salt concentration and composition due to screening and ion correlations. Given the importance of electrostatic interactions, a reliable and straightforward theory of charge regulation would be of utmost importance. This Article presents a theory that accounts for salt screening, site, and ion correlations. Our approach shows an impeccable agreement as compared to Monte Carlo simulations and experiments of 1:1 and 2:1 salts. We furthermore disentangle the relative importance of site-site, ion-ion, and ion-site correlations. Contrary to previous claims, we find that ion-site correlations for the studied cases are subdominant to the two other correlation terms.

Ground State Configurations and Metastable Phases of Charged Linear Rods.

This computational study investigates the energy minimum, that is, ground state, of suspensions of monodisperse (single-component) charged linear rods at various densities and screening lengths. We find that closed-packed unidirectional configurations have the lowest energies for all studied cases. We further specify the lattice parameters for these crystalline structures. In addition, we identify a few metastable phases, including heliconical structures. These metastable heliconical phases are composed of hexagonal smectic C layers with particle orientations forming a conical helicoid with a short pitch of three layers. We evidence this by zero-temperature Monte Carlo simulations starting from an energy-minimized hexagonal cholesteric configuration, which rapidly transforms to a heliconical phase. Furthermore, this heliconical phase is remarkably stable even at finite temperatures and melts to a disordered phase at high temperatures. Finally, we conduct simulations at room temperature and conditions typical for cellulose nanocrystal suspensions to study the onset of nematic order and compare our results to available experimental data. Our findings suggest that electrostatics play an important role in the isotropic/anisotropic transition for dense suspensions of charged rods.

Directional shear jamming of frictionless ellipses.

In this work we study shear reversals of dense non-Brownian suspensions composed of cohesionless elliptical particles. By numerical simulations, we show that a new fragility appears for frictionless ellipses in the flowing states, where particles can flow indefinitely in one direction at applied shear stresses but shear jam in the other direction upon shear stress reversal. This new fragility, absent in the isotropic particle case, is linked to the directional order of the elongated particles at steady shear and its reorientation at shear stress reversal, which forces the suspensions to pass through a more disordered state with an increased number of contacts in which it might get arrested.

Transition from steady shear to oscillatory shear rheology of dense suspensions.

Recent studies have highlighted that oscillatory and time-dependent shear flows might help increase the flowability of dense suspensions. While most focus has been on cross-flows we here study a simple two-dimensional suspensions where we apply simultaneously oscillatory and stationary shear along the same direction. We first show that the dissipative viscosities in this set-up significantly decrease with an increasing shear-rate magnitude of the oscillations and given that the oscillatory strain is small, in a similar fashion as found previously for cross-flow oscillations. As for cross-flow oscillations, the decrease can be attributed to the large decrease in the number of contacts and an altered microstructure as one transitions from a steady shear to an oscillatory shear dominated rheology. As subresults we find both an extension to the µ(J) rheology, a constitutive relationship between the shear stresses and the shear rate, valid for oscillatory shear flows and that shear-jamming of frictional particles at oscillatory shear dominated flows occurs at higher packing fractions compared to steady shear dominated flows.

Strong-coupling theory of counterions with hard cores between symmetrically charged walls.

By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on pointlike counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two subpopulations, one for each plate, and integrates out one subpopulation to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard-sphere overlap are unavoidable, and thus rule out configurations.

Local Rheology Relation with Variable Yield Stress Ratio across Dry, Wet, Dense, and Dilute Granular Flows.

Dry, wet, dense, and dilute granular flows have been previously considered fundamentally different and thus described by distinct, and in many cases incompatible, rheologies. We carry out extensive simulations of granular flows, including wet and dry conditions, various geometries and driving mechanisms (boundary driven, fluid driven, and gravity driven), many of which are not captured by standard rheology models. For all simulated conditions, except for fluid-driven and gravity-driven flows close to the flow threshold, we find that the Mohr-Coulomb friction coefficient µ scales with the square root of the local Péclet number Pe provided that the particle diameter exceeds the particle mean free path. With decreasing Pe and granular temperature gradient M, this general scaling breaks down, leading to a yield condition with a variable yield stress ratio characterized by M.

Modeling the assembly of oppositely charged lock- and key-colloids.

The interaction of oppositely charged lock- and key-colloids is investigated using computer simulations. We show that indented spheres, i.e., lock-particles, can be specifically assembled with spherical key-particles using solely electrostatic interactions in addition to a hard overlap potential. An analytic description of the entropic and energetic contributions is derived and supported by simulations and explicit energy calculations, respectively. The analytic expression of the electrostatic contribution is further employed to build up a schematic model allowing for efficient large-scale Monte Carlo simulations. The influence of the charge/ionic strength, the degree of indentation, and the size/number ratio is discussed by analyzing the specific and unspecific associations from the simulations. Herein, both particle design and mixing conditions lead to the formation of stable specific clusters analogous to colloidal molecules whose valence is defined by the number of lock-particles associated with a key-particle. In addition, the approach is extended to the encapsulation of an excess of small key-particles in largely indented lock-particles. These two examples exemplify that highly specific pairwise interactions can be implemented by using solely oppositely charged particles with complementary geometries, which opens the road for a rational design of complex hierarchical self-assemblies of complementary building blocks.

Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases.

We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance d. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner strong-coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of d comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.

Bare and Effective Charge of Mesoporous Silica Particles.

We develop and combine a novel numerical model, within the Poisson-Boltzmann framework, with classical experimental titration techniques for mesoporous silica particles to study the charging behavior as both pH and the amount of monovalent salt are varied. One key finding is that these particles can be considered to have an effectively or apparent electroneutral inner core with an effectively charged rim. As a consequence, the total apparent charge of the particle is several orders of magnitude smaller than that of the bare silica charge, which accounts only for the charged silanol groups of the mesoporous silica particles and which has its major contribution from the interior. Hence, the interior dictates the mesoporous silicas' bare charge while the rim its effective charge. We furthermore report density, charge, and accumulated charge profiles across the particle's interface.

Non-local rheology in dense granular flows: Revisiting the concept of fluidity.

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. (Phys. Rev. Lett 103, 036001 (2009)) for soft matter, and adapted for granular matter by Kamrin et al. (Phys. Rev. Lett. 108, 178301 (2012)), and the gradient expansion of the local rheology µ(I) that we have proposed (Phys. Rev. Lett. 111, 238301 (2013)). We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

Direct summation of dipole-dipole interactions using the Wolf formalism.

We present an expanded Wolf formalism for direct summation of long-range dipole-dipole interactions and rule-of-thumbs how to choose optimal spherical cutoff (Rc) and damping parameter (α). This is done by comparing liquid radial distribution functions, dipole-dipole orientation correlations, particle energies, and dielectric constants, with Ewald sums and the Reaction field method. The resulting rule states that ασ < 1 and αRc > 3 for reduced densities around ρ(∗) = 1 where σ is the particle size. Being a pair potential, the presented approach scales linearly with system size and is applicable to simulations involving point dipoles such as the Stockmayer fluid and polarizable water models.

A new dipolar potential for numerical simulations of polar fluids on the 4D hypersphere.

We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three-dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions: when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all the formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.

On the origin of the halo stabilization.

Monte Carlo simulations show that charge-regulation alone can cause highly charged zirconium nanoparticles to adsorb to a similarly charged or neutral silica particle and thereby stabilizing the latter. This mechanism, referred to as halo stabilization, is quite general and applicable in a range of systems provided that pH, van der Waals forces, and dissociation constants of the charge-regulating particles are properly chosen. In our modeling we see an overall attraction at low volume fractions of nanoparticles, while at higher a repulsive barrier is created, stabilizing the microparticles and protecting them from aggregation. The charge-regulation mechanism also turns the silica surface from positively charged, without nanoparticles, to negatively charged in the presence of nanoparticles.

Nonlocal rheology of granular flows across yield conditions.

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A nonlocal constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square root of the distance to the yield point, on both sides of that point.

Transition from the viscous to inertial regime in dense suspensions.

Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behavior at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This setup is conceptually identical to recent experiments of Boyer, Guazzelli, and Pouliquen [Phys. Rev. Lett. 107, 188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces, respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.

Classical van der Waals interactions between spherical bodies of dipolar fluid.

The van der Waals interaction free energy A(int) between two spherical bodies of Stockmayer fluid across a vacuum is calculated using molecular simulations and classical perturbation theory. The results are decomposed into their electrostatic and Lennard-Jones parts, and the former is shown to agree excellently with predictions from dielectric continuum theory. A(int) is decomposed into its energetic and entropic contributions and the results are compared with analytical predictions. Finally, we expand the electrostatic part of A(int) in a multipole expansion, and show that the surprisingly good agreement between the molecular and continuum descriptions is likely due to a cancellation of errors coming from the neglect of the discrete nature of the fluid within the dielectric description.

Some comments and corrections regarding the calculation of electrostatic potential derivatives using the Ewald summation technique.

A review of the literature on the calculation of electrostatic potentials, fields, and field gradients in systems consisting of charges and dipoles using the Ewald summation technique is presented. Discrepancies between the previous formulas are highlighted, and an error in the derivation of the reciprocal contributions to the electrostatic field and field gradient is corrected. The new formulas for the field and field gradient are shown to exhibit a termwise identity with the ones for the electrostatic energy.

A classical density functional theory of ionic liquids.

We present a simple, classical density functional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer density functional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.