The dynamics of spherical particles near a single plane wall are computed using an extension of the Stokesian dynamics method that includes long-range many-body and pairwise lubrication interactions between the spheres and the wall in Stokes flow. Extra care is taken to ensure that the mobility and resistance tensors are symmetric, positive, and definite-something which is ineluctable for particles in low-Reynolds-number flows. We discuss why two previous simulation methods for particles near a plane wall, one using multipole expansions and the other using the Rotne-Prager tensor, fail to produce symmetric resistance and mobility tensors. Additionally, we offer some insight on how the Stokesian dynamics paradigm might be extended to study the dynamics of particles in any confining geometry.

Nanoparticles offer clear advantages for both passive and active penetration into biologically important membranes. However, the uptake and localization mechanism of nanoparticles within living plants, plant cells, and organelles has yet to be elucidated.1 Here, we examine the subcellular uptake and kinetic trapping of a wide range of nanoparticles for the first time, using the plant chloroplast as a model system, but validated in vivo in living plants. Confocal visible and near-infrared fluorescent microscopy and single particle tracking of goldcysteine-AF405 (GNP-Cys-AF405), streptavidin-quantum dot (SA-QD), dextran and poly(acrylic acid) nanoceria, and various polymer-wrapped single-walled carbon nanotubes (SWCNTs), including lipid-PEG-SWCNT, chitosan-SWCNT and 30-base (dAdT) sequence of ssDNA (AT) 15 wrapped SWCNTs (hereafter referred to as ss(AT) 15 -SWCNT), are used to demonstrate that particle size and the magnitude, but not the sign, of the zeta potential are key in determining whether a particle is spontaneously and kinetically trapped within the organelle, despite the negative zeta potential of the envelope. We develop a mathematical model of this lipid exchange envelope and penetration (LEEP) mechanism, which agrees well with observations of this size and zeta potential dependence. The theory predicts a critical particle size below which the mechanism fails at all zeta potentials, explaining why nanoparticles are critical for this process. LEEP constitutes a powerful particulate transport and localization mechanism for nanoparticles within the plant system.

Reversible self-association of therapeutic antibodies is a key factor in high protein solution viscosities. In the present work, a coarse-grained computational model accounting for electrostatic, dispersion, and long-ranged hydrodynamic interactions of two model monoclonal antibodies is applied to understand the nature of self-association, predicting the solution microstructure and resulting transport properties of the solution. For the proteins investigated, the structure factor across a range of solution conditions shows quantitative agreement with neutron-scattering experiments. We observe a homogeneous, dynamical association of the antibodies with no evidence of phase separation. Calculations of self-diffusivity and viscosity from coarse-grained dynamic simulations show the appropriate trends with concentration but, respectively, over- and under-predict the experimentally measured values. By adding constraints to the self-associated clusters that rigidify them under flow, prediction of the transport properties is significantly improved with respect to experimental measurements. We hypothesize that these rigidity constraints are associated with missing degrees of freedom in the coarse-grained model resulting from patchy and heterogeneous interactions among coarse-grained domains. These results demonstrate how structural anisotropy and anisotropy of interactions generated by features at the 2-5 nm length scale in antibodies are sufficient to recover the dynamics and rheological properties of these important macromolecular solutions.

Suspensions of paramagnetic colloids are driven to phase separate and self-assemble by a toggled magnetic field. Initially, all suspensions form network structures that span the sample cell. When the magnetic field is toggled, this network structure coarsens diffusively for a time that scales exponentially with frequency. Beyond this break through time, suspensions cease diffusive coarsening and undergo an apparent instability. The magnetic field drives suspensions to condense into dispersed, domains of bodycentered tetragonal crystals. Within these domains the crystalline order depends on the pulse frequency. Because the scaling of the break through time with respect to frequency is exponential, the steady state limit corresponding to an infinite pulse frequency is kinetically arrested and the equilibrium state is unreachable. These experiments show that there is an out-of-equilibrium pathway that can be used to escape a kinetically arrested state as well as a diverging time scale for phase separation as the critical frequency for condensation is approached. Rather than fine tuning the strength of the interactions among particles, a simple annealing scheme - toggling of the magnetic field - is used to create a broad envelope for assembly of ordered particle structures.

We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-PragerYamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform Fast Fourier Transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. For geometrically dense microstructures (fractal dimension equal three), the performance is independent of volume fraction, while for tenuous microstructures (fractal dimension less than three), such as gels and polymer solutions, the performance improves with decreasing volume fraction. This is in stark contrast with other related linear-scaling methods such as the Force Coupling Method and the Fluctuating Immersed Boundary method, for which performance degrades with decreasing volume fraction. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4 × 10 6 particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable the cost of computing deterministic displacements in BD simulations. A high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.