Biophysical Considerations in the Rational Design and Cellular Targeting of Flexible Polymeric Nanoparticles.

How nanoparticle (NP) mechanical properties impact multivalent ligand-receptor-mediated binding to cell surfaces, the avidity, propensity for internalization, and effects due to crowding remains unknown or unquantified. Through computational analyses, the effects of NP composition from soft, deformable NPs to rigid spheres, effect of tethers, the crowding of NPs at the membrane surface, and the cell membrane properties such as cytoskeletal interactions are addressed. Analyses of binding mechanisms of three distinct NPs that differ in type and rigidity (core-corona flexible NP, rigid NP, and rigid-tethered NP) but are otherwise similar in size and ligand surface density are reported; moreover, for the case of flexible NP, NP stiffness is tuned by varying the internal crosslinking density. Biophysical modeling of NP binding to membranes together with thermodynamic analysis powered by free energy calculations is employed, and it is shown that efficient cellular targeting and uptake of NP functionalized with targeting ligand molecules can be shaped by factors including NP flexibility and crowding, receptor-ligand binding avidity, state of the membrane cytoskeleton, and curvature inducing proteins. Rational design principles that confer tension, membrane excess area, and cytoskeletal sensing properties to the NP which can be exploited for cell-specific targeting of NP are uncovered.

Nanoparticle transport phenomena in confined flows.

Nanoparticles submerged in confined flow fields occur in several technological applications involving heat and mass transfer in nanoscale systems. Describing the transport with nanoparticles in confined flows poses additional challenges due to the coupling between the thermal effects and fluid forces. Here, we focus on the relevant literature related to Brownian motion, hydrodynamic interactions and transport associated with nanoparticles in confined flows. We review the literature on the several techniques that are based on the principles of non-equilibrium statistical mechanics and computational fluid dynamics in order to simultaneously preserve the fluctuation-dissipation relationship and the prevailing hydrodynamic correlations. Through a review of select examples, we discuss the treatments of the temporal dynamics from the colloidal scales to the molecular scales pertaining to nanoscale fluid dynamics and heat transfer. As evident from this review, there, indeed has been little progress made in regard to the accurate modeling of heat transport in nanofluids flowing in confined geometries such as tubes. Therefore the associated mechanisms with such processes remain unexplained. This review has revealed that the information available in open literature on the transport properties of nanofluids is often contradictory and confusing. It has been very difficult to draw definitive conclusions. The quality of work reported on this topic is non-uniform. A significant portion of this review pertains to the treatment of the fluid dynamic aspects of the nanoparticle transport problem. By simultaneously treating the energy transport in ways discussed in this review as related to momentum transport, the ultimate goal of understanding nanoscale heat transport in confined flows may be achieved.

Nanofluid Dynamics of Flexible Polymeric Nanoparticles Under Wall Confinement.

Describing the hydrodynamics of nanoparticles in fluid media poses interesting challenges due to the coupling between the Brownian and hydrodynamic forces at the nanoscale. We focus on multiscale formulations of Brownian motion and hydrodynamic interactions (HI) of a single flexible polymeric nanoparticle in confining flows using the Brownian Dynamics method. The nanoparticle is modeled as a self-avoiding freely jointed polymer chain that is subject to Brownian forces, hydrodynamics forces, and repulsive interactions with the confining wall. To accommodate the effect of the wall, the hydrodynamic lift due to the wall is included in the mobility of a bead of the polymer chain which depends on its proximity to the wall. Using the example of a flexible polymeric nanoparticle, we illustrate temporal dynamics pertaining to the colloidal scale as well as the nanoscale.

Stiffness can mediate balance between hydrodynamic forces and avidity to impact the targeting of flexible polymeric nanoparticles in flow.

We report computational investigations of deformable polymeric nanoparticles (NPs) under colloidal suspension flow and adhesive environment. We employ a coarse-grained model for the polymeric NP and perform Brownian dynamics (BD) simulations with hydrodynamic interactions and in the presence of wall-confinement, particulate margination, and wall-adhesion for obtaining NP microstructure, shape, and anisotropic and inhomogeneous transport properties for different NP stiffness. These microscopic properties are utilized in solving the Fokker-Planck equation to obtain the spatial distribution of NP subject to shear, margination due to colloidal microparticles, and confinement due to a vessel wall. Comparing our computational results for the amount of NP margination to the near-wall adhesion regime with those of our binding experiments in cell culture under shear, we found quantitative agreement on shear-enhanced binding, the effect of particulate volume fraction, and the effect of NP stiffness. For the experimentally realized polymeric NP, our model predicts that the shear and volume fraction mediated enhancement in targeting has a hydrodynamic transport origin and is not due to a multivalent binding effect. However, for ultrasoft polymeric NPs, our model predicts a substantial increase in targeting due to multivalent binding. Our results are also in general agreement with experiments of tissue targeting measurements in vivo in mice, however, one needs to exercise caution in extending the modeling treatment to in vivo conditions owing to model approximations. The reported combined computational approach and results are expected to enable fine-tuning of design and optimization of flexible NP in targeted drug delivery applications.

Excess area dependent scaling behavior of nano-sized membrane tethers.

Thermal fluctuations in cell membranes manifest as an excess area ([Formula: see text]) which governs a multitude of physical process at the sub-micron scale. We present a theoretical framework, based on an in silico tether pulling method, which may be used to reliably estimate [Formula: see text] in live cells. We perform our simulations in two different thermodynamic ensembles: (i) the constant projected area and (ii) the constant frame tension ensembles and show the equivalence of our results in the two. The tether forces estimated from our simulations compare well with our experimental measurements for tethers extracted from ruptured GUVs and HeLa cells. We demonstrate the significance and validity of our method by showing that all our calculations performed in the initial tether formation regime (i.e. when the length of the tether is comparable to its radius) along with experiments of tether extraction in 15 different cell types collapse onto two unified scaling relationships mapping tether force, tether radius, bending stiffness κ, and membrane tension σ. We show that [Formula: see text] is an important determinant of the radius of the extracted tether, which is equal to the characteristic length [Formula: see text] for [Formula: see text], and is equal to [Formula: see text] for [Formula: see text]. We also find that the estimated excess area follows a linear scaling behavior that only depends on the true value of [Formula: see text] for the membrane, based on which we propose a self-consistent technique to estimate the range of excess membrane areas in a cell.

Rheology of colloidal suspensions in confined flow: Treatment of hydrodynamic interactions in particle-based simulations inspired by dynamical density functional theory.

We investigate the microstructure and rheology of a hard-sphere suspension in a Newtonian fluid confined in a cylindrical channel and undergoing pressure-driven flow using Monte Carlo simulations. We develop a hydrodynamic framework inspired by dynamical density functional theory approaches in which the contributions due to various flow-induced hydrodynamic interactions (HI) are included in the form of thermodynamic work done by these HI-derived forces in displacing the hard spheres. Using this framework, we can self-consistently determine the effect of the local microstructure on the average flow field, and vice versa, and coevolve the inhomogeneous density distribution and the flattening velocity profile with increase in the density of suspended particles. Specifically, we explore the effect on the local microstructure due to the inclusion of forces arising from confinement-induced inertial effects, forces due to solvent-mediated interparticle interactions, and the dependence of the diffusivity on the local density. We examine the dependence of the apparent viscosity of the suspension on the volume fraction of hard spheres in the cylinder, the flow rate, and the diameter of the cylinder and investigate their effects on the local microstructure.

Microstructure of Flow-Driven Suspension of Hardspheres in Cylindrical Confinement: A Dynamical Density Functional Theory and Monte Carlo Study.

We have studied the microstructure of a flow-driven hardsphere suspension inside a cylinder using dynamical density functional theory and Monte Carlo simulations. In order to be representative of various physical conditions that may prevail in experiments, we investigate the problem using both the grand canonical (µVT) ensemble and the canonical (NVT) ensemble. In both ensembles, the hydrodynamic effect on the suspension mediated by the presence of the confining wall is implemented in a mean-field fashion by incorporating the thermodynamic work done by the inertial lift force on the particle given the average flow field. The predicted particle distribution in the µVT ensemble displays strong structural ordering at increasing flow rates due to the correspondingly higher particle concentrations inside the cylinder. In the NVT ensemble, for dilute suspensions we observe a peak in the distribution of density at a location similar to that of the Segré-Silberberg annulus, while for dense suspensions the competing effects of the inertial lift and the hardsphere interaction lead to the formation of several annuli.

Computational Models for Nanoscale Fluid Dynamics and Transport Inspired by Nonequilibrium Thermodynamics.

Traditionally, the numerical computation of particle motion in a fluid is resolved through computational fluid dynamics (CFD). However, resolving the motion of nanoparticles poses additional challenges due to the coupling between the Brownian and hydrodynamic forces. Here, we focus on the Brownian motion of a nanoparticle coupled to adhesive interactions and confining-wall-mediated hydrodynamic interactions. We discuss several techniques that are founded on the basis of combining CFD methods with the theory of nonequilibrium statistical mechanics in order to simultaneously conserve thermal equipartition and to show correct hydrodynamic correlations. These include the fluctuating hydrodynamics (FHD) method, the generalized Langevin method, the hybrid method, and the deterministic method. Through the examples discussed, we also show a top-down multiscale progression of temporal dynamics from the colloidal scales to the molecular scales, and the associated fluctuations, hydrodynamic correlations. While the motivation and the examples discussed here pertain to nanoscale fluid dynamics and mass transport, the methodologies presented are rather general and can be easily adopted to applications in convective heat transfer.

Nanoparticle stochastic motion in the inertial regime and hydrodynamic interactions close to a cylindrical wall.

We have carried out direct numerical simulations (DNS) of the fluctuating Navier-Stokes equation together with the particle equations governing the motion of a nanosized particle or nanoparticle (NP) in a cylindrical tube. The effects of the confining boundary, its curvature, particle size, and particle density variations have all been investigated. To reveal how the nature of the temporal correlations (hydrodynamic memory) in the inertial regime is altered by the full hydrodynamic interaction due to the confining boundaries, we have employed the Arbitrary Lagrangian-Eulerian (ALE) method to determine the dynamical relaxation of a spherical NP located at various positions in the medium over a wide span of time scales compared to the fluid viscous relaxation time τv = a2/v, where a is the spherical particle radius and v is the kinematic viscosity. The results show that, as compared to the behavior of a particle in regions away from the confining boundary, the velocity autocorrelation function (VACF) for a particle in the lubrication layer initially decays exponentially with a Stokes drag enhanced by a factor that is proportional to the ratio of the particle radius to the gap thickness between the particle and the wall. Independent of the particle location, beyond time scales greater than a2/v, the decay is always algebraic followed by a second exponential decay (attributed to the wall curvature) that is associated with a second time scale D2/v, where D is the vessel diameter.

Biophysically inspired model for functionalized nanocarrier adhesion to cell surface: roles of protein expression and mechanical factors.

In order to achieve selective targeting of affinity-ligand coated nanoparticles to the target tissue, it is essential to understand the key mechanisms that govern their capture by the target cell. Next-generation pharmacokinetic (PK) models that systematically account for proteomic and mechanical factors can accelerate the design, validation and translation of targeted nanocarriers (NCs) in the clinic. Towards this objective, we have developed a computational model to delineate the roles played by target protein expression and mechanical factors of the target cell membrane in determining the avidity of functionalized NCs to live cells. Model results show quantitative agreement with in vivo experiments when specific and non-specific contributions to NC binding are taken into account. The specific contributions are accounted for through extensive simulations of multivalent receptor-ligand interactions, membrane mechanics and entropic factors such as membrane undulations and receptor translation. The computed NC avidity is strongly dependent on ligand density, receptor expression, bending mechanics of the target cell membrane, as well as entropic factors associated with the membrane and the receptor motion. Our computational model can predict the in vivo targeting levels of the intracellular adhesion molecule-1 (ICAM1)-coated NCs targeted to the lung, heart, kidney, liver and spleen of mouse, when the contributions due to endothelial capture are accounted for. The effect of other cells (such as monocytes, etc.) do not improve the model predictions at steady state. We demonstrate the predictive utility of our model by predicting partitioning coefficients of functionalized NCs in mice and human tissues and report the statistical accuracy of our model predictions under different scenarios.

Effect of wall-mediated hydrodynamic fluctuations on the kinetics of a Brownian nanoparticle.

The reactive flux formalism (Chandler 1978 J. Chem. Phys.68, 2959-2970. (doi:10.1063/1.436049)) and the subsequent development of methods such as transition path sampling have laid the foundation for explicitly quantifying the rate process in terms of microscopic simulations. However, explicit methods to account for how the hydrodynamic correlations impact the transient reaction rate are missing in the colloidal literature. We show that the composite generalized Langevin equation (Yu et al. 2015 Phys. Rev. E91, 052303. (doi:10.1103/PhysRevE.91.052303)) makes a significant step towards solving the coupled processes of molecular reactions and hydrodynamic relaxation by examining how the wall-mediated hydrodynamic memory impacts the two-stage temporal relaxation of the reaction rate for a nanoparticle transition between two bound states in the bulk, near-wall and lubrication regimes.

Hydrodynamic interactions of deformable polymeric nanocarriers and the effect of crosslinking.

We report theoretical as well as numerical investigations of deformable nanocarriers (NCs) under physiologically relevant flow conditions. Specifically, to model the deformable lysozyme-core/dextran-shell crosslinked polymer based NC with internal nanostructure and subject it to external hydrodynamic shear, we have introduced a coarse-grained model for the NC and have adopted a Brownian dynamics framework, which incorporates hydrodynamic interactions, in order to describe the static and dynamic properties of the NC. In order to represent the fluidity of the polymer network in the dextran brush-like corona, we coarse-grain the structure of the NC based on the hypothesis that Brownian motion, polymer melt reptations, and crosslinking density dominate their structure and dynamics. In our model, we specify a crosslinking density and employ the simulated annealing protocol to mimic the experimental synthesis steps in order to obtain the appropriate internal structure of the core-shell polymer. We then compute the equilibrium as well as steady shear rheological properties as functions of the Péclet number and the crosslinking density, in the presence of hydrodynamic interactions. We find that with increasing crosslinking, the stiffness of the nanocarrier increases, the radius of gyration decreases, and as a consequence the self-diffusivity increases. The nanocarrier under shear deforms and orients along the direction of the applied shear and we find that the orientation and deformation under shear are dependent on the shear rate and the crosslinking density. We compare various dynamic properties of the NC as a function of the shear force, such as orientation, deformation, intrinsic stresses etc., with previously reported computational and experimental results of other model systems. The computational approach described here serves as a powerful tool for the rational design of NCs by taking both the physiological as well as the hydrodynamic environments into consideration. Development of such models is essential in order to gain useful insights that may be translated into the optimal design of NCs for diagnostic as well as targeted drug delivery applications.

Composite generalized Langevin equation for Brownian motion in different hydrodynamic and adhesion regimes.

We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics.

Modelling of Binding Free Energy of Targeted Nanocarriers to Cell Surface.

We have developed a numerical model based on Metropolis Monte Carlo (MC) and the weighted histogram analysis method (WHAM) that enables the calculation of the absolute binding free energy between functionalized nanocarriers (NC) and endothelial cell (EC) surfaces. The binding affinities are calculated according to the free energy landscapes. The model predictions quantitatively agree with the analogous measurements of specific antibody coated NCs (100∼nm in diameter) to intracellular adhesion molecule-1 (ICAM-1) expressing EC surface in in vitro cell culture experiments. The model also enables an investigation of the effects of a broad range of parameters that include antibody surface coverage of NC, glycocalyx in both in vivo and in vitro conditions, shear flow and NC size. Using our model we explore the effects of shear flow and reproduce the shear-enhanced binding observed in equilibrium measurements in collagen-coated tube. Furthermore, our results indicate that the bond stiffness, representing the specific antibody-antigen interaction, significantly impacts the binding affinities. The predictive success of our computational protocol represents a sound quantitative approach for model driven design and optimization of functionalized nanocarriers in targeted vascular drug delivery.

Nanocarrier Hydrodynamics and Binding in Targeted Drug Delivery: Challenges in Numerical Modeling and Experimental Validation.

This review discusses current progress and future challenges in the numerical modeling of targeted drug delivery using functionalized nanocarriers (NC). Antibody coated nanocarriers of various size and shapes, also called functionalized nanocarriers, are designed to be injected in the vasculature, whereby they undergo translational and rotational motion governed by hydrodynamic interaction with blood particulates as well as adhesive interactions mediated by the surface antibody binding to target antigens/receptors on cell surfaces. We review current multiscale modeling approaches rooted in computational fluid dynamics and nonequilibrium statistical mechanics to accurately resolve fluid, thermal, as well as adhesive interactions governing nanocarrier motion and their binding to endothelial cells lining the vasculature. We also outline current challenges and unresolved issues surrounding the modeling methods. Experimental approaches in pharmacology and bioengineering are discussed briefly from the perspective of model validation.

Computational simulation of hematocrit effects on arterial gas embolism dynamics.

BACKGROUND: Recent computational investigations have shed light into the various hydrodynamic mechanisms at play during arterial gas embolism that may result in endothelial cell (EC) injury. Other recent studies have suggested that variations in hematocrit level may play an important role in determining the severity of neurological complications due to decompression sickness associated with gas embolism. METHODS: To develop a comprehensive picture, we computationally modeled the effect of hematocrit variations on the motion of a nearly occluding gas bubble in arterial blood vessels of various sizes. The computational methodology is based on an axisymmetric finite difference immersed boundary numerical method to precisely track the blood-bubble dynamics of the interface. Hematocrit variations are taken to be in the range of 0.2-0.6. The chosen blood vessel sizes correspond to small arteries and small and large arterioles in normal humans. RESULTS: Relevant hydrodynamic interactions between the gas bubble and EC-lined vessel lumen have been characterized and quantified as a function of hematocrit levels. In particular, the variations in shear stress, spatial and temporal shear stress gradients, and the gap between bubble and vascular endothelium surfaces that contribute to EC injury have been computed. DISCUSSION: The results suggest that in small arteries, the deleterious hydrodynamic effects of the gas embolism on an EC-lined cell wall are significantly amplified as the hematocrit levels increase. However, such pronounced variations with hematocrit levels are not observed in the arterioles.

Multiscale Modeling of Functionalized Nanocarriers in Targeted Drug Delivery.

Targeted drug delivery using functionalized nanocarriers (NCs) is a strategy in therapeutic and diagnostic applications. In this paper we review the recent development of models at multiple length and time scales and their applications to targeting of antibody functionalized nanocarriers to antigens (receptors) on the endothelial cell (EC) surface. Our mesoscale (100 nm-1 µm) model is based on phenomenological interaction potentials for receptor-ligand interactions, receptor-flexure and resistance offered by glycocalyx. All free parameters are either directly determined from independent biophysical and cell biology experiments or estimated using molecular dynamics simulations. We employ a Metropolis Monte Carlo (MC) strategy in conjunction with the weighted histogram analysis method (WHAM) to compute the free energy landscape (potential of mean force or PMF) associated with the multivalent antigen-antibody interactions mediating the NC binding to EC. The binding affinities (association constants) are then derived from the PMF by computing absolute binding free energy of binding of NC to EC, taking into account the relevant translational and rotational entropy losses of NC and the receptors. We validate our model predictions by comparing the computed binding affinities and PMF to a wide range of experimental measurements, including in vitro cell culture, in vivo endothelial targeting, atomic force microscopy (AFM), and flow chamber experiments. The model predictions agree closely and quantitatively with all types experimental measurements. On this basis, we conclude that our computational protocol represents a quantitative and predictive approach for model driven design and optimization of functionalized NCs in targeted vascular drug delivery.

Protein assembly at the air-water interface studied by fluorescence microscopy.

Protein assembly at the air-water interface (AWI) occurs naturally in many biological processes and provides a method for creating biomaterials. However, the factors that control protein self-assembly at the AWI and the dynamic processes that occur during adsorption are still underexplored. Using fluorescence microscopy, we investigated assembly at the AWI of a model protein, human serum albumin minimally labeled with Texas Red fluorophore. Static and dynamic information was obtained under low subphase concentrations. By varying the solution protein concentration, ionic strength, and redox state, we changed the microstructure of protein assembly at the AWI accordingly. The addition of pluronic surfactant caused phase segregation to occur at the AWI, with fluid surfactant domains and more rigid protein domains revealed by fluorescence recovery after photobleaching experiments. Protein domains were observed to coalesce during this competitive adsorption process.

Dynamic factors controlling carrier anchoring on vascular cells.

This article reviews experimental and modeling methods for determining the critical roles played by the various factors that control nanocarrier drug delivery to vascular endothelial cells.

Multivalent binding of nanocarrier to endothelial cells under shear flow.

We investigate the effects of particle size, shear flow, and resistance due to the glycocalyx on the multivalent binding of functionalized nanocarriers (NC) to endothelial cells (ECs). We address the much- debated issue of shear-enhanced binding by computing the binding free-energy landscapes of NC binding to the EC surface when the system is subjected to shear, using a model and simulation methodology based on the Metropolis Monte Carlo approach. The binding affinities calculated based on the free-energy profiles are found to be in excellent agreement with experimental measurements for different-sized NCs. The model suggests that increasing the size of NCs significantly increases the multivalency but only moderately enhances the binding affinities due to the entropy loss associated with bound receptors on the EC surface. A significant prediction of our model is that under flow conditions, the binding free energies of NCs are a nonmonotonic function of the shear force. They show a well-defined minimum at a critical shear value, and thus quantitatively mimic the shear-enhanced binding behavior observed in various experiments. More significantly, our results indicate that the interplay between multivalent binding and shear force can reproduce the shear-enhanced binding phenomenon, which suggests that under certain conditions, this phenomenon can also occur in systems that do not show a catch-bond behavior. In addition, the model also suggests that the impact of the glycocalyx thickness on NC binding affinity is exponential, implying a highly nonlinear effect of the glycocalyx on binding.