Particles of variable size and shape have been increasingly investigated in the literature due to their effect on biological systems both in vitro and in vivo. In terms of flow-dynamics, reports have shown that the SAV may affect the propagation of particles in both interstitial and intravascular compartments, margination toward capillary walls, clearance through fenestrations, and alignment and turbulence in flow fields. For cellular association, the SAV and associated curvature effects influence antibody interaction area and adhesion strength,107 opsonization,108 and internalization kinetics and mechanisms.49 The SAV also affects intracellular aspects through nuclear alignment and particle degradation. This section will therefore focus on these effects within the context of recent literature.
2.2.1. Flow Dynamics and Biodistribution
According to fundamental fluid dynamic science, the movement of a particle within a flow regime is governed by both shape and size. The size of particles administered in blood vessels may dictate their velocity and diffusion,109 while particle movement in tissue is limited by size due to steric hindrance within the extracellular matrix.49 For nonspherical particles, angular movement under flow is often described using the rotational Peclet number, , which takes into account Brownian and non-Brownian motions of particles. The rotary diffusivity, Dr, is closely related to the aspect ratio of the particle, and quantifies the extent of Brownian motion. For high Pe values, anisometric particles are not prone to Brownian effects and solely “tumble” end over end periodically, as described by Jeffery.110 The rate of “tumbling”, , can be quantified according to Equation 1:
Where is the strain rate, re is the effective particle aspect ratio, and ϕ is the angle between the long particle axis and the plane orthogonal to the flow direction.111, 112 Larson states that for a Jeffery orbit, the period of rotation increases for increasing aspect ratio. Large-aspect-ratio particles decelerate in rotational velocity when the long axis is nearly parallel to the flow direction, and accelerate otherwise.112 Mueller and co-workers verified that re, which is determined experimentally and related to the actual aspect ratio, impacts dramatically upon angular velocity, and in turn determines the particle position probability density.111 This is shown in Figure 3 for prolate and oblate ellipsoidal particles. It is important to note that a nonspherical particle will therefore spend a greater amount of time aligned with a flow field, reducing the available cross-sectional area for interaction with other particles or cells. This was recently observed experimentally in vitro by Discher and colleagues for long filomicelles, which avoid interaction with phagocytic cells, using flow rates similar to those found in the spleen.48 As the filomicelle length increased from 1 to 3 μm, uptake into macrophages decreased dramatically and logarithmically due to alignment of the filomicelle within the flow field.
Figure 3. The effect of particle geometry on capillary flow behavior. a) The aspect ratio (re) governs the magnitude of angular velocity under simple shearing flow. Reproduced with permission.111 Copyright 2010, Royal Society Publications. b) Platelets interact heavily with the endothelial wall due to their irregular shape. 1) Tethering, 2) rolling angular velocity and activation, and 3) firm adhesion with the wall are all affected by the platelet geometry.
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When investigating the effect of the SAV on the shear rate and the turbulent nature of a particle suspension within a flow regime, a modified Reynolds number, , can be adopted where G is the shear rate, and ν the kinematic viscosity.113 Qi and Luo investigated the effect of aspect ratio on Rep and particle rotational state in Couette flow, and observed that particle shape had a clear impact upon Rep. The authors observed several distinct regions of Rep where independent rotational states such as “tumbling”, “wagging”, flow aligning, “log-rolling”, and “kayaking” occurred.113 In terms of particle size, Decuzzi and co-workers showed that for silica microspheres initially adhered to a flow-chamber substrate, the critical shear rate increased dramatically as the particle diameter increased from 1.3 to 5 μm,25 which is consistent with the conclusions of both Goetz et al. and Lamprecht et al.54, 55 This illustrates that particle geometry has a large influence on the shear experienced in both the capillary and vasculature, affecting cellular interaction and adhesion with immune-system cells under flow conditions.
These observations can be placed further in a biological context by examining literature describing the margination properties of particles. Margination is defined as the movement and interaction of particles toward the endothelial wall in blood capillary channels. This is a critical aspect of therapeutic delivery to endothelial cells and also in being able to exploit the enhanced retention and permeability (EPR) effect for passive delivery to tumor sites, where EPR is a size dependent process with a maximum limit of approximately 500 nm.114 Decuzzi and co-workers discussed the margination propensity of particles with different geometries, where due to the core movement of red blood cells in capillaries, there exists a cell-free layer within close proximity of the endothelial wall in which particles with little propensity for longitudinal and lateral drift would remain.115 This result was also found by Goldman et al. for spherical particles, which were found to reside within this laminar phase layer unless an external lateral force was applied.116 Nonspherical particles, however, exhibit an intrinsic hydrodynamic lateral force and torque, meaning that these particles marginate highly, interacting with the endothelial wall to a greater extent than spherical particles. This has been validated by experiments performed by Gentile and co-workers using a parallel plate flow chamber to measure the margination propensity of silica particles with different sizes, densities, and shapes.117 It was reported that while higher mass particles were overcome by gravity and moved towards the walls as expected, as the aspect ratio and SAV increased, margination increased and a greater number of particles adhered to the chamber substrate. Similarly, this is found in a biological setting for the margnination of leukocytes due to platelet aggregation altering their co-geometry,118 as well as interactions between the endothelial wall and irregularly shaped platelets, as shown in Figure 3.119
The action of natural fenestrations during circulation is inherently connected to particle geometry. Small particles with a hydrodynamic radius of 5.5 nm120 and free molecules with a size limit of 5 kDa121 are often removed in the kidney through glomerular filtration, while particles with a diameter less than 100 nm pass through fenestrations in the endothelial lining,3 and rigid particles larger than 200 nm may be filtered in the spleen.5 Larger microparticles are often cleared through phagocytic interactions with Kupffer cells in the liver or trapped in capillary beds; however, smaller particles can also be removed via endocytosis by phagocytic or non-phagocytic cells.3 Kostarelos and co-workers reported that carbon nanotube bundles with a diameter of 10 to 40 nm and length of 0.3 to 1 μm showed rapid clearance, predominantly due to renal excretion via active glomerular filtration.72 However, it was shown by Bhatia and co-workers that renal excretion of gold nanorods with a similar minor axis length could be comprehensively reduced by attaching a 5 kDa PEG outer layer using thiol chemistry, thereby increasing the hydrodynamic radius.20 In addition to particle clearance through fenestrations, an increased SAV can help exploit passive tumor targeting via the EPR effect. Bhatia and co-workers also showed that passive tumor accumulation was high for the gold nanorods due to both size effects and reduced renal clearance,20 while Decuzzi et al. reasoned that particle shape impacts heavily upon the rational design of particulate systems in the exploitation of the EPR effect.115
All of these geometry-dependant flow properties culminate in affecting biodistribution outcomes in vivo. Discher and co-workers observed that the alignment of long filomicelles in flow fields affecting macrophage interaction in vitro paralleled the in vivo behavior of long filomicelles.48 Increased length resulted in higher blood circulation half-lives and passive accumulation in the lung. When compared to spherical PEGylated stealth vehicles, which are generally cleared within a day, long filomicelles exhibited circulation lifetimes of up to five days. Muro showed that elliptical disks were able to better target the lung using anti-ICAM targeting moieties compared to a range of sphere sizes, evidenced through a high immunospecificity index (ISI).122 Interestingly for the anti-ICAM functionalized PS spheres, the smaller the diameter the better the ISI and consequently the percentage of particles in the blood was also greater, which also correlates well with the impact of SAV on critical shear and flow-alignment, as previously mentioned. Devarajan et al. found that irregular shaped glycerylmonostearate polymer lipid nanostructures (LIPOMERs) avoided macrophages in circulation, achieving high concentrations in the spleen when compared to spherical LIPOMERs, which accumulated in the liver.51 This could have important consequences for splenotropic drug delivery, due to avoiding Kupffer cell clearance while still demonstrating high spleen retention. Decuzzi et al. also recently showed that discoidal particles actively avoided Kupffer cells and consequently liver accumulation, boosting accumulation in non-MPS organs.25
2.2.2. Cellular Interaction and Uptake
It is generally suggested that phagocytosis of particles is predominantly mediated by molecular recognition between cells and particles. One important example is the presence of integrin-associated protein CD47 on red blood cells, preventing phagocytosis. Lindberg and co-workers showed that CD47 interacts with a corresponding protein on macrophages, preventing internalization.123 Besides molecular recognition, the SAV of particles also plays an important role in both phagocytosis and target cell interaction. Long filomicelles align in flow fields, reducing phagocytic association.48 Decuzzi and co-workers observed that firm adhesion between particles and cells is obtained when hydrodynamic and dislodging forces are balanced by ligand–receptor interactions combined with other adhesion forces.115 These forces have been shown to depend on shape,107, 115 and have also been extensively proven to depend on size.107, 124 Decuzzi et al. and Gao et al. both noted that geometry and ligand density, in a similar vein to membrane adhesion, will determine the rate of receptor-mediated endocytosis of particles into a cell,107, 124 while Muro and co-workers showed that high SAV elliptical disks achieve high targeting specificity for endothelial cells due to improved interaction when compared to spheres.122
Cellular uptake of particles involves endocytosis, a process of internalizing materials by engulfing them with the cell membrane. Several mechanisms, including phagocytosis, macropinocytosis, clathrin-mediated endocytosis, and caveolar-mediated endocytosis can be used for particle internalization depending on the physicochemical properties of the particles and the cell physiology. Generally these endocytic pathways differ with regard to the size of the particles. Particles larger than 0.5 μm are more likely internalized by macropinocytosis or phagocytosis, as the inherent portal size for clathrin-mediated endocytosis is about 120 nm and approximately 90 nm for cavolae-mediated endocytosis. Foged et al. investigated the uptake of PS spheres with diameters ranging between 0.04 and 15 μm, some with modified surfaces, into dendritic cells.53 It was found that the cellular uptake rate increased as the diameter of the PS spheres decreased, similar to the results of Muro et al. who reported more rapid uptake, and lysosomal trafficking, of 0.1 μm diameter PS spheres when compared to 1 μm particles.122 Muro et al. postulated that this was due to increased small particle surface interaction, witnessed through double-positive flow cytometry experiments, combined with a macropinocytosis uptake mechanism, compared to a phagocytic mechanism for the larger spheres. This size effect was also observed by Rejman et al. in a study of the compartmentalization of both 200 and 500 nm PS beads, where only the 200 nm particles were able to accumulate in late endosomal and lysosomal compartments.125 Although to a large extent particle size determines the internalization mechanism from the viewpoint of the space limits in each endocytic pathway, varied findings have suggested the interplay between size, shape and chemical properties of particles on internalization mechanisms. Hoekstra and co-workers found that clathrin-mediated endocytosis dominated for PS-based microspheres with a diameter less than 200 nm incubated with eukaryotic cells, with a shift towards caveolae-mediated internalization as the microsphere size increased.125
While the cellular uptake of particles is influenced by the size, more recent studies have also demonstrated the significant impact of the shape on cell dynamics. DeSimone and co-workers investigated cationic PRINT particles with various sizes and shapes, examining both uptake kinetics and mechanisms.126 Cylinders (150 nm × 450 nm) were internalized quicker and to a greater extent than 200 nm diameter spherical particles in HeLa cells, even though the internal volume of the cylinders was greater. By using endocytic inhibitors, it was found that the cylinders utilized multiple mechanisms to a greater extent than the spheres to enter the cells, correlating with other extensive studies by DeSimone and co-workers for 1 μm cylindrical PRINT particles with both positive and negative charges, which showed both dual clathrin-mediated endocytosis and macropinocytosis uptake routes were predominantly utilized in a range of cell lines.24 This is consistent with the observation that the increased SAV of cylinders would further promote interaction between the cationic surface and the cell membrane proteins. Mitragotri and co-workers compared the cellular internalization of 1 μm PS spherical and elliptical particles with the same internal volume in endothelial cells.52 It was found that the spheres internalized much more rapidly, however this difference was seen to decrease over time. This work was extended by examining the effect of the alignment of the particle major axis to the cellular membrane, quantified by the initial contact angle (Ω), on cell membrane penetration velocity and internalization using rat alveolar macrophages.127 Particles with their major axis oriented tangentially to the cell membrane, that is as Ω approaches 90°, exhibited dramatically reduced internalization. This was mainly attributed to the necessary expansion required to form an actin cup for phagocytosis, while similar internalization trends were seen for the static incubation of long worm-like polymer particles with phagocytes, as seen in Figure 4.15, 48 Similar time-dependant high-aspect-ratio particle alignment was also seen by Mitragotri and co-workers for elliptical disk-shaped PLGA particles tangentially aligning in the cytoplasm with the nucleus of pooled human umbilical vein endothelial cells.52 Over long time scales spherical particles were found to have a shorter average distance to the cell nucleus, which has important implications for the delivery of therapeutics that have limited diffusion coefficients in the cell cytoplasm.
Figure 4. Phagocytosis of nonspherical particles. Images of PS disks orientated end-on (a), disks side-on (b), spheres (c), and IgG adsorbed worms (d) fabricated via mechanical stretching of spherical beads. a–c) Reproduced with permission.127 Copyright 2006, Natioanl Academy of Sciences. d) Reproduced with permission.15 Copyright 2009, Springer.
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Yang and Ma also simulated the effect of Ω for different SAV nanoparticles on the penetration of a model lipid bilayer.128 They showed that the minimum driving force of the ellipsoidal particle for breaching the lipid bilayer was dependent upon internal volume, aspect ratio, and approach angle. It was also shown that the process was time dependent; with time, the ellipsoid aligned itself tangentially with the bilayer, altering the angle Ω. Placing this in context with experimental gold nanoparticle interactions with cell-lines, Chan and co-workers showed that 14 nm × 40 nm and 14 nm × 74 nm gold nanorods internalized into HeLa cells at a much slower rate than spherical nanoparticles with a diameter of 74 nm.19 This correlates well with the modeling of Yang and Ma128 and experimental work on surfactant-stabilized gold nanorod internalization into human breast adenocarcinoma cells, where increasing the aspect ratio slowed uptake.129 Chan and co-workers also demonstrated that gold nanoparticles with a diameter of 50 nm were optimal for HeLa internalization, an effect most likely due to harnessing multi-mechanism internalization, and differences in adsorption of serum proteins due to curvature effects.19 In addition to the work on gold nanorods, several groups have also studied DNA or protein delivery using carbon nanorods, and have found them to deliver effectively into the cellular cytoplasm via an endocytotic mechanism.130, 131
In therapeutic delivery applications, cargo must be often released in a controlled manner, and delivered into the cytoplasm in order to interact with the cell nucleus. In some cases, degradation and cargo release may depend upon the particle SAV. Dunne and co-workers investigated PLGA microsphere mass loss due to hydrolysis, and found that larger spheres degraded at almost twice the rate of smaller ones, primarily due to longer diffusion path lengths allowing autocatalytic degradation.132 However for a similar system, Labhasetwar and co-workers found that a 100-fold decrease in particle diameter had limited effect on bovine serum albumin release.133