Nanoparticle delivery and particle diffusion in confined and complex environments

Accepted Manuscript Nanoparticle delivery and particle diffusion in confined and complex environments Hisham Al-Obaidi, Alexander T. Florence

PII:

S1773-2247(15)00112-4

DOI:

10.1016/j.jddst.2015.06.017

Reference:

JDDST 56

To appear in:

Journal of Drug Delivery Science and Technology

Received Date: 10 May 2015 Revised Date:

23 June 2015

Accepted Date: 23 June 2015

Please cite this article as: H. Al-Obaidi, A.T. Florence, Nanoparticle delivery and particle diffusion in confined and complex environments, Journal of Drug Delivery Science and Technology (2015), doi: 10.1016/j.jddst.2015.06.017. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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COMPLEX ENVIRONMENTS FOR NANOPARTICLE DIFFUSION

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DIFFUSION IN CORRALS

Microvilli X section

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SINGLE FILE DIFFUSION CELL

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Lymph

EXTRAVASATION

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Blood

JAMMING

Extracellular space

OBSTRUCTED DIFFUSION

ACCEPTED MANUSCRIPT REVIEW Nanoparticle delivery and particle diffusion in confined and complex environments Hisham Al-Obaidi1 and Alexander T. Florence2* 1 Department

of Pharmacy, King’s College London, Stamford Street, London SE1 9NH,UK UCL School of Pharmacy, University College London, Brunswick Square, London WC1N 1AX, UK

Abstract

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Multiple biological, chemical and physical factors influence and dictate the success or otherwise of nanocarrier mediated drug delivery and targeting. One issue is diffusion. This review considers aspects of the movement of nanoparticles in their passage from the selected point of administration to their intended locus of action, with an emphasis on the effects of particle diffusion in the often confined and complex spaces of the body. Diffusion of drugs and carriers rarely takes place in free unbounded spaces in vivo, it being more likely to occur, in part at least, in complex, heterogeneous locations, for example between villi and microvilli in the intestine, in the extracellular matrix of tumours and in the crowded environment of cell interiors. Flow in capillaries involves changing pressures, changing capillary radii and asymmetric bifurcations of vessels. Nanocarrier passage through pores and fenestrae in the process of extravasation, which itself is a stochastic process, may be impeded by particle jamming thus hindering procession towards cellular goals. While many of these processes have been difficult to study in vivo, there are many basic studies of these phenomena which can be applied to the biological situation. This overview examines diffusion-related phenomena and speculates on their importance in attaining the still elusive goal of achieving a significant proportion of the administered dose of nanoparticles (and hence drug) in target tissues.

Keywords: nanoparticles, targeting, anomalous diffusion, obstruction, jamming

A paper for the Special Issue of the Journal of Delivery Science and Technology dedicated to the founder of the journal, Professor Dominique Duchêne.

Corresponding author: Alexander T. Florence * [email protected];

ACCEPTED MANUSCRIPT REVIEW Nanoparticle delivery and particle diffusion in confined and complex environments Hisham Al-Obaidi1 and Alexander T. Florence2* 2

of Pharmacy, King’s College London, Stamford Street, London SE1 9NH,UK UCL School of Pharmacy, University College London, Brunswick Square, London WC1N 1AX, UK

Abstract

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Multiple biological, chemical and physical factors influence and dictate the success or otherwise of nanocarrier mediated drug delivery and targeting. One issue is diffusion. This review considers aspects of the movement of nanoparticles in their passage from the selected point of administration to their intended locus of action, with an emphasis on the effects of particle diffusion in the often confined and complex spaces of the body. Diffusion of drugs and carriers rarely takes place in free unbounded spaces in vivo, it being more likely to occur, in part at least, in complex, heterogeneous locations, for example between villi and microvilli in the intestine, in the extracellular matrix of tumours and in the crowded environment of cell interiors. Flow in capillaries involves changing pressures, changing capillary radii and asymmetric bifurcations of vessels. Nanocarrier passage through pores and fenestrae in the process of extravasation, which itself is a stochastic process, may be impeded by particle jamming thus hindering procession towards cellular goals. While many of these processes have been difficult to study in vivo, there are many basic studies of these phenomena which can be applied to the biological situation. This overview examines diffusion-related phenomena and speculates on their importance in attaining the still elusive goal of achieving a significant proportion of the administered dose of nanoparticles (and hence drug) in target tissues.

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Keywords: nanoparticles, targeting, anomalous diffusion, obstruction, jamming

A paper for the Special Issue of the Journal of Delivery Science and Technology dedicated to the founder of the journal, Professor Dominique Duchêne.

Corresponding author: Alexander T. Florence * [email protected]; 1

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Contents

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1. Introduction 2. Brownian motion and diffusion 3. Particulate diffusion 4. Corralled, anomalous and obstructed diffusion 5. Convection, flow and diffusion 6. Interactions with the biological environment 7. intestinal uptake of nanoparticles 8. The intravenous route: capillary flow, extravasation and jamming 9. Diffusion in extracellular matrices 10. Diffusion in brain tissue 11. Diffusion in cells 12. Conclusions

At worst, one is in motion; and at best Reaching no absolute in which to rest, One is always nearer by not keeping still.

1. Introduction

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Thom Gunn from a poem in The Sense of Movement, Faber, 1957

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Targeting and delivery of drugs in nanoparticulate carriers is obviously dependant for success on both significant accumulation in target structures such as tumours and the release of the active agent at the appropriate site and rate to achieve an optimum concentration profile. To achieve this following intravenous administration, particles must extravasate (a stochastic process), pass into the extracellular matrix and then diffuse towards target cellular structures and perhaps also into cell nuclei. Extracellular matrices are not simple channels [1], and all cells have “crowded” environments [2]. There are of course advantages of drug administration in carrier systems which can result from a change in the biodistribution of active ingredients avoiding non-target organs, but the ultimate goal is normally specific organ targeting. Reduction in the rate of diffusion of particles in many circumstances impedes their ability to navigate readily to these ultimate sites. There are many consequences of diffusional behaviour which are not fully resolved: does reduction in the rate of diffusion of particles in the extracellular space of tumours decrease or enhance the possibility of optimal drug release from perhaps ultimately motionless particles? It is clear that it is dangerous to generalise: what applies to nanoparticles with one specific drug does not necessarily apply to systems of different construction, size, shape, flexibility and surface characteristics. Demetzos and Pippa [3] have recently

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ACCEPTED MANUSCRIPT provided one means of addressing the “nanosimilarity” or otherwise of constructs. And if tumours are targets they are in a sense moving targets often changing physically and biologically with time as they grow.

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Diffusion of both drug molecules and particles may occur under a range of conditions, in static systems such as in unstirred media, in flowing or turbulent media, in systems which have obstacles to their movement, or close to the walls of vessels and cells where there might be interactions between particles and walls. So-called anomalous diffusion is a feature of fractal systems [4] where particles are trapped in various bottlenecks and structural dead-ends.

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We became interested in the topic of diffusion in complex or confined spaces when studying the dynamics of microparticles “corralled” inside isolated lipid vesicles [5] (a simple but instructive model system) and by an earlier encounter with the obstruction effect [6]. This short overview in considering diffusion and related issues elaborates on concerns expressed by many on the separation of expectations of nanoparticle targeting and the physical and biological realities in present approaches [7]. The challenges of the body’s intricacies must be better understood. It is unlikely that an all-encompassing theoretical treatment will for some time predict particle flow and diffusion from administration via complex pathways to geometrically complex target elements. Here we can only address some of the issues in discussing particle diffusion in static and flowing media, in confined elements of the body such as capillaries, fenestrae, extracellular matrices, the intestinal epithelia, villi and microvilli, cells and nuclear pores.

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2. Brownian motion and diffusion The diffusion of small molecules, macromolecules and particles is evident in all biological systems and is the main mechanism by which biochemical messages are transferred [8, 9]. The 19th century Scottish botanist Robert Brown [10] first described the motion of pollen particles in a static liquid suspension; the relationship between this Brownian motion caused by thermal motions in the liquid and the coefficient of diffusion of the particles (D), their radius (r) and the viscosity (η) of the continuous phase at a temperature (T) was solved by Einstein [11] and is embodied in the Stokes-Einstein equation (equation 1) for a single spherical particle of radius, r, where k is the Boltzmann constant. As D = kT/f where f is the particle’s frictional coefficient, (f = 6πηr) in a medium of viscosity η such that:

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D = kT/6πηr

[1]

Equation 1 provides the stationary (self) diffusion coefficient in the absence of a concentration gradient (as in Brownian motion) and also in some of the situations discussed in the review. 3

ACCEPTED MANUSCRIPT The flux (J) of material, where dc/dx is the concentration gradient is given by J = -D (dc/dx)

[2]

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These equations have assisted in explaining many biological and physical processes such as the movement of DNA and proteins [12, 13] and the absorption of drugs across epithelia [14]. R.K. Jain and colleagues [see for example:15] have done much to illuminate the physicochemical and biological issues of tumour targeting.

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The Stokes-Einstein equation is used widely to determine the radius of particles through techniques such as dynamic light scattering [16]. There are limits to its use, a lower size limit [17] (of around 2nm) and an upper limit perhaps where sedimentation of larger particles is more dominant. Tuteja et al [18] discuss the diffusion of particles in polymer liquids finding this to be faster than predicted by the Stokes-Einstein equation due to the fact - they surmise - that the particles have a smaller size than the polymer mesh.

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The Brownian movement of asymmetric particles is clearly of interest with the advent of carbon nanotubes and other constructs as potential drug carriers. There are both the rotational and translational aspects of the behaviour of nonspherical carriers to be considered (see, for example references [19, 20]). Brownian motion of ellipsoids has been addressed [21] considering the diffusion coefficient related to two frictional coefficients, γa and γb , respectively for parallel and perpendicular diffusion, hence Do = KT/γo. As γa < γb Da > Db when free rotation is impeded as it might be in restricted spaces. If the particles can rotate, rotational diffusion “washes out directional memory” in the words of Han et al [21]. Fig 1 represents the areas considered in this review in relation to three possible routes of particle administration, namely the intravenous, and oral routes and direct administration into the brain, the last to avoid a discussion here of the penetration of particles across the blood-brain barrier, a topic in itself.

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[FIGURE 1]

The cytoplasm of individual cells is very heterogeneous in nature with organelles such as the Golgi complex in the micrometre size range to others with a size range of around 100nm such as the endoplasmic reticulum (ER). The presence and size of cell organelles implies that hindrance to diffusion of nanoparticles is likely and considerable [22, 23], and this at the end of the tortuous journey from site of administration. As suggested by Figure 1, the procession to the site of 4

ACCEPTED MANUSCRIPT action is challenging. Sinek and colleagues [24] summarise the general situation so well writing “the performance of micro-and nanodevices must be considered in the context of a dynamic, biological environment, spanning several scales and modes, including the intravascular, the intratumoral and even the intracellular…it is not only what such devices do in isolation that requires investigation, but also what they do in the body, and what the body does, or attempts to do, to them”.

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Orally administered nanosystems are a case in point. They will be present in the heterogeneous contents of the gastrointestinal tract. Some will escape and interact with the gut associated lymphoid tissue and Peyer’s patches where a degree of uptake can occur [25] and they are then transported via the lymphatic system towards the blood circulation; others are absorbed by enterocytes. The presence of villi and microvilli which facilitate the absorption of drug molecules may have an influence on the uptake of nanoparticles, but the question is in which way? Uptake of nanoparticles may result from the entrapment of the nanoparticles within the confines of the villi despite the movement of the intestinal contents towards the colon. Does hindered diffusion result in enhanced absorption of particles entrapped close to the villous surfaces? It is perhaps a balance between the convective flow of the fluid versus entrapment. Outcomes will depend on the properties of the nanoparticles such as their shape and surface charge or decoration. Hydrophilic poloxymer coatings deter nanoparticle uptake by the gut-associated lymphoid tissue (GALT) [26] perhaps by making close contact with absorbing surfaces difficult.

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Even in tissue culture – on which much exploratory work depends - particles “diffuse, settle and agglomerate” cellular dose is therefore a function of these factors as pointed out by Teeguarden et al [27]. The same group [28]) have developed a computational model to encompass these phenomena to better estimate in vitro dosimetry of nanoparticles.

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3. Particulate diffusion Normal patterns of unfettered particulate diffusion as a function of time are shown in Fig 2. As time progresses particles move out from the point of origin but not in an equal manner. Thus in this situation few particles would have reached the extremities. This model does not encompass convection, flow and the other factors which can propel particles in vivo. [FIGURE 2]

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ACCEPTED MANUSCRIPT Particle size is of key importance as the Stokes-Einstein equation (1) for a single particle dictates. Particle concentration matters also. The diffusion coefficient of such a particle (DS) differs from that of a collection of particles, DC. If the volume fraction of particles is Φ DC = DS (1 + λΦ)

(3)

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where λ is a factor related to particle interactions. For charged particles interactions will of course depend on electrolyte concentration [29], λ decreasing with increasing electrolyte so that any significant effect of volume fraction on Dc can be reduced to zero. The coupling of particle motion through fluid – hydrodynamic interactions, also occurs [30]. When particles are trapped in crevices for example between microvilli, their concentration might increase, but there will be in these confined spaces closer particulate proximity to an absorbing membrane, as we discuss later. Normal Brownian motion and hence diffusion depends on the freedom to move in the medium in which the particles are suspended. Any restriction to movement results in sub-diffusion. The extent of pharmacological action at target sites therefore depends on a series of both free and corralled diffusion processes of the nanocarriers and also to those drug molecules which have been released. 4. Corralled, anomalous and obstructed diffusion

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Despite the fact that “confined” or “corralled” diffusion has been discussed in many basic physical and mathematical studies, there is perhaps a need to summarize the main findings with regard to the impact of spatial confinements on the flux of nanoparticles and to pose questions such as what is the impact on diffusion when the particles are moving close to any confining structure? and what is known about surface properties of the nanoparticles and their interactions within corrals?

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The time to leave a corralled structure though an opening is an important factor if particles are trapped in otherwise unproductive spaces, that is where they can exert no biological action. If the confines of the corral are permeable to nanoparticles the “escape time” (t ESC) is inversely proportional to the particle diffusion coefficient D as shown in equation 4 [31], t ESC /τ = F(hl) where τ = A/4D, hence t ESC = [AF.hl/4D] (4) where A is the corral area, l is the characteristic length of the corral, h is the permeability of the membrane and F is a function related to the shape of the 6

ACCEPTED MANUSCRIPT confines. Reductions in diffusivity of the particle can thus have a significant impact on particle escape time at any given permeability. In other words, corrals can dramatically affect the translocation of a moving particle in a concentration gradient. To estimate this accurately one needs of course to understand the mechanism(s) and rate of particle escape, and the permeability of any corral barrier.

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Biological environments such as the intracellular and extracellular fluids are so heterogeneous that for a particle to move freely is almost impossible. Diffusion will be restricted in the presence of any barriers or objects that hinder movement. Fig 3 illustrates the main types of obstacles for any particle wherever obstructions to free movement may occur; the particle may then experience periods of free diffusion but in the process of circumventing barriers pathways are lengthened, with an increase in tortuosity.

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To understand the impact of such hindrance on flux, previous studies have evaluated the impact of confines when 1μm polystyrene particles suspended in water/D2O are kept parallel or perpendicular to a wall. It was shown that there was a drift in the direction of the gradient, which leads to a net flux of particles equal to zero [32, 33]. These structures represent “obstructions” which when particles move past them travel longer (tortuous) pathways than free particles. The obstruction effect explored by Mackie and Meares [34] and by Fricke [35] causes the measured diffusion coefficient in the complex medium (Dcm) to be decreased compared, say, to diffusion in water, D0 , and this is a function of the volume fraction Φ of the obstructing object: Dcm/Do = [(1 – Φ)3/(1+ Φ)2]

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If the volume fraction of an obstructing object is 0.2, Dcm is reduced to one third of the value in water. In more crowded environments (Φ > 0.5), the diffusion coefficient is reduced to extremely low values. More complex derivations allow for heterogeneous obstructive objects being present. The obstruction effect applies to small molecules, ions, macromolecules and particles, hence also drugs released from nanocarriers in crowded environments. Using particle tracking methods the movement of particles in any physical or biological system can be monitored and the trajectories of the traced object can be determined. The displacements performed by the moving particle can then be quantified and expressed as the mean squared displacement (MSD). Diffusion patterns can then be categorised as sub-diffusion, super-diffusion or normal diffusion based on the

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[FIGURE 4]

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where t is the time lag or time between steps within a defined trajectory, the exponent (α) represents the degree of deviation from a normal Brownian diffusion (α =1). Higher α values reflect super-diffusion and lower α values subdiffusion. Fig 4 illustrates the correlation between the MSD and time of trajectory. A plateau at higher time scales represents sub-diffusion while linearity reflects normal Brownian motion.

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A drift in the value of the MSD may result from accelerated movement due to interactions with other particles (super-diffusion). Our own observations showed four patterns for diffusion when the number of entrapped polystyrene 1μm particles inside large vesicles was increased [5]. The diffusion coefficients were  0.27 × 10−9 cm2 s-1 for single entrapped particle,  0.61 × 10−9 cm2 s-1 for two particles, 1.26 × 10−9 cm2 s-1 for three particles, and 1.3 × 10−9 cm2 s-1 for multiple particles [5]. A free polystyrene particle has a diffusion coefficient in water of 5.1 x 10-9 cm2 s-1. Figure 5 traces the Brownian motion of the four particles in the model system. [FIGURE 5]

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Anomalous diffusion of small lipid nanogranules has been reported in yeast cells [36], an α value (see equation 6) of 0.75 indicating sub-diffusion attributable to the mechanical hindrance of the cytoplasmic polymeric networks of the cytoskeleton and other vesicles as in mammalian cells. It has been observed that at longer time scales (>23ms) the movement of particles becomes more restricted resulting in the typical sub-diffusive pattern [37].

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5. Convection, flow and diffusion Convection, through movement of the fluid medium, can dominate simple diffusional processes. Equation 6 is modified when there is diffusion plus flow of the medium such that MSD = 4Dtα + v2t2

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When a protein such as insulin is administered subcutaneously its movement in the interstitial fluid and extracellular matrix to the site of action can thus be predicted. Reddy et al. [39] used an in-vivo model to measure the interstitial transport of injected macromolecules and nanoparticles and were able to evaluate interstitial convection. Using a convection coefficient (ψ), the ratio between the mean velocities of the solute (μ) compared to velocity of the fluid (ν) was assumed to be linear, that is μ= ψ υ (8)

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Convection across the interstitial fluid was estimated by comparing the movement of macromolecules against the movement of a reference material. Different parameters were taken into account such as the shape, size, charge and mass of the system (dextrans, albumin and polystyrene nanoparticles (1 to 20nm in diameter). Apart from obvious size dependence, larger species moving more slowly, the authors [31] predicted a significant charge contribution towards the convection of the molecules, which resulted in mechanical hindrance. The latter seemed to counterbalance or cancel the impact of size on convection of the macromolecules [39]. Convection has been used to supplement the slow diffusion of macromolecules in the brain [40].

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Combining external forces with diffusion presents many opportunities for enhancement of performance. Aggregates of small PLGA nanoparticles carrying tissue plasminogen activator (tPA) targeted to vessels obstructed by platelets can be induced to release the active by a combination of shear-induced disintegration and self-diffusion. Shear stress from the blood flow cause these particulate aggregates to disintegrate into smaller particles that adhere to the surface of the blood vessels; the aggregates’ size limits their diffusion to injured tissues and therefore undesirable effects are reduced [41]. Brownian motion in shear flow is clearly of importance in the delivery of nanosystems. Miyazaki and Bedeaux [42] have attempted to find a mathematical or physical equation to “disentangle” the effects of diffusion of a particle from the effects of convection.

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Flow is not only important in terms of nanoparticle distribution but it also impacts on deposition of particles and molecules on surfaces. Deposition reduces with increase in the Reynolds number and larger particles, which were found to have a lower tendency to adsorb at the same Reynolds number, are more affected by flow [43], a finding paralleled with dendrimer adsorption, flow removing particles adsorbed to cells in quiescent media [44]. 6. Interactions with the biological environment

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The decoration of nanoparticle surfaces e.g. with hydrophilic poly(oxyethylene)glycol (PEG) molecules for the purpose of preventing uptake into the RES or with proteins as targeting agents [45] takes on an importance other than these primary functions. The interpretation in vivo of the significance of entropic and enthalpic interactions between particles and membrane surfaces or gels is not clear. In vivo this is the result of the changing nature of the opsonisation of proteins onto particles surface in the circulation [45].

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Interaction and filtering events have been used to explain size-related diffusion in extracellular microenvironments (Fig 6) [46]. Hydrogels can interact with diffusing particles and as such exchange of materials between different spatial regions will depend on the properties of the diffusing particles such as their size, shape and charge or other surface properties.

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The presence of the gel state in many biological sites means that studies of diffusion in hydrogels are of particular relevance in understanding diffusion in vivo. Deviation of diffusion coefficients from the Stokes-Einstein norm occurs with latex nanoparticles diffusing in hydroxypropyl methylcellulose (HPMC) gels [47]. The surface charge of the nanoparticles can hinder the movement of anionic nanoparticles, while cationic nanoparticles adsorb to plasma membranes and eventually diffuse significantly faster, due to the net negative charge present at the surface of cells [48]. Diffusion of poly(acrylic acid) (PAA) and poly(allylamine) (PAM) systems was found to be around 2 times slower than the diffusion of neutral nanoparticles [49].

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Studies on biofilms perhaps can shed light on access to diseased organ targets. In addition to diffusion, convective fluid flow can contribute towards movement of solutes, but because of biofilm formation, fluid convective flow can be significantly reduced rendering diffusion the main mechanism for the movement of solutes. In a typical cell, diffusion may occur rapidly because of the short pathways involved, but biofilm dimensions are significantly larger and diffusion distances are also [50]. The heterogeneous nature of biofilm structures has been proposed as the reason for increased resistance of the bacterial population to hostile conditions [51, 52]. Surface properties seem of special importance for diffusion of nanoparticles across biofilms. In a recent study, diffusion of silica nanoparticles across biofilms of Pseudomonas aeruginosa depended to a larger extent on the hydrophilicity/lipophilicity of the silica nanoparticles surface than on the size of the nanoparticles [53]. Similar findings have also been reported for anionic carboxylate polystyrene beads (50nm) whose diffusion was influenced by the properties of the bacterial membrane, higher hydrophobicity encouraging faster nanoparticle diffusion [54]. The impact of the surface of the

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bacterial biofilms may therefore impede the adhesion of the nanoparticles and result in retarded diffusion, a trend typical for diffusion within boundaries, due to the presence of interfacial bacterial components such as peptidoglycans and pili. Despite the fact that sub-diffusive patterns are clear for particles moving across different biofilms of a Burkholderia cepacia complex (BCC), differences between the moving particles in terms of their charge properties were minimal. This may support previous studies where surface hydrophobicity seemed critical for diffusion. PEGylation of the particles was suggested to improve diffusivity in biofilms and fresh cystic fibrosis sputum while charge on the surface immobilized the particles [55]. Stroh et al. [56] identified slow diffusion of neurotrophin factor (BDNF) as the main reason for its limited penetration in tissues. Modification with PEG however enhances interstitial diffusion, explained by the PEG molecules “sheathing” the BDNF from “unfavourable binding interactions”

7. Intestinal uptake of nanoparticles

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Fig 7 illustrates schematically some of the issues of nanoparticle delivery to the intestinal epithelium. Nanoparticle uptake has been studied for over 80 years and has been the subject of several reviews to consider the relatively poor percentage uptake of systems, which it has been suggested is optimal with particles around 50nm in diameter [57-61]. The holy grail of protein (especially insulin) delivery by the oral route is still to be attained some 90 years after it was first attempted. Hence it is useful to consider here some of the issues. Most of the particulate absorption achieved is by way of the GALT where the domes of Peyer’s patches are free of villi and mucus. The specialised M-cells allow viral, antigen and particle uptake, depending on the nature of the particles. The access to both the Peyer’s patches and the intestinal villous regions are topographically complex, leading to obstructive effects on diffusion, but there are many factors which lead to a reduction in the probability of particle interaction with the epithelial cells and thus absorption, not least that of the admixture of nanoparticles with gut contents.

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[FIGURE 7]

The presence of mucus, unstirred water layers, the rheology in the interstices of the villi, the motion of the villi in affects fluid flow and also the bifurcations – the “choice” the particle has to make of villous “cavity”. Many of these aspects of nanoparticle flux have been discussed in the literature from a basic point of view, but some do address the issue of drug and particle absorption. It has been demonstrated that oral absorption of nanoparticles is limited to around 5% of the administered dose of hydrophobic particles [62, 63]. Few if any papers have 11

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shown values significantly higher with all manner of constructs. It has to be emphasised that the dose of nanoparticle does not indicate dose of drug as few nanoparticles comprise only drug. Many experimental systems have only very low loading capacity, hence not only the total dose delivered to the specific site is compromised but the rate at which drug will diffuse from the system may also be reduced. Success will thus be difficult to achieve. The nanoparticles also are not in a straightforward suspension but mixed with gut contents: their “availability” for absorption is compromised. For any drug particle successfully absorbed the journey towards sites of action starts with passage via the lymph and bile ducts [64] to the systemic circulation. Within the gut, nanoparticles can be endogenous particles formed from recrystallization/precipitation of calcium phosphate and it is thought these are reabsorbed through the Peyer’s patches. On the other hand, exogenous nanoparticles can reach the gut through ingestion of organic and inorganic nutrients such as titanium oxide and ferritin nanoparticles [65]. The extent of oral absorption of the gamut of nanoparticles now under investigation is still the focus of research [64, 66]. It is hazardous to generalise.

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An analogy to what happens in the small intestine may be seen in a perhaps rather extreme physical model of “dead ends” [67-69]. Particles can diffuse along a tube with repeated dead ends separated from each other by a distance (l) (Fig 8) [67]. As a particle moves along the tube, it may enter the dead ends where subdiffusion causes its movement to be restricted until it is able to escape. The dimensions of the tube are defined as the radius (r), length (l) and volume for the dead ends (Vcav). The diffusion coefficient (D) at time (t) and position x can be defined (equation 9) , thus defining the probability (P) of finding the particle in a dead end along the tube at time (t) in relation to its original position (x0). The larger the number of the dead ends the greater the probability for the particle to be confined and therefore corralled diffusion is directly proportional to the formed cavities within the suggested tube [67].

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D(t) =

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It is interesting that when considering effective diffusion in the ECS of the brain that dead-end pores increase tortuosity and hence reduce the overall diffusion of particles and molecules, by “providing an extra space where molecules can be delayed” [64] [FIGURE 8]

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[FIGURE 9]

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Multiple tracking has been used to understand the impact of the thickness of mucus on the diffusion of particles across the gut epithelium (Fig 9) [70]. Polystyrene particles (0.5 µm) were tracked using ex vivo preparations of the wall of the terminal ileum and proximal colon of the exotic model - the brushtail possum (Trichosurus vulpecula). Heterogeneous viscoelastic regions were found on the mucosa while other elements were covered by Newtonian fluid with a viscosity close to water. Differences in terms of viscosity and areas of viscoelasticity were observed between the ileal and the colonic mucosa while insignificant differences were observed within the intestinal mucosa (see Figure 9).

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The questions to be posed here include : a) does the sub-diffusion of particles in the cavity created by the villus structures lead to an advantage in terms of allowing access to the epithelium and hence absorption by way of enterocytes?; b) do the bifurcations (which we discuss below) reduce the opportunity for access to absorbing membranes? c) what is the role of mucus? d) what is the role played by the microvilli? Villi lengths range up to 400μm in humans. They are not static and their “wavy and whip-like” motion causes there to be fluid eddies around the villi; without this motion Wang and coworkers [71] suggest that due to the tight packing of the villi the fluid between would be static, or in their words, “nearly stagnant”. Hence diffusion of particles will be accompanied by their forced motion through eddies, when fluid is transported to and from the villi. Diffusion is thus enhanced, but not readily estimated. The evidence that the GALT is the preferred mode of entry of nanoparticles suggests that the villous and microvillous “cavities” might themselves impede uptake. So do the microvilli have a role in capturing nanoparticles? The dimensions of human jejunal microvilli have been reported [72] to be, on the crest cells, some 1360nm in height and 80nm in diameter, with a spacing of 200nm, while those on the intervillous surfaces were on average 1000nm in height and 100nm in diameter. Hence the microvilli provide corrals, as a 100nm particle will have a tight fit if the distance between microvilli is, as it appears to be around at most 200nm. Fig 10 shows the possible impact of microvilli on nanoparticles uptake by the intestinal epithelium. The limits of space in the corral suggest that contacts with the epithelial cells will be frequent, although the concentration of particles might be low. There seem to be few publications with visual evidence of nanoparticles close to the microvilli. Transmission electron micrographs of 17-23nm gold nanoparticles show clusters adjacent to the gut microvilli of Daphnia magnum and a particle which appears to have entered a microvillus, overall uptake was very low [73]. Wickline et al. [74, 75] showed that large

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numbers of particles bearing an αϒβ3–integrin binding ligand were associated with the microvilli and plasma membranes of C32 melanoma cells, while the undecorated particles were not. Fast absorption of nanoparticles may be attributed, Mesiha and colleagues suggest, to the increased chances of the ultra fine particles below 100 nm being entrapped between the villi and microvilli of the intestine” [76].

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8. The intravenous route: capillary flow, extravasation and jamming

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The intravenous route is the primary and perhaps most direct route of administration of experimental nanosystems. When injected intravenously there is of course immediate contact with blood. Some particles adhere to red blood cells (RBCs) hence their movement is dictated not only by the properties of the nanoparticle but by those of the erythrocytes. Diffusion of RBCs has been the focus of different studies because of the importance of understanding the movement of the blood cells for essential body functions. The first requirement for a drug delivery carrier is to escape reticuloendothelial selective uptake and thus to maintain longer circulation times [77].

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Particle flow clearly occurs in the complex medium of the blood itself and in the network of vessels and capillaries which provide particle traps. En route to extravasation sites particles circulate in vessels with their varying dimensions, branches and sometimes blockages. Decuzzi et al [78] have discussed carrier shape and size effects in vascular delivery. If particles are to reach distant targets - that is non-vascular targets – they must extravasate in sufficient numbers. This preliminary part of the enhanced permeation and retention (EPR) effect is a stochastic process: not every particle enters the extracellular space or tumours. Those that do – and the statistical chances are enhanced by recirculation of the particles - may not reach their target because of jamming of particles at exits from the circulation. Extravasation thus involves the particle “finding” the escape, and this will depend on the relative size of the particle, its charge and the diameter of the “window”. Perrault et al. [68] have discussed the effect of particle size and surface chemistry on the extent of diffusion across tumor tissues [79] to evaluate the payload at the tumor site, using a series of core particles decorated with PEG chains of different length. The correlation between half-life and uptake is not necessarily intuitive. Both the core diameter and the hydrodynamic diameter appear to be important. With core diameters

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The constrained Brownian movement and the hindered diffusion of particles in pores [80] is relevant to extravasation. Jamming might occur when nanoparticles pass through the fenestrae. “What is the volume of suspension that flows through a small orifice before it clogs?” is the title of a paper by Goldsztein [81]. He replies by saying this depends on the volume fraction of the suspension, the frictional forces at play and the ratio of orifice to particle diameters. There will be hindered diffusion (up to an order of magnitude) even if the (solid) particle radius is only one third of radius of the pore [82]. Flexible systems such as colloidal gels and macromolecular carriers might be less susceptible to arrest. Jamming is important in many situations in vivo. It is discussed in a review by Siemens and van Hecke [83]. The physics involved is not trivial! A free-flowing suspension may be converted to the solid state but can be refluidised by applied stress, temperature or vibration [84]. Disc-shaped particles can be jammed by application of shear stress [85], hence the size, shape, charge and surface nature of particles is clearly important in this and other critical processes in the movement of particles from administration site to target site. These interactions and jamming, can be enhanced by attraction between particle and pore or channel surface but they occur also with particles much smaller than the orifice (Fig 12) [86]. Ellipsoidal particles have been shown to jam randomly more readily than spherical particles [87-89]. The interest, in the context of this review, however, is the effect that these processes have on overall transport times, how to avoid them and to what extent such physicochemical events prevent full access to the extracellular matrix. 9. Diffusion in the extracellular matrix

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Normal and tumour tissues are composed of three different compartments, vascular, interstitial, and cellular. For the drug molecules to reach tumour cells they must distribute across the vascular space, diffuse through the interstitial space and finally diffuse across cell membranes. All these steps can happen providing the systems do not undergo non-specific binding to plasma proteins or other structures nor are metabolised or degraded.. The biological structures of a solid tumour have been known to be distinctly different from normal tissues. Reasons for these differences include the high interstitial fluid pressure (IFP) and increased stiffness of tumor extracellular matrix (ECM). These modifications of the tumor structure can significantly limit drug diffusion. For the drug to reach the core of the tumor mass it has to diffuse across the collagen fibers and 15

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distribute throughout the tumour tissue. Accumulation of the drug in the interstitial space of the tumor is essential to achieve maximum treatment efficiency. The extracellular matrix of tumour tissue is structurally heterogeneous as it consists of proteoglycans, hyaluronic acid, collagen, elastin, laminin, and other structural proteins. The heterogeneity of the matrix represents a changing barrier to diffusion of nanoparticles or molecules. Different types of interactions exist such as steric interactions with the matrix fibers, solvation interactions and, for charged partiles molecules, electrostatic interactions with charged organelles within the matrix.

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In order to give cells rigidity, support and networks through which nutrients can be distributed, cells are surrounded by an extracellular space (ECS), which is largely made-up of a network of macromolecules forming the extracellular matrix (ECM). The extracellular space is comprised of the interstitial fluid, blood lymph and the extracellular matrix. Protein fibres along with a network of glycosamino-glycan (negatively charged polysaccharides) chains form the bulk of the matrix, the latter constituting a gel layer in which the cells are embedded. Elastic fibres along with collagen form the bulk of the ECM of many tissues such as skin, blood and lungs. The structure of the matrix influences the mechanical properties of cells by affecting cytoskeleton structure; as the matrix covers the cell, the composition of the matrix can also affect cell function by binding to cellsurface receptors and altering the intracellular uptake mechanisms [90]. The extracellular spaces change in diameter as cells divide and grow. A tortuosity factor λ describes the hindrance in diffusion in situations where there are obstructions. It is defined as

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(λ = √[D/D*])

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where D is the diffusion coefficient in free suspensions and D* is the effective diffusion coefficient in the medium in question. The volume of the ECS divided by the total volume of the tissue results in the volume fraction of the ECS. For example in the grey matter of the brain the volume fraction is about 20% and the tortuosity factor is thus circa 1.6 [91]. It has been was found that the hindrance to diffusion depends mainly on the volume fraction of the ECS and is independent of cell shape [92] but this is difficult to follow if we consider the diagram in Figure 11 where changes in cell shape clearly affect, through pathway constrictions, the free movement of particles. These varied channel widths also can explain the causes of the heterogeneous nature of drug molecule and particle distribution in tumours. Single-file diffusion may occur in the narrowest constrictions, a topic that is dealt with by Burada and colleagues [93]. Particles may be constrained in static fluid or dragged by fluid flow; particles which are close to the dimensions of the space can be “hampered” by the presence of neighbouring particles which become in effect, in the words of these

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The charge on the drug carrier has been shown to be vital to achieve higher accumulation of the drug in some tumour tissues. This is in line with the heterogeneous nature of the extracellular matrix and the significant occurrence of polysaccharides. Interaction of nanocarriers with protein chains can also decrease particulate diffusion. The organization of collagen and elastin within the extracellular space is not uniform and largely depends on the function of the tissue. In addition to glycosaminoglycan, hydrophilic hyaluronan chains are extensively hydrated and may therefore contribute to the higher viscosity of the matrix. However it is the microscopic viscosity – that experienced by the individual particles that is key, rather than the overall bulk rheological characteristics of the medium. Diffusion coefficients of 30nm gold particles in the ECM range from 1.1 –1.7 x 10-9 cm2 s-1, a factor of 5x lower than the diffusion coefficients in simple fluids (5.4-9.5 x 10-9 cm2 s-1). Larger particles would be expected to experience greater retardation. 10. Diffusion in brain tissues (after access)

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There have been many reports on the uptake of nanoparticles after intravenous injection across the blood-brain barrier (BBB) , notably by Kreuter and colleagues [94]. The role of simple diffusion was questioned for delivery of polysorbate 20 coated nanoparticle loaded with loperamide crossing the blood brain barrier [95]. This topic of access via the BBB is not discussed here. Rather we concentrate on the fate of nanoparticles once they reach the brain tissue whether by this route or by direct injection into diseased tissue. As discussed elsewhere [96], both diffusion of the active from the formulation and diffusion and transport of the nanoparticles and released drug is important. Some drugs themselves, such as paclitaxel, diffuse over only small distances (millimetres) from delivery systems deposited in the brain. A pellet loaded with NGF spreads only 2-3mm into rat brain tissue [97]. Hence the transport and positioning of nanoparticles is crucial in reaching target tissue. Stereotaxic administration now is aided by advances in imaging technology. The release of neurotransmitters at the presynaptic junctions in the brain is a diffusional process involving GABA, serotonin and acetylcholine and other agents, hence understanding diffusion can be critical to understanding these basic mechanisms as well as drug and particle delivery. The role of the extracellular matrix is essential in oxygen diffusion along with other essential nutrients and ions. The processes of signalling, transmission and nutrients exchange are all based on diffusion. It is especially important to recognise that diffusion might depend also on the presence of brain

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ACCEPTED MANUSCRIPT disorders such as inflammatory and demyelinating diseases [98]. The diffusion of C14-orotic acid across hippocampal slice preparations was seen in one study to be enhanced significantly when the drug was loaded into nanoparticles [99].

11. Diffusion in cells

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The geometric and viscous elements of the tortuosity of the brain ECS has been studied [100]. The width of the ECS has been estimated in some cases to be around 20 - 64nm [101, 102] and that in ischemia it is smaller [103]. Clearly this has implications for nanocarrier delivery, but there have been divergent views about the maximum size for nanoparticle diffusion. These results suggest that diffusion of nanoparticles is extremely challenging and may require modification to the nanoparticle surface to allow penetration of the brain parenchyma. One study suggests that after penetration, paclitaxel-loaded nanoparticles coated with a low molecular weight polyethylene glycol (PEG) were able to spread rapidly with a rat brain [104]. The size of these nanoparticles was between 40-100nm, but delivery of particles up to 200nm was suggested to be possible. The nature of the surface coating was found to be significant as -COOH coated nanoparticles diffused 2300 times more slowly than PEG coated nanoparticles. Polysorbate 80 coated nanoparticles have incidentally also been found to be able to cross the blood brain barrier [105].

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The ultimate destination of many targeted systems are the cells of tumours or diseased organs. For gene therapy the target is the nucleus. It is sometimes at these latter stages that therapies based on nanosystems fail, at the last hurdle in a difficult course. Fig 13 indicates in simple terms the barriers present to free diffusion of systems within a cell with organelles such as the endoplasmic reticulum, Golgi bodies and mitochondria. [FIGURE 12]

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A balance between the adhesion of diffusing nanoparticles and hydrodynamic radius is necessary for maximum uptake by cells; nanoparticles from 100-200nm diameter are able to cross the cell membrane without the need of clathrins [20]. This balance determines the interaction with the surface of the cell membrane and also determines how fast the nanoparticles can diffuse across the cell membrane [20, 106]. Regardless of the mechanisms of cellular uptake, nanoparticles must reach the interior of the cell. If drug is released inside the cell, perhaps nanoparticle diffusion is less of an issue, but to enter the nucleus particles or drugs must have access to the nuclear pores. Once nanoparticles reach the cell their fate may depend on the extent that diffusion is controlling movement, and on the point of the cell cycle as reported by Selhuber-Unkel et al for endogenous lipid granules [107]. The cytoplasm is less viscous during 18

ACCEPTED MANUSCRIPT interphase in the system studied. Cytoplasmic streaming can also affect diffusional processes, so the cell contents are far from static. In addition to normal Brownian motion of solutes and particles there is a disturbance of the cytoplasm by the action of molecular motors [108] to produce “enhanced diffusion dynamics” which they surmise may resemble the “vital activity” observed by Robert Brown.

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[FIGURE 13]

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Gene delivery systems, drugs such as doxorubicin and other nanosystems require entry to the nucleus. This occurs by either passive and/or facilitated modes; it is in the former that diffusion is to the fore.

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Entry is naturally constrained but somewhat less than has been thought, being for proteins greater than the 60kDa postulated [109]. Much will depend on the shape and flexibility of the transporting material, but the 9-12nm diameter limit has been applied to proteins. Other figures of 30-40nm and 20-70nm have been suggested. If this is considered to be the limit for nanoparticles, many systems being investigated now would not succeed in entering the nucleus. However Jang and colleagues have shown otherwise: that nanoparticles larger than the nuclear pore by spontaneously degrading and allowing free diffusion of their encapsulated load of doxorubicin to diffuse and enter the nucleus to intercalate with DNA [110]. The nuclear pore complex and its action as a gateway has been declared a mystery [111]. Each pore, of which there are an estimated 1000 to 10,000 per cell, is not a simple object but, it is argued, a pore filled with a reversible gel [111] or a polymer brush [112]. There is support for both, where size is a criterion for entry, and surface charge might also lead to additional complications should there interactions with the polymeric material inside the pore. It is also argued that a reversible gel structure would allow faster diffusion of material via the pore [113, 114]. Movement within the nucleus is a specialised topic in itself.

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12. Conclusions This overview has highlighted some of the areas and factors which affect diffusion of nanocarriers and ultimately the drugs and actives that they carry. While many individual factors such as obstruction effects can be quantified, there is no analysis which will a priori determine overall outcomes. The extent to which the diffusional characteristics can be manipulated (e.g. by using smaller particle dimensions, avoiding blockage and jamming or by deaggregating complexes) may go some way to avoid poor performance. Simple diffusion plays a major role in many biological, chemical and physical processes. However,

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diffusion of nanoparticles is affected not only by the properties of the particles themselves, but also by particle-particle and particle-barrier interactions, by fluid flow in vivo and by the many obstacles they encounter after administration. The balance between the different types of diffusion (subdiffusion, superdiffusion and normal diffusion) and the role of convection and fluid flow depends on the nature of the environment. Drug release from drug macroscopic and nanoscopic vehicles depends to an extent on the viscosity of the environment, which can slow down diffusion leading to sub-diffusion. The size of the nanoparticles is always a major factor, as is the nature of the natural, modified or decorated surface of the particles which can influence their behaviour in suspension and flow and interaction with the biological environment. The rate at which molecules or nanoparticles move around is complex and requires further understanding of diffusion in all circumstances and the impact of sub-diffusion or super-diffusion on overall transport kinetics.

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Nearly all the topics discussed in this short review can be investigated in more theoretical depth. Above all we need further information on the rate-limiting steps in the trajectory from administration to target, and the summation of probabilities for each step. All this has to go hand in hand with achieving maximal loading of nanocarriers with the most potent drugs and therapeutic actives.. “One is always nearer by not keeping still” refers to both nanoparticles and to our collective scientific endeavours.

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ACCEPTED MANUSCRIPT H.Al-Obaidi and A.T. Florence: Figure legends Figure 1: A scheme (images not to scale) showing some of the corrals, dead-ends, archipelagos

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and presque-îles (not unlike geographic coastlines) and other causes of sub-diffusion of nanoparticles. After oral administration of nanoparticles, a proportion of which can be absorbed by the gut associated lymph tissue (GALT) given the right surface structures and size, and then translocate via the mesenteric lymph into the blood supply and some may cross the blood brain barrier (BBB). In the lymph vessels particles of a certain size may move in single file as shown. Others may be absorbed by enterocytes after movement in between villi and microvilli. The IV route supplies nanoparticles directly into the blood where a proportion can be extravasated after each circulation before entering the anisotropic extracellular space (ECS) and the extracellular matrix (ECM). The crowded interior of the cell and the nucleus provide further barriers to free diffusion. The brain provides additional challenges, even after direct administration of particles or implants.

Figure 2: A simulation of particle movement by means of diffusion (N=500) . The particles are

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red, the areas “visited” are in white while the as yet unexplored territory is in black. From H. Larralde et al. Nature, 1992, 355, 423-426.

Figure 3: Representation of the Brownian movement of particles in simple and confined systems, in convective situations, or with physical barriers, rafts or where there are for example repulsive interactions between particles (which can accelerate particles). From S. Jin and A.S. Verkman, J.Phys.Chem.,B, 2007, 111, 3625-3622.

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Figure 4: Schematic showing correlation between time and mean squared displacement (MSD) for a moving particle in different environments. If movement if not restricted then normal Brownian motion is expected, while within boundaries corralled diffusion or subdiffusion of the particles would be observed. When there is an accelerated movement of the particle due to repulsion between the particles then superdiffusion results. Figure 5: Left diagram: schematic (showing the trajectory of four 1μm polystyrene particles of

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the total of more than 15 microparticles inside a large liposome. The particles may exhibit (see diagram on right) electrostatic and van der Waals interactions (1, 2, and 3) or electrostatic repulsion (4, 5, and 6) with the membrane as well as with other particles. From H. Al-Obaidi et al., J. Drug Targeting, 2010, 18, 821-830

Figure 6: Diffusion in gels and other media may be complicated by interactions and trapping between the diffusing particles and structures. Two types of filtering can occur inbiopolymerbased hydrogels (a) Size filtering allows particles that are smaller than the cut-off size of the hydrogel to pass, while larger particles cannot; (b) Interaction filtering is a mechanism whereby oppositely charged particles interact with the polymer chains leading to passage of neutral particles while the charged particles are prevented. From Lieleg, O. and K. Ribbeck. Trends in Cell Biology, 2011. 21, 543-551.

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Schematic (upper histological sections; below a diagrammatic representation) showing the factors that can affect delivery of nanoparticles across the intestinal epithelium. The main portal of entry of nanoparticles (and antigens) are the M-cells of the Peyer’s patches in the gut-associated lymphoid tissue (GALT). There freedom from villi and mucus allows more secure access to the absorbing M-cells. The topography of the villus membranes is complex. The villi are not static which complicates flow patterns around them. As listed (Top Right) the first barrier to uptake is the mucus covering in part the epithelium. The unstirred water layers can also hinder movement. Bifurcations at the base of the villi can trap some of the nanoparticles. Microvilli offer a tighter environment (see Figure 10). Absorption via the lymphoid tissue allows particles to enter the lymphatic system and hence the blood.

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Figure 8. The model consisting of a tube with multiple dead ends – which could be considered to be an idealised (but extreme) unilateral model of the villous structures and opportunities for particle ingress and escape. From Dagdug, L., et al., J Chem Phys, 2007. 127, 224712.

Figure 9: Viscoelastic regions estimated to surround the GI villi as postulated by Y.F. Lim et al.,

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J. R. Soc, Interface 2013, 201, 210121008.

Figure 10: Schematic showing a suggested model for presence of nanoparticles in villous

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regions (upper drawing). Initially the particles will diffuse towards the epithelium covered by the villi by means of Brownian motion. The particles are then expected to experience hindered diffusion in corrals formed by the microvilli. The arrows in the top image indicate the movement of the nanoparticles due to concentration gradient from the lumen towards the surface while arrows in the insert image represent restricted movement of the nanoparticles. The movement of the villi causes additional complications to interpretation.

Figure 11: A model based on microscopy illustrating the markedly different channels in the

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ECS. The change in the size of tumour cells during growth puts pressure on the channels hence the routes for particle movement are constantly changing in length and width. It is possible to that constriction of the spaces lead to the formation of “dead ends” discussed earlier. Diagram from K.C. Chen and C. Nicholson, Proc. Nat. Ac. Sci.,USA, 2000, 97, 8306-8311.

Figure 12: Cartoon to illustrate the crowded interior of a cell illustrating the likelihood of

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corralled and obstructed diffusion can occur inside human cells, because of impedance by cellular organelles such as the cytoskeleton of the cell. Eventually, the particles may cross the nucleus through the nuclear pores of which there are estimated to be over 1000 per cell. The cytoplasm is believed to be stirred by the movement of molecular motors(not shown).

Figure 13: Diagram of the nuclear pore complex NPC) showing the reversible gel or polymer brush entrance. Picture from S.S. Patel et al., Cell, 2007,129, 83-96.

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