Diffusion of Particles in the Extracellular Matrix: The Effect of Repulsive Electrostatic Interactions

Diffusive transport of macromolecules and nanoparticles in charged fibrous media is of interest in many biological applications, including drug delivery and separation processes. Experimental findings have shown that diffusion can be significantly hindered by electrostatic interactions between the diffusing particle and charged components of the extracellular matrix. The implications, however, have not been analyzed rigorously. Here, we present a mathematical framework to study the effect of charge on the diffusive transport of macromolecules and nanoparticles in the extracellular matrix of biological tissues. The model takes into account steric, hydrodynamic, and electrostatic interactions. We show that when the fiber size is comparable to the Debye length, electrostatic forces between the fibers and the particles result in slowed diffusion. However, as the fiber diameter increases the repulsive forces become less important. Our results explain the experimental observations that neutral particles diffuse faster than charged particles. Taken together, we conclude that optimal particles for delivery to tumors should be initially cationic to target the tumor vessels and then change to neutral charge after exiting the blood vessels.     

A theoretical study of rotational diffusion models for rod-shaped viruses. The influence of motion on 31P nuclear magnetic resonance lineshapes and transversal relaxation.

Information about the interaction between nucleic acids and coat proteins in intact virus particles may be obtained by studying the restricted backbone dynamics of the incapsulated nucleic acids using 31P nuclear magnetic resonance (NMR) spectroscopy. In this article, simulations are carried out to investigate how reorientation of a rod-shaped virus particle as a whole and isolated nucleic acid motions within the virion influence the 31P NMR lineshape and transversal relaxation dominated by the phosphorus chemical shift anisotropy. Two opposite cases are considered on a theoretical level. First, isotropic rotational diffusion is used as a model for mobile nucleic acids that are loosely or partially bound to the protein coat. The effect of this type of diffusion on lineshape and transversal relaxation is calculated by solving the stochastic Liouville equation by an expansion in spherical functions. Next, uniaxial rotational diffusion is assumed to represent the mobility of phosphorus in a virion that rotates as a rigid rod about its length axis. This type of diffusion is approximated by an exchange process among discrete sites. As turns out from these simulations, the amplitude and the frequency of the motion can only be unequivocally determined from experimental data by a combined analysis of the lineshape and the transversal relaxation. In the fast motional region both the isotropic and the uniaxial diffusion model predict the same transversal relaxation as the Redfield theory. For very slow motion, transversal relaxation resembles the nonexponential relaxation as observed for water molecules undergoing translational diffusion in a magnetic field gradient. In this frequency region T2e is inversely proportional to the cube root of the diffusion coefficient. In addition to the isotropic and uniaxial diffusion models, a third model is presented, in which fast restricted nucleic acid backbone motions dominating the lineshape are superimposed on a slow rotation of the virion about its length axis, dominating transversal relaxation. In an accompanying article the models are applied to the 31P NMR results obtained for bacteriophage M13 and tobacco mosaic virus.     

Subdiffusive Dynamics Lead to Depleted Particle Densities near Cellular Borders

It has long been known that the complex cellular environment leads to anomalous motion of intracellular particles. At a gross level, this is characterized by mean-squared displacements that deviate from the standard linear profile. Statistical analysis of particle trajectories has helped further elucidate how different characteristics of the cellular environment can introduce different types of anomalousness. A significant majority of this literature has, however, focused on characterizing the properties of trajectories that do not interact with cell borders (e.g., cell membrane or nucleus). Numerous biological processes ranging from protein activation to exocytosis, however, require particles to be near a membrane. This study investigates the consequences of a canonical type of subdiffusive motion, fractional Brownian motion, and its physical analog, generalized Langevin equation dynamics, on the spatial localization of particles near reflecting boundaries. Results show that this type of subdiffusive motion leads to the formation of significant zones of depleted particle density near boundaries and that this effect is independent of the specific model details encoding those dynamics. Rather, these depletion layers are a natural and robust consequence of the anticorrelated nature of motion increments that is at the core of fractional Brownian motion (or alternatively generalized Langevin equation) dynamics. If such depletion zones are present, it would be of profound importance given the wide array of signaling and transport processes that occur near membranes. If not, that would suggest our understanding of this type of anomalous motion may be flawed. Either way, this result points to the need to further investigate the consequences of anomalous particle motions near cell borders from both theoretical and experimental perspectives.     

Selective Filtering of Particles by the Extracellular Matrix: An Electrostatic Bandpass

The transport of microscopic particles such as growth factors, proteins, or drugs through the extracellular matrix (ECM) is based on diffusion, a ubiquitous mechanism in nature. The ECM shapes the local distribution of the transported macromolecules and at the same time constitutes an important barrier toward infectious agents. To fulfill these competing tasks, the hydrogels have to employ highly selective filtering mechanisms. Yet, the underlying microscopic principles are still an enigma in cell biology and drug delivery. Here, we show that the extracellular matrix presents an effective electrostatic bandpass, suppressing the diffusive motion of both positively and negatively charged objects. This mechanism allows uncharged particles to easily diffuse through the matrix, while charged particles are effectively trapped. However, by tuning the strength of this physical interaction of the particles with the biopolymer matrix, the microscopic mobility of formerly trapped particles can be rescued on demand. Moreover, we identify heparan sulfate chains to be one important key factor for the barrier function of the extracellular matrix. We propose that localized charge patches in the ECM are responsible for its highly unspecific but strongly selective filtering effect. Such localized interactions could also account for the observed tunability and selectivity of many other important permeability barriers that are established by biopolymer-based hydrogels, e.g., the mucus layer of endothelial cells or the hydrogel in the nuclear core complex.     

PEGylation of nanoparticles improves their cytoplasmic transport

The efficacy of nucleus-targeted drug- or gene-carrying nanoparticles may be limited by slow transport through the molecularly crowded cytoplasm following endosome escape. Cytoskeletal elements and cellular organelles may pose steric and/or adhesive obstacles to the efficient intracellular transport of nanoparticles. To potentially reduce adhesive interactions of colloids with intracellular components, the surface of model nanoparticles was coated with polyethylene glycol (PEG). Subsequently, multiple-particle tracking (MPT) was used to quantify the cytoplasmic transport rates of particles microinjected into the cytoplasm of live cells. PEGylation increased average nanoparticle diffusivities by 100% compared to unPEGylated particles (time scale of 10 s) in live cells. Faster particle transport correlated with a marked decrease in the number of particles that underwent hindered transport, from 79.2% (unmodified) to 48.8% (PEGylated). This result adds to an impressive list of positive benefits associated with PEGylation of drug and gene delivery vectors.     

Particle Transport through Hydrogels Is Charge Asymmetric

Transport processes within biological polymer networks, including mucus and the extracellular matrix, play an important role in the human body, where they serve as a filter for the exchange of molecules and nanoparticles. Such polymer networks are complex and heterogeneous hydrogel environments that regulate diffusive processes through finely tuned particle-network interactions. In this work, we present experimental and theoretical studies to examine the role of electrostatics on the basic mechanisms governing the diffusion of charged probe molecules inside model polymer networks. Translational diffusion coefficients are determined by fluorescence correlation spectroscopy measurements for probe molecules in uncharged as well as cationic and anionic polymer solutions. We show that particle transport in the charged hydrogels is highly asymmetric, with diffusion slowed down much more by electrostatic attraction than by repulsion, and that the filtering capability of the gel is sensitive to the solution ionic strength. Brownian dynamics simulations of a simple model are used to examine key parameters, including interaction strength and interaction range within the model networks. Simulations, which are in quantitative agreement with our experiments, reveal the charge asymmetry to be due to the sticking of particles at the vertices of the oppositely charged polymer networks.     

Mannitol-guided delivery of Ciprofloxacin in artificial cystic fibrosis mucus model

Abnormal airway mucus presents a significant challenge for inhalational drug delivery. Recognizing the thick and tenacious airway mucus seen in the cystic fibrosis (CF) patients as a critical barrier to effective drug delivery, both into the mucus layer itself as well as across that layer to the underlying airway epithelium, we hypothesize that mannitol or NaCl can form inhalable drug carriers, improve drug penetration into the mucus, and ultimately enhance the drug's therapeutic effect. The objective of this study is to test whether mannitol and NaCl particles, as inhalable drug carriers, improve drug delivery into and enhance a drug's activity within a mucus-like material. Microparticles containing Ciprofloxacin (Cipro), an active ingredient, and either mannitol or NaCl were produced by spray-drying. Cipro encapsulated in mannitol particles (Cipro-mannitol) was significantly more effective at killing Pseudomonas aeruginosa (P. aeruginosa) grown in artificial mucus (AM) than Cipro encapsulated in either NaCl particles (Cipro-NaCl) or in hydrophobic particles consisting of dipalmitoylphosphatidylcholine (DPPC), albumin, and lactose (Cipro-DAL). The relatively high antibacterial effectiveness of Cipro-mannitol was not due to the effect of mannitol on bacteria or on Cipro. Rather, the unique performance of the mannitol-based particles in AM is attributable to its ability to increase local water content in the AM and enhance drug penetration into it. Mannitol is a promising excipient for inhalable microparticles that facilitate the drug delivery into the CF mucus.     

Spatial configuration of charge and hydrophobicity tune particle transport through mucus

Mucus is a selectively permeable hydrogel that protects wet epithelia from pathogen invasion and poses a barrier to drug delivery. Determining the parameters of a particle that promote or prevent passage through mucus is critical, as it will enable predictions about the mucosal passage of pathogens and inform the design of therapeutics. The effect of particle net charge and size on mucosal transport has been characterized using simple model particles; however, predictions of mucosal passage remain challenging. Here, we utilize rationally designed peptides to examine the integrated contributions of charge, hydrophobicity, and spatial configuration on mucosal transport. We find that net charge does not entirely predict transport. Specifically, for cationic peptides, the inclusion of hydrophobic residues and the position of charged and hydrophobic residues within the peptide impact mucosal transport. We have developed a simple model of mucosal transport that predicts how previously unexplored amino acid sequences achieve slow versus fast passage through mucus. This model may be used as a basis to predict transport behavior of natural peptide-based particles, such as antimicrobial peptides or viruses, and assist in the engineering of synthetic sequences with desired transport properties.     

Development of a computational fluid dynamics model for mucociliary clearance in the nasal cavity

Intranasal drug delivery has attracted significant attention because of the opportunity to deliver systemic drugs directly to the blood stream. However, the mucociliary clearance poses a challenge in gaining high efficacy of intranasal drug delivery because cilia continuously carry the mucus blanket towards the laryngeal region. To better understand mucus flow behaviour on the human nasal cavity wall, we present computational model development, and evaluation of mucus motion on a realistic nasal cavity model reconstructed from CT-scans. The model development involved two approaches based on the actual nasal cavity geometry namely: (i) unwrapped-surface model in 2D domain and (ii) 3D-shell model. Conservation equations of fluid motion were applied to the domains, where a mucus production source term was used to initiate the mucus motion. The analysis included mucus flow patterns, virtual saccharin tests and quantitative velocity magnitude analysis, which demonstrated that the 3D-shell model results provided better agreement with experimental data. The unwrapped-surface model also suffered from mesh-deformations during the unwrapping stage and this led to higher mucus velocity compared to experimental data. Therefore, the 3D-shell model was recommended for future mucus flow simulations. As a first step towards mucus motion modelling this study provides important information that accurately simulates a mucus velocity field on a human nasal cavity wall, for assessment of toxicology and efficacy of intranasal drug delivery.     

Local motion analysis reveals impact of the dynamic cytoskeleton on intracellular subdiffusion

Intracellular transport is a complex interplay of ballistic transport along filaments and of diffusive motion, reliably delivering material and allowing for cell differentiation, migration, and proliferation. The diffusive regime, including subdiffusive, Brownian, and superdiffusive motion, is of particular interest for inferring information about the dynamics of the cytoskeleton morphology during intracellular transport. The influence of dynamic cytoskeletal states on intracellular transport are investigated in Dictyostelium discoideum cells by single particle tracking of fluorescent nanoparticles, to relate quantitative motion parameters and intracellular processes before and after cytoskeletal disruption. A local mean-square displacement (MSD) analysis separates ballistic motion phases, which we exclude here, from diffusive nanoparticle motion. In this study, we focus on intracellular subdiffusion and elucidate lag-time dependence, with particular focus on the impact of cytoskeleton compartments like microtubules and actin filaments. This method proves useful for binary motion state distributions. Experimental results are compared to simulations of a data-driven Langevin model with finite velocity correlations that captures essential statistical features of the local MSD algorithm. Specifically, the values of the mean MSD exponent and effective diffusion coefficients can be traced back to negative correlations of the motion's increments. We clearly identify both microtubules and actin filaments as the cause for intracellular subdiffusion and show that actin-microtubule cross talk exerts viscosifying effects at timescales larger than 0.2 s. Our findings might give insights into material transport and information exchange in living cells, which might facilitate gaining control over cell functions.     

Crowding Effects in Vehicular Traffic

While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of crowding due to car density and driving fluctuations on the transport of vehicles. Using a microscopic model for traffic, we found that crowding can push car movement from a superballistic down to a subdiffusive state. The transition is also associated with a change in the shape of the probability distribution of positions from a negatively-skewed normal to an exponential distribution. Moreover, crowding broadens the distribution of cars’ trap times and cluster sizes. At steady state, the subdiffusive state persists only when there is a large variability in car speeds. We further relate our work to prior findings from random walk models of transport in cellular systems.     

Intracellular transport dynamics of endosomes containing DNA polyplexes along the microtubule network

We have explored the transport of DNA polyplexes enclosed in endosomes within the cellular environment by multiple particle tracking (MPT). The polyplex-loaded endosomes demonstrate enhanced diffusion at short timescales (t<7 s) with their mean-square displacement (MSD) Deltax(t)2 scaling as t1.25. For longer time intervals they exhibit subdiffusive transport and have an MSD scaling as t0.7. This crossover from an enhanced diffusion to a subdiffusive regime can be explained by considering the action of motor proteins that actively transport these endosomes along the cellular microtubule network and the thermal bending modes of the microtubule network itself.     

Engineering Lipid Vesicles of Enhanced Intratumoral Transport Capabilities: Correlating Liposome Characteristics with Penetration into Human Prostate Tumor Spheroids

Liposomes have been widely used delivery systems, particularly relevant to the development of cancer therapeutics. Numerous liposome-based drugs are in the clinic or in clinical trials today against multiple tumor types; however, systematic studies of liposome interactions with solid or metastatic tumor nodules are scarce. This study is describing the in vitro interaction between liposomes and avascular human prostate (LNCaP-LN3) tumor spheroids. The ability of fluorescently labelled liposomal delivery systems of varying physicochemical characteristics to penetrate within multicellular tumor spheroids has been investigated by confocal laser scanning microscopy. A variety of liposome characteristics and experimental parameters were investigated, including lipid bilayer composition, duration of liposome-spheroid interaction, mean liposome size, steric stabilization of liposomes. Electrostatic binding between cationic liposomes and spheroids was very efficient; however, it impeded any significant penetration of the vesicles within deeper layers of the tumor spheroid. Small unilamellar liposomes of neutral surface character did not bind as efficiently but exhibited enhanced penetrative transport capabilities closer to the tumor core. Polymer-coated (sterically stabilised) liposomes exhibited almost no interaction with the spheroid, indicating that their limited diffusion within avascular tissues may be a limiting step for their use against micrometastases. Multicellular tumor spheroids were used as models of solid tumor interstitium relevant to delivery systems able to extravasate from the microcapillaries or as models of prevascularized micrometastases. This study illustrates that interactions between liposomes and other drug delivery systems with multicellular tumor spheroids can offer critically important information with respect to optimizing solid or micrometastatic tumor delivery and targeting strategies.     

Derivation of an Analytical Solution to a Reaction-Diffusion Model for Autocatalytic Degradation and Erosion in Polymer Microspheres

A mathematical reaction-diffusion model is defined to describe the gradual decomposition of polymer microspheres composed of poly(D,L-lactic-co-glycolic acid) (PLGA) that are used for pharmaceutical drug delivery over extended periods of time. The partial differential equation (PDE) model treats simultaneous first-order generation due to chemical reaction and diffusion of reaction products in spherical geometry to capture the microsphere-size-dependent effects of autocatalysis on PLGA erosion that occurs when the microspheres are exposed to aqueous media such as biological fluids. The model is solved analytically for the concentration of the autocatalytic carboxylic acid end groups of the polymer chains that comprise the microspheres as a function of radial position and time. The analytical solution for the reaction and transport of the autocatalytic chemical species is useful for predicting the conditions under which drug release from PLGA microspheres transitions from diffusion-controlled to erosion-controlled release, for understanding the dynamic coupling between the PLGA degradation and erosion mechanisms, and for designing drug release particles. The model is the first to provide an analytical prediction for the dynamics and spatial heterogeneities of PLGA degradation and erosion within a spherical particle. The analytical solution is applicable to other spherical systems with simultaneous diffusive transport and first-order generation by reaction.     

Engineering lipid vesicles of enhanced intratumoral transport capabilities: correlating liposome characteristics with penetration into human prostate tumor spheroids

Liposomes have been widely used delivery systems, particularly relevant to the development of cancer therapeutics. Numerous liposome-based drugs are in the clinic or in clinical trials today against multiple tumor types; however, systematic studies of liposome interactions with solid or metastatic tumor nodules are scarce. This study is describing the in vitro interaction between liposomes and avascular human prostate (LNCaP-LN3) tumor spheroids. The ability of fluorescently labelled liposomal delivery systems of varying physicochemical characteristics to penetrate within multicellular tumor spheroids has been investigated by confocal laser scanning microscopy. A variety of liposome characteristics and experimental parameters were investigated, including lipid bilayer composition, duration of liposome-spheroid interaction, mean liposome size, steric stabilization of liposomes. Electrostatic binding between cationic liposomes and spheroids was very efficient; however, it impeded any significant penetration of the vesicles within deeper layers of the tumor spheroid. Small unilamellar liposomes of neutral surface character did not bind as efficiently but exhibited enhanced penetrative transport capabilities closer to the tumor core. Polymer-coated (sterically stabilised) liposomes exhibited almost no interaction with the spheroid, indicating that their limited diffusion within avascular tissues may be a limiting step for their use against micrometastases. Multicellular tumor spheroids were used as models of solid tumor interstitium relevant to delivery systems able to extravasate from the microcapillaries or as models of prevascularized micrometastases. This study illustrates that interactions between liposomes and other drug delivery systems with multicellular tumor spheroids can offer critically important information with respect to optimizing solid or micrometastatic tumor delivery and targeting strategies.     

Spatial Configuration and Composition of Charge Modulates Transport into a Mucin Hydrogel Barrier

The mucus barrier is selectively permeable to a wide variety of molecules, proteins, and cells, and establishes gradients of these particulates to influence the uptake of nutrients, the defense against pathogens, and the delivery of drugs. Despite its importance for health and disease, the criteria that govern transport through the mucus barrier are largely unknown. Studies with uniformly functionalized nanoparticles have provided critical information about the relevance of particle size and net charge for mucus transport. However, these particles lack the detailed spatial arrangements of charge found in natural mucus-interacting substrates, such as certain viruses, which may have important consequences for transport through the mucus barrier. Using a novel, to our knowledge, microfluidic design that enables us to measure real-time transport gradients inside a hydrogel of mucins, the gel-forming glycoprotein component of mucus, we show that two peptides with the same net charge, but different charge arrangements, exhibit fundamentally different transport behaviors. Specifically, we show that certain configurations of positive and negative charges result in enhanced uptake into a mucin barrier, a remarkable effect that is not observed with either charge alone. Moreover, we show that the ionic strength within the mucin barrier strongly influences transport specificity, and that this effect depends on the detailed spatial arrangement of charge. These findings suggest that spatial charge distribution is a critical parameter to modulate transport through mucin-based barriers, and have concrete implications for the prediction of mucosal passage, and the design of drug delivery vehicles with tunable transport properties.     

Mucoadhesive nanoparticles may disrupt the protective human mucus barrier by altering its microstructure

Mucus secretions typically protect exposed surfaces of the eyes and respiratory, gastrointestinal and female reproductive tracts from foreign entities, including pathogens and environmental ultrafine particles. We hypothesized that excess exposure to some foreign particles, however, may cause disruption of the mucus barrier. Many synthetic nanoparticles are likely to be mucoadhesive due to hydrophobic, electrostatic or hydrogen bonding interactions. We therefore sought to determine whether mucoadhesive particles (MAP) could alter the mucus microstructure, thereby allowing other foreign particles to more easily penetrate mucus. We engineered muco-inert probe particles 1 μm in diameter, whose diffusion in mucus is limited only by steric obstruction from the mucus mesh, and used them to measure possible MAP-induced changes to the microstructure of fresh human cervicovaginal mucus. We found that a 0.24% w/v concentration of 200 nm MAP in mucus induced a ～10-fold increase in the average effective diffusivity of the probe particles, and a 2- to 3-fold increase in the fraction capable of penetrating physiologically thick mucus layers. The same concentration of muco-inert particles, and a low concentration (0.0006% w/v) of MAP, had no detectable effect on probe particle penetration rates. Using an obstruction-scaling model, we determined that the higher MAP dose increased the average mesh spacing ("pore" size) of mucus from 380 nm to 470 nm. The bulk viscoelasticity of mucus was unaffected by MAP exposure, suggesting MAP may not directly impair mucus clearance or its function as a lubricant, both of which depend critically on the bulk rheological properties of mucus. Our findings suggest mucoadhesive nanoparticles can substantially alter the microstructure of mucus, highlighting the potential of mucoadhesive environmental or engineered nanoparticles to disrupt mucus barriers and cause greater exposure to foreign particles, including pathogens and other potentially toxic nanomaterials.     

Identifying the Interaction of Vancomycin With Novel pH-Responsive Lipids as Antibacterial Biomaterials Via Accelerated Molecular Dynamics and Binding Free Energy Calculations

Nano-drug delivery systems have proven to be an efficient formulation tool to overcome the challenges with current antibiotics therapy and resistance. A series of pH-responsive lipid molecules were designed and synthesized for future liposomal formulation as a nano-drug delivery system for vancomycin at the infection site. The structures of these lipids differ from each other in respect of hydrocarbon tails: Lipid1, 2, 3 and 4 have stearic, oleic, linoleic, and linolenic acid hydrocarbon chains, respectively. The impact of variation in the hydrocarbon chain in the lipid structure on drug encapsulation and release profile, as well as mode of drug interaction, was investigated using molecular modeling analyses. A wide range of computational tools, including accelerated molecular dynamics, normal molecular dynamics, binding free energy calculations and principle component analysis, were applied to provide comprehensive insight into the interaction landscape between vancomycin and the designed lipid molecules. Interestingly, both MM-GBSA and MM-PBSA binding affinity calculations using normal molecular dynamics and accelerated molecular dynamics trajectories showed a very consistent trend, where the order of binding affinity towards vancomycin was lipid4?>?lipid1?>?lipid2?>?lipid3. From both normal molecular dynamics and accelerated molecular dynamics, the interaction of lipid3 with vancomycin is demonstrated to be the weakest (?G_binding?=??2.17 and ?11.57, for normal molecular dynamics and accelerated molecular dynamics, respectively) when compared to other complexes. We believe that the degree of unsaturation of the hydrocarbon chain in the lipid molecules may impact on the overall conformational behavior, interaction mode and encapsulation (wrapping) of the lipid molecules around the vancomycin molecule. This thorough computational analysis prior to the experimental investigation is a valuable approach to guide for predicting the encapsulation ability, drug release and further development of novel liposome-based pH-responsive nano-drug delivery system with refined structural and chemical features of potential lipid molecule for formulation development.     

Subdiffusive-Brownian crossover in membrane proteins: a generalized Langevin equation-based approach

In this work, we propose a generalized Langevin equation-based model to describe the lateral diffusion of a protein in a lipid bilayer. The memory kernel is represented in terms of a viscous (instantaneous) and an elastic (noninstantaneous) component modeled through a Dirac δ function and a three-parameter Mittag-Leffler type function, respectively. By imposing a specific relationship between the parameters of the three-parameter Mittag-Leffler function, the different dynamical regimes—namely ballistic, subdiffusive, and Brownian, as well as the crossover from one regime to another—are retrieved. Within this approach, the transition time from the ballistic to the subdiffusive regime and the spectrum of relaxation times underlying the transition from the subdiffusive to the Brownian regime are given. The reliability of the model is tested by comparing the mean-square displacement derived in the framework of this model and the mean-square displacement of a protein diffusing in a membrane calculated through molecular dynamics simulations.