Multivalent binding of nanocarrier to endothelial cells under shear flow

Drug-loaded nanoparticles for cancer therapy: a high-throughput multicellular agent-based modeling study

Interactions between biological systems and engineered nanomaterials have become an important area of study due to the application of nanomaterials in medicine. In particular, the application of nanomaterials for cancer diagnosis or treatment presents a challenging opportunity due to the complex biology of this disease spanning multiple time and spatial scales. A system-level analysis would benefit from mathematical modeling and computational simulation to explore the interactions between anticancer drug-loaded nanoparticles (NPs), cells, and tissues, and the associated parameters driving this system and a patient's overall response. Although a number of models have explored these interactions in the past, few have focused on simulating individual cell-NP interactions. This study develops a multicellular agent-based model of cancer nanotherapy that simulates NP internalization, drug release within the cell cytoplasm, "inheritance" of NPs by daughter cells at cell division, cell pharmacodynamic response to the intracellular drug, and overall drug effect on tumor dynamics. A large-scale parallel computational framework is used to investigate the impact of pharmacokinetic design parameters (NP internalization rate, NP decay rate, anticancer drug release rate) and therapeutic strategies (NP doses and injection frequency) on the tumor dynamics. In particular, through the exploration of NP "inheritance" at cell division, the results indicate that cancer treatment may be improved when NPs are inherited at cell division for cytotoxic chemotherapy. Moreover, smaller dosage of cytostatic chemotherapy may also improve inhibition of tumor growth when cell division is not completely inhibited. This work suggests that slow delivery by "heritable" NPs can drive new dimensions of nanotherapy design for more sustained therapeutic response.

The role of the cell surface glycocalyx in drug delivery to and through the endothelium

Cell membranes are key interfaces where materials engineering meets biology. Traditionally regarded as just the location of receptors regulating the uptake of molecules, we now know that all mammalian cell membranes are 'sugar coated'. These sugars, or glycans, form a matrix bound at the cell membrane via proteins and lipids, referred to as the glycocalyx, which modulate access to cell membrane receptors crucial for interactions with drug delivery systems (DDS). Focusing on the key blood-tissue barrier faced by most DDS to enable transport from the place of administration to target sites via the circulation, we critically assess the design of carriers for interactions at the endothelial cell surface. We also discuss the current challenges for this area and provide opportunities for future research efforts to more fully engineer DDS for controlled, efficient, and targeted interactions with the endothelium for therapeutic application.

Targeting vascular inflammation through emerging methods and drug carriers

Acute inflammation is a common dangerous component of pathogenesis of many prevalent conditions with high morbidity and mortality including sepsis, thrombosis, acute respiratory distress syndrome (ARDS), COVID-19, myocardial and cerebral ischemia-reperfusion, infection, and trauma. Inflammatory changes of the vasculature and blood mediate the course and outcome of the pathology in the tissue site of insult, remote organs and systemically. Endothelial cells lining the luminal surface of the vasculature play the key regulatory functions in the body, distinct under normal vs. pathological conditions. In theory, pharmacological interventions in the endothelial cells might enable therapeutic correction of the overzealous damaging pro-inflammatory and pro-thrombotic changes in the vasculature. However, current agents and drug delivery systems (DDS) have inadequate pharmacokinetics and lack the spatiotemporal precision of vascular delivery in the context of acute inflammation. To attain this level of precision, many groups design DDS targeted to specific endothelial surface determinants. These DDS are able to provide specificity for desired tissues, organs, cells, and sub-cellular compartments needed for a particular intervention. We provide a brief overview of endothelial determinants, design of DDS targeted to these molecules, their performance in experimental models with focus on animal studies and appraisal of emerging new approaches. Particular attention is paid to challenges and perspectives of targeted therapeutics and nanomedicine for advanced management of acute inflammation.

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

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

Multiscale modeling of protein membrane interactions for nanoparticle targeting in drug delivery

Nanoparticle (NP)-based imaging and drug delivery systems for systemic (e.g. intravenous) therapeutic and diagnostic applications are inherently a complex integration of biology and engineering. A broad range of length and time scales are essential to hydrodynamic and microscopic molecular interactions mediating NP (drug nanocarriers, imaging agents) motion in blood flow, cell binding/uptake, and tissue accumulation. A computational model of time-dependent tissue delivery, providing in silico prediction of organ-specific accumulation of NPs, can be leveraged in NP design and clinical applications. In this article, we provide the current state-of-the-art and future outlook for the development of predictive models for NP transport, targeting, and distribution through the integration of new computational schemes rooted in statistical mechanics and transport. The resulting multiscale model will comprehensively incorporate: (i) hydrodynamic interactions in the vascular scales relevant to NP margination; (ii) physical and mechanical forces defining cellular and tissue architecture and epitope accessibility mediating NP adhesion; and (iii) subcellular and paracellular interactions including molecular-level targeting impacting NP uptake.

Thermodynamic analysis of multivalent binding of functionalized nanoparticles to membrane surface reveals the importance of membrane entropy and nanoparticle entropy in adhesion of flexible nanoparticles

We present a quantitative model for multivalent binding of ligand-coated flexible polymeric nanoparticles (NPs) to a flexible membrane expressing receptors. The model is developed using a multiscale computational framework by coupling a continuum field model for the cell membrane with a coarse-grained model for the polymeric NPs. The NP is modeled as a self-avoiding bead-spring polymer chain, and the cell membrane is modeled as a triangulated surface using the dynamically triangulated Monte Carlo method. The nanoparticle binding affinity to a cell surface is mainly determined by the delicate balance between the enthalpic gain due to the multivalent ligand-receptor binding and the entropic penalties of various components including receptor translation, membrane undulation, and NP conformation. We have developed new methods to compute the free energy of binding, which includes these enthalpy and entropy terms. We show that the multivalent interactions between the flexible NP and the cell surface are subject to entropy-enthalpy compensation. Three different entropy contributions, namely, those due to receptor-ligand translation, NP flexibility, and membrane undulations, are all significant, although the first of these terms is the most dominant. However, both NP flexibility and membrane undulations dictate the receptor-ligand translational entropy making the entropy compensation context-specific, i.e., dependent on whether the NP is rigid or flexible, and on the state of the membrane given by the value of membrane tension or its excess area.

Nanoparticle transport phenomena in confined flows

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

Multivalent Binding of a Ligand-Coated Particle: Role of Shape, Size, and Ligand Heterogeneity

We utilize a multiscale modeling framework to study the effect of shape, size, and ligand composition on the efficacy of binding of a ligand-coated particle to a substrate functionalized with the target receptors. First, we show how molecular dynamics along with steered molecular dynamics calculations can be used to accurately parameterize the molecular-binding free energy and the effective spring constant for a receptor-ligand pair. We demonstrate this for two ligands that bind to the α₅β₁-domain of integrin. Next, we show how these effective potentials can be used to build computational models at the meso- and continuum-scales. These models incorporate the molecular nature of the receptor-ligand interactions and yet provide an inexpensive route to study the multivalent interaction of receptors and ligands through the construction of Bell potentials customized to the molecular identities. We quantify the binding efficacy of the ligand-coated-particle in terms of its multivalency, binding free-energy landscape, and the losses in the configurational entropies. We show that 1) the binding avidity for particle sizes less than 350 nm is set by the competition between the enthalpic and entropic contributions, whereas that for sizes above 350 nm is dominated by the enthalpy of binding; 2) anisotropic particles display higher levels of multivalent binding compared to those of spherical particles; and 3) variations in ligand composition can alter binding avidity without altering the average multivalency. The methods and results presented here have wide applications in the rational design of functionalized carriers and also in understanding cell adhesion.

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

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

Effect of flow on targeting and penetration of angiopep-decorated nanoparticles in a microfluidic model blood-brain barrier

The blood-brain barrier (BBB) limits transport of nanoparticles from the circulation to the brain parenchyma. Angiopep-2, a peptide which functions as a brain transport vector, can be coupled to nanoparticles in order to facilitate binding and internalization by brain endothelial cells (ECs), and subsequent BBB penetration. This multi-step process may be affected by blood flow over brain ECs, as flow influences endothelial cell phenotype as well as interactions of nanoparticles with ECs. In the present study a microfluidic BBB model was constructed to evaluate binding and internalization by brain ECs, as well as BBB penetration of Angiopep-2 coupled liposomes (Ang2-Liposomes) in static and flow conditions. Ang2 conjugation to liposomes markedly improved binding relative to unconjugated liposomes. Ang2-Liposomes bound and were internalized efficiently by brain endothelial cells after static incubation or with 1 dyne/cm² of fluid shear stress (FSS), while binding was reduced at a FSS of 6 dyne/cm². Penetration of the model microfluidic BBB by Ang2-Liposomes was higher at a FSS of 1 dyne/cm² and 6 dyne/cm² than with static incubation. Analysis of barrier function and control experiments for receptor-mediated penetration provided insight into the magnitude of transcellular versus paracellular transport at each tested FSS. Overall, the results demonstrate that flow impacted the binding and BBB penetration of Ang2-functionalized nanoparticles. This highlights the relevance of the local flow environment for in vitro modeling of the performance of nanoparticles functionalized with BBB penetrating ligands.

Nanoparticle localization in blood vessels: dependence on fluid shear stress, flow disturbances, and flow-induced changes in endothelial physiology

Nanoparticles in the bloodstream are subjected to complex fluid forces as they move through the curves and branches of healthy or tumor vasculature. While nanoparticles are known to preferentially accumulate in angiogenic vessels, little is known about the flow conditions in these vessels and how these conditions may influence localization. Here, we report a methodology which combines confocal imaging of nanoparticle-injected transgenic zebrafish embryos, 3D modeling of the vasculature, particle mapping, and computational fluid dynamics, to quantitatively assess the effects of fluid forces on nanoparticle distribution in vivo. Six-fold lower accumulation was found in zebrafish arteries compared to the lower velocity veins. Nanoparticle localization varied inversely with shear stress. Highest accumulation was present in regions of disturbed flow found at branch points and curvatures in the vasculature. To further investigate cell-particle association under flow, human endothelial cells were exposed to nanoparticles under hemodynamic conditions typically found in human vessels. Physiological adaptations of endothelial cells to 20 hours of flow enhanced nanoparticle accumulation in regions of disturbed flow. Overall our results suggest that fluid shear stress magnitude, flow disturbances, and flow-induced changes in endothelial physiology modulate nanoparticle localization in angiogenic vessels.

Stochastic simulations of nanoparticle internalization through transferrin receptor dependent clathrin-mediated endocytosis

BACKGROUND

Receptor dependent clathrin-mediated endocytosis (CME) is one of the most important endocytic pathways for the internalization of bioparticles into cells. During CME, the ligand-receptor interactions, development of clathrin-coated pit (CCP) and membrane evolution all act together to drive the internalization of bioparticles. In this work, we develop a stochastic computational model to investigate the CME based on the Metropolis Monte Carlo simulations.

METHODS

The model is based on the combination of a stochastic particle binding model with a membrane model. The energetic costs of membrane bending, CCP formation and ligand-receptor interactions are systematically linked together.

RESULTS

We implement our model to investigate the effects of particle size, ligand density and membrane stiffness on the overall process of CME from the drug delivery perspectives. Consistent with some experiments, our results show that the intermediate particle size and ligand density favor the particle internalization. Moreover, our results show that it is easier for a particle to enter a cell with softer membrane.

CONCLUSIONS

The model presented here is able to provide mechanistic insights into CME and can be readily modified to include other important factors, such as actins. The predictions from the model will aid in the therapeutic design of intracellular/transcellular drug delivery and antiviral interventions.

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

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

Nonspecific Colloidal-Type Interaction Explains Size-Dependent Specific Binding of Membrane-Targeted Nanoparticles

Emerging biomedical applications such as molecular imaging and drug delivery often require directed binding of nanoparticles to cell-membrane receptors. The specific apparent affinity of such ligand-functionalized particles is size-dependent, an observation so far solely attributed to multivalent receptor-ligand interaction. We question the universality of this explanation by demonstrating that the binding kinetics also depends on weak, attractive colloidal-type interaction between nanoparticles and a lipid membrane. Applying label-free single-particle imaging, we correlate binding of nanoparticles targeted to a cell-mimetic lipid membrane with the distribution of nontargeted particles freely diffusing close to the membrane interface. This analysis shows that already a weak, k_BT-scale attraction present between 50 nm gold nanoparticles and the membrane renders these particles an order of magnitude higher avidity compared to 20 nm particles. A stronger emphasis on nonspecific particle-membrane interaction might thus be required to accurately predict nanoparticle targeting and other similar processes such as cellular uptake of exosomes and viruses.

Endothelial glycocalyx conditions influence nanoparticle uptake for passive targeting

Cardiovascular diseases are facilitated by endothelial cell (EC) dysfunction and coincide with EC glycocalyx coat shedding. These diseases may be prevented by delivering medications to affected vascular regions using circulating nanoparticle (NP) drug carriers. The objective of the present study was to observe how the delivery of 10 nm polyethylene glycol-coated gold NPs (PEG-AuNP) to ECs is impacted by glycocalyx structure on the EC surface. Rat fat pad endothelial cells were chosen for their robust glycocalyx, verified by fluorescent immunolabeling of adsorbed albumin and integrated heparan sulfate (HS) chains. Confocal fluorescent imaging revealed a ~3 µm thick glycocalyx layer, covering 75% of the ECs and containing abundant HS. This healthy glycocalyx hindered the uptake of PEG-AuNP as expected because glycocalyx pores are typically 7 nm wide. Additional glycocalyx models tested included: a collapsed glycocalyx obtained by culturing cells in reduced protein media, a degraded glycocalyx obtained by applying heparinase III enzyme to specifically cleave HS, and a recovered glycocalyx obtained by supplementing exogenous HS into the media after enzyme degradation. The collapsed glycocalyx waŝ2 µm thick with unchanged EC coverage and sustained HS content. The degraded glycocalyx showed similar changes in EC thickness and coverage but its HS thickness was reduced to 0.7 µm and spanned only 10% of the original EC surface. Both dysfunctional models retained six- to sevenfold more PEG-AuNP compared to the healthy glycocalyx. The collapsed glycocalyx permitted NPs to cross the glycocalyx into intracellular spaces, whereas the degraded glycocalyx trapped the PEG-AuNP within the glycocalyx. The repaired glycocalyx model partially restored HS thickness to 1.2 µm and 44% coverage of the ECs, but it was able to reverse the NP uptake back to baseline levels. In summary, this study showed that the glycocalyx structure is critical for NP uptake by ECs and may serve as a passive pathway for delivering NPs to dysfunctional ECs.

Binding kinetics and multi-bond: Finding correlations by synthesizing interactions between ligand-coated bionanoparticles and receptor surfaces

The number of bonds formed between one single bionanoparticle and many surface receptors is an important subject to be studied but is seldom quantitatively investigated. A new evaluation of the correlation between binding kinetics and number of bonds is presented by varying ligand density and receptor density. An experimental system was developed using measurements with surface plasmon resonance spectroscopy. A corresponding multi-site adsorption model elucidated the correlation. The results show that with the increase of the receptor density, the adsorption rate first decreased when the number of bonds was below a maximum value and then increased when the number of bonds stayed at this maximum value. The investigation on ligand density variation suggests that the coating density on top of the bionanoparticle surface may have a particular value below which more ligand will accelerate the adsorption rate. The ratio of ligand amount bound by the receptors to the total ligand amount associated with a single bionanoparticle will remain constant even if one attaches more ligands to a bionanoparticle. We envision that the bionanoparticle desorption will not depend on density changes from either ligand or receptor when the number of bonds reaches a specific efficient value.

Thermodynamic free energy methods to investigate shape transitions in bilayer membranes

The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morphological transitions in bilayer membranes, induced either by the action of curvature remodeling proteins or due to the application of external forces. Using a triangulated surface as a model for the cell membrane and using the framework of dynamical triangulation Monte Carlo, we have focused on the methods of Widom insertion, thermodynamic integration, Bennett acceptance scheme, and umbrella sampling and weighted histogram analysis. We have demonstrated how these methods can be employed in a variety of problems involving the cell membrane. Specifically, we have shown that the chemical potential, computed using Widom insertion, and the relative free energies, computed using thermodynamic integration and Bennett acceptance method, are excellent measures to study the transition from curvature sensing to curvature inducing behavior of membrane associated proteins. The umbrella sampling and WHAM analysis has been used to study the thermodynamics of tether formation in cell membranes and the quantitative predictions of the computational model are in excellent agreement with experimental measurements. Furthermore, we also present a method based on WHAM and thermodynamic integration to handle problems related to end-point-catastrophe that are common in most free energy methods.

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

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

Non-affinity factors modulating vascular targeting of nano- and microcarriers

Particles capable of homing and adhering to specific vascular biomarkers have potential as fundamental tools in drug delivery for mediation of a wide variety of pathologies, including inflammation, thrombosis, and pulmonary disorders. The presentation of affinity ligands on the surface of a particle provides a means of targeting the particle to sites of therapeutic interest, but a host of other factors come into play in determining the targeting capacity of the particle. This review presents a summary of several key considerations in nano- and microparticle design that modulate targeted delivery without directly altering epitope-specific affinity. Namely, we describe the effect of factors in definition of the base carrier (including shape, size, and flexibility) on the capacity of carriers to access, adhere to, and integrate in target biological milieus. Furthermore, we present a summary of fundamental dynamics of carrier behavior in circulation, taking into account interactions with cells in circulation and the role of hemodynamics in mediating the direction of carriers to target sites. Finally, we note non-affinity aspects to uptake and intracellular trafficking of carriers in target cells. In total, recent findings presented here may offer an opportunity to capitalize on mitigating factors in the behavior of ligand-targeted carriers in order to optimize targeting.

Cell and nanoparticle transport in tumour microvasculature: the role of size, shape and surface functionality of nanoparticles

Through nanomedicine, game-changing methods are emerging to deliver drug molecules directly to diseased areas. One of the most promising of these is the targeted delivery of drugs and imaging agents via drug carrier-based platforms. Such drug delivery systems can now be synthesized from a wide range of different materials, made in a number of different shapes, and coated with an array of different organic molecules, including ligands. If optimized, these systems can enhance the efficacy and specificity of delivery compared with those of non-targeted systems. Emerging integrated multiscale experiments, models and simulations have opened the door for endless medical applications. Current bottlenecks in design of the drug-carrying particles are the lack of knowledge about the dispersion of these particles in the microvasculature and of their subsequent internalization by diseased cells (Bao et al. 2014 J. R. Soc. Interface 11, 20140301 (doi:10.1098/rsif.2014.0301)). We describe multiscale modelling techniques that study how drug carriers disperse within the microvasculature. The immersed molecular finite-element method is adopted to simulate whole blood including blood plasma, red blood cells and nanoparticles. With a novel dissipative particle dynamics method, the beginning stages of receptor-driven endocytosis of nanoparticles can be understood in detail. Using this multiscale modelling method, we elucidate how the size, shape and surface functionality of nanoparticles will affect their dispersion in the microvasculature and subsequent internalization by targeted cells.

Hydrodynamic interactions of deformable polymeric nanocarriers and the effect of crosslinking

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

Collaborative Enhancement of Endothelial Targeting of Nanocarriers by Modulating Platelet-Endothelial Cell Adhesion Molecule-1/CD31 Epitope Engagement

Nanocarriers (NCs) coated with antibodies (Abs) to extracellular epitopes of the transmembrane glycoprotein PECAM (platelet endothelial cell adhesion molecule-1/CD31) enable targeted drug delivery to vascular endothelial cells. Recent studies revealed that paired Abs directed to adjacent, yet distinct epitopes of PECAM stimulate each other's binding to endothelial cells in vitro and in vivo ("collaborative enhancement"). This phenomenon improves targeting of therapeutic fusion proteins, yet its potential role in targeting multivalent NCs has not been addressed. Herein, we studied the effects of Ab-mediated collaborative enhancement on multivalent NC spheres coated with PECAM Abs (Ab/NC, ∼180 nm diameter). We found that PECAM Abs do mutually enhance endothelial cell binding of Ab/NC coated by paired, but not "self" Ab. In vitro, collaborative enhancement of endothelial binding of Ab/NC by paired Abs is modulated by Ab/NC avidity, epitope selection, and flow. Cell fixation, but not blocking of endocytosis, obliterated collaborative enhancement of Ab/NC binding, indicating that the effect is mediated by molecular reorganization of PECAM molecules in the endothelial plasmalemma. The collaborative enhancement of Ab/NC binding was affirmed in vivo. Intravascular injection of paired Abs enhanced targeting of Ab/NC to pulmonary vasculature in mice by an order of magnitude. This stimulatory effect greatly exceeded enhancement of Ab targeting by paired Abs, indicating that '"collaborative enhancement"' effect is even more pronounced for relatively large multivalent carriers versus free Abs, likely due to more profound consequences of positive alteration of epitope accessibility. This phenomenon provides a potential paradigm for optimizing the endothelial-targeted nanocarrier delivery of therapeutic agents.

The influence of flow, shear stress and adhesion molecule targeting on gold nanoparticle uptake in human endothelial cells

The uptake of nanoparticles by endothelial cells is dependent on shear stress adaptation and flow exposure conditions. Adaptation of primary human umbilical vein endothelial cells (HUVECs) to shear stress for 24 h was associated with reduced internalisation of unmodified 80 nm spherical gold nanoparticles (AuNPs) (mean hydrodynamic size of 99 nm in culture medium) after exposure to flow conditions compared with cells that were cultured and exposed to static conditions. Under static conditions, targeting of 80 nm AuNPs conjugated with antibodies against the intracellular adhesion molecule 1 (ICAM-1) (mean hydrodynamic size of 109 nm in culture medium) markedly increased the internalisation of AuNPs in HUVECs that were activated with the tumour necrosis factor (TNF), a treatment that markedly increased the surface expression of ICAM-1. Shear stress-adapted and TNF-activated HUVECs, which were exposed to flow conditions, had higher association with anti-ICAM-1 AuNPs than cells that were not TNF-activated or exposed to particles under static conditions. Hence, shear stress adaptation reduces the uptake of unmodified AuNPs and increases the association between anti-ICAM-1 AuNPs and TNF-activated HUVECs.

Temperature- and flow-enhanced detection specificity of mutated DNA against the wild type with reporter microspheres

Detection of mutated (MT) deoxyribonucleic acid (DNA) amongst the wild type (WT) requires the probe DNA (pDNA) that is complementary to the MT to discriminate the WT by one or two nucleotide mismatches. Traditionally this is achieved by raising the temperature to above the melting temperature (Tm) of the WT (TWT) but below that of the MT (TMT). However, a raised temperature is also accompanied by a weakened binding of the MT to the pDNA which can reduce the detection sensitivity. In this study, we investigated flow as a way to enhance MT detection specificity at a lower temperature. Gold-coated glass (GCG) slides immobilized with pDNA complementary to the target MT were placed at the center of the flow cell. The detection was done by flowing MT or WT at various concentrations followed by flowing 10(5) ml(-1) fluorescent reporter microspheres (FRMs) that were 6 μm in size and coated with reporter DNA complementary to the MT or WT but different from the pDNA at various flow rates and temperatures. The detection of MT or WT was characterized by counting the FRMs captured on the GCG. Hepatitis B virus 1762/1764 double mutation (HBV DM) was the model MT and the TMT and TWT were 47 °C and 22 °C, respectively. It was shown that at room temperature, flow initially increased the binding of both the MT and WT at lower flow rates but decreased the binding at flow rates ≥4 ml min(-1) due to the increase in the flow-induced impingement force on the FRMs to overcome the binding of the MT and the WT to the GCG at higher flow rates. At ≥30 °C the decrease in binding of the WT with an increasing flow rate was more than that of the MT because 30 °C was above the TWT but still well below the TMT. As a result, the detection of MT at 30 °C with a flow rate of 4 ml min(-1) was more specific than at 35 °C without flow. These results indicate that flow can diminish WT binding at a lower temperature than without flow and allow MT detection to occur at a lower temperature with high specificity.

Modelling of Binding Free Energy of Targeted Nanocarriers to Cell Surface

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

Quantitation of nanoparticle accumulation in flow using optimized microfluidic chambers

BACKGROUND

The vascular cell adhesion molecule-1 (VCAM-1) targeting peptide sequence, VHPKQHR, is a promising moiety for targeting atherosclerosis through incorporation into nanoparticles such as dendrimers and liposomes.

PURPOSE

We aim to develop VCAM-1-targeted nanoparticles that effectively accumulate on the endothelium under shear conditions and to develop robust microfluidic chambers able to house sufficient cells for flow cytometric measurements.

METHODS

Carboxyfluorescein-labeled monomeric VHP-peptide, tetrameric VHP-dendrimers (bisbidentate or radial architecture, with or without N-terminal acetylation) and VHP-peptide liposomes were prepared. Human umbilical vein endothelial cells were treated with nanoparticles under 0 or 2.9 dyne/cm(2) shear, and particle binding was quantified. Flow chambers cured at various temperatures, with or without glass backings were fabricated, characterized for deformation and applied in experiments.

RESULTS

Although liposomes accumulated with highest efficiency, dendrimers also demonstrated specific binding. N-terminal acetylation significantly reduced dendrimer binding, and despite shorter movement range, bisbidentate dendrimers outperformed radial dendrimers, suggesting multiple epitope presence within its estimated arm-span of 57 Å. Under shear, while liposome binding increased 300%, dendrimer binding to cells decreased 65%. Through higher temperature curing and glass backing insertion, polydimethylsiloxane flow chambers maintaining rectangular cross-section with aspect-ratio as low as 1:111 were achieved.

CONCLUSION

Optimized dendrimers and liposomal nanocarriers specifically accumulated onto cells within microfluidic chambers.

Temporal Multiscale Approach for Nanocarrier Motion with Simultaneous Adhesion and Hydrodynamic Interactions in Targeted Drug Delivery

We present a fluctuating hydrodynamics approach and a hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics to resolve the motion of a nanocarrier when subject to both hydrodynamic interactions and adhesive interactions. Specifically, using these approaches, we compute equilibrium probability distributions at constant temperature as well as velocity autocorrelation functions of the nanocarrier subject to thermal motion in a quiescent Newtonian fluid medium, when tethered by a harmonic spring force mimicking a tether due to a single receptor-ligand bond. We demonstrate that the thermal equipartition of translation, rotation, and spring degrees of freedom are preserved by our formalism while simultaneously resolving the nature of the hydrodynamic correlations. Additionally, we evaluate the potential of mean force (or free energy density) along a specified reaction coordinate to faciltate extensive conformational sampling of the nanocarrier motion. We show that our results are in excellent agreement with analytical results and Monte Carlo simulations, thereby validating our methodologies. The frameworks we have presented provide a comprehensive platform for temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion in vascular targeted drug delivery.

Multiscale perspectives of virus entry via endocytosis

Most viruses take advantage of endocytic pathways to gain entry into host cells and initiate infections. Understanding of virus entry via endocytosis is critically important for the design of antiviral strategies. Virus entry via endocytosis is a complex process involving hundreds of cellular proteins. The entire process is dictated by events occurring at multiple time and length scales. In this review, we discuss and evaluate the available means to investigate virus endocytic entry, from both experimental and theoretical/numerical modeling fronts, and highlight the importance of multiscale features. The complexity of the process requires investigations at a systems biology level, which involves the combination of different experimental approaches, the collaboration of experimentalists and theorists across different disciplines, and the development of novel multiscale models.

Reduction of nanoparticle avidity enhances the selectivity of vascular targeting and PET detection of pulmonary inflammation

Targeting nanoparticles (NPs) loaded with drugs and probes to precise locations in the body may improve the treatment and detection of many diseases. Generally, to achieve targeting, affinity ligands are introduced on the surface of NPs that can bind to molecules present on the cell of interest. Optimization of ligand density is a critical parameter in controlling NP binding to target cells, and a higher ligand density is not always the most effective. In this study, we investigated how NP avidity affects targeting to the pulmonary vasculature, using NPs targeted to ICAM-1. This cell adhesion molecule is expressed by quiescent endothelium at modest levels and is upregulated in a variety of pathological settings. NP avidity was controlled by ligand density, with the expected result that higher avidity NPs demonstrated greater pulmonary uptake than lower avidity NPs in both naive and pathological mice. However, in comparison with high-avidity NPs, low-avidity NPs exhibited several-fold higher selectivity of targeting to pathological endothelium. This finding was translated into a PET imaging platform that was more effective in detecting pulmonary vascular inflammation using low-avidity NPs. Furthermore, computational modeling revealed that elevated expression of ICAM-1 on the endothelium is critical for multivalent anchoring of NPs with low avidity, while high-avidity NPs anchor effectively to both quiescent and activated endothelium. These results provide a paradigm that can be used to optimize NP targeting by manipulating ligand density and may find biomedical utility for increasing detection of pathological vasculature.

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

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

Nanocarrier-Cell Surface Adhesive and Hydrodynamic Interactions: Ligand-Receptor Bond Sensitivity Study

A hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics is employed to study the motion of a neutrally buoyant nanocarrier in an incompressible Newtonian stationary fluid medium. Both hydrodynamic interactions and adhesive interactions are included, as are different receptor-ligand bond constants relevant to medical applications. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed for the simulation. The flow around the particle and its motion are fully resolved. The temperatures of the particle associated with the various degrees of freedom satisfy the equipartition theorem. The potential of mean force (or free energy density) along a specified reaction coordinate for the harmonic (spring) interactions between the antibody and antigen is evaluated for two different bond constants. The numerical evaluations show excellent comparison with analytical results. This temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion has important implications for designing nanocarriers for vascular targeted drug delivery.

A hybrid approach for the simulation of a nearly neutrally buoyant nanoparticle thermal motion in an incompressible Newtonian fluid medium

A hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed in simulating the thermal motion of the particle suspended in the fluid contained in a cylindrical vessel. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery.

Microcantilever-Based Label-Free Characterization of Temperature-Dependent Biomolecular Affinity Binding

This paper presents label-free characterization of temperature-dependent biomolecular affinity binding on solid surfaces using a microcantilever-based device. The device consists of a Parylene cantilever one side of which is coated with a gold film and functionalized with molecules as an affinity receptor to a target analyte. The cantilever is located in a poly(dimethylsiloxane) (PDMS) microfluidic chamber that is integrated with a transparent indium tin oxide (ITO) resistive temperature sensor on the underlying substrate. The ITO sensor allows for real-time measurements of the chamber temperature, as well as unobstructed optical access for reflection-based optical detection of the cantilever deflection. To test the temperature-dependent binding between the target and receptor, the temperature of the chamber is maintained at a constant setpoint, while a solution of unlabeled analyte molecules is continuously infused through the chamber. The measured cantilever deflection is used to determine the target-receptor binding characteristics. We demonstrate label-free characterization of temperature-dependent binding kinetics of the platelet-derived growth factor (PDGF) protein with an aptamer receptor. Affinity binding properties including the association and dissociation rate constants as well as equilibrium dissociation constant are obtained, and shown to exhibit significant dependencies on temperature.

Multiscale systems biology and physics of thrombosis under flow

Blood clotting under hemodynamic conditions involves numerous multiscale interactions from the molecular scale to macroscopic vessel and systemic circulation scales. Transmission of shear forces to platelet receptors such as GPIbα, P-selectin, α(2)β(1), and α(2b)β(3) controls adhesion dynamics. These forces also drive membrane tether formation, cellular deformation, and mechanosignaling in blood cells. Blood flow results in red blood cell (RBC) drift towards the center of the vessel along with a near-wall plasma layer enriched with platelets. RBC motions also dramatically enhance platelet dispersion. Trajectories of individual platelets near a thrombotic deposit dictate capture-activation-arrest dynamics as these newly arriving platelets are exposed to chemical gradients of ADP, thromboxane, and thrombin within a micron-scale boundary layer formed around the deposit. If shear forces are sufficiently elevated (>50 dyne/cm(2)), the largest polymers of von Willebrand Factor may elongate with concomitant shear-induced platelet activation. Finally, thrombin generation enhances platelet recruitment and clot strength via fibrin polymerization. By combination of coarse-graining, continuum, and stochastic algorithms, the numerical simulation of the growth rate, composition, and occlusive/embolic potential of a thrombus now spans multiscale phenomena. These simulations accommodate particular flow geometries, blood phenotype, pharmacological regimen, and reactive surfaces to help predict disease risk or response to therapy.

A hybrid formalism combining fluctuating hydrodynamics and generalized Langevin dynamics for the simulation of nanoparticle thermal motion in an incompressible fluid medium

A novel hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of the nanoparticle is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian (ALE) based finite element method (FEM) is employed in simulating the thermal motion of a particle suspended in the fluid confined in a cylindrical vessel. The results for thermal equilibrium between the particle and the fluid are validated by comparing the numerically predicted temperature of the nanoparticle with that obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation function (VACF) and mean squared displacement (MSD) with well-known analytical results. For nanoparticle motion in an incompressible fluid, the fluctuating hydrodynamics approach resolves the hydrodynamics correctly but does not impose the correct equipartition of energy based on the nanoparticle mass because of the added mass of the displaced fluid. In contrast, the Langevin approach with an appropriate memory is able to show the correct equipartition of energy, but not the correct short- and long-time hydrodynamic correlations. Using our hybrid approach presented here, we show for the first time, that we can simultaneously satisfy the equipartition theorem and the (short- and long-time) hydrodynamic correlations. In effect, this results in a thermostat that also simultaneously preserves the true hydrodynamic correlations. The significance of this result is that our new algorithm provides a robust computational approach to explore nanoparticle motion in arbitrary geometries and flow fields, while simultaneously enabling us to study carrier adhesion mediated by biological reactions (receptor-ligand interactions) at the vessel wall at a specified finite temperature.