Cell nanoparticle dynamics within blood

I am trying to mathematically model the dynamics of a particular cell in circulation and its binding to another nanoparticle that is intravenously injected. The concentration of this cell is very low (about 5 cells per mL of blood). I want to see how many nanoparticles are needed to bind to as many of these rare cells as possible.

So first, I am trying to model the cell dynamics in the blood flow. I am not sure how to start. I wanted to model the cell movement through the entire cardiovascular system, but I would have to simplify it. I am thinking of modeling the blood flow through some of the major organ systems, and estimating the absorption through the capillaries. I am thinking something like the physiologically-based pharmacokinetic model (PBPK). However, there would be some parameters that I wouldn't know about that I would need for the model (at least that is what I think, I am new to pharmacokinetics) Also for the actual fluid dynamics, I'm not sure how to model this, because the blood isn't just a fluid, and has many other cells, so I don't know if there are some other effects.

So, my question is, in what direction should I go to model the dynamics of this cell in circulation? I want to model the circulation in the entire cardiovascular system, because I need to also model the other nanoparticle dynamics, and how likely it is to find and bind to some of the receptors on the cell. Is there an example of a similar model that has been done?

To go the PBPK route:

I would recommend using the organism parameters and structure from the whole body platform model by Shah and Betts.

  • Shah, D.K. & Betts, A.M. J Pharmacokinet Pharmacodyn (2012) 39: 67. doi:10.1007/s10928-011-9232-2

They have assigned a plasma space volume, plasma flow, blood cell space volume and blood cell flow for each organ and the total body. The base model structure for circulation is complete if you use the equations for the blood cell space in this paper as the foundation (Eq 2 and Eq 5).

Once the model structure is complete, step 2 is to model all processes that can affect the cell in each compartment. If the cell is adhering to a nanoparticle, a compartment equation could then be:

d[cell]/dt = (flow in - flow out)/volume + Kon x [nano] x [cell] - Koff x [cell-nano complex]

To model the interaction of the cell with the nanoparticle you will need to model both within the same structure. A review of PBPK modelling for nanoparticles can be found here:

  • Physiologically Based Pharmacokinetic Modeling of Nanoparticles Mingguang Li, Khuloud T. Al-Jamal, Kostas Kostarelos, and Joshua Reineke ACS Nano 2010 4 (11), 6303-6317 doi: 10.1021/nn1018818

A pharmacokinetic (top-down, classical) model for nanoparticles in the circulatory system may also give insight to how to model the processes that affect nanoparticles in vivo. This model accounts for fluid dynamics, pore size and specific nanoparticle properties.

  • Kirtane, A. R., Siegel, R. A. and Panyam, J. (2015), A Pharmacokinetic Model for Quantifying the Effect of Vascular Permeability on the Choice of Drug Carrier: A Framework for Personalized Nanomedicine. J. Pharm. Sci., 104: 1174-1186. doi:10.1002/jps.24302

Modelling the Transport of Nanoparticles under Blood Flow using an Agent-based Approach

Blood-mediated nanoparticle delivery is a new and growing field in the development of therapeutics and diagnostics. Nanoparticle properties such as size, shape and surface chemistry can be controlled to improve their performance in biological systems. This enables modulation of immune system interactions, blood clearance profile and interaction with target cells, thereby aiding effective delivery of cargo within cells or tissues. Their ability to target and enter tissues from the blood is highly dependent on their behaviour under blood flow. Here we have produced an agent-based model of nanoparticle behaviour under blood flow in capillaries. We demonstrate that red blood cells are highly important for effective nanoparticle distribution within capillaries. Furthermore, we use this model to demonstrate how nanoparticle size can selectively target tumour tissue over normal tissue. We demonstrate that the polydispersity of nanoparticle populations is an important consideration in achieving optimal specificity and to avoid off-target effects. In future this model could be used for informing new nanoparticle design and to predict general and specific uptake properties under blood flow.

Nanoparticles can limit inflammation by distracting the immune system

A surprise finding suggests that an injection of nanoparticles may be able to help fight the immune system when it goes haywire, researchers at the University of Michigan have shown. The nanoparticles divert immune cells that cause inflammation away from an injury site.

Inflammation is a double-edged sword. When it works, it helps the body heal and fights off infections. But sometimes, the immune system overreacts. An acute lung injury, sustained by inhaling smoke, for instance, can lead to runaway fluid production that essentially drowns a person.

Now, experiments in mice suggest that simple plastic nanoparticles, delivered by IV, may be able to keep a type of immune cell -- called a neutrophil -- too busy to cause inflammation. Other diseases in which neutrophils cause excessive inflammation include sepsis and the hardening of the arteries, or atherosclerosis.

"Neutrophils are the first line of defense. They are the most active and the most optimized to mount an inflammatory response," said Omolola Eniola-Adefeso, a professor of chemical engineering and biomedical engineering at U-M, who led the research. "They're the underdogs of white blood cells, and we're seeing that maybe we need to pay more attention to them."

She didn't start out looking to redirect the immune system with nanoparticles. Rather, her work has been exploring the dynamics within blood vessels that help or hurt the ability of nanoparticles to deliver drugs to the blood vessel wall and beyond. In experiments, her students ran blood through artificial blood vessels -- channels etched into a chip and lined with the same kind of cells that line blood vessel walls.

At first, they saw only that the neutrophils were banishing their plastic particles, which were designed to attach to the blood vessel wall. This was a problem because if the particles couldn't bind, they couldn't deliver drugs to diseased tissue. But after watching the microscope video footage many times, they realized that the neutrophils also vanished -- they weren't binding to the blood vessel wall either.

"The 'oh my God' of horror about our particle turned into an excitement over these particles doing something to cells that had not previously been explored," Eniola-Adefeso said. "These cool interactions between cells and particles got in the way of either one being able to do what they wanted to do."

Her team designed an experiment injuring part of the blood vessel wall in the microfluidic chips and confirmed that the neutrophils were redirecting their attention from creating inflammation at the injury site to carting the foreign particles away.

Then, Eniola-Adefeso connected with Michael Holinstat, a professor of pharmacology at Michigan Medicine, who has technology that can see into the blood vessels of live mice. In mice with acute lung injury, they found that injecting nanoparticles by IV could reduce the number of neutrophils congregating at the injury site by half or more.

In fact, the neutrophil concentration was similar to the concentration found in the blood of uninjured mice. Instead, the neutrophils were taking the particles to the liver, where they could be removed from circulation. Eniola-Adefeso intends to continue the research in this direction, finding out whether an injection of nanoparticles is a viable treatment for conditions with excessive inflammation.

Her group will also continue troubleshooting nanoparticles as vehicles for targeted drug delivery. One way to keep the neutrophils away is to coat the particles with so-called nonfouling materials -- materials that are resistant to picking up proteins from the blood.

Because the chemicals that the team uses to attach the nanoparticles to the blood vessel walls are the same as those used by the neutrophils themselves, a coating that combines nonfouling materials with the targeting chemicals will throw most white blood cells off the scent.

"To date, we've tried many nonfouling materials. But in the end, they foul because nature is very sophisticated," she said.

Alternatively, other research groups have tried taking the membranes from cells that naturally travel to the targeted tissue -- for instance, the neutrophils that attach to the blood vessel wall -- and putting nanoparticles inside them. Like the alien in human skin from the film "Men in Black."

Results and Discussion

Optical trapping of nanoparticles inside living zebrafish

The optical transparency of the thin zebrafish larvae (Supplementary Movie 1 Supplementary Fig. 1) is unique among in vivo vertebrate models and one of the main reasons for its immense popularity as a model system. With this in mind, we tested whether the zebrafish was also ‘optically see-through’ for the infrared laser beam of the optical tweezers and whether this approach could be used to manipulate different structures inside the living larva.

One recent emerging application of zebrafish as a model system is in the nanomedicine field 12 . For this, nanoparticles loaded with drugs and decorated on their surface with (potentially) targeting factors can be injected, enabling their biodistribution and blood circulation to be monitored using live imaging. To determine whether such injected particles can be trapped inside the complex environment of the fish, we injected latex particles into 2-day-old fish larvae (according to a recently developed protocol 12 , see also Methods, Supplementary Movie 2 and Supplementary Fig. 2). The particles readily distributed throughout the circulation of the blood stream and with time an increasing portion of the nanoparticles either adhered to the endothelium lining of the blood vessels or were taken up by macrophages.

After mounting the fish in the optical tweezers microscope (Supplementary Fig 3), we used transmission microscopy to select particles of interest that had adhered to the endothelium lining the caudal vein (Fig. 1a). Next, the OT were turned on and we were able to carefully move away some particles off the endothelium (Fig. 1a at 3.5 s, see also Supplementary Movie 3). Subsequently, the particles could be displaced and also moved against the direction of fast blood flow (200 μm s −1 in the vein and ∼ 700 μm s −1 in the artery 14 ) indicating strong trapping. In the example shown (Fig. 1a), at time point 5.4 s an erythrocyte hits the optical trap, thereby dislodging the particle from the trap. Intriguingly, the dislodged particle was subsequently pulled back, spring-like, to the original adhesion point. This indicated that the particle was connected through a nanotube (as described previously 15 ), which exerted a pulling force on the particle, that re-incorporated the tether into the endothelium after retraction. These manipulations could be done at a trapping laser power settings of 500 mW, about 10% of the maximum force available (corresponding to about max 75 mW in the sample). This demonstrates that statically adhering particles can be trapped in the zebrafish, making possible the investigating of details of interaction that are not possible with other methods.

(a) A particle (green arrowhead) adhered to the endothelium of the caudal vein (indicated with blue dotted lines) is pulled away from the endothelium into the fast blood flow (purple arrow) using optical tweezers (black crosshairs). At time 5.5 s an erythrocyte is drawn into the trap. This replaces the particle in the trap which is subsequently pulled back towards the original adhesion point of the endothelium, presumably due to a connecting nanotube. Experiment repeated at least 80 times. (b) Four separate particles (numbered) are fished out of the blood flow and moved towards a sheltered region at the tip of the tail. Purple arrows indicate flow direction. Experiment was repeated at least 10 times. Scale bar, 5 μm.

After having established that an already adhered particle could be trapped, we next investigated whether it was possible to catch particles that were injected into the blood stream and moving with the flow at high speed 14 . To do this, we made use of the available time-sharing multiplexing option of the optical tweezers system by scanning the trapping laser at high speed over several positions, multiple traps can be created that can be used to trap in parallel a high number of objects 16 . We thus distributed several ‘fishing’ traps throughout the blood stream. In Fig. 1b (Supplementary Movie 4) using two traps, two particles (marked with ‘1’ and ‘2’) had already been moved towards the tail to a region with lower flow velocity outside the main blood flow (purple arrows). Next, another particle (‘3’) was caught (19.7 s) and moved together with the two other particles while another particle (‘4’) was trapped in the flow at t=20 s. To demonstrate the positioning control that the multiplexed tweezers allow in vivo, the particles were positioned first in a straight line (32 s) and next repositioned into a square shape (39.1 s). The trapping of multiple particles within the blood flow and the subsequent reorganization of their relative positions demonstrates the robustness of the trapping, and the versatility of experiments that are possible for example, by establishing simultaneous contact between several particles and specific cells (Supplementary Movie 5 Supplementary Fig. 4).

Trapping was possible throughout the fish and up to depths of 100 μm away from the bottom cover glass (including zebrafish and medium, Supplementary Fig. 3) and we for example trapped cells and particles inside the beating heart. However, we found that most straightforward trapping could be done in the caudal vein and artery in the (thinner) tail region of the fish, at a depth of about 50 μm, where the arterial blood flow turns from retrograde transport towards the tail to anterograde transport towards the head of the fish. The experiments demonstrate that the adhesive properties of particles can be tested inside the living fish using micromanipulation, even in the fast flowing blood in the caudal artery. We successfully trapped and moved polystyrene particles of 200 nm to 1 μm diameter, but conducted most experiments with particles of 840 nm diameter (see Methods section, fluorescence emission peak at ∼ 700 nm) or 1 μm (non-fluorescent) because of their clear visibility and higher trapping stiffness 17 . Slowing down the blood flow using the anaesthetic tricaine 18 facilitates optical trapping, and allows also smaller particles down to 200 nm to be moved, although this was more difficult due to the lower trapping stiffness and the fact that smaller particles were difficult to discriminate using bright field transmission microscopy. However, using confocal fluorescence microscopy the particles could be identified. The larger particles could be trapped without obvious heating damage for extended periods of time inside the vasculature with laser powers 100 mW to 3 W (about 15 mW to ∼ 450 mW in the sample). However, a few scattered darker areas (possibly pigments that had developed despite use of phenylthiourea (PTU), see Methods) interacted strongly with the OT, and when the OT was moved transiently over these areas they became visibly damaged, presumably due to heating. However, by avoiding these areas no discernable damage was observed over the course of the experiments.

Trapping of cells in living zebrafish

Traditionally for experiments with optical tweezers spherical particles with high refractive index are used because they can be trapped with a high stiffness and they are especially suitable for trap calibration for quantitative experiments. However, for other applications, spatial micromanipulation is the crucial feature, as objects such as cells, particles or other nano–micron scale objects can be brought into contact with each other at well-defined time points and positions, opening up the possibility for analysing dynamics not accessible through passive observation.

As we found that particles can be easily and robustly trapped throughout the whole zebrafish, we next asked whether cells could also be micromanipulated inside the fish. In the absence of particles and using higher laser powers (about 2 W system setting, ∼ 250 mW in the sample), we activated the optical trap in the middle of the caudal vein, which almost instantly resulted in the immobilization of an erythrocyte in the trap. These cells could be stably held in position against the full flow of the blood stream (Fig. 2a Supplementary Movie 6) and could even be moved in the direction against the blood flow. We found that the nucleus of the zebrafish erythrocytes 19 was trapped most strongly. In Fig. 2a, a membrane in a ‘bag’-like shape can be observed behind the stably trapped nucleus, this deformation is caused by the drag force that the blood exerts and resembles the blebs that form due to local heating of cells 20 . This experiment shows that in the zebrafish optical trapping of erythrocytes is strong and seems more robust than that achieved in mouse ear 8 , where trapping had to be done gradually while making crucial use of the wall of the blood vessel. A possible explanation for this may be that erythrocytes in mice lack a nucleus.

(a) An erythrocyte is trapped and moved in the blood flow. Scale bar, 10 μm. Experiment repeated at least 10 times. (b) A blood-resident fluorescent macrophage (yellow, green outline in t=0 s) was micromanipulated and moved in 3D in a blood vessel. The white outline indicates another, non-mobile macrophage. The red dots are injected particles. Scale bar, 5 μm. Experiment repeated at least 5 times. (c) An injected particle (red colour) that was associated with a macrophage was tested for adhesion. First the particle was moved away (t=0–21.7 s) after which the OT was briefly shut off. This did not result in the particle flowing away with the blood, suggesting that a nanotube (not visible) was tethering the particle next the particle was carefully brought into contact and moved away again (52.3–101.6 s), indicating that no strong binding was established. Finally, the particle was moved further into the macrophage with a higher pushing force after which the particle could not be detached anymore (t=107.6–136.1 s). Scale bar, 10 μm. Experiment was repeated at least 5 times.

Next, we tested whether other cell types could also be trapped in the zebrafish larva. However, it is not always trivial to identify different cell types based on solely using transmission imaging in the crowded and dynamic environment of a living organism. We therefore made use of a feature we implemented on the optical tweezers imaging system used here (adapted Nanotracker JPK Instruments AS, Berlin, see Methods), namely the possibility to do parallel trapping and confocal and transmission imaging (see also ref. 21). Using a transgenic zebrafish line with fluorescent macrophages, (Tg(mpeg1:mcherry)) 22 we thus set out to test the trapping potential of these cells. In this fish line, a relatively high number of macrophages are resident in the tissue and these cells cannot be manipulated using OT. However, several macrophages were also present freely in the lumen of blood vessels. In Fig. 2b (see also Supplementary Movie 7) an area with two macrophages in the caudal vein was selected these macrophages could be identified using fluorescence imaging, one that was immobile (white contour) and another that could be moved using the OT. First, the macrophage was moved relative to the fish (using acousto-optic deflection-based repositioning t=0–18 s and 39–81 s), while at t=20 s the whole stage, including the fish and the non-mobile macrophage, was moved (horizontally and axially), while the trap was held in a stable position. The combined trapping and confocal imaging in the zebrafish demonstrates that specific cell types can be identified and trapped using this versatile system. A plethora of transgenic zebrafish lines are available 10 and different cell types and physiological questions can thereby be addressed. As another example, in Supplementary Movie 8 (and Supplementary Fig. 5) a particle (red colour, emission 640 nm) was moved in zebrafish with (green) fluorescent endothelial cells (Tg(fli1:EGFP) 23 .

We then asked whether particles that were associated with a macrophage could be moved using the tweezers specifically, we wondered whether they were adhering to the macrophage surface or had been internalized by the cell. For this, we again used tricaine to slow the blood flow. In Fig. 2c (Supplementary Movie 9), a fluorescent macrophage was identified in the caudal vein of the zebrafish larva using confocal imaging. Next, a particle (red colour, indicated with a green arrow) was trapped with the tweezers and moved away, which resulted in its detachment from the macrophage (t=0–21.7 s), thus indicating that it was not inside the macrophage. Shutting the OT off briefly did not result in the particle flowing away with the blood as other particles (the red dots) can be observed to do while they move past the stationary macrophage and stationary red nanoparticles. This suggests that the particle remained tethered to the macrophage through a nanotube (not visible either because of it being in a different plane than the confocal imaging plane or because it was very thin and not very bright). Next, the particle was moved towards the macrophage again however, no interaction could be observed (52.3–101.6 s). Finally, the particle was moved with a higher pushing force against the macrophage after which it adhered robustly, and it was not possible to detach the particle anymore (even at 5 W, the highest power available on our system). Macrophages play a central role in clearing of larger objects 24 , and it is crucial to understand this interaction for nanoparticle-based nanomedicine and delivery of drugs. The zebrafish-optical tweezers system makes it possible to study the dynamics of the interactions, make contact with a specific area of the cell, and may also be used to investigate the role of the contact forces with which particle interact when they are pushed against a macrophage in a controlled manner.

Multiple traps for in vivo nanotube formation

To study in more detail the particle adhesion to endothelial cells in vivo, a more complex system was tested involving multiple cells. In a zebrafish where the blood flow was slowed down (using tricaine), we first located a particle that adhered to the endothelium. Next, we applied several optical traps to clear the operation area of all cells: four erythrocytes that were present close to the adhered particle were removed (Fig. 3a Supplementary Movie 10). First, cell ‘1’ was moved away (behaving like a billiard ball pushing the other cells forward) and after moving it away it was kept trapped at a distance, allowing the assembly of a ‘fence’ together with several other traps placed in adjacent positions. Next, cell ‘2’ was moved and placed behind cell ‘1’ the ‘fence’ formed by several optical traps prevented the cells from flowing and diffusing back into the operation region. In addition, cells that were out of focus experienced a scattering force that ‘blew’ them away from the area of the fence. At t=36.4 s the earlier identified particle was next moved away from the endothelium. However, this particle did not fully detach, as a thin membrane protrusion was pulled out from the endothelial cell. Such membrane tethers or nanotubes have been studied in great detail in vitro since they can reveal information about, for example, membrane-cytoskeleton interactions, continuity of the membrane and its biophysical properties 25,26,27 . Our experiments using OT inside the live zebrafish larva show for the first time that nanotubes can be formed in a multicellular organism in vivo using active micromanipulation and that these nanotubes could function as a flexible adhesion, where adhered objects can be moved away while remaining tethered.

(a) In a smaller blood vessel several erythrocytes are cleared (0–36.4 s) and fenced off, after which an adhered particle was moved away from the endothelium, and a tethering nanotube was formed (36.4–42.2 s). Scale bar, 5 μm. (b) Quantification of the adhesion probability of naked and PEG-coated particles, classified as: detachable (white), strongly adhered (solid) and tethered (lines). Experiment was repeated at least 60 times.

Quantification of adhesion and ‘stealth’ properties

Understanding how nanoparticles adhere to different cell types and how the dynamics of adhesion is regulated is crucial for nanoparticle-based drug delivery. We therefore wanted to test systematically the adhesion of particles to the endothelium cells lining the vessels. To do this we experimented with two types of particles: ‘naked’—and polyethylene glycol (PEG)-coated polystyrene particles (1 μm diameter). The PEG should provide a coat that lowers the non-specific affinity of the particles for cells such as macrophages. PEG has been widely used to provide ‘stealth’ properties to nanoparticles designed for, for example, cancer therapy, facilitating a longer circulation time in the blood stream. In another project we used PEG-coated particles in ZF and effectively monitored their biodistribution and characterized their targeting and ‘stealth’ properties to cancer cells 11 . Injected 1 μm particles adhering to the endothelium were detected and attempts were made to pull them away at a fixed laser power of 500 mW. For the naked polystyrene particles we found that the majority of the particles adhered strongly to the endothelium (Fig. 3b) and it was not possible to move them away at the laser power used (often also not at higher powers as they were strongly adhered). Out of 30 particles tested in the larvae, 29 could not be moved and only 1 could be pulled away but nevertheless remained connected through a tether and was pulled back after the trap was shut off (Fig. 3b, left bar). Next, we tested injected particles with a PEG-coating. These particles were also found to be adhered to the endothelium, and we determined the binding of these PEGylated particles (Fig. 3b, right). Out of the 30 PEG-coated particles that were found immobilized to the endothelium 26 could be detached, whereas four formed a tether. None of these particles were attached so strongly that it was impossible to move them away from the endothelium. This demonstrates that PEG lowers the binding affinity of the polystyrene particles for endothelial cells in vivo, even though they still adhered to some extent to the endothelium.

The fact that the PEG-coated particles more often form tethers indicates that the particles do adhere, but with a significantly lower strength than non-coated particles. The initial force required for tether formation depends strongly on the size of the adhesion zone and more frequent tether formation implies that the area of adhesion to endothelial cells is smaller in the PEGylated-particle-case. Naked-particles likely adhere through larger areas resulting in a higher threshold force for nanotube formation 15,28 than the tweezers can provide.

We then investigated whether heparin 29 would affect the binding of nanoparticles to the endothelial lining, given that proteins and drugs with heparin binding sites that bind the endothelium can be detached in the presence of heparin. We evaluated this first by comparing the circulation of fluorescent particles in ZF injected with mixtures (3 nl) of particles (non-coated polystyrene) together with or without heparin (concentrations 40 and 100 mg ml −1 ). Confocal fluorescence imaging revealed no difference in adhesion properties in the presence or absence of heparin even at the highest drug concentration. We then used optical tweezers to evaluate whether the adhesion properties of particles had changed on a ‘more subtle level’ in the presence of heparin. As with the PEG-coated particles (Fig. 3b) we used the OT to pull on nanoparticles adhered to the endothelium (500 mW laser power). These experiments show that there was no significant difference in the adhesion properties in the presence or absence of heparin (Supplementary Fig. 6).

Optical trapping and manipulation of injected bacteria

After having demonstrated trapping of injected particles and naturally occurring zebrafish cells inside the living zebrafish larva, we tested whether this approach can also be applied to study injected bacteria. Bacteria were amongst the first biological particles to be optically trapped in vitro in aqueous solutions 2 , but as far as we know there are no reports of trapping bacteria inside living vertebrates. Rod-shaped bacteria are more difficult to trap than spherical (polystyrene) particles and they are smaller than macrophages and erythrocytes. As a proof of principle of optical manipulation of bacteria in zebrafish, we injected the fish bacterium M. marinum, which causes fish tuberculosis, and which has been widely and effectively used as a model for human tuberculosis in the zebrafish larva 12,30 .

For this experiment we selected a region where the blood flow was very slow (again using tricaine), and using either fluorescence or transmission imaging, we could detect the presence of (red fluorescent) bacteria that had been injected (Fig. 4). Next, a bacterium was trapped and moved against the endothelium using the OT (Supplementary Movie 11). Before the trap was activated, the bacterium was seen moving in a Brownian manner through the blood vessel, rotating and diffusing. It could be imaged in a snapshot while oriented in the imaging plane (Fig. 4a, see also Supplementary Movie 11). Activating the optical tweezers (Fig. 4b) resulted in the bacterium becoming orientated in a direction perpendicular to the imaging plane (in the direction of the tweezer beam). This reorientation is expected for elongated objects. Next, the bacterium was pushed against the endothelium (Fig. 4c). Intriguingly, in Fig. 4d a cell (presumably a macrophage 31 ) could be observed crawling towards the contact point. After the bacterium was repeatedly moved against the endothelium, the immune cell was seen to arrest its movement and finally seemed to ‘decide’ to move across the endothelial barrier (Fig. 4g-i). Macrophages are known to collect bacteria 31 , and controlling the position and timing of bacteria and interactions with different cells makes it possible to study this phenomenon in a controlled manner. The OT can for example be used to determine how long a bacterium needs to stay in contact to adhere to a cell or to evoke a response, or whether multiple bacteria will increase the recruitment of macrophages or influence phagocytosis dynamics.

(a) A diffusing bacterium (purple arrow) is (bd) trapped, pushed against and moved away from the endothelium (red line in a). This seems to activate an immune cell (green arrowheads), which moves towards the contact point (cf). Repeated contact with the endothelium seems to again attract the attention of the crawling cell, which (gi) finally moves into the vein. The total duration of experiment is ∼ 2 min. Scale bar, 10 μm. Experiment was repeated at least 4 times.

We also tested the effects of anti-inflammatory drugs on the migration of immune cells to bacteria-invaded areas. Our preliminary experiments using fish lines with either fluorescent neutrophils or fluorescent macrophages confirmed that the anti-inflammatory drugs diclofenac and indomethacin 32 inhibited the recruitment of neutrophils (and macrophages to a lesser degree, unpublished results) to sites where bacteria had been injected 12 . However, these experiments need a systematic follow-up for their significance to be verified.

Collectively, the experiments we have described demonstrate for the first time active micromanipulation of a full scale of nano- to micron-sized structures inside a living vertebrate using the transparent zebrafish larva. The manipulated structures ranged from injected nanoparticles and bacteria to naturally occurring zebrafish cells as erythrocytes and macrophages.

We foresee many uses of this approach such as (but not limited to), the characterization of interaction properties of nanoparticles with specific cells for nanomedicine applications. In particular the properties of nanoparticles could be studied, for example, by functionalizing them with ligands for targeting to specific cells or with coats such as PEG to prevent interactions with other cells. Alternatively, optically manipulated nanoparticles releasing a specific compound could be brought in the proximity of the organismal structure of interest for testing of local cellular responses to chemicals (as has been already demonstrated elegantly with cells in vitro 33 ) such as for studies of vascular function and endothelial integrity.

Controlled investigations of recruitment and activation of immune cells, by micromanipulating bacteria, other microorganisms or antigen-coated particles to specific regions in the organism will make possible to investigate adhesion to and activation/recruitment of immune cells, for example in the presence of anti-inflammatory drugs, especially in combination with imaging. Finally, quantitative optical tweezers have been instrumental to understanding cellular biomechanical properties and their regulatory role in function. However, this has been mostly done in vitro with cells in culture, and the work presented here opens up many possibilities to perform such experiments throughout a living vertebrate.

4. Nanoparticle applications in biology

4.1 Nanoparticles as sensors

NP platforms such as gold NPs have been extensively used as sensors due to their surface chemistry. One method of using the unique surface chemistry of gold NPs for signal transduction amplification is the bio-barcode method developed by the Mirkin group. This method has been applied for protein 50 and DNA 51 target detection. For target DNA detection, PCR-like sensitivity can be achieved. This technique has been reported for the detection of cytokines at a concentration of 30 aM (attomolar) 52 and for the detection of a soluble pathogenic biomarker for Alzheimer's disease at a concentration around 100 aM. 53 More recently, the group used this method to detect prostate-specific antigen (PSA), a commonly investigated cancer biomarker that can indicate the presence of prostate cancer when expressed at elevated levels. 54 In the bio-barcode assay approach, DNA-functionalized gold NPs (30 nm) are conjugated to PSA-specific antibodies to generate PSA gold NP probes (Fig. 2). 55,56 The DNA strands are the bio barcodes. A magnetic microparticle (MMP) functionalized with monoclonal antibodies to PSA is mixed with the PSA target protein. After a washing step, the PSA gold NP probes are added to the MMP-bound PSA. After further separation by magnetic field application and wash steps, the PSA-specific DNA barcodes are released into solution and analyzed using the scanometric assay, which takes advantage of gold NP catalyzed silver enhancement. This assay achieved a sensitivity of 330 fg mL −1 of PSA.

Fig. 2 The bio-barcode method. (A) Development of the NP probe. (B) Method of detection using prostate specific antigen-conjugated gold NP probes. Reproduced from ref. 56.

The DNA bio-barcode method combines the ability to conjugate a large number of DNA strands onto gold NP surfaces and the detection of these DNA strands using techniques such as PCR amplification or scanometric assays. Another approach for sensing that uses optical properties of the NP surface has been developed by the Rotello group. 57 They found that anionic fluorescent polymers may reversibly bind and dissociate from functionalized cationic gold NPs through non-covalent chemical interactions. When the fluorescent polymer is bound to the NP, its fluorescence is quenched. When it is dissociated from the NP, the fluorescence is restored. This phenomenon is the basis of a “chemical nose” system. 58 In this system, the target protein is detected according to its different fluorescence responses upon binding to different types of surface-modified gold NPs. A fluorescence response pattern is generated and then analyzed through statistical methods. This process can detect, quantify, and distinguish different molecular targets from each other. This process was initially developed for the detection and sensing of proteins, 58 but has also been adapted for the detection and sensing of bacteria, 59 for the detection of physicochemical differences between healthy, cancerous and metastatic human breast cells, and for the differentiation of isogenic healthy and transformed cells (Fig. 3). 60,61 “Chemical nose” sensing also provides the advantage of not using antibodies for detection since the identity of the target analyte does not need to be known in order to detect the analyte.

Fig. 3 Interactions between NP–GFP complexes and cell surfaces generate different fluorescence patterns. Reproduced from ref. 61.

Gold NPs can also enhance surface-enhanced Raman scattering (SERS) for detection and identification of biomolecules at the NP surface. The SERS technique has been frequently used to detect specific analytes through their unique vibrational spectra. The narrow width of SERS spectra allows for multiple analyte detection within complex mixtures, including detection down to the single-molecule level. 33 Thus, SERS techniques have been used for ultrasensitive detection of biomolecules such as glucose, 62 hemoglobin, 63 bacteria, 64 and viruses. 65 Using this approach, a group demonstrated that gold NPs encoded with Raman reporters and conjugated with single-chain variant fragment (ScFv) antibodies can target cancer biomarkers such as epidermal growth factor receptors (EGFR) in vitro and in vivo (Fig. 4). 66,67 Recently, investigators also demonstrated a SERS system based on a thin-film NP array self-assembled at the liquid–liquid interphase for multi-phase trace analyte detection. 68 The group was able to detect single phase analytes as well as multiple analytes dissolved in water and organic phases.

Fig. 4 Surface-enhanced Raman scattering (SERS) spectra and the correlated surface plasmon imaging of single cancer cells tagged with ScFv-conjugated gold NPs. Reproduced from ref. 67.

Nanosensors have also been developed that exploit the magnetic properties of magnetic NPs such as SPIONs. There is considerable interest in magnetic NPs since they have strong magnetic properties and most biological samples exhibit negligible magnetic susceptibility. 69 SPIONs have been used as magnetic tags for many different types of sensors including giant magnetoresistive (GMR) biosensors, which are based on the binding of magnetic particles to a sensor surface. 70 The magnetic fields of the particles can alter the magnetic fields of the sensor, resulting in changes in the electrical resistance of the sensor. Recently, Wang and colleagues at Stanford University have demonstrated the use of this technique for a protein detection assay in which an array of GMR sensors is used to detect binding events of proteins to arrays of surface-bound antibodies with the use of SPIONs as magnetic tags. 71 In this assay, the target antigen is between two antibodies, one bound to the sensor and the other tagged with a SPION. The presence or absence of the magnetized NP is detected by the underlying sensor. The group demonstrated the assay to be matrix insensitive to various biological fluids, but still capable of detecting proteins down to attomolar concentrations and over an extensive range of concentrations. Using a similar strategy, they have also demonstrated the detection of cancer-associated proteins in 50% serum at sub-picomolar concentrations using MACS particles (commercialized SPIONs for cell separation). 72 Recently, they have used streptavidin functionalized antiferromagnetic NPs to detect DNA with high sensitivity (10 pM). 73

The superparamagnetic property of IONPs is also the basis of magnetic relaxation switching. The Weissleder group has studied magnetic relaxation switches consisting of 3–5 nm SPIONs coated with 10 nm thick dextran and stabilized by crosslinking. 74 Targeted SPIONs are developed by functionalizing them with amino groups for the attachment of a range of sulfhydryl-bearing molecules. 75 The nanoswitches can undergo reversible assembly (clustering and declustering) in the presence of a molecule that is recognized by the ligands immobilized on the NP, resulting in a change in the transverse magnetic relativity (1/ T 2) of surrounding water protons. The changes in relaxation rates as a result of NP assembly can be used to detect a variety of biological targets including DNA and proteins at the low femtomole level (0.5–10 fmol). 76 Recently, the Weissleder group developed a portable chip-based diagnostic magnetic resonance (DMR) system for rapid and quantitative detection of biological targets. 77 The DMR also uses IONPs as sensors to amplify molecular interactions caused by assemblies of SPIONs. They demonstrated proof of concept by detecting with high sensitivity the presence of proteins in parallel and by detecting bacteria. Compared to the benchtop NMR relaxometer, the DMR system had a mass detection limit improved by two orders of magnitude (detection limit of 15 fmol).

Magnetic NP relaxation sensors have also been used in assays in which the basis of the assay is the relaxation of the magnetic moments within magnetic NPs. 78 Brownian relaxation is the dominant mechanism for these NP biosensors. In this method, NPs form aggregates upon recognition of target analytes, leading to a larger hydrodynamic size and thus slower Brownian relaxation responses than individual NPs. Using this principle, a group recently detected a bacterial antibody at the sensitivity of 0.3 nM with an AC susceptometer. 79

The Weissleder group has also used antibody-coated NPs in a microfluidic device to detect bacteria. 82 They also reported that core–shell NPs with Fe metal cores have enhanced sensitivity compared to IONPs for the detection of bacterial cells. Recently, the group also developed an assay based on a magnetic barcoding strategy that did not require antibodies and could detect single-gene mutations. 83 In this approach, PCR-amplified mycobacterial genes are sequence-specifically captured on polymeric beads that are modified with complementary DNA, labeled by SPIONs, and detected by NMR. The platform could detect M. tuberculosis and identify drug-resistance strains from sputum samples within 2.5 h. The investigators also developed a similar system that uses rRNA as a target marker for NP labeling. 84 The approach used a universal and specific nucleic acid probe that detects 16S rRNA, which is abundant in and common to many bacterial species. The device was sensitive enough to detect as few as 1–2 E. coli bacteria in 10 mL of blood and accurately estimate bacterial load.

Many groups have also utilized small molecule functionalized NPs to label bacteria. One group developed a magnetic glyco-NP based system that could detect E. coli strains in 5 minutes and enable up to 88% removal from the sample by exploiting the bacterial interaction with carbohydrates on mammalian cell surfaces (Fig. 5). 85,86 Another group reported the use of vancomycin-modified SPIONs in a magnetic capture assay for various Gram-positive and Gram-negative bacteria. 87 They also demonstrated that as size and ligand coverage on the NP increase, the time required for efficient labeling to the bacteria with the NPs decreases.

Optical biosensing of bacteria has also been employed using both metallic NPs and QDs. The bio-barcode assay approach 50 provides amplification and the possibility of simultaneously detecting many different targets in one sample. Using this method, Bacillus subtilis double-stranded genomic DNA was detected at a 2.5 fM concentration. 88 Similarly, Salmonella enteritidis was detected at 0.2 fM. 89 QDs have also been used as pathogen sensors. Edgar et al. reported a technique that combined in vivo biotinylation of engineered host-specific bacteriophage and attachment of the phage to streptavidin-coated QDs. 90 The method provides specific detection of E. coli among several different bacterial strains and can detect as few as 10 bacteria per mL of the experimental samples.

NP immunomagnetic techniques are some of the more commonly used methods for the identification and capture of CTCs. These techniques involve the use of magnetic NPs to target and isolate CTCs using a ligand–receptor based mechanism. Currently, the CellSearch device, which uses an immunomagnetic technique, is the only FDA-approved test for CTC assessment. 92,93 CellSearch is based on a positive epithelial cell adhesion molecule (EpCAM) selection of the CTCs and utilizes iron NPs coated with a polymer layer carrying biotin analogues and conjugated with anti-EpCAM, for the capture of CTCs in vitro . This system can also be used for the labeling and identification of leukocytes using an anti-CD45-APC antibody as the NP targeting ligand. Recently, a group also demonstrated that IONPs functionalized with anti-HER2 or anti-HER2/neu could be used to separate 73.6% of HER2/neu over-expressing cancer cells that were spiked in 1 mL of blood. 94 The receptor–ligand interactions resulted in the preferential capture of the cancer cells. In another preclinical study, in vivo CTC detection approach was achieved using PEGylated magnetic NPs. 95 Investigators dually targeted CTCs in vivo with magnetic NPs conjugated with plasminogen activator (uPA) and folate-targeted nanotubes for subsequent detection using photoacoustic flow cytometry.

The incorporation of polymers, which can enable targeted detection and surface capturing, in other organic and inorganic NP platforms can potentially lead to novel NP sensors for CTC detection. 96 Recently, a group used targeted polymer coated gold NPs and the SERS technique to directly measure CTCs in the presence of white blood cells (Fig. 6). 97,98 EGF peptides were conjugated to the polymer coated gold NPs that were encoded with QSY reporters. The NPs successfully identified CTCs in the peripheral blood of 19 patients with squamous cell carcinoma of the head and neck, with a sensitivity range of 1 to 720 CTCs per mL of whole blood.

Fig. 6 Surface-enhanced Raman scattering (SERS) detection of circulating tumor cells. (A) Schematic of EGF peptide-conjugated NPs. (B) SERS spectra of different numbers of cancer cells spiked into the white blood cell sample. (C) SERS spectra of a blood sample incubated with targeted and non-targeted NPs. Reproduced from ref. 98.

Other techniques for identification and separation of cells include the use of biomimetic nanotechnology, which takes advantage of naturally occurring processes. The Hong group has investigated biomimetic approaches to develop microfluidic devices for the identification and separation of cells. These devices exploit the natural process of cell rolling, which results from adhesive interactions between selectin molecules expressed on the endothelial venules and glycoprotein receptors on the cancer cells. 99 Recently, the cell rolling process using E-selectin was applied to CTC detection for enhanced surface sensitivity and specificity. 100 Seventh-generation (G7) poly(amidoamine) (PAMAM) dendrimers were also used to engineer cell capture surfaces for simultaneous binding of multiple ligands to multiple receptors (multivalent binding). The biomimetic combinations of dendrimer-mediated multivalent effect and cell rolling significantly enhanced the surface capture of CTCs.

4.2 Nanoparticles as imaging agents

Inorganic NPs such as QDs are among the most promising fluorescent labels for cellular imaging. QDs can emit light of specific wavelengths and also be tuned to emit in the NIR region of the spectrum, in which tissue autofluorescence is reduced and excitation light penetration increased. 110 Monofunctionalized QDs have been used to track individual proteins in cells 111 and receptors involved in cell movement during development and metastasis. 112 QDs have been used for imaging of specific tumor biomarkers, such as the use of arginine–glycine–aspartic acid (RGD) peptide-conjugated NIR QDs for the targeting of integrin αvβ3. 113 Targeted QDs have also been studied for their capability for multiplex imaging, which involves simultaneous imaging of many molecular targets using different QDs that use different emission wavelengths. Recently, QDs have been applied for multiplex molecular imaging of lymph nodes, 114 embryonic stem cells, 115 as well as tumor cells and vasculature. 116,117

Gold NPs have been studied as a non-invasive modality for in vivo cancer imaging using small organic molecules as near-infrared (NIR) SERS reporters. Recently, antibody conjugated gold NPs were used in conjunction with a sensitive and stable cyanine reporter that was developed and screened from a combinatorial library of SERS reporters for the detection of HER2-positive tumors in xenograft models. 118 Other recent in vivo imaging efforts have been directed towards the use of several targeted SERS gold NPs for multiplexed imaging in mouse models. 119,120

Magnetic NPs are one of the more well studied NP platforms for targeted molecular imaging. Magnetic NP imaging systems have shown potential for real-time visualization of biological events, such as cell migration/trafficking, 121–123 enzyme activities, 124 and other biological interactions at the molecular and cellular level. 25 Magnetic NPs have also shown promising use as contrast agents in magnetic resonance imaging (MRI), a biomedical technique based on nuclear magnetic resonance of various interacting nuclei. SPIONs, formed from iron oxide crystals coated with dextran or carboxydextran, are widely used MRI contrast agents for cancer imaging. 20 When injected into patients, SPIONs have been shown to remain in the tumors 24 hours after injection compared with 1 hour for gadolinium-based MR agents. 125 This difference is due to easier uptake of the NP by the tumor and lower diffusivity of the NP out of the tumor.

Many studies have investigated the use of SPIONs for the targeted detection of tumors and their metastases. 126–129 SPIONs have also been targeted to cancer cells without using targeting ligands. In one study, it was demonstrated that a recombinant human heavy-chain ferritin protein shell containing IONPs targeted tumor cells overexpressing transferrin receptor 1. 130 The iron oxide core also catalyzed the oxidation of peroxidase substrates in the presence of hydrogen peroxide to produce a color reaction that is used to visualize tumor tissues. In another study, investigators assembled SPIONs and targeting peptides on a modified viral scaffold to increase the number of SPIONs reaching tumor cells. 129 Glutamic acid residues were introduced into the protein coat of M13, a virus that infects bacteria. The negatively charged residues promoted the electrostatic assembly of NPs along the M13 coat's filamentous structure. The viral coat was also rendered to display a peptide that targets SPARC glycoprotein, which is overexpressed in various cancers. Compared to traditional approaches where NPs are directly functionalized with targeting ligands, this approach may amplify the contrast when performing MR imaging.

Novel NPs with advanced magnetic properties have also been pursued for visualizing biological events. One such class is metal-doped ferrite NPs with a composition of MFe2O4, where M is +2 cation of Mn, Fe, Co or Ni, to tune specific magnetic properties. 127 MnFe2O4 NPs were found to be non-toxic in vitro and possess the highest magnetic susceptibility, suggesting that they may make better MRI probes. When these NPs were conjugated with antibodies, they showed enhanced MRI sensitivity for the detection of cancer markers. Other NP platforms have been combined with SPIONs including dendrimers (magnetodendrimers) 123 and liposomes (magnetoliposomes). 131 These SPIONs have been used for applications such as monitoring the migration of cells or visualizing bone marrow in vivo . 132

4.3 Nanoparticles as delivery vehicles

NPs offer a potential solution to the challenges in siRNA delivery. Cationic lipid or polymer NPs have been used to transport anionic nucleic acids into cells due to their ability to form a condensed complex with nucleic acids. 136 This stabilizes and protects them from enzymatic degradation. Cationic materials can also help NPs escape sequestration in endosomes/lysosomes. Groups such as the nitrogens in the cationic polymer polyethyleneimine (PEI), which become protonated in the pH environment of the endosomes/lysosomes, can facilitate endosomal escape by increasing Cl influx in response to protonation at acidic pH. The result is an increase in osmotic pressure and swelling, which leads to organelle burst and delivery of the siRNA NPs. This phenomenon is referred to as the “proton sponge effect”. However, a recent study showed that siRNA delivery in a cationic lipid NP system was substantially reduced as approximately 70% of the internalized siRNA was recycled to the extracellular media due to the exit of the lipid NPs from late endosomes/lysosomes. 137 Thus, siRNA delivery might be improved by designing novel NP vehicles that can escape the recycling pathways. Active targeting methods of non-endocytic uptake of NP delivery of nucleic acids have also been explored using fusogenic peptides and cell penetrating peptides. 138 To better understand siRNA NP interactions with biological systems, siRNA probes have been used to study intracellular trafficking 139 as well as assembly and disassembly of siRNA NPs. 140

Recently, NPs have been used to deliver siRNA to silence genes in immune cells since these cells can have pivotal roles in homeostasis and disease. 141 In one study, NPs were used to selectively silence Cyclin D1 (CyD1), a cell cycle-regulatory molecule, in leukocytes in vivo to determine the exact role of the molecule in gut inflammation. 141 NPs were loaded with CyD1 siRNA and functionalized with antibodies to β7 integrin. The study revealed that these targeted NPs silenced CyD1 in leukocytes and reversed experimentally induced colitis in mice by suppressing leukocyte proliferation and T helper cell 1 cytokine expression. Another recent report also described the use of lipid NPs for the in vivo delivery of siRNA to silence disease genes in immune cells. 142 The study demonstrated siRNA-mediated silencing in myeloid cell types of nonhuman primates and established the feasibility of targeting multiple gene targets in rodent myeloid cells. The therapeutic potential was validated using siRNA targeting tumor necrosis factor-α (TNFα). Another study used NPs to explore the immunological mechanisms triggering nonalcoholic steatohepatitis (NASH). 142 The investigators found that TNFα produced by Kupffer cells can trigger the development of NASH through the enhanced production of chemokines IP-10 and MCP-1. Moreover, TNFα silencing in myeloid cells reduced the chemokine production and prevented the development of NASH, suggesting potential of TNFα as a novel therapeutic target in NASH.

NPs have also been used as vehicles to deliver siRNA in plant cells to study cellular pathways at the single cell level. 143 One group used amine-conjugated polymeric NPs as vehicles to deliver siRNA targeting specific genes in the cellulose biosynthesis pathway. They found that NtCesA-1 , a factor involved in cell wall synthesis in whole plants, also plays an essential role in cell wall regeneration in isolated protoplasts.

The ability to easily modify and functionalize NPs has resulted in recent interest in using these vehicles to deliver agents to subcellular organelles. Targeted NPs can bind to targets localized on the cell surface and enter the cell through endocytosis. However, if the target is located intracellularly, NPs and their cargo may not be able to reach the target of interest due to intracellular sequestration of the NP or due to the lack of subcellular targeting capabilities. In particular, NPs carrying oligonucleotides need to escape the endosome and then be targeted to be effective. Tools for effective subcellular targeting are emerging for targeted delivery to the nucleus, 146 cytosol, 147 mitochondria, 148 endosomes, 149 and lysosomes. 150 In general, two approaches are being investigated for the design of NPs for subcellular targeting: (1) passive targeting of NPs to a particular organelle by varying NP characteristics such as size, shape, and composition 151 and (2) active targeting of NPs to the organelle of interest by functionalizing NP surfaces with targeting ligands directed towards the organelle. These approaches have been applied with varying levels of success.

Hurdles to successful sub-cellular targeting include biological barriers specific to the target organelle. For example, NPs targeted to the nucleus must enter the cell membrane, escape endosomal–lysosomal pathways, possess a way to interact with the nuclear pore complex, and be small enough to cross the nuclear membrane. 146 Targeting ligands such as the nuclear localization signal (NLS) have been used to enhance nuclear delivery by the active transport mechanism. 152 In one study, the localization of NLS conjugated gold NPs at the nucleus of a cancer cell damaged the DNA. 152 In contrast, in another study, NLS conjugated gold NPs were not able to target the nucleus of cells from outside the plasma membrane because they were unable to enter the cells or were trapped in the endosomes. Instead, NPs conjugated with both NLS and receptor-mediated endocytosis (RME) peptides reached the nucleus. 153

For NPs targeted to the mitochondria, biological barriers include intracellular transport to the mitochondria and outer and inner mitochondrial membranes and toxicity. 154 Thus far, most studies have primarily developed metal oxide or liposomal NPs for delivery to the mitochondria. Delivery to the mitochondria has also been based on electrostatic interactions between the NP and the organelle. The mitochondria have a negative membrane potential compared to other cellular membranes, which can lead to the accumulation of lipophilic cations. 155 This concept was utilized in the fabrication of stearyl triphenyl phosphonium (STPP) targeted liposomes with anti-cancer agents ceramide 156 and scarleol 157 to target the mitochondria. STPP was chosen since it exhibits both cationic and lipophilic properties. Another group used a polymeric NP system to deliver mitochondria-acting therapeutics to their destination. 158 The NPs were synthesized with a lipophilic triphenylphosphonium (TPP) cation, which is known to cross into the mitochondrial matrix space. Through in vitro screening of a library of NPs with varying charge and size, the group identified an optimized targeted NP that improved the efficacy and decreased the toxicity for cancer, Alzheimer's disease, and obesity compared with non-targeted NPs or the small molecule therapeutics. 158

4.4 Effects of biology on NPs

Recently, it has been shown that the uptake of NPs by cells in vitro can be influenced by the cell cycle phase. 104 The study found that NPs internalized by cells are not exported from cells, but are split between daughter cells when the cell divides. The results may have implications for clearance or accumulation of NPs in vivo . Another recent study demonstrated that the global immune status, such as the balance of Th1–Th2 cytokines and M1–M2 macrophages, can also affect the NP clearance process. 105 The investigators showed that mouse strains that are prone to Th1 immune responses cleared NPs at a slower rate than Th2-prone mice. Macrophages isolated from the Th1 strains also took up fewer particles in vitro than macrophages from Th2 strains. The results were confirmed in human monocyte-derived macrophages, suggesting that global immune regulation may affect NP clearance in humans.

Due to their small sizes and the EPR effect, NPs are often passively or actively targeted to cancer tumors. 106 Yet the clearance and distribution of NPs can also greatly depend on the tumor vasculature. Jain and colleagues have suggested that leaky and poorly organized blood vessels of cancerous tumors can result in an increase in the interstitial fluid pressure inside tumors, reducing blood supply to them and thus impairing delivery of agents to the tumors. 107 They showed that repairing the abnormal vessels in mammary tumors, by blocking vascular endothelial growth factor receptor-2, improves the delivery of smaller NPs (12 nm), while hindering the delivery of larger NPs (125 nm). The role of other proteins such as TGF-β in normalizing tumor vasculature for NP delivery in tumors has also been explored. 108 TGF-β blockade was found to significantly decrease tumor growth and metastasis in mice. It also increased the recruitment and incorporation of perivascular cells into tumor blood vessels, increased the fraction of perfused vessels, and decreased the collagen I content of the tumor interstitial matrix. The investigators found that as a result of the vessel and interstitial matrix normalization, TGF-β blockade improved the intratumoral uptake of NP therapeutics, leading to better control of tumor growth.

4.5 Nanoparticles to study biological processes

NP platforms can also enable the local perturbation of protein activities in cells at a subcellular scale. In particular, magnetic NPs can be coated with a biocompatible surface layer that can be functionalized with ligands that target specific cell-surface receptors, which then can be activated remotely by applied magnetic fields. In a recent study, investigators used this approach to study how NP mediated activation of specific signaling pathways can lead to changes in cellular responses. 161 The magnetic NPs are attached with active signaling proteins, and can be displaced by magnetic forces into different locations of the cell. Once these protein-conjugated NPs are inserted into the cells, they bind partner proteins at their surfaces and locally stimulate signal transduction pathways. This strategy was applied to members of the Rho-GTPases, a set of molecular switches known to regulate cell morphology. NP mediated Rac1 signal was found to induce actin polymerization in protrusive areas of cells while no NP induced actin polymerization was observed in the other areas of the cell, suggesting that Rac1 associates with another partner to polymerize actin in the regions of high membrane activity. The investigators demonstrated that the NP-mediated activation of signaling pathways could also lead to a local alteration of cellular morphology and remodeling of the actin cytoskeleton. Thus, the strategies used in this study could be used to enhance understanding of how other biomolecules are spatially modulated and integrated at the cellular level.

The use of magnetic NPs for controlling cell signaling pathways was demonstrated in another study by Cheon and colleagues. 162 The group showed that functionalized magnetic NPs could turn on apoptosis cell signaling when a magnetic field is applied. The magnetic switch developed consisted of zinc-doped IONPs conjugated with a targeting antibody for death receptor 4 (DR4) of DLD-1 colon cancer cells. When a magnetic field was applied to aggregate DR4-conjugated IONPs bound to cell surface receptors, an apoptosis signaling pathway was promoted. This magnetic control of apoptosis was demonstrated in vivo using zebrafish as a model organism. IONPs can also be used to activate cells and remotely regulate protein production. 163,164 Stanley and colleagues used anti-His conjugated IONPs to bind to a modified epitope tagged TRPV1 channel. The temperature sensitive TRPV1 channel was activated with local heating of bound anti-His IONPs, resulting in activation of a Ca 2+ -sensitive promoter that stimulated the synthesis and release of bioengineered insulin. This result along with lowered blood glucose was confirmed in vivo with mice expressing the bioengineered insulin gene. The investigators further showed that cells can be engineered to synthesize genetically encoded ferritin NPs and inducibly release insulin. The use of IONPs in noninvasive techniques for cell manipulation potentially provides a useful tool for basic biology research.

Other inorganic NP platforms have also shown potential as tools to regulate cellular activities with spatial and temporal control. Recently, infrared-absorbing gold NPs were used as optical switches of gene interference and were remotely controlled using light. 165 The technique involved functionalizing the NPs with double-stranded oligonucleotides and at specific times and intracellular locations, NIR illumination was used to photothermally heat the gold NPs, causing the double-stranded oligonucleotides to denature at their melting temperature and the antisense oligonucleotides to be released from the carriers.

On a macroscopic scale, the spatial organization of cells in cell culture can be important in basic biology research. Since cellular activities in conventional 2D cell culture differ from those found in vivo , many efforts have focused on developing 3D cell culture for a more physiologically relevant microenvironment. Recently, Pasqualini and colleagues reported an innovative approach to 3D tissue culture based on the magnetic levitation of cells with a hydrogel consisting of gold NPs, IONPs, and M13-derived phage particles that display integrin-targeting ligands. 163 By spatially controlling the magnetic field, the authors were able to control the geometry of the cell mass and produce concentrated clustering of different cell types in co-culture. They also found that magnetically levitated human glioblastoma cells showed similar protein expression profiles to those observed in human tumor xenografts. The results indicate that magnetic levitation of cells may be a useful method for recapitulating in vivo protein expression without the use of a specific medium, engineered scaffolds or matrices.

Nanoparticles disguised as red blood cells to deliver cancer-fighting drugs

Researchers at the University of California, San Diego have developed a novel method of disguising nanoparticles as red blood cells, which will enable them to evade the body's immune system and deliver cancer-fighting drugs straight to a tumor. Their research will be published next week in the online Early Edition of the Proceedings of the National Academy of Sciences.

The method involves collecting the membrane from a red blood cell and wrapping it like a powerful camouflaging cloak around a biodegradable polymer nanoparticle stuffed with a cocktail of small molecule drugs. Nanoparticles are less than 100 nanometers in size, about the same size as a virus.

"This is the first work that combines the natural cell membrane with a synthetic nanoparticle for drug delivery applications." said Liangfang Zhang, a nanoeningeering professor at the UC San Diego Jacobs School of Engineering and Moores UCSD Cancer Center. "This nanoparticle platform will have little risk of immune response."

Researchers have been working for years on developing drug delivery systems that mimic the body's natural behavior for more effective drug delivery. That means creating vehicles such as nanoparticles that can live and circulate in the body for extended periods without being attacked by the immune system. Red blood cells live in the body for up to 180 days and, as such, are "nature's long-circulation delivery vehicle," said Zhang's student Che-Ming Hu, a UCSD Ph.D. candidate in bioengineering, and first author on the paper.

Stealth nanoparticles are already used successfully in clinical cancer treatment to deliver chemotherapy drugs. They are coated in a synthetic material such as polyethylene glycol that creates a protection layer to suppress the immune system so that the nanoparticle has time to deliver its payload. Zhang said today's stealth nanoparticle drug delivery vehicles can circulate in the body for hours compared to the minutes a nanoparticle might survive without this special coating.

But in Zhang's study, nanoparticles coated in the membranes of red blood cells circulated in the bodies of lab mice for nearly two days. The study was funded through a grant from the National Institute of Health.

A shift towards personalized medicine

Using the body's own red blood cells marks a significant shift in focus and a major breakthrough in the field of personalized drug delivery research. Trying to mimic the most important properties of a red blood cell in a synthetic coating requires an in-depth biological understanding of how all the proteins and lipids function on the surface of a cell so that you know you are mimicking the right properties. Instead, Zhang's team is just taking the whole surface membrane from an actual red blood cell.

"We approached this problem from an engineering point of view and bypassed all of this fundamental biology," said Zhang. "If the red blood cell has such a feature and we know that it has something to do with the membrane -- although we don't fully understand exactly what is going on at the protein level -- we just take the whole membrane. You put the cloak on the nanoparticle, and the nanoparticle looks like a red blood cell."

Using nanoparticles to deliver drugs also reduces the hours it takes to slowly drip chemotherapy drug solutions through an intravenous line to just a few minutes for a single injection of nanoparticle drugs. This significantly improves the patient's experience and compliance with the therapeutic plan. The breakthrough could lead to more personalized drug delivery wherein a small sample of a patient's own blood could produce enough of the essential membrane to disguise the nanoparticle, reducing the risk of immune response to almost nothing.

Zhang said one of the next steps is to develop an approach for large-scale manufacturing of these biomimetic nanoparticles for clinical use, which will be done through funding from the National Science Foundation. Researchers will also add a targeting molecule to the membrane that will enable the particle to seek and bind to cancer cells, and integrate the team's technology for loading drugs into the nanoparticle core so that multiple drugs can be delivered at the same time.

Zhang said being able to deliver multiple drugs in a single nanoparticle is important because cancer cells can develop a resistance to drugs delivered individually. By combining them, and giving the nanoparticle the ability to target cancer cells, the whole cocktail can be dropped like a bomb from within the cancer cell.

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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. Interface11, 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.

1. Introduction

A number of biophysical barriers can prevent circulating agents from accumulating at tumour sites at satisfactory levels. Thus, the delivery efficiency of drug molecules as well as imaging agents can be very low. The biophysical barriers include the sequestration in the reticulo-endothelial system (RES) organs [1,2], cellular uptake by immune cells [3,4], degradation by protein absorption (opsonization) within the blood flow [5], low permeability of the blood vessels and adverse interstitial fluid pressure in solid tumours [6–10]. Therefore, the freely administrated drug molecules cannot be efficiently delivered into the tumour site. For instance, only less than 0.1% of the injected drug molecules can be found in 1 g of tumour tissue, signalling the inefficient delivery of these free molecules. However, when these molecules are encapsulated into liposomes, their peak accumulation can be improved by one or two orders of magnitude. Thus, it opens a new avenue for the nanoparticle (NP)-based drug carriers to efficiently deliver the drug molecules or imaging agents into the diseased sites.

In cancer treatment and imaging, the standard strategy for maximizing NP accumulation at the tumour sites relies on the enhanced permeation and retention (EPR) effect [11–14]. At the tumour sites, the vessel walls tend to be discontinuous with fenestrations. The size of these fenestrations is approximately 100–200 nm for mice, depending on the tumour type, stage and location [11]. Therefore, sufficiently small NPs (smaller than the size of fenestrations) can passively exit tumour vessels and diffuse into the tumour tissue. The accumulation of these NPs usually reaches a peak 12–24 h after injection. Then, these NPs should be sterically stabilized and opsonization-resistant within the blood flow, in order to allow long circulation times (hours to days). However, major RES organs, such as the liver and spleen, are also characterized by a fenestrated endothelium and adopt the same mechanism to sequester the foreign circulating objects, i.e. drug molecules and NPs. Thus, not surprisingly, most of the systemically injected drug molecules and NPs accumulate in the RES organs. In addition to this, we should emphasize that the EPR-based delivery strategy is solely and exclusively limited to cancer therapy and imagining, and does not provide a general method for drug delivery, as discussed by Nie [15]. Therefore, the design principle for drug carriers has been extended by not only considering the EPR effect (passive targeting) but also the local environment (active targeting), such as pH value [16,17], for targeted drug delivery.

Up to date, there are several classes of NPs demonstrating promising properties as therapeutic carriers, such as solid lipid NPs, liposomes, quantum dots, dendrimers and polymer micelles. By loading the drug molecules into these NPs, their bio-distribution, pharmacokinetics and toxicity can be dramatically improved, in comparison to their freely administrated counterparts [19–21]. Nevertheless, the accumulation of these NPs in the diseased sites is still undesirably low and can be improved. To resolve this issue, there are many strategies developed for designing efficient NP-based drug carriers [22–24]. For example, vascular targeting has been proposed as a general strategy to enhance the concentration of NPs and the associated drug molecules, within the diseased tissue. In this case, injected NPs are decorated with targeting moieties (ligands) that specifically recognize and firmly bind to the over-expressed specific receptors on the abnormal vessels walls [25–27].

The physiochemical properties of NPs, such as size, shape, surface functionality and stiffness (4S parameters), can affect their biological clearance [18,23,24,28,29]. Therefore, NPs can be modified in various ways to extend their circulation time [13,14]. In the past decades, the design of NPs for biomedical applications has been advanced by studying their biological responses. The evolution of the NP carriers has followed advances in understanding of how 4S parameters affect their efficacy. As shown in figure 1, there are three generations of NPs developed for biomedical applications [18,23]. In the first generation of NPs, they are functionalized with basic surface chemistries (charges/ligands) and are evaluated through their biocompatibility and toxicity. However, these NPs are unstable and usually internalized by the immune cells (macrophages) during circulation. To overcome these problems, in the second generation, the surfaces of NPs are grafted with polymer chains, improving their water solubility and allowing them to avoid aggregation and opsonization. Compared with the first generation, the second generation of NPs demonstrate improved stability and targeting in biological systems. However, the active targeting of these NPs to the tumour cells or other diseased cells is still disappointing. Thus, the third-generation NPs shifts the design paradigm from stable materials to ‘intelligent’ and environmentally responsive materials with improved targeting capabilities. Local environmental (i.e. pH value) changes cause the properties of these NPs to change in a prescribed way. Here we should emphasize that although the design of NPs shifts from the first generation to the third generation, the first- and second-generation NPs still have many applications in different areas, but their behaviours are still poorly understood. Moreover, a comprehensive understanding on the first- and second-generation NPs will help us to efficiently design the third-generation NPs, which will be pursued in this study.

Figure 1. Evolution of the design of nanoparticles with their properties and biological challenges. MPS, EPR and PEG denote mononuclear phagocyte system, enhanced permeation and retention and polyethylene glycol, respectively. See the main text for more discussions. Adapted from [18]. (Online version in colour.)

When the NP-based drug carriers are injected into the blood flow, they will experience several important steps during their life journey to be delivered into the diseased site [28]: (i) microcirculation with red blood cells (RBCs), white blood cells (WBCs), platelets and many others in the blood flow, (ii) firm absorption by the vessel wall around the tumour site, (iii) diffusing to the tumour site, and (iv) recognition and uptake by the tumour cells. Owing to the complexity of drug delivery process, it is usually difficult to trace the behaviours of NPs step by step in this process and understand their behaviours. On the contrary, with the advancements in computational modelling, the behaviours of NPs within blood flow and their interactions with disease cells can be more accurately quantified [18,28,30–32]. Therefore, the detailed physical mechanisms underpinning the NP-mediated drug delivery can be understood through these simulations, which will be useful in guiding the design of NPs with high efficacy.

This paper is organized as follows. Section 2 summarizes the current knowledge of NP-mediated drug delivery by focusing on the transport of NPs within the blood flow and their subsequent internalization by diseased cells. The effects of NP size and shape will be further explored through immersed molecular finite-element method (IMFEM) simulations in §3. Section 4 will demonstrate how the NPs’ shape and surface functionalization will influence their internalization behaviours. Finally, §5 concludes the present study and discusses the future research directions with the advancements in multiscale modelling.

2. State of knowledge

2.1. Vascular dynamics of nanoparticles

2.1.1. Margination behaviour of nanoparticles

Blood is a dense suspension of deformable cells in plasma, with RBCs comprising approximately 35–45% by volume while WBCs and platelets occupy less than 1%. The volume fraction of RBCs is called haematocrit. In large vessels, due to the high shear rates, blood can simply be modelled as a Newtonian fluid. However, in the microcirculation and near the vessel walls, the transport, rolling and adhesion dynamics of NPs are affected by the presence of RBCs. In particular, it is well documented that fast moving RBCs tend to push circulating WBCs and NPs laterally, thus affecting their dynamics and wall deposition [26,33]. Therefore, in the microcirculation and in proximity of the vessel walls, the potential importance of non-Newtonian effects warrants careful investigation.

In experiments, different components in the blood flow, including the RBCs, WBCs, platelets and NPs, are found to segregate under normal physiological conditions [34,35]. The RBCs tend to migrate away from the vessel wall and concentrate in the middle of the vessel. Thus, a ‘cell-free layer’ is formed near the vascular wall, which is approximately 1 µm thick [36]. However, the WBCs, platelets and some of the NPs prefer to migrate into this ‘cell-free layer’. This behaviour is called ‘margination’. In NP-mediated drug delivery, the drug molecules can be more efficiently delivered to the tumour through the margination behaviour of NPs, which increases NPs' interaction with the vascular wall. This allows the NPs to better ‘sense’ the biophysical and biological abnormalities, such as the presence of fenestrations or the expression of specific receptors, on the surface of endothelial cells. Afterwards, the NP can firmly adhere to the vessel wall under flow, if the hydrodynamic forces are balanced out by the interfacial adhesive interactions between the NP and vessel wall. The adhesive interaction can be specific, i.e. formation of ligand–receptor bonds, and non-specific, i.e. van der Waals, electrostatic and steric interactions. Margination and the subsequent adhesion of NPs to the endothelium allow the NPs to transmigrate across the endothelial wall and enter a diseased area of tissue, eventually delivering the drug molecules. Therefore, irrespective of the targeting mechanism (specific or non-specific), an efficient drug carrier should be able to migrate into the ‘cell-free layer’ at the tumour site, thereby maximizing its interaction with the tumour vascular wall.

2.1.2. 4S parameter effects on margination propensity

Margination propensity depends on the 4S parameters of NPs. The effects of these parameters on NP margination are summarized in table 1. The size of the NP is an important parameter in designing drug carriers. The NPs smaller than 10 nm will be cleaned from the blood stream through the kidney or via extravasation from a tumour [49]. However, the NPs larger than 200 nm are at risk of being filtered out by the liver or spleen or destroyed by the bone marrow. Charoenphol et al. [40] studied the NP size effect by using spheres with diameters ranging from 0.5 to 10 µm in the blood. The margination propensity is found to increase with the sphere diameter. Recently, Lee et al. [38] explored the NP size effect through combined in vivo and in silico studies, by using spherical polystyrene NPs with diameters of 10–1000 nm. The simulation and experimental results confirm that larger NPs (greater than 500 nm) can migrate into the ‘cell-free layer’, while smaller NPs (less than 200 nm) are mostly trapped between RBCs in the core region. However, to date, there is not a consensus on an optimal NP size for margination [31,34,37,38,40].

Table 1. Summary of the effects of 4S parameters on NP margination.

The margination and adhesion of different shaped NPs have been theoretically and experimentally (in vitro) studied. Spherical, quasi-hemispherical and discoidal NPs have been compared [34,35]. Thin discoidal NPs are found to exhibit larger lateral drift velocities (migration rate) than other NPs, under the influence of hydrodynamic forces [34,35]. These results indicate that thin discoidal NPs more probably interact with the vascular wall. Some of the theoretical, in vitro and in vivo experimental results have revealed that thin discoidal particles can more firmly adhere to the lateral walls under shear flow when compared with spherical and slender cylindrical particles [26,50,51]. The thin discoidal NPs are observed to offer a larger surface of adhesion and a smaller cross section, leading to lower hydrodynamic forces and larger adhesive interaction. Similarly, Gentile et al. [35] found that disc-shaped and hemispherical NPs migrated more compared with their spherical counterparts. Moreover, gold nanorods exhibit much higher margination propensity than gold nanospheres, as revealed by Toy et al. [37]. The evidence clearly demonstrates that NP shape can dramatically affect their vascular dynamics.

The effect of NP stiffness has been explored through the margination of WBCs. Freund studied the mixture of RBCs and WBCs in flow [45]. When the stiffness of RBCs was enlarged by a factor of 10, the observed change of margination propensity for WBCs was negligible. Thus, the author concluded that the deformability of RBCs does not affect the margination behaviours of WBCs. Kumar & Graham [46] modelled a dilute suspension of elastic capsules under simple shear flow. Contradictory to the results reported by Freund [45], they found that stiff particles (such as WBCs) tend to marginate, while the soft (‘floppy’) particles (such as RBCs) accumulate near the centre of the channel [46]. Later, they studied a system containing both type of particles and found that the stiff and soft particles mimicked the behaviours of WBCs and RBCs in the blood flow [47], respectively. The margination of stiff particles is attributed to the heterogeneous collisions between these particles [48]. Recently, the deformability (stiffness) of particles and its effect on transport in blood circulation has been noted by the group of DeSimone [52]. They adopted the PRINT approach, which is similar to the hydrogel-template strategy, to demonstrate that deformable microparticles (5 µm) with concave shape can circulate longer than their rigid counterparts [52].

Through Monte Carlo simulations, Wang & Dormidontova [53,54] have studied the binding between a spherical NP tethered with ligands and a planar cell surface with mobile receptors. The core size of the NP, grafting density, tether length and the per cent of functionalization by ligands are found to play important roles in the binding affinity of NPs for the cell surface. Radhakrishnan and co-workers [55,56] have developed a Monte Carlo method to calculate the binding free energy between functionalized NPs and endothelial cell surfaces. The obtained results demonstrate that there exists a critical antibody density, below which the binding affinity drops dramatically. All these results demonstrate the important role played by the surface properties of NPs, i.e. grafted chains and their length, grafting density and ligand density. In addition, the shape and size of NPs are also theoretically found to have great influence on the adhesive strength [26,50]. Thus, studying the binding affinity between NPs and vessel wall under the combined influence of the 4S parameters and the shear flow is essential to fully understand the mechanisms controlling drug-delivery efficacy [57].

Although extensive experimental studies have been carried out to understand the effect of 4S parameters of NPs on their drug-delivery efficacy, many conflicting results have been reported for varied conditions. For example, Toy et al. [37] measured the margination of spherical NPs with diameters ranging from 60 to 130 nm in a bloodless solution. They found that the smaller NPs diffused much faster than larger NPs due to the Brownian motion [21]. However, through a combined in vivo and in silico study, Lee et al. [38] found that 1 µm NPs exhibited near wall dispersion, whereas 200 nm NPs were distributed randomly in the blood vessel when RBCs were present. The smaller NPs appear to get trapped within the spaces between RBCs, slowing their diffusion toward the vascular wall and suggesting that smaller NPs may not always be better. The different results reported by these studies are induced by different haematocrit. To resolve above controversy and provide a unified picture of how to design efficient NPs, we need to create a multiscale computational method for studying the vascular transport and deposition of NPs with different 4S properties, under the same relevant physiological conditions such as vessel diameter, shear rate and haematocrit.

2.2. Internalization of nanoparticles

After the NP approaches the surface of tumour cells, it has to be internalized to deliver the attached drug molecules into the interior of the cell. This process, so-called ‘endocytosis’, involves several important steps: (i) NPs are specific-bound to the cell membrane, (ii) NPs are wrapped by the membrane and a membrane-bound NP complex is formed, (iii) an early stage endosome is formed due to the pinching-off of the membrane budding, and (iv) endosomal release of the NP during the late stage of the endosome. Note that endocytosis is also an important process for cells to internalize small molecules, such as proteins and other macromolecules.

The size and shape of NPs have been identified as two key parameters to control their internalization behaviours [58–60]. Aoyama and co-workers explored the size effect of endocytosis in the subviral region, by using the lipophilic CdSe quantum dot coated with trioctylphosphine oxide [59]. Comparing the NPs with different diameters, i.e. 5, 15 and 50 nm, they found a dramatic size effect as Later on, Chan and co-workers have systematically studied the NP size effect by using Au NPs with different diameters from 10 to 100 nm [60]. The uptake half time of Au NPs with diameters of 14, 50 and 74 nm is 2.1, 1.90 and 2.24 h, respectively. Again, they find that Au NPs with diameter of 50 nm can be most efficiently taken up by the diseased cells. Thus, both the kinetics and saturation concentrations of NPs can be highly influenced by their physical dimensions. They also explored the potential NP shape effect by using the spherical and rod-like NPs. The NP uptake is found to be dependent on the shape and uptake of rod-like NPs is less efficient than their spherical counterparts [60]. For instance, 500 and 375% more 74 and 14 nm spherical NPs can be internalized by cells than 74 × 14 nm rod-like NPs, respectively. Further studies reveal that the local curvature of non-spherical NPs controls the endocytic kinetics when the NPs approach the cell surface [61,62].

To understand the NP size and shape effects, both theoretical and computational studies have been pursued in the past years [63–68]. The pioneering work done by Gao et al. [63] points out that the endocytosis of NPs relies on competition between the bending of membrane and diffusion of free receptors to the docking site when the NP approaches cell surface. Therefore, both small and large NPs cannot be efficiently taken up due to the energy barrier of membrane bending and limitation of free receptors, respectively. Their theoretical model predicts the optimal size of NP of approximately 25–50 nm [63], which agrees well with previous experimental observations. However, due to the complex kinetic process involved during the endocytosis of non-spherical NPs, the theoretical study can only be used to qualitatively explain the NP shape effect. More information has been revealed through large scale molecular simulations (e.g. [67,69–71]). These simulation results show that the spherical NPs are the most efficient carriers to be accepted by diseased cells. The membrane bending energy is the major reason why the non-spherical NPs are less efficient to be delivered into the diseased cell. The kinetics of endocytosis plays an important role in design of drug carriers. For instance, the efficacy of drug carriers does not only depend on how many, but also relies on how fast they can enter the diseased cell. As demonstrated in the present study, both the NP surface property and shape can dramatically affect the endocytic kinetics, which should be taken into consideration in the design of drug carriers.

In recent years, the stiffness of NPs has also been recognized as a key parameter to control their endocytic kinetics. Theoretical [74], computational [75] and experimental [76,77] studies have uncovered that the stiff NPs can be more easily internalized by cells, comparing with their soft counterparts. The theoretical model developed by Yi et al. [74] has excellently explained how the stiffness of NPs can control their internalization. For example, when a soft NP approaches the cell membrane, it can spread out on the cell surface with a large wet angle. Then, the highly spread out NP introduces a large local curvature at the spreading front. In this way, the endocytosis of a soft NP encounters a very large membrane bending energy barrier akin to the spread shape. Eventually, the membrane wrapping of the soft NP may be prevented by the large energy barrier (table 2).

Table 2. Summary of the effects of 4S parameters on NP internalization.

Molecular-specific NPs have been developed with the goal of improving tumour-specific accumulation. The surface of these NPs is coated with ligand molecules capable of recognizing and binding receptors expressed on the target cells [72]. Despite their extraordinary in vitro efficiency, this approach has demonstrated limited success in vivo. Potential reasons include changes in ligand binding affinity, ligand immunogenicity and constraints on the ligand presentation, particularly on small NPs with limited surface area. As a result, tumour targeting with molecular-specific NPs remains controversial, as highlighted by Nie and co-workers [15,73]. Therefore, designing the surface functionality of the NPs is still a challenge, which needs to be further explored in detail.

3. Vascular transport of nanoparticles predicted by immersed molecular finite-element method

3.1. Model and methodology

The IMFEM [78–83] is a computational framework to concurrently deal with the relevant physical interactions in biological environments [80,84,85], including fluid–structure interaction (FSI) [82,86,87], cell–cell interaction [81,88,89], thermal fluctuation [78,79,90], electrokinetics [83,91,92], self-assembly behaviour [79,93–95] and other mesoscale and molecular effects [96]. In this work, the IMFEM will be used to simulate the blood flow as well as the microcirculation of NPs. In this case, the deformable RBCs will be immersed into a Newtonian fluid, representing the blood plasma. The microcirculation of NPs within the blood will be analysed as a function of the 4S parameters, and the local vascular conditions, i.e. vessel diameter and flow velocity. Then, the cell–cell, cell–NP and NP–NP interactions will be explicitly accounted for as described below and will be coupled with an Eulerian fluid domain within IMFEM. The NPs are treated as Lagrangian solids in the Eulerian fluid domain, as described in figure 2. The FSI forces are calculated on the surfaces of RBCs and NPs, and subsequently distributed onto the surrounding fluid domain through a Dirac delta function or reproducing kernel particle method (RKPM) [97,98]. The underlying governing equation for the Eulerian fluid is the Navier–Stokes equation, which can be directly solved by a fluid solver. The movement of RBCs and NPs is determined by the hydrodynamic forces and thermal fluctuations, as well as their interactions.

Figure 2. Mathematical framework for immersed molecular finite-element method, which is based on a Navier–Stokes equation solver. The structural equation is treated as a fluid–structure interaction force distributed into the fluid domain by the reproducing kernel particle method function. (Online version in colour.)

The initial shape of the RBC is a biconcave discoid with its cross-sectional profile defined by a mathematical expression [81]. The deformation of RBCs is defined by a hyper-elastic, Mooney–Rivlin, strain energy function. The material properties of the RBC membrane have been calibrated from the experimental results on the uniaxial tension of a single RBC [99], as given in figure 3. The RBC–RBC interaction is described by a Morse-type potential, which has been theoretically provided by Neu et al. [100,101]. To prevent overlap between RBCs and NPs in the simulations, we adopt a Lennard-Jones potential for RBC–NP and NP–NP interactions [31,38]. To correctly capture the multiphase nature of the plasma–cell–NP mixtures, their interactions are also coupled with the Navier–Stokes equation for the fluid domain. The interaction forces are calculated for each element on the surfaces of RBCs or NPs by using a cut-off distance to determine which elements of nearby cells are within the domain of influence. The interactions forces are integrated over the surface area within the affected domain. The calculated forces on the surfaces of RBCs and NPs are distributed onto the surrounding fluid domain through the RKPM [97,98]. These FSIs are also included into the equations of motion for the fluid domain. After solving the governing equations, the velocities of the fluid domain are interpolated onto the surfaces of RBCs and NPs, which ensures the no-slip boundary condition on the surfaces of RBCs or NPs. Here we should emphasize that although the fluid domain is modelled as a Newtonian fluid, the non-Newtonian behaviour in the microcirculation emerges from the multiphase mixture of RBCs and NPs, and is correctly captured through our IMFEM simulations.

Figure 3. Validation of immersed finite-element method on a single red blood cell (RBC): (a) deformation behaviour of the RBC under uniaxial tension, (b) deformation of RBC along the tensile and transverse directions when it is under uniaxial tension and (c) tank-treading behaviour of RBC under a shear flow (maximum shear velocity is 100 µm s –1 ). The experimental assumptions and results in (a) and (b) are reproduced with permission from [99]. The tank-treading behaviour of RBC under the shear flow has been observed in experiments by [102]. (Online version in colour.)

The IMFEM simulation of blood flow has been validated and verified through comparisons with the following experiments: (i) RBC deformation along the tensile and transverse directions when it is under uniaxial tension [99], (ii) tank-treading behaviour of RBC under a shear flow [102,103], (iii) discharge haematocrit out of the vessel [104], (iv) discharge haematocrit out of the vessel [104], and (v) cell-free-layer thickness at different haematocrits [105,106], as discussed in our recent study [38]. For all of these cases, experimental results are found to be in good agreement with our simulations, supporting the accuracy and validity of the proposed approach. After the model and methods are validated, the coefficient of radial dispersion Dr of NPs regulating their near-wall accumulation in blood vessels can be determined through the IMFEM simulations. For a given number of NPs, N, the dispersion coefficient Dr is defined as

3.2. Effects of nanoparticle size and shape on microcirculation behaviour

To understand the NP size effect on its microcirculation behaviour, 100 rigid, spherical NPs with equal diameter (varying between simulations from 20 to 1000 nm) are randomly distributed within the capillary in the initial configurations, as described in figure 4. Under the normal physiological conditions, we find that the deformation of RBCs modifies the local surrounding flow field. Specifically, the deformed RBCs are pushed away from the vessel wall and tend to accumulate within the centre of the blood vessel, leading to the formation of a ‘cell-free layer’. The modified local flow field around RBCs dramatically changes the microcirculation behaviours of the NPs (cf. figure 4). When the diameter of NPs is larger than 500 nm, the NPs are pushed away from the centre of blood vessel, due to the tumbling of RBCs. Thus, the large NPs migrate into the ‘cell-free layer’ and tend to accumulate near the vessel wall. Such margination behaviour of large NPs mimics WBCs and platelets during circulations. When the diameters of the NPs are smaller than 500 nm, they can stay within the space between RBCs during circulation. Interestingly, the NPs distributed within the centre of the blood vessel cannot escape away, as their movements are blocked by the RBCs. The radial dispersion coefficients Dr of different sized NPs are also calculated during the simulations. Dr of NPs with 1000 nm diameters are found to be six times larger than those of 100 nm NPs, indicating the important role played by the size of NPs.

Figure 4. (a) Initial configuration of deformable red blood cells (RBCs) and spherical rigid particles dispersed within a 20 × 60 µm capillary. A parabolic velocity profile is assigned at the inlet section with a maximum velocity of 100 µs −1 . (b) Complex flow field is formed around the particles, in the vicinity of RBCs. Adapted from [38]. (Online version in colour.)

The concentration of the RBCs is also found to play an important role in this process. For example, the trajectories of 100 and 1000 nm NPs in a capillary with different haematocrits, namely 0, 15 and 30%, are given in figures 5 and 6. Clearly, in the absence of RBCs (0% haematocrit), the NPs follow the streamlines without appreciable lateral drifting, regardless of the NP size. However, for the case with 15 and 30% haematocrits, lateral motions for NPs are found to deviate away from the core region and move toward the midline. The largest and more rapid fluctuations along the radial direction of the vessel were observed for the small NPs (100 nm in diameter), at the lower haematocrit (15%). Indeed, with a lower RBC volume fraction, the separation distance between adjacent cells is larger and NPs can more easily move through the circulating cells, thus leading to a more hectic NP dynamics. Overall, these results further demonstrate that larger, sub-micrometre- and micrometre-sized NPs can be more efficiently excluded by the vessel core, pushed laterally by the fast moving RBCs, whereas the smallest NPs would benefit far less from this exclusion mechanism and would stay confined with the vessel core for a longer time.

Figure 5. Trajectories for spherical particles with 100 nm diameter in a capillary with different haematocrits: (a) 0%, (b) 15% and (c) 30%.

Figure 6. Trajectories for spherical particles with 1000 nm diameter in a capillary with different haematocrits: (a) 0%, (b) 15% and (c) 30%.

To quantify the effective dispersion of NPs during microcirculation, we further introduce the effective radial dispersion coefficient, defined as Dr/DB, where DB is the diffusion coefficient of NPs induced by the Brownian motion. According to the classical Stokes–Einstein relation, we have

where kB and T are the Boltzmann constant and temperature, respectively, d is the diameter of particles and η is the viscosity of the fluid. Then, the effective radial dispersion coefficients for NPs with diameters of 100 and 1000 nm can be obtained and are given in figure 7a with haematocrits of 15%. The effective dispersion ratio Dr/DB is larger for NPs in the vessel core and reduced for NPs in the ‘cell-free layer’. Comparing with the 1000 nm NPs, the effective dispersion ratio is always smaller for the 100 nm NPs, signalling that the larger sized NPs are more efficient. Moreover, the contribution of RBCs to the dispersion of smaller NPs is relatively small. Finally, the NP shape effect can be explored by the same method. As given in figure 7b, the different shaped NPs, such as sphere, capsule and ellipsoid, can be studied and their lateral drifting velocities are calculated. The ellipsoid-shaped NP is found to more efficiently drift away from the core region of the vessel. Further studies will be pursued to understand the NP shape effect in detail.

Figure 7. (a) Effective radial dispersion coefficients for particles of 100 and 1000 nm in diameter with 15% haematocrit. (b) Drift velocity of the different shaped particles in a capillary with 30% haematocrit. (Online version in colour.)

4. Molecular simulation on internalization of nanoparticles

4.1. Model and methodology

To study the internalization behaviour of the NPs, we adopt the dissipative particle dynamics (DPD) method [107,108], which can accurately account for the hydrodynamic interactions by considering the water molecules explicitly. In the DPD method, a single bead represents a group of atoms or molecules. Thus, DPD can approach larger temporal and spatial scales in comparison to classical molecular simulations. Additionally, the interactions between different molecular species can be accurately reproduced by the conservative force in the DPD simulations [71,109]. As a result, the DPD method is well suited to study the endocytosis of NPs as different molecules involved.

As presented in figure 8, the lipid molecule is represented by the H3(T5)2 model. Each lipid molecule consists of a lipid head with two tails, formed by three hydrophilic (H) and five hydrophobic (T) beads, respectively. Then, the neighbouring beads are connected together by a simple harmonic spring. To ensure the linearity of the lipid heads and tails, a harmonic bending potential is applied on the adjacent three beads. To represent the hydrophilic/hydrophobic property of the head and tail beads, the repulsive interaction parameters for the same type of beads are the same while it has been enlarged for different beads. Then, the lipid molecules can self-assemble into a stable lipid bilayer in the water environment. For the detailed set-up of the DPD simulation, the readers are referred to our previous studies [71,109]. For the model of NPs, we consider that the NP is formed by a rigid core with a surface coated polymer [110]. A typical model system will be the PEGylated Au NPs, with the core and shell representing Au NP and PEG polymer, respectively. In the DPD simulation, the relative position of the core beads for the NP is fixed by considering a rigid core. The tethered polymer chains are rather flexible and hydrophilic, preventing the clustering of NPs in the solution. Each pair of beads on a tethered polymer chain is connected through a harmonic bond with adjacent three beads constrained through a harmonic bending potential, ensuring the persistent length of the polymer chains is realistic. The potentials of the bond and angle are calibrated through the statistical distributions of the bond and angle of the PEG polymer immersed into the water, which are obtained through the all-atomic simulations [109]. In this way, the conformation of the tethered PEG polymers can be accurately represented in our DPD simulations. All the potential parameters for the grafted PEG polymers and their interactions with lipid molecules are reported in our recent studies [71,109]. The representative DPD models for PEGylated NPs are shown in figure 8. With these models at hand, the internalization of PEGylated NPs can be studied by our DPD simulations.

Figure 8. (a) H3(T5)2 model for the lipid molecule and corresponding lipid bilayer in the simulation box. The hydrophilic heads and hydroponic tails of lipid molecules are coloured by blue beads and silver lines, respectively. For clarity, the solvent (water) molecules are made invisible. (b) Models for PEGylated NPs with grafted PEG chain length N = 18, corresponding to molecular weight of 815 Da. The core diameter of the NP is approximately 8 nm, coloured by yellow. The grafted PEG chains and targeting moieties bound to their free ends are coloured by cyan and blue, respectively. For clarity, the solvent molecules are made invisible. (Online version in colour.)

Here we assume that the NPs have already reached the tumour cells in simulations. Therefore, the endocytosis of these NPs by the cell can directly indicate the efficacy of these drug carriers in treating the disease. To mimic the receptor-mediated endocytosis in our simulations, the cell membrane is considered to contain rich-receptor embedded regimes, which is the typical situation for tumour cells. Then, the free ends of tethered PEG chains are covalently bound with specific ligands, which can recognize and bind with these receptors. In this way, our simulation model could well reproduce the receptor-mediated endocytosis pathway [71,109].

4.2. Effects of nanoparticle surface functionality and shape on internalization behaviour

The endocytoic kinetics of the PEGylated NPs with spherical core are given in figure 9. The diameter of the core is approximately 8 nm and the molecular weight of tethered chain is approximately 838 Da, which falls within the experimentally relevant range. Owing to the different grafting density of PEG, we can observe quantitatively different behaviours of these PEGylated NPs. For example, when the grafting density is low, e.g. 0.2 chains nm −2 , the PEGylated NP can be absorbed on the surface of cell membrane at the beginning. However, after a long simulation time (more than 2000 ns), the PEGylated NP is still on the surface of membrane and cannot be delivered into the interior of the cell. When the grafting density has been increased to 1.6 chains nm −2 , the PEGylated NP will be wrapped by the cell membrane at the beginning, which is the so-called ‘membrane-bending’ stage. This is followed by the ‘membrane-extruding’ stage, as the upper leaflet of the membrane will extrude to wrap around the surface of the NP. Eventually, the NP will be fully wrapped by the membrane and form a NP–membrane complex. In this way, the PEGylated NP can be delivered into the diseased cell for targeted drug delivery.

Figure 9. Representative DPD simulation snapshots for the internalization process of PEGylated NP with grafting densities of (a) 0.2 and (b) 1.6 chains nm −2 . The core diameter is approximately 8 nm. The grafted PEG chain length is N = 18. Same colour scheme as in figure 8 is used. (Online version in colour.)

Given these different behaviours of PEGylated NPs, we may wonder why the different grafting densities of PEG polymer play an important role. In our recent studies [28,71,109], it has been revealed that three major free energy changes are involved during endocytosis: (i) specific ligand–receptor interactions, (ii) membrane bending energy, and (iii) non-specific entropy change of tethered chains. In these free energy contributions, the specific ligand–receptor interaction provides the driving force for the PEGylated NP to be wrapped by the lipid bilayer and eventually delivered into the cell. However, the bending energy change and the entropy loss of tethered chains create energy barriers, preventing the internalization of NPs. In this case, if the driving force provided by the ligand–receptor interaction is not strong enough to overcome the energy barrier created by the membrane bending and entropy loss of tethered chains, the NP cannot be internalized. According to the above argument, we have developed a theoretical method (mean-field approach) to estimate the entropy loss of the tethered chains [71,109]. The free change per chain during this process is found to be approximately 1kBT, where kB and T are the Boltzmann constant and temperature, respectively. When the grafting density is low, i.e. 0.2 chains nm −2 , the corresponding entropy loss is also small. However, the ligand–receptor interaction is also weak, as the ligands are conjugated to the free ends of tethered chains. Thus, the PEGylated NPs cannot be internalized. On the contrary, the PEGylated NPs with large grafting density can be quickly accepted by the cell, as the specific ligand–receptor interaction is strong enough to overcome the energy barriers. These observations highlight the important role played by the surface functionalization of NPs during endocytosis.

The simulation results have also been compared with experimental studies on the J774A.1 uptake of PEGylated Au NPs in serum-free media, done by Walkey et al. [111], as shown in figure 10. When the grafting density of PEG polymer is high, the interaction between the PEGylated NP and cell membrane is very strong, due to the direct interactions between the distal methoxy group at the free ends of the PEG chains and the membrane surface proteins or lipids [111]. However, when the grafting density is low, the interaction between PEGylated NPs and cell membrane becomes very weak. Thus, the PEGylated NPs with high grafting densities could be easily accepted by the cell whereas low grafting density ones cannot. All these phenomena have been confirmed by molecular simulations and experimental results (cf. figure 10). Nevertheless, the PEGylated NPs could enter the cell through other pathways, such as clathrin-mediated endocytosis, which is beyond the scope of this study [106].

Figure 10. Effect of grafting density on the cellular uptake efficiency, which is proportional to the internalization rate of PEGylated NPs. (a) Experimental results by Walkey et al. [111] for J774A.1 uptake of PEGylated Au NPs are shown for comparison with our DPD results. (b) Representative transmission electron microscopy images of the intracellular distribution of PEGylated Au NPs with grafting density of 0.96 chains nm −2 and core diameter of 15 nm (B1: scale bar, 1000 nm. B2–B4: scale bar, 100 nm). Images B1–B4 are reproduced with permission from [111]. (Online version in colour.)

The NP shape is also an important design parameter for internalization. As demonstrated in figure 11, the different shaped NPs display different endocytic kinetics, although they have the same ligand–receptor interaction with equal amount of grafted PEG polymers. The spherical, rod-like, cubic and disc-like NPs are compared with the same surface areas for their cores. Under a fixed grafting density, 0.6 chains nm −2 , the spherical NP can be most efficiently accepted by the cell, followed by cubic and rod-like NPs, while the disc-like NP can only be found on the surface of cell membrane. The related membrane bending energies are found to be about 8πκ, [8,12)πκ, 12πκ and 27.33πκ for spherical, cubic, rod- and disc-like NPs [71], respectively. κ is the membrane bending modulus, of the order of 10–20 kBT [71]. Therefore, the different membrane bending energies for these NPs determine their efficiency during endocytosis.

Figure 11. Representative DPD simulation snapshots for the internalization process of PEGylated NPs with different shaped cores: sphere, rod, cube and disc. All these cores have equal surface area. The grafted PEG chain length is N = 30. Same colour scheme as in figure 8 is used. Adapted from [71]. (Online version in colour.)

We should emphasize that the effect of NP shape is always ambiguously evaluated in the experiments due to the interplay between the NP shape and its surface properties. For example, the different shaped NPs have different surface area-to-volume ratios, which makes discerning size effect from surface effect difficult, especially when only a few different shapes are considered. Besides, different shaped NPs have different numbers of ligands per grafted chain due to their different surface curvatures [112]. To clarify the shape effect of NPs, we can first fix the size (diameter) of spherical NPs, and then study the rod or disc NPs under equal surface area-to-volume ratio and ligand-to-grafted-chain ratio. Such precisely defined conditions will allow us to unambiguously explore the shape effect of NPs during endocytosis, which is only achievable through computer simulations.

5. Concluding remarks and perspective

In this work, we have demonstrated that the transport of NPs within the tumour microvasculature can be greatly influenced by their 4S parameters, such as size, shape, surface functionality and stiffness. The microcirculation of NPs and their subsequent internalization by disease cells can be understood through IMFEM and DPD simulations, respectively. The important roles played by the 4S parameters can be elucidated through these simulations. Thus, by combing the IMFEM with DPD simulations, the life journey of the NP-based drug carriers can be predicted through our multiscale modelling approach.

Through these multiscale simulations, fundamental mechanisms underpinning the NP-mediated drug delivery can be elucidated. These detailed physical insights can provide useful guidelines in the design of NPs. For instance, larger sized NPs are found to be able to migrate into the ‘cell-free layer’ through IMFEM simulations, whereas smaller sized NPs could be more efficiently taken up by the diseased cells through theoretical analysis and computer simulations. Based on these observations, a multistage delivery platform has been designed by Ferrari and co-workers [113]. In the design of this platform, biodegradable and biocompatible mesoporous silicon particles are used to carry nano-sized quantum dots or carbon nanotubes. During the microcirculation process, these mesoporous silicon particles can be more easily accumulated at the tumour sites due to the EPR and margination effects. Then, the carried NPs can be gradually released and diffuse into the tumour cells. Through receptor-mediated endocytosis and other pathways, these NPs will be internalized by tumour cells. Comparing with traditional design of NPs, this multistage platform has considered different physical mechanisms during the NP-mediated drug-delivery process. Note that the traditional design of NPs relies on the slow and inefficient ‘Edisonian’ approaches. Such a process is very time-consuming and cost-inefficient. According to the multiscale modelling approach, the design of NPs can be more easily achieved through these computer simulations. In the near future, we hope that simulation-based design paradigms can guide experimental design of next-generation NPs, with enhanced active targeting, low toxicity and limited side effects.


The pathological complications of atherosclerosis, namely heart attacks and strokes, remain the leading cause of worldwide mortality [1]. Because atherosclerosis is fundamentally a disease that involves inflammation of the endothelium, the monolayer of cells that lines the inside of blood vessels, a particularly promising idea is the use of nanoparticles as cargo vehicles for targeted delivery of anti-inflammatory agents to arterial endothelial cells. Recent studies have established that nanoparticle internalization into endothelial cells depends on a number of factors including nanoparticle size and surface functionalization [2–4]. Elucidating the basis for these observations is of primary interest.

A critical component in the development of an effective nanoparticle-based endovascular drug delivery system is the interaction between particles and the endothelial cell surface. To specifically target inflamed endothelial cells at an atherosclerotic lesion, nanoparticles can be coated with antibodies against endothelial cell adhesion molecules, such as selectins, VCAM-1, PECAM-1, or ICAM-1 [5]. Out of these different receptors, intercellular adhesion molecule-1 (ICAM-1) is a particularly relevant target, since its level of expression in vascular endothelial cells is enhanced significantly by pathological stimuli such as oxidants, cytokines, and abnormal fluid mechanical shear stresses [3]. Specifically, a 20 to 100 fold increase in ICAM-1 expression in activated over quiescent cells has been reported [6]. ICAM-1-mediated nanoparticle internalization into endothelial cells has been the subject of a number of recent experimental studies [3, 6–10]. Nanoparticles coated with anti-ICAM-1 antibodies activate a specific endocytosis pathway termed CAM-mediated endocytosis [7]. Unlike endocytosis mediated by other membrane receptors, CAM-mediated endocytosis requires multivalent binding: a single anti-ICAM-1 antibody is not internalized by an endothelial cell, whereas a particle carrying several antibodies can be internalized. CAM-mediated endocytosis is actin-dependent, but it involves different protein machineries than clathrin-mediated endocytosis, caveoli, macropynocytosis, or phagocytosis [3, 7].

In this article we develop a mathematical model to describe receptor-mediated nanoparticle internalization, specifically considering the case of ICAM-1-mediated endocytosis. Several theoretical models of nanoparticle internalization have previously been proposed. A first group of theoretical models describes receptor-mediated internalization of spherical and non-spherical particles limited by diffusion of receptors within the cell membrane [11–13]. These models assume the particle ligand density to be much larger than the cell membrane receptor density, thus making receptor diffusion towards the particle wrapping zone a limiting physical mechanism. This assumption does not appear applicable to ICAM-1-mediated nanoparticle endocytosis into inflamed endothelial cells, where receptor and ligand densities are both of the order of 1000 molecules/μm 2 [14], and diffusion of receptors thus becomes negligible. Another group of theoretical models uses energetic approaches to describe membrane wrapping of a nanoparticle (see the recent review by Bahrami et al. [15]). These models have investigated the role of nanoparticle shape and orientation [16, 17], nanoparticle deformability [18], and interactions between multiple nanoparticles [19, 20], but they often leave out the cell’s cytoplasmic rigidity and the bond formation dynamics, as well as the kinetics of the wrapping process. Recent advances in modeling the wrapping of a nanoparticle by a membrane have incorporated stochastic thermal fluctuations to study the kinetics of wrapping [21] or conformational changes of membrane proteins, which are described by particle dynamics simulations [22].

Here we develop a new theoretical model to study the kinetics of nanoparticle internalization under the following premises: (i) we consider the case where receptor and ligand density are comparable, so we neglect receptor diffusion (ii) we include both membrane bending and viscoelastic deformation of the cytoskeleton (iii) we account for the dynamics of bond formation under force. Unlike most of the previous theoretical models, which are based on energy formulations, we develop our model in terms of force balances. Our formulation is inspired by that proposed by Dembo et al. to study the kinetics of detachment of a membrane from a surface [23]. Our model enables us to understand how receptor-mediated internalization is affected by particle size, bond characteristics, cell mechanical properties, and external forces exerted on the nanoparticle.


The potential toxicity of NPs is the main problem of their use in medicine. Therefore, not only positive results of the use of NPs, but also the possible unpredictable negative consequences of their action on the human body, should be scrutinized. The toxicity of NPs is related to their distribution in the bloodstream and lymph stream and their capacities for penetrating into almost all cells, tissues, and organs and interacting with various macromolecules and altering their structure, thereby interfering with intracellular processes and the functioning of whole organs. The NP toxicity strongly depends on their physical and chemical properties, such as the shape, size, electric charge, and chemical compositions of the core and shell. Many types of NPs are not recognized by the protective systems of cells and the body, which decreases the rate of their degradation and may lead to considerable accumulation of NPs in organs and tissues, even to highly toxic and lethal concentrations. However, a number of approaches to designing NPs with a decreased toxicity compared to the traditional NPs are already available. Advanced methods for studying the NP toxicity make it possible to analyze different pathways and mechanisms of toxicity at the molecular level, as well as reliably predict the possible negative effect at the body level.

Thus, it is obvious that designing NPs that have small or no negative effects is impossible unless all qualitative and quantitative physical and chemical properties of NPs are systematically taken into consideration and a relevant experimental model for estimating their influence on biological systems is available.