3. Parameters determining the NP-CM interaction

3.1. Nanoparticle Size

It is intuitive to believe that the difficulty for nanoparticles entering the cell membrane will raise with the increasing particle size. Essentially, many researchers have also found that some nanomaterials with greater size will cause more critical changes in the morphology and surface composition of cell membranes. Jirasak43 et al. have found that small-sized nanoparticles similar to fullerenes can quickly enter the hydrophobic region of the lipid-bilayer without causing significant cell membrane deformation. Similarly, Rai Beena44 et al. have used a rigid nanoparticle model to measure the impact of the size effect of nanoparticles on cell membranes by analyzing some structure factor of membrane plane projection area, area compressibility, and order parameters. It has been found that larger-sized nanoparticle will obviously cause changes in the morphology and physical properties of the cell membrane (Figure. 4A). In addition, it was also found that small graphene sheets can quickly enter the inside of the bilayer, while large graphene sheets can only be partially embedded in the cell membrane and lead to more complex cell membrane deformations45. For graphene sheets adsorbed on the cell membrane surface, the orientation of lipid molecules in the area covered by the graphene sheets alters significantly driven by the hydrophobic interaction, and there is the phenomenon of more obvious the horizontal orientation of the lipid hydrophobic chains to be discovered with enlarging the size of graphene sheet model46.
However, recent studies have shown that the size effect and the difficulty of entering the cell membrane are not a simple linear relationship, which indicates that there is theoretically a minimum and an optimal radius for entering the cell membrane47,48. As the radius is lower than the minimum radius, the cell membrane cannot be endocytosed, entering the cell only through direct penetration49. Meanwhile, for nanoparticles smaller than the optimal radius, large-sized particles can be more easily wrapped by cell membranes than small-sized particles (Figure. 4B)50.
The existence of the minimum radius lies in the competition of the adsorption energy and the cell membrane bending energy47. For larger nanoparticles, the number of receptors on the surface will be relatively higher, resulting in higher adsorption energy. Simultaneously, to wrap large-size nanoparticles, the curvature of the cell membrane’s bending deformation should be larger, the membrane bending energy barrier, which is negatively related to the bending curvature51, would also be lower. On the contrary, nanoparticles of too small size cannot provide sufficient binding sites and small curvature, resulting in lower adsorption energy and greater membrane bending energy, rendering it more difficult to be wrapped by cell membranes. Therefore, only nanoparticles larger than the critical size can be endocytosed by the cell membrane. Gao47,50 et al. have also proposed another pair of competing interactions, the diffusion kinetics of nanoparticles near the cell membrane and the nanoparticle-cell membrane’s thermodynamic attraction. Larger size nanoparticles may carry a larger number of ligands, and their diffusion performance is weaker due to their size effect, so they are more likely to be wrapped by cell membranes. In comparison, the higher diffusion coefficient of small-sized particles in the solution may give rise to an adverse effect on entering the cell membrane. However, for nanoparticles with an excessively large size, the wrapping time will increase significantly52, and the cytotoxicity caused by larger deformations will also affect the nanoparticles’ therapeutic efficiency, so there is supposed to exist an optimal wrapping radius for the nanoparticles. To determine the optimal radius, some researchers have already begun to put forward insights on this issue from the perspective of the diffusion dynamics of nanoparticles. Yan53 et al. have studied the diffusion kinetics of graphene in cell membranes. They have pointed out that the diffusion kinetics of graphene sheets in cell membranes are affected by graphite interaction with hydrophobic phospholipid tails. Several typical graphene diffusion dynamics models have also been summarized: Brown dynamics-Levy dynamics-directional dynamics. Many studies have established a variety of mathematical models for the diffusion of nanoparticles, and their influencing factors are also be analyzing, which would assist people to find the optimal nanoparticle radius54.

3.2. Nanoparticle Shape

Shape is also a significant factor in determining how nanoparticles enter cells. For nanoparticles with good isotropy, such as spherical and cubic nanoparticles, the way they enter the cell is determined by their size: small-sized nanoparticles will directly penetrate through the cell membrane31,55. In contrast, larger nanoparticles need to be wrapped by the cell membrane to accomplish cell internalization56. For non-isotropic materials, the researchers have found that, under a strong driving force (concentration gradient, ligand-receptor interaction, etc.), the sharp end of materials can also penetrate the cell membrane57. By adjusting the surface chemistry of such nanoparticles, the kinetic process of nanoparticles piercing the cell membrane can be optimized (detailed discussion will be carried out in the next section). For the process of endocytosis, anisotropic materials possess a particular dynamic process: orientation-wrapping-reorientation58. Their initial conformation plays an extremely important role for anisotropic materials, such as rod-shaped, disc-shaped, and elliptical nanoparticles. Taking rod-shaped particles as an example, if the particles’ initial conformation is perpendicular to the cell membrane, direct wrapping needs to overcome a large amount of membrane bending energy. Therefore, the nanoparticle will preferentially adjust its original orientation so that its morphological long axis could be parallel to the cell membrane, resulting in the lower bending energy (Figure. 5A). After being wrapped by the cell membrane, some nanoparticles may continue to rotate due to the residual rotational momentum (Figure. 5B)19. As reported in the previous study, this special internalization kinetics will reduce the efficiency of nanoparticles entering cells. Li59 et al. have used DPD simulations to verify that spherical and cubic nanoparticles with better isotropy can be wrapped by cell membranes within simulation time of 7 - 9 ns, while rod-like and disc-like particles with poor isotropy would not finished the internalization within 13.5 ns (Figure. 5C). However, this preferentially oriented dynamic behavior can help cell membranes abate the membrane bending energy needed to overcome in the process of the endocytosis59. Chen et al. have also used Langevin’s molecular dynamics simulation to demonstrate that some deformable spherical nanoparticles will also deform into an asymmetric structure and then be wrapped by cell membranes (Figure. 5D)26.
From the above discussion, it can be seen that the study of the rotation dynamics of nanoparticles is very indispensable for understanding nanoparticle internalization. Chen60 and his colleagues have studied the diffusion mechanism of nanoparticles by analyzing the mean square displacement. It has been found that charged particles possess better diffusion ability than neutral particles. Simultaneously, the nanoparticles with randomly distributed electric charges conform to the law of super diffusion (the nonlinear power-law relationship between the mean square displacement and the simulation time61,62), while the diffusion of uniformly distributed nanoparticles is more in line with the law of linear diffusion. By analyzing the typical trajectory and turning angle distribution of nanoparticles, it has been found that nanoparticles with randomly distributed charges would be inclined to diffuse in a specific direction due to more complex asymmetric forces and torques to be given to nanoparticles with random charge distribution, while nanoparticles with uniform charge distribution have almost the same probability of diffusing in all directions. Ji63 et al. have also found that nanoparticles modified with more or shorter ligands are more likely to interact with cell membranes, since longer modifiers may destroy the anisotropy of the nanoparticles, leading to the inhibition of the nanoparticle rotation59. However, the rotation of nanoparticles can also bring disadvantages. Both experiments and DPD simulations have indicated that the rotation of nanoparticles will damage the surface structure of the cell membrane64. Balancing the relationship between cytotoxicity caused by the rotation of nanoparticles and optimizing the energy barrier of cell internalization is the next essential research topic in this field.

3.3. Chemical property of nanoparticle surface

The surface chemistry of nanoparticles is supposed to be the most critical factor affecting the interaction with cell membranes. In this review, more emphasis would be laid on three aspects: hydrophilic / hydrophobic properties, charge properties, and ligand-receptor interaction. In every aspect, the density surface pattern and the covalent bonding of the modification would have an important influence.
The hydrophilic surface modification of nanoparticles is the basis for successful drug delivery. For one thing, hydrophobic nanoparticles would reduce the biocompatibility of the drug delivery system65,66. For another, under the protection of the hydrophilic modifier, the bioavailability of nanoparticles will be guaranteed by avoiding being adsorb to plasma proteins30. However, it can be seen from Figure. 6A that the hydrophilic surface also affects the interaction between nanoparticles and cell membranes. Driven by the hydrophobic attraction, the nanoparticles can be trapped into the cell membrane faster, while nanoparticles with hydrophilic surfaces can only adsorb on the phospholipid head layer of the cell membrane, requiring to overcome a higher free energy barrier due to the incompatibility between the nanoparticle and the phospholipid tail67. Similarly, in the study of graphene and cell membranes, researchers have also found that graphene can form a sandwich shape with cell membranes, while graphene oxide can be adsorbed on the cell membrane surface or vertically pass through the cell membrane conformation46,68. Therefore, researchers should appropriately adjust the hydrophilic / hydrophobic ratio of the nanoparticle surface. Furthermore, many experimental and theoretical studies have indicated that the hydrophilic / hydrophobic surface pattern can also have bearing on the cell internalization69. Compared with Janus particles, the nanoparticles in which two kinds of surface patterns alternately distributed will increase the probability of entering the cell. The study of Wang and his colleagues25 has pointed out that the more alternate surface pattern stratification, the higher the efficiency of cell internalization. Zhang67 et al. have also proved that nanoparticles with randomly distributed hydrophilic / hydrophobic surfaces can penetrate cell membranes, while Janus particles can only be trapped in cell membranes. In addition to affecting the efficiency of cell internalization, the surface properties of nanoparticles will also change cell membranes’ physical and chemical properties. On the one hand, passing through the cell membrane will cause the cell membrane deformation. On the other hand, Lin70 et al. have discovered that hydrophobic nanoparticles will not change the cell membrane’s phase transition temperature. As the degree of surface modification strengthens, the phase transition temperature would first increase with the subsequent decrease, leaving the final phase transition temperature higher than the original value.
Compared with normal cells, the cell membrane of cancer cells contains a higher density of negative charges71. Hence, the charge modification of nanoparticles is also an effective alternative means to enhance drug delivery efficiency. For example, researchers have proved that nanoparticles modified with zwitterionic polymers are better capable of consummating the cell internalization72. It has been reported that different charge types determine distinct cell membrane deformation mechanisms: neutral nanoparticles will not significantly change the lateral curvature of the cell membrane. Positively charged nanoparticles would cause the cell membrane to bulge upwards, while negatively charged particles cause the cell membrane to dent downwards (Figure. 6B)60. Moreover, for pH amphoteric drug-loaded nanoparticles, the charge effect is particularly significant. As the degree of ionization increases, the charge effect can help improve the efficiency of nanoparticles penetrating through the cell membrane. However, nanoparticles would disintegrate before being internalized by the cell with too much mounting degrees of ionization23. Therefore, these simulation results suggest that people need to adjust the relationship between nanoparticle cohesion and ionization. Another major factor, manifested from several studies, lies in choosing the covalent bond and non-covalent bond modification73. Rigid nanoparticles covalently linked to the modified polymer containing ligands can be wrapped by the cell membrane more productively due to the strengthening connection between nanoparticles and modifiers. Adversely, non-covalently attached nanoparticles cannot be wrapped by the cell membrane as the modification polymer detaching from the nanoparticle. Under the pH trigger, the modification polymer connected by non-covalent bonds has a significant increase in hydrophilicity then falls apart from the surface of the nanoparticle so that the core of the hydrophobic nanoparticle has the opportunity to enter the middle layer of the cell membrane.
Another key chemical modification is the ligand-receptor distribution, which assists nanoparticles specifically recognize targeted cells without damaging normal cells. Only sufficient ligand density and ligand-receptor interaction strength can induce cell membrane deformation and encapsulate nanoparticles. Therefore, understanding the relationship between the strength of the nanoparticle ligand-receptor interaction and the membrane tension can provide more insights to understand the mechanism of nanoparticle-cell interaction. As shown in Figure. 6C, the stronger the ligand density (f ) on the surface of the nanoparticle, the greater extent of the cell membrane deformation, which results in more complete membrane wrapping. Nevertheless, the mounting cell membrane tension (σ ) increase the difficulty of the membrane deformation, the nanoparticles thus tend to penetrate the cell. Therefore, by adjusting the relationship between f and σ , five nanoparticle-cell membrane interaction mechanisms can be observed: (1) Direct penetration (lower f and higher σ ). (2) Penetration or partial wrapping (lower f and moderate σ ). (3) Full wrapping (higher f and lower σ ). (4) Wrapping following penetration (higher f and appropriate σ ). (5) Wrapping- penetration-rewrapping (lower f and lower σ ).

3.4. Nanoparticle concentration

The concentration gradient is also one of the driving forces for the interaction between nanoparticles and cell membranes. Therefore, both experimental and theoretical studies have indicated that nanoparticle concentration has a huge impact on internalization efficiency43. Multiple nanoparticles will aggregate or disperse on the cell membrane surface, which adjusts the nanoparticles’ size and shape to affect the nanoparticle-cell membrane interaction mechanism.
For example, high-concentration nanoparticles lead to larger aggregates. As described in section 3.1 , large size aggregates can reduce the membrane bending energy, thereby promoting the cell membrane to encapsulate the nanoparticles. Sometimes, the aggregates of nanoparticles will rearrange and recombine into various shape to increase the required curvature of the cell membrane, improving the efficiency of nanoparticle cell internalization. Hu74et al. have explored the effect of peptide concentration alteration, and it can be seen from the simulation results that peptides can be adsorbed on the surface of the cell membrane and can open perforations in the cell membrane to enter the cell as the concentration is high. Bundling multiple small peptides into large individuals will also accelerate the pore-forming effect, which is similar to the concentration effect.
Inspired by the concentration effect, the researchers have proposed a method of cooperative internalization of multiple nanoparticles75. As mentioned in section 3.3 , hydrophilic nanoparticles can be adsorbed on the hydrophilic surface of the cell membrane, but it is challenging to enter the hydrophobic inner layer of the cell membrane. With the aid of a partner nanoparticle, the hydrophilic nanoparticle can smoothly penetrate cell membranes under their synergistic effect, and the difference in nanoparticle surface properties can produce different degrees of cooperative internalization (Figure. 7A). A single hydrophilic nanoparticle is adsorbed on the cell membrane surface, while four hydrophilic nanoparticles can penetrate the cell membrane together. A single nanoparticle with a random hydrophilic / hydrophobic surface distribution can penetrate the cell membrane but can only be embedded in the cell membrane after increasing the concentration. Zhang74 et al. have analyzed the force spectrum of nanoparticles and the distance between nanoparticles. They have concluded that nanoparticle synergistic effect is greatly relevant to the dispersion behaviour of the nanoparticles. The aggregation of nanoparticles is more conducive to penetration, which is related to the difference in force status of the nanoparticles on the horizontal plane. Although the influencing factors and mechanisms of synergistic interaction are given, there are still counter-intuitive aspects. Cite an instance, the diffusion performance of hydrophilic nanoparticles in an aqueous solution should be better than that of hydrophobic nanoparticles. However, according to their simulation results, the distance between hydrophilic nanoparticles is smaller than that of hydrophobic nanoparticles. Li76 et al. have also studied the influence of nanoparticle charge on the synergistic penetration effect. It has been found that two positively charged nanoparticles can still enter the cell membrane since the interaction between the nanoparticle and the cell membrane weakens the electrostatic repulsion. In addition to the nanoparticle surface properties, the difference in their shapes will also cause different synergistic effects. For example, vertically-oriented asymmetric nanoparticles can further promote cell membrane penetration28. In order to promote the cooperative internalization between the nanoparticles, many researchers would choose to use polymers to connect the two nanoparticles. According to Figure. 7B, two nanoparticles connected by a polymer can increase the degree of engulfment by the cell membrane under the synergistic effect. The chemical properties, length, and molecular rigidity of the polymer connecting the nanoparticles should be systematically optimized when designing such a system. If too long and rigid polymer molecular chain has been utilized, it will increase the distance between the nanoparticles and reduce the synergistic effect of the nanoparticles77.

3.5. Nanoparticle elastic modulus

Although most researchers use rigid nanoparticle models to simulate the cell internalization process, with the diversification of modelling methods, more emphasis has been paid to nanoparticle mechanical properties, especially the elastic modulus78. As illustrated in Figure 8A, rigid hydrophilic nanoparticles have a higher free energy barrier to penetrate the cell membrane due to the incompatibility between the hydrophilic nanoparticle surface and the interior of the lipid bimolecular membrane. After appropriately reducing the nanoparticle elastic modulus, the nanoparticles would undergo a certain degree of deformation, which reduces the contact area between the nanoparticles and the lipid tail. Therefore, a lower energy barrier is supposed to be overcome by the softer hydrophilic nanoparticles. On the contrary, since the good attractive interaction with the middle part of the cell membrane for rigid hydrophobic nanoparticles, the free energy will decrease during the process of the nanoparticle penetrating the cell, which reaches a minimum as the nanoparticle is trapped in the middle of the cell membrane. The deformation of the softer nanoparticles changes the contact state between the nanoparticles and the cell membrane, enlarging the minimum value of free energy, making it more arduous for the nanoparticles to penetrate the cell membrane25. For the process of endocytosis, the effect of elastic modulus is also twofold. For one thing, Yi79 et al. have used the framework of Helfrich theory to propose a theoretical model for the interaction between elastic nanoparticles and cell membranes. From the numerical simulation results, it can be found that soft nanoparticles are more challenging to be wrapped by cell membranes than rigid nanoparticles because the deformation of nanoparticles will bring more energy. For another, the nanoparticle deformation will adjust the nanoparticle shape. If the deformation leads to an appropriate shape, which needs enlarged cell membrane curvature, thereby improving the nanoparticle internalization efficiency (Figure. 8B)26. Excessively lower nanoparticle elastic modulus will bring more negative effects, such as low nanoparticle stability under the shear of fluid and even the disintegration before being internalized by cells80.