Continuum Modeling And Analyses Of Coupled Mechanical Behaviors Of Low-Dimensional Nanomaterials And Biomembranes

With the rapid development of nanotechnology,the chances of exposure to nanomaterials increase dramatically.The nanomaterials can enter the human body via a number of pathways,such as the dermal,ocular,respiratory and gastrointestinal systems,which might lead to series of complicated biological reactions.During the interactions with the immune cells and the subsequent cells,the nanomaterials can transport across the membranes and enter the interiors of cells.Moreover,due to the unique physicochemical properties,the nanomaterials hold great potential in bio-imaging,diagnosis and drug delivery.To achieve the specified functions,the nanomaterials will interact with the cell membranes frequently.Therefore,a fundamental understanding of the interactions between the nanomaterials and the cell membranes is essential to assess the safety of the nanomaterials and provide guidelines to the design of nanomaterial-based biomedical applications.This dissertation focuses on the continuum modelling and analyses of the coupled mechanical behaviors of the low-dimensional nanomaterials and cell membranes.The influences of the size,shape,rigidity of the nanomaterial,the surface tension of the cell membrane and the adhesion strength on the nanomaterial—membrane interactions are systematically investigated.The main contents of this dissertation are divided into the following six parts:Firstly,for the interactions between substrate-supported carbon nanotubes and the cell membrane,a continuum model considering the radial deformation and the long-range van der Waals interactions between carbon atoms is established.Based on the continuum model,the conditions of the carbon nanotubes to collapse under the dual interactions of the substrate and the cell membrane are analyzed.The results show that nanotubes tend to collapse when the bending rigidity of the membrane is large whereas the nanotubes prefer not to collapse when the nanotube-membrane adhesion strength is strong.An approximately theoretical model is proposed to derive the critical conditions of the collapses of the nanotubes.Besides,the minimum energy paths of the collapses of the nanotubes are calculated.Moreover,for the system xwith the cell membrane wrapping on the arrays of nanotubes,the cell membrane can be regulated to be adhered on the substrate or be detached from the substrate,depending on the separation distance of nanotubes and the rigidity of the cell membrane.Secondly,for the interactions between a deformable nanoparticle and the cell membrane,a continuum model considering the deformation and the relative location of the nanoparticle is proposed.Based on the model,the equilibrium configurations and the full wrapping conditions during the endocytosis and exocytosis of a deformable nanoparticle are investigated.Results show that the soft nanoparticle requires lower adhesion strength to be shallowly wrapped but higher adhesion strength to be fully wrapped compared with the rigid nanoparticle.The influences of the relative location indicate that the nanoparticle is easier to be shallowly wrapped but harder to be fully wrapped when the nanoparticle is inside than outside the cell.Additionally,as the size of the cell increases,the adhesion strength for the full wrapping configuration decreases when the nanoparticle is inside,while it increases after a plateau when the nanoparticle is outside.Thirdly,a dynamical model considering the rotation of nanoparticle is derived to theoretically imvestisate the receptor-mediated endocytosis of the cylindrical nanoparticle with elliptical cross-section.By coupling the rotation of the nanoparticle with the diffusion of the receptors on the membrane to bind with the ligands,the model successfully captures the dynamical wrapping process of the elliptical nanoparticle.Based on this model,the influences of the size and shape of the nanoparticle are investigated.Results show that the endocytosis consists of two stages.In the first stage,the nanoparticle remains fixed and is wrapped by the membrane symmetrically,whereas the nanoparticle starts to rotate and is wrapped by the membrane asymmetrically in the second stage.Through the rotation of the nanoparticle,the deformation energy is effectively reduced and the wrapping speed is accelerated.Moreover,the nanoparticle can be fully wrapped by the membrane only in a certain size range and the size range is narrower for the nanoparticle with more irregular shape.Fourthly,for the protrusion of a nanorod against the cell membrane,a continuum model with the nanorod protrudes with arbitrary orientation angle is established to investigate the equilibrium configuration and resistance force of the cell membrane.By considering the deformation of the cell membrane in three-dimensional case,the model is able to describe the asymmetrical configuration when the nanorod protrudes with a tilted angle.It is found that increasing the protrusion height and the surface tension of the membrane will change the equilibrium configuration from the open configuration to the folded configuration.The critical protrusion height and the surface tension of the membrane for the transition of the equilibrium configuration increase as the nanorod protrudes with a larger orientation angle.Moreover,the resistance force of the cell membrane is found to be minimal when the nanorod protrudes from the membrane vertically.Furthermore,the results are applied to the analyses of the buckling of filopodia and the penetration of nanowires into the cells.Fifthly,for the cooperative wrapping of cylindrncal nanoparticles,a continuum model considering the nanoparticle-nanoparticle electrostatic interaction and van der Waals interaction is proposed.The conditions for the nanoparticles to be wrapped cooperatively and the corresponding configurations are investigated.Three types of nanoparticles,namely the rigid nanoparticles with circular and elliptic cross-sections and the deformable nanoparticles are systematically investigated to reveal the influences of the shapes and rigidities of the nanoparticles.Results show that the electrostatic interaction will enhance the tendency of the independent wrapping and inhibit the rotation of the elongated nanoparticles with elliptic cross-sections.The van der Waals interaction between the nanoparticles leads the nanoparticles to be wrapped cooperatively or independently.Specifically,the elongated nanoparticles with elliptic cross-sections are more likely to be wrapped cooperatively as the cross-sections approach circular shape.Moreover,the softer nanoparticles are more likely to be wrapped cooperatively compared with the stiff nanoparticles.Finally,for the aggregation of nanoparticles on the cell membrane,a continuum model considering the nanoparticles of the same size,the nanoparticles of different sizes and ellipsoidal nanoparticles are established.By adopting the nonlocal adhesive potential,the established model can effectively capture the variations of the adhesive areas of the nanoparticles during the aggregation,which overcome the limitations of the traditional models that fix the adhesive areas.Based on the model,the influences of the sizes,shapes of the nanoparticles and the surface tension of the membrane are systematically investigated.Results show that the aggregation is tension-dependent,that is,increasing the membrane tension will modulate the membrane-mediated interaction between the nanoparticles from attractive to attractive-repulsive and finally to purely repulsive force.For the aggregation of nanoparticles of different sizes,there is a height difference between the nanoparticles and the large-size nanoparticle is wrapped in a greater extent than the small-size nanoparticle.For the ellipsoidal nanoparticles,small aspect ratio and weak nanoparticles-membrane adhesion strength lead to the side-to-side configuration,whereas the system with a large aspect ratio and strong nanoparticles-membrane adhesion strength prefers the tip-to-tip configuration.