The Mechanics-Statistical Physics Coupling Mechanism Of Nanoparticle-Media Interaction

Commonly,most enveloped viruses infect cells via receptor-mediated endocytosis,which causes the disease onset and,in turn,affect human health.Inspired by this natural biological process,various types of nanoparticles(NPs)are often used as carriers of targeted drugs to ensure that,drugs can be transported to abnormal organs,tissues and cells to reduce toxic effects.Thus,exploring a series of geometric and mechanical optimization conditions for the efficient targeting and internalization of NPs into cells can not only provide theoretical guidance for the prevention of viral infectious diseases,but also help to reasonably design functional NPs for targeting drug carriers.Therefore,it’s crucial to quantitatively understand the mechanical process of the interaction between NPs and cells.The mechanical interaction between NPs and cells is an extremely complex dynamical process coupling mechanical,physical,chemical and physiological factors,spanning multiple length and time scales.Regarding traditional modeling,on the one hand,although the continuum theoretical model show efficiency and can better analyze the biomechanical events at the cell level,it cannot quantitatively determine the statistical mechanical effect at the molecular scale.On the other hand,although the discrete model can provide all the details at the molecular scale,the amount of calculation will be too large to achieve effective analysis due to too much freedom of the real system in the face of the multi space-and time-scales.In addition,the interaction between NPs and cells is also affected by thermal disturbance,and the mechanical deformation is coupled with the random diffusion and chemical reaction of adhesion molecules.Therefore,how to establish an effective multi-scale model comprehensively to realize the quantitative analysis on the mechanism between NPs and media is still a major challenge.In this paper,based on the analysis of multi length scale(cytoskeleton,cell membrane,nanoparticles and adhesion molecules)and multi time scale(skeleton creep,molecular reaction and diffusion),a mechanistic-statistical physical quantitative theoretical model on the interaction between NPs and media is established to study the influence laws of various factors on their statistical mechanical properties and discuss the effective applications of relevant theoretical prediction.The main innovative research achievements are as follows:(1)A mechanistic-statistical physical model widely applicable to the interaction between NPs and cells is established.Firstly,the free energy of the nanoparticle(NP)-cell media system is given.And then,through the principle of variation,the boundary driving force which drives the growth of the NP-cell adhesion area and the diffusion driving force which drives the diffusion of receptors on the membrane are obtained,respectively.Finally,the stochastic process of NP-cell interaction under thermal fluctuations is given by considering transitions of all metastable states which are obtained through randomly growing or decreasing the contact area between the NP and cell.(2)A theoretical model for the interaction between NP with any receptor density and the membrane-skeleton media is also established.The influences of the viscosity of the extracellular matrix,the stiffness of the cytoskeleton,and the density of the receptor are systematically analyzed,respectively.Correspondingly,the diffusion mechanism,the viscous mechanism,the non-viscous mechanism,the skeleton-free mechanism and the non-diffusion mechanism are discussed one by one through different simplification of this theoretical model.Specially,this model is broadly applicable to any receptor density,and can successfully degenerate to the receptormediated endocytosis model developed by Gao et al.for sparse receptors and the viscoelastic creep endocytosis model proposed by Wang et al.for dense receptors.(3)A theoretical model for the interaction between vesicle NP with any stiffness distribution and membrane media is established.Through minimum of free energy and the sequential quadratic programming,the effect of the ligand density coupled with the elasticity of NP is analyzed.Results show that both the elasticity and ligand density of NP regulate the endocytosis.As a result of the energy competition,there is an optimal ligand density,the median value of which corresponds to the maximum wrapping degree for NP-media system.In particular,ligand and receptor shortage regimes are determined for low and high ligand densities,respectively.(4)Optimal ligand distribution and stiffness distribution are provided for the efficient internalization of NP,respectively.The influence of the non-uniform ligand distribution coupled with different shapes and different cytoskeleton stiffness on cellular uptake is discussed.From an optimization point of view,the optimal ligand distribution for spherical and cylindrical NPs is uniform,and this optimal ligand distribution is also related to the local curvature of the NP and the local cytoskeleton stiffness of the cell.Furthermore,from steady-state wrapping morphology to stochastic kinetic analysis,the effect of stiffness distribution of NP on cellular uptake is systematically investigated.For NP with heterogeneous membrane structures,cell tend to complete the final encapsulation near the soft regions of the NP.(5)Considering the experimental measurement of atomic force microscopy(AFM),a probe-NP-cell viscoelastic model is established by analyzing the force-tracking experiments on the endocytosis of single NP.This model can quantitatively explain experimental mechanisms and calibrate experimental measurements.Based on this model,the analytical formulas for the engulfment duration,velocity and driving force is successfully deduced,and it is found that the theoretically predicted endocytic force is in good agreement with the experimental measurement result.