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Enhanced effect of dimension of receptor-ligand complex and depletion effect on receptor-mediated endocytosis of nanoparticles

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Chinese Physics B 2017年第12期26卷 48-54页

作者：刘野高庆庆刘益军赵闯毛宗良胡林刘艳辉 College of Physics Guizhou University CAS Key Laboratory for Mechanical Behavior and Design of Materials University of Science and Technology of China

We present an extended analytical model including the depletion effect and the dimension of ligand-receptor complex, aiming to elucidate their influences on endocytosis of spherocylindrical nanoparticles （NPs）. It is found that the dimension of ligand-receptor complex （δ） and the depletion effect interrelatedly govern the optimal conditions of NP endocytosis. The endocytosis phase diagram constructed in the space of NP radius and relative aspect ratio indicates that the endocytosis of NP is enhanced evidently by reducing the optimal radius and the threshold radius of endocytosed NP. Meanwhile, through thermodynamic and kinetic analysis of the diffusion of receptors, the dependence of diffusion length on depletion effect and the dimension of ligand-receptor complex can be identified in great detail. For small aspect ratio, diffusion length decreases with increasing concentration c of small bioparticles in cellular environment. Endocytosis speed corresponding to large radius R and high concentration c of small bioparticles strongly depends on the increasing （2r-δ）. These results may show some highlights into the conscious design of NPs for diagnostic agents and therapeutic drug delivery applications.

关键词： cellular uptake depletion effect dimension of receptor-ligand complex elasticity theory

General compliance transformation relations for all seven crystal systems

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Science China(Physics,Mechanics & Astronomy) 2013年第4期56卷 694-700页

作者： ZHANG Yan JI Vincent ICMMO/LEMHE UMR CNRS 8182 Université Paris-Sud 11Orsay Cedex 91405 France

For crystals, the compliance (sij) and the stiffness (cij) matrices are specified in the orthogonal coordinate systems (Yi), which do not coincide with the crystal axes (Xi) commonly used except for cubic and orthorhombic crystal systems. Transformations have been done in this paper and the general compliance transformation relations from the orthogonal coordinate systems (Yi) to the measurement systems (Mi) are given for all seven crystal systems. Accordingly, useful expressions for Young's modulus E and Poisson's ratio are also derived.

关键词： elasticity theory compliance Young’s modulus Poisson’s ratio

The Elastic Continuum Limit of the Tight Binding Model

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Chinese Annals of Mathematics,Series B 2007年第6期28卷 665-676页

作者： Weinan E Jianfeng LU Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA

The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.

关键词： Continuum limit elasticity theory Cauchy-Born rule Tight binding model

Optimal aspect ratio of endocytosed spherocylindrical nanoparticle

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Frontiers of physics 2015年第1期10卷 119-123页

作者： Ying-Bing Chen Yan-Hui Liu Yah Zeng Wei Mao Lin Hu Zong-Liang Mao Hou-Qiang Xu Key Laboratory of Animal Genetics Breeding and Reproduction in the Plateau Mountainous Region Ministry of Education College of Animal Science Guizhou University Guiyang 550025 China Soft Condensed Matter Laboratory College of Science Guizhou University Guiyang 550025 China State Key Laboratory of Theoretical Physics Institute of Theoretical Physics Chinese Academy of Sciences Beijing 100190 China College of Civil Engineering Guizhou University Guiyang 550025 China

Recent simulations have demonstrated that bioparticle size and shape modulate the process of endocytosis, and studies have provided more quantitative information that the endocytosis efficiency of spherocylindrical bioparticles is decided by its aspect ratio. At the same time, the dimensions of the receptor-ligand complex have strong effects on the size-dependent exclusion of proteins within the cellular environment. However, these earlier theoretical works including simulations did not consider the effects of ligand-receptor complex dimension on the endocytosis process. Thus, it is necessary to resolve the effects of ligand-receptor complex dimension and determine the optimal aspect ratio of spherocylindrical bioparticles in the process of endocytosis. Accordingly, we proposed a continuum elastic model, of which the results indicate that the aspect ratio depends on the ligand-receptor complex dimension and the radius of the spherocylindrical bioparticle. This model provides a phase diagram of the aspect ratio of endocytosed spherocylindrical bioparticles, the larger aspect ratio of which appears in the phase diagram with increasing ligand density, and highlights the bioparticle design.

关键词： cellular uptake depletion effects dimension of ligand-receptor complex elasticity theory

Evaluation of Some Fourier Integrals in N-Dimensional Space for the theory of Dislocations in Quasicrystals

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Wuhan University Journal of Natural Sciences 2001年第4期6卷 787-790页

作者： Yao Duan-zheng Ding Di-hua Wang Ren-hui Hu Cheng-zheng School of Physics and Technology Wuhan University Wuhan 430072 China

A method to evaluate some Fourier integrals is extended from two-dimensional (2-D) and three dimensional (3-D) spaces ton-dimensional (n-D) space, which are often used in the elasticity theory of dislocations in quasi... 详细信息

关键词： quasicrystals dislocation Fourier integral elasticity theory

Airy, Beltrami, Maxwell, Einstein and Lanczos Potentials Revisited

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Journal of Modern Physics 2016年第7期7卷 699-728页

作者： J.-F. Pommaret CERMICS Ecole des Ponts ParisTech Marne-la-Vallée France

The purpose of this paper is to revisit the well known potentials, also called stress functions, needed in order to study the parametrizations of the stress equations, respectively provided by G.B. Airy (1863) for 2-dimensional elasticity, then by E. Beltrami (1892), J.C. Maxwell (1870) for 3-dimensional elasticity, finally by A. Einstein (1915) for 4-dimensional elasticity, both with a variational procedure introduced by C. Lanczos (1949, 1962) in order to relate potentials to Lagrange multipliers. Using the methods of Algebraic Analysis, namely mixing differential geometry with homological algebra and combining the double duality test involved with the Spencer cohomology, we shall be able to extend these results to an arbitrary situation with an arbitrary dimension n. We shall also explain why double duality is perfectly adapted to variational calculus with differential constraints as a way to eliminate the corresponding Lagrange multipliers. For example, the canonical parametrization of the stress equations is just described by the formal adjoint of the components of the linearized Riemann tensor considered as a linear second order differential operator but the minimum number of potentials needed is equal to for any minimal parametrization, the Einstein parametrization being “in between” with potentials. We provide all the above results without even using indices for writing down explicit formulas in the way it is done in any textbook today, but it could be strictly impossible to obtain them without using the above methods. We also revisit the possibility (Maxwell equations of electromagnetism) or the impossibility (Einstein equations of gravitation) to obtain canonical or minimal parametrizations for various equations of physics. It is nevertheless important to notice that, when n and the algorithms presented are known, most of the calculations can be achieved by using computers for the corresponding symbolic computations. Finally, though the paper is mathemati

关键词： Stress Equations Stress Functions elasticity theory Lagrange Multipliers Formal Adjoint Control theory General Relativity Einstein Equations Lanczos Potentials Algebraic Analysis Riemann Tensor Weyl Tensor