With the full treatment of the Helfrich model we theoretically study the symmetrical adhesion of two cylindrical colloids to a tubular membrane. The adhesion of the rigid cylinders with different radius from the membr...With the full treatment of the Helfrich model we theoretically study the symmetrical adhesion of two cylindrical colloids to a tubular membrane. The adhesion of the rigid cylinders with different radius from the membrane tube surface can produce both shallow wrapping with relatively small wrapping angle and deep wrapping with big wrapping angle. These significant structural behaviors can be obtained by analyzing the system energy. A second order adhesion transition from the desorbed to weakly adhered states is found, and a first order phase transition where the cylindrical colloids undergo an abrupt transition from weakly adhered to strongly adhered states can be obtained as well.展开更多
The interaction of nanoparticles with cell membranes is of great importance because of their potential biomedical applications. In this paper, we investigate the adhesion of stripe-patterned cylinders to a fluid membr...The interaction of nanoparticles with cell membranes is of great importance because of their potential biomedical applications. In this paper, we investigate the adhesion of stripe-patterned cylinders to a fluid membrane with a full consideration of the Helfrich free energy. Three situations are considered: one striated cylindrical particle, two pure cylindrical particles, and two Janus cylindrical particles. It is found that, with the adhesion of a single sparse striated cylinder, there are a variety of steady-states with energy barriers and the stable state is determined by the pattern of the cylinder. However,when the particle is densely striped, it has no effect on the stable state. By comparing the wrapping degree of two cylindrical particles with that of a single cylindrical particle, we find that two pure cylindrical particles can promote or suppress their interaction with the membrane under different situations. However, two Janus cylindrical particles can only inhibit their interaction with the membrane. Besides, this interaction is related to a first-order transition which is a shallow-to-deep wrapping transition for two pure cylinders while it is a shallow-to-half wrapping transition for two Janus cylinders. Furthermore, the position where the transition happens as a function of adhesion energy is given for fixed membrane tension and the precondition of the transition is presented.展开更多
On the basis of Helfrich＇s bending energy model, we show that the adsorption process of a small spherical particle to a closed vesicle can be analytically studied by retaining the leading terms in an expansion of the...On the basis of Helfrich＇s bending energy model, we show that the adsorption process of a small spherical particle to a closed vesicle can be analytically studied by retaining the leading terms in an expansion of the shape equation. Our general derivation predicts the optimal binding sites on a vesicle, where the local membrane shape of the binding site could be non-axisymmetric before the continuous adhesion transition takes place. Our derivation avoids directly solving the shape equation and depends on an integration of the contact-line condition. The results are verified by several examples of independent numerical solutions.展开更多
We investigate the structure of multiple spherical particles confined in a soft membrane tube that originally has a cylindrical shape. Assuming an attraction energy between the surface of the spherical particle and th...We investigate the structure of multiple spherical particles confined in a soft membrane tube that originally has a cylindrical shape. Assuming an attraction energy between the surface of the spherical particle and the inner wall of the membrane tube, we show that a variety of conformational structures can be stabilized on the basis of analyzing a Helfrich energy for the soft tube. Using a numerical approach, we calculate the phase diagram in terms of basic parameters in the system. Structures that prefer close contact of spheres and structures that contain well separated spheres are found in this calculation.展开更多
Membrane fusion is an important process by which biological membranes perform their life activities. Simulations show that the membrane fusion process happens mainly through three pathways, where the Stalk-Pore hypoth...Membrane fusion is an important process by which biological membranes perform their life activities. Simulations show that the membrane fusion process happens mainly through three pathways, where the Stalk-Pore hypothesis, in which two membranes come into close contact to form a stalk to a hemifusion intermediate, and then the fusion pore opens to achieve completely fusion, is widely accepted, and there exist two free energy barriers that break the current structural steady state for lipid rearrangement. Factors of lipid composition, mechanical environment, protein and ion have regulatory roles in the membrane fusion process by effecting membrane curvature structurally and the free energy barriers from energetic perspective. Meanwhile, many theoretical models, represented by the Helfrich model, have been proposed to predict the membrane fusion process. In this paper, we review the research process of membrane fusion and mainly introduce the dynamics of membrane fusion, regulation factors and typical theoretical models.展开更多
For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy,including the Willmore and the Helfrich flows,we consider a numerical approach.In this study,we construct a s...For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy,including the Willmore and the Helfrich flows,we consider a numerical approach.In this study,we construct a structure-preserving method based on a discrete variational derivative method.Furthermore,to prevent the vertex concentration that may lead to numerical instability,we discretely introduce Deckelnick’s tangential velocity.Here,a modification term is introduced in the process of adding tangential velocity.This modified term enables the method to reproduce the equations’properties while preventing vertex concentration.Numerical experiments demonstrate that the proposed approach captures the equations’properties with high accuracy and avoids the concentration of vertices.展开更多
We propose a mathematically rigorous method to measure the spontaneous curvature of a bilayer membrane by molecular dynamics(MD)simulation,which provides description of the molecular mechanisms that cause the spontane...We propose a mathematically rigorous method to measure the spontaneous curvature of a bilayer membrane by molecular dynamics(MD)simulation,which provides description of the molecular mechanisms that cause the spontaneous curvature.As a main result,for the membrane setup investigated,the spontaneous curvature is proved to be a constant plus twice the mean curvature of the membrane in its tensionless ground state.The spontaneous curvature due to the built-in transbilayer asymmetry of the membrane in terms of lipid shape is studied by the proposed method.A linear dependence of the spontaneous curvature with respect to the head-bead diameter difference and the lipid mixing ratio is discovered.The consistency with the theoretical results provides evidence supporting the validity of our method.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11074151)the National Key Basic Research and Development Program of China(Grant No.2011CB808100)
文摘With the full treatment of the Helfrich model we theoretically study the symmetrical adhesion of two cylindrical colloids to a tubular membrane. The adhesion of the rigid cylinders with different radius from the membrane tube surface can produce both shallow wrapping with relatively small wrapping angle and deep wrapping with big wrapping angle. These significant structural behaviors can be obtained by analyzing the system energy. A second order adhesion transition from the desorbed to weakly adhered states is found, and a first order phase transition where the cylindrical colloids undergo an abrupt transition from weakly adhered to strongly adhered states can be obtained as well.
基金supported by the National Natural Science Foundation of China(Grant Nos.91027040 and 21274062)
文摘The interaction of nanoparticles with cell membranes is of great importance because of their potential biomedical applications. In this paper, we investigate the adhesion of stripe-patterned cylinders to a fluid membrane with a full consideration of the Helfrich free energy. Three situations are considered: one striated cylindrical particle, two pure cylindrical particles, and two Janus cylindrical particles. It is found that, with the adhesion of a single sparse striated cylinder, there are a variety of steady-states with energy barriers and the stable state is determined by the pattern of the cylinder. However,when the particle is densely striped, it has no effect on the stable state. By comparing the wrapping degree of two cylindrical particles with that of a single cylindrical particle, we find that two pure cylindrical particles can promote or suppress their interaction with the membrane under different situations. However, two Janus cylindrical particles can only inhibit their interaction with the membrane. Besides, this interaction is related to a first-order transition which is a shallow-to-deep wrapping transition for two pure cylinders while it is a shallow-to-half wrapping transition for two Janus cylinders. Furthermore, the position where the transition happens as a function of adhesion energy is given for fixed membrane tension and the precondition of the transition is presented.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11074047 and 11274075)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.RFDP-20100071110006)the Natural Science and Science Engineering Council of Canada
文摘On the basis of Helfrich＇s bending energy model, we show that the adsorption process of a small spherical particle to a closed vesicle can be analytically studied by retaining the leading terms in an expansion of the shape equation. Our general derivation predicts the optimal binding sites on a vesicle, where the local membrane shape of the binding site could be non-axisymmetric before the continuous adhesion transition takes place. Our derivation avoids directly solving the shape equation and depends on an integration of the contact-line condition. The results are verified by several examples of independent numerical solutions.
基金Project supported by the National Natural Science Foundation of China(Grant No.11074151)
文摘We investigate the structure of multiple spherical particles confined in a soft membrane tube that originally has a cylindrical shape. Assuming an attraction energy between the surface of the spherical particle and the inner wall of the membrane tube, we show that a variety of conformational structures can be stabilized on the basis of analyzing a Helfrich energy for the soft tube. Using a numerical approach, we calculate the phase diagram in terms of basic parameters in the system. Structures that prefer close contact of spheres and structures that contain well separated spheres are found in this calculation.
基金supported by the National Natural Science Foundation of China (Grants 32130061 and 12172366)。
文摘Membrane fusion is an important process by which biological membranes perform their life activities. Simulations show that the membrane fusion process happens mainly through three pathways, where the Stalk-Pore hypothesis, in which two membranes come into close contact to form a stalk to a hemifusion intermediate, and then the fusion pore opens to achieve completely fusion, is widely accepted, and there exist two free energy barriers that break the current structural steady state for lipid rearrangement. Factors of lipid composition, mechanical environment, protein and ion have regulatory roles in the membrane fusion process by effecting membrane curvature structurally and the free energy barriers from energetic perspective. Meanwhile, many theoretical models, represented by the Helfrich model, have been proposed to predict the membrane fusion process. In this paper, we review the research process of membrane fusion and mainly introduce the dynamics of membrane fusion, regulation factors and typical theoretical models.
基金This work was supported by JSPS KAKENHI Grant Nos.19K14590,21K18301,Japan.
文摘For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy,including the Willmore and the Helfrich flows,we consider a numerical approach.In this study,we construct a structure-preserving method based on a discrete variational derivative method.Furthermore,to prevent the vertex concentration that may lead to numerical instability,we discretely introduce Deckelnick’s tangential velocity.Here,a modification term is introduced in the process of adding tangential velocity.This modified term enables the method to reproduce the equations’properties while preventing vertex concentration.Numerical experiments demonstrate that the proposed approach captures the equations’properties with high accuracy and avoids the concentration of vertices.
基金the financial support through the Natural Science Foundation of China No.11004131the financial support by the Natural Science Foundation of China No.50930003.
文摘We propose a mathematically rigorous method to measure the spontaneous curvature of a bilayer membrane by molecular dynamics(MD)simulation,which provides description of the molecular mechanisms that cause the spontaneous curvature.As a main result,for the membrane setup investigated,the spontaneous curvature is proved to be a constant plus twice the mean curvature of the membrane in its tensionless ground state.The spontaneous curvature due to the built-in transbilayer asymmetry of the membrane in terms of lipid shape is studied by the proposed method.A linear dependence of the spontaneous curvature with respect to the head-bead diameter difference and the lipid mixing ratio is discovered.The consistency with the theoretical results provides evidence supporting the validity of our method.
