红细胞的高效粗粒化无溶剂分子动力学模型

红细胞作为人体内最常见的细胞之一，其形态的变化对于人体生理功能的维持至关重要，对其进行建模研究可以帮助揭示红细胞在生理条件下的结构、形态和功能。红细胞主要依靠调节跨膜渗透压差来调节其形态，此外，肌动球蛋白分子马达在此过程中也起着重要作用。在之前的红细胞无溶剂分子动力学模型中，缺少对渗透压和分子马达的建模与研究。在上述背景下，本文发展了高效的粗粒化红细胞分子动力学模型，引入渗透压和分子马达，构建了一个更为完整的红细胞计算力学模型，并研究了渗透压、膜骨架、分子马达对红细胞形态的影响。

本文建立的红细胞模型分为三层：磷脂膜、膜骨架和分子马达。其中磷脂膜采用Yuan等建立的高效粗粒化无溶剂模型。通过LAMMPS提供的用户子程序接口和C++面向对象编程，将该模型集成到LAMMPS的官方程序包中，并将脂质粒子之间的相互作用势命名为YLZ势，YLZ势通过LAMMPS中的非球形对势ASPHERE类来实现。膜骨架以长链分子网络的形式建模，其通过膜蛋白粒子与磷脂膜动态连接，且与磷脂膜之间存在空间位阻效应。

本文在YLZ势中给单个粒子添加一个沿其对称轴方向的力，来对红细胞中的磷脂膜施加沿囊泡内侧法向的力，以模拟渗透压。通过调节渗透压的大小，分别对磷脂膜和红细胞进行力学形态仿真研究，观察到在不同渗透压下的各种形状，如双凹形、杯形和多脊形，并计算稳态时的体积减小比，验证了渗透压体积调节方式的有效性。进一步对磷脂膜和红细胞施加渗透压再撤除，对比发现红细胞中膜骨架的存在能帮助红细胞维持形态。

红细胞模型第三层的分子马达通过长度可变的化学键来实现。由于分子马达所产生的收缩力在细胞各处并不均匀，本文设置了三种分子马达的分布方式：均匀分布、不均匀分布、仅分布在红细胞内凹区。在红细胞达到稳态后，通过逐渐缩短分子马达的平衡键长，比较在三种分布下红细胞形态的变化情况，探究了分子马达对于红细胞形态调节的作用。

[1] DIEZ-SILVA M, DAO M, HAN J, et al. Shape and Biomechanical Characteristics of Human Red Blood Cells in Health and Disease[J]. MRS bulletin / Materials Research Society, 2010, 35(5): 382-388.
[2] MOHANDAS N, EVANS E. Mechanical Properties of the Red Cell Membrane in Relation to Molecular Structure and Genetic Defects[J/OL]. Annual Review of Biophysics, 1994, 23(Volume 23, 1994): 787-818.
[3] GALLAGHER P G. Disorders of red cell volume regulation[J/OL]. Current Opinion in Hematology, 2013, 20(3): 201.
[4] SINGER S J, NICOLSON G L. The Fluid Mosaic Model of the Structure of Cell Membranes[J/OL]. Science, 1972, 175(4023): 720-731.
[5] GARDEL M L, KASZA K E, BRANGWYNNE C P, et al. Chapter 19: Mechanical response of cytoskeletal networks[J/OL]. Methods in Cell Biology, 2008, 89: 487-519.
[6] EHRLICHER A J, NAKAMURA F, HARTWIG J H, et al. Mechanical strain in actin networks regulates FilGAP and integrin binding to filamin A[J/OL]. Nature, 2011, 478(7368): 260-263.
[7] HOFFMAN J F. Questions for Red Blood Cell Physiologists to Ponder in This Millenium[J/OL]. Blood Cells, Molecules, and Diseases, 2001, 27(1): 57-61.
[8] METROPOLIS N, ROSENBLUTH A W, ROSENBLUTH M N, et al. Equation of State Calculations by Fast Computing Machines[J/OL]. The Journal of Chemical Physics, 1953, 21(6): 1087-1092.
[9] KARPLUS M, PETSKO G A. Molecular dynamics simulations in biology[J/OL]. Nature, 1990, 347(6294): 631-639.
[10] ANDERSEN H C. Molecular dynamics simulations at constant pressure and/or temperature[J/OL]. The Journal of Chemical Physics, 1980, 72(4): 2384-2393.
[11] PELITI L, LEIBLER S. Effects of Thermal Fluctuations on Systems with Small Surface Tension[J/OL]. Physical Review Letters, 1985, 54(15): 1690-1693.
[12] MILNER S T, SAFRAN S A. Dynamical fluctuations of droplet microemulsions and vesicles[J/OL]. Physical Review A, 1987, 36(9): 4371-4379.
[13] ALDER B J, WAINWRIGHT T E. Phase Transition for a Hard Sphere System[J/OL]. The Journal of Chemical Physics, 1957, 27(5): 1208-1209.
[14] 严六明,朱素华编著.分子动力学模拟的理论与实践[M].科学出版社,2013.
[15] WANG Y, SHAO H, ZHANG C, et al. Molecular dynamics for electrocatalysis: Mechanism explanation and performance prediction[J/OL]. Energy Reviews, 2023, 2(3): 100028.
[16] GULLAPALLI R R, DEMIREL M C, BUTLER P J. Molecular dynamics simulations of DiI-C18(3) in a DPPC lipid bilayer[J/OL]. Physical Chemistry Chemical Physics, 2008, 10(24): 3548.
[17] SIMONS K, VAZ W. Model Systems, Lipid Rafts, and Cell Membranes 1[J/OL]. Annual review of biophysics and biomolecular structure, 2004, 33: 269-295.
[18] NOGUCHI H, TAKASU M. Fusion pathways of vesicles: A Brownian dynamics simulation[J/OL]. The Journal of Chemical Physics, 2001, 115(20): 9547-9551.
[19] GAO L, LIPOWSKY R, SHILLCOCK J. Tension-induced vesicle fusion: pathways and pore dynamics[J/OL]. Soft Matter, 2008, 4(6): 1208-1214.
[20] HU W F, KIM Y, LAI M C. An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier–Stokes flows[J/OL]. Journal of Computational Physics, 2014, 257: 670-686.
[21] PENG Z, LI X, PIVKIN I V, et al. Lipid bilayer and cytoskeletal interactions in a red blood cell[J/OL]. Proceedings of the National Academy of Sciences, 2013, 110(33): 13356-13361.
[22] DROUFFE J M, MAGGS A C, LEIBLER S. Computer Simulations of Self-Assembled Membranes[J/OL]. Science, 1991, 254(5036): 1353-1356.
[23] DESERNO M. Mesoscopic Membrane Physics: Concepts, Simulations, and Selected Applications[J/OL]. Macromolecular Rapid Communications, 2009, 30(9-10): 752-771.
[24] NOGUCHI H, GOMPPER G. Meshless membrane model based on the moving least-squares method[J/OL]. Physical Review E, 2006, 73(2): 021903.
[25] SMITH K A, JASNOW D, BALAZS A C. Designing synthetic vesicles that engulf nanoscopic particles[J/OL]. The Journal of Chemical Physics, 2007, 127(8): 084703.
[26] COOKE I R, KREMER K, DESERNO M. Tunable generic model for fluid bilayer membranes[J/OL]. Physical Review E, 2005, 72(1): 011506.
[27] YUAN H, HUANG C, LI J, et al. One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes[J/OL]. Physical Review E, 2010, 82(1): 011905.
[28] LI J, LYKOTRAFITIS G, DAO M, et al. Cytoskeletal dynamics of human erythrocyte[J/OL]. Proceedings of the National Academy of Sciences, 2007, 104(12): 4937-4942.
[29] FU S P, PENG Z, YUAN H, et al. Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS[J/OL]. Computer Physics Communications, 2017, 210: 193-203.
[30] COOKE I R, DESERNO M. Solvent-free model for self-assembling fluid bilayer membranes: Stabilization of the fluid phase based on broad attractive tail potentials[J/OL]. The Journal of Chemical Physics, 2005, 123(22): 224710.
[31] BOAL D H. Mechanics of the cell[M]. 2nd ed. Cambridge (GB): Cambridge university press, 2012.
[32] YANAGISAWA M, IMAI M, TANIGUCHI T. Shape Deformation of Vesicle Coupled with Phase Separation[J/OL]. Progress of Theoretical Physics Supplement, 2008, 175: 71-80.
[33] MILNER S T, SAFRAN S A. Dynamical fluctuations of droplet microemulsions and vesicles[J/OL]. Physical Review A, 1987, 36(9): 4371-4379.
[34] LIU P, LI J, ZHANG Y W. Pressure-temperature phase diagram for shapes of vesicles: A coarse-grained molecular dynamics study[J/OL]. Applied Physics Letters, 2009, 95(14): 143104.
[35] TANAKA M, SACKMANN E. Polymer-supported membranes as models of the cell surface[J/OL]. Nature, 2005, 437(7059): 656-663.
[36] MIAO L, FOURCADE B, RAO M, et al. Equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles[J/OL]. Physical Review A, 1991, 43(12): 6843-6856.
[37] CHIEN S. Red Cell Deformability and its Relevance to Blood Flow[J/OL]. Annual Review of Physiology, 1987, 49(Volume 49, 1987): 177-192.
[38] DYRDA A, CYTLAK U, CIURASZKIEWICZ A, et al. Local membrane deformations activate Ca2+-dependent K + and anionic currents in intact human red blood cells[J/OL]. PLoS ONE, 2010, 5(2): e9447.
[39] CAHALAN S M, LUKACS V, RANADE S S, et al. Piezo1 links mechanical forces to red blood cell volume[J/OL]. eLife, 2015, 4: e07370.
[40] SVETINA S, ŠVELC KEBE T, BOŽIČ B. A Model of Piezo1-Based Regulation of Red Blood Cell Volume[J/OL]. Biophysical Journal, 2019, 116(1): 151-164.
[41] MARKVOORT A J, SPIJKER P, SMEIJERS A F, et al. Vesicle Deformation by Draining: Geometrical and Topological Shape Changes[J/OL]. The Journal of Physical Chemistry B, 2009, 113(25): 8731-8737.
[42] WONG A J, KIEHART D P, POLLARD T D. Myosin from human erythrocytes.[J/OL]. Journal of Biological Chemistry, 1985, 260(1): 46-49.
[43] SALBREUX G, CHARRAS G, PALUCH E. Actin cortex mechanics and cellular morphogenesis[J/OL]. Trends in Cell Biology, 2012, 22(10): 536-545.
[44] VICENTE-MANZANARES M, MA X, ADELSTEIN R S, et al. Non-muscle myosin II takes centre stage in cell adhesion and migration[J/OL]. Nature Reviews Molecular Cell Biology, 2009, 10(11): 778-790.
[45] HEISSLER S M, MANSTEIN D J. Nonmuscle myosin-2: mix and match[J/OL]. Cellular and Molecular Life Sciences, 2013, 70(1): 1-21.
[46] CONTI M A, ADELSTEIN R S. Nonmuscle myosin II moves in new directions[J/OL]. Journal of Cell Science, 2008, 121(3): 404-404.
[47] AGARWAL P, ZAIDEL-BAR R. Principles of Actomyosin Regulation In Vivo[J/OL]. Trends in Cell Biology, 2019, 29(2): 150-163.
[48] GORFINKIEL N, BLANCHARD G B. Dynamics of actomyosin contractile activity during epithelial morphogenesis[J/OL]. Current Opinion in Cell Biology, 2011, 23(5): 531-539.
[49] KASZA K E, ZALLEN J A. Dynamics and regulation of contractile actin–myosin networks in morphogenesis[J/OL]. Current Opinion in Cell Biology, 2011, 23(1): 30-38.
[50] HEISENBERG C P, BELLAÏCHE Y. Forces in Tissue Morphogenesis and Patterning[J/OL]. Cell, 2013, 153(5): 948-962.
[51] YAMADA K M, SIXT M. Mechanisms of 3D cell migration[J/OL]. Nature Reviews Molecular Cell Biology, 2019, 20(12): 738-752.
[52] SMITH A S, NOWAK R B, ZHOU S, et al. Myosin IIA interacts with the spectrin-actin membrane skeleton to control red blood cell membrane curvature and deformability[J/OL]. Proceedings of the National Academy of Sciences of the United States of America, 2018, 115(19): E4377-E4385.
[53] ALIMOHAMADI H, SMITH A S, NOWAK R B, et al. Non-uniform distribution of myosin-mediated forces governs red blood cell membrane curvature through tension modulation[J/OL]. PLOS Computational Biology, 2020, 16(5): e1007890.
[54] THOMPSON A P, AKTULGA H M, BERGER R, et al. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales[J/OL]. Computer Physics Communications, 2022, 271: 108171.
[55] CANHAM P B, BURTON A C. Distribution of Size and Shape in Populations of Normal Human Red Cells[J/OL]. Circulation Research, 1968, 22(3): 405-422.
[56] GRATZER W B. The red cell membrane and its cytoskeleton[J/OL]. The Biochemical Journal, 1981, 198(1): 1-8.
[57] FOWLER V M. The human erythrocyte plasma membrane: a Rosetta Stone for decoding membrane-cytoskeleton structure[J/OL]. Current Topics in Membranes, 2013, 72: 39-88.
[58] GOKHIN D S, FOWLER V M. Feisty filaments: actin dynamics in the red blood cell membrane skeleton[J/OL]. Current Opinion in Hematology, 2016, 23(3): 206-214.
[59] LI N, CHEN S, XU K, et al. Structural basis of membrane skeleton organization in red blood cells[J/OL]. Cell, 2023, 186(9): 1912-1929.e18.
[60] ALBERTS B. Molecular biology of the cell[M]. Sixth edition. New York, NY: Garland Science, Taylor and Francis Group, 2015.
[61] MARKVOORT A J, VAN SANTEN R A, HILBERS P A J. Vesicle Shapes from Molecular Dynamics Simulations[J/OL]. The Journal of Physical Chemistry B, 2006, 110(45): 22780-22785.
[62] NOSÉ S. A molecular dynamics method for simulations in the canonical ensemble[J/OL]. Molecular Physics, 2002, 100(1): 191-198.
[63] Gerald L H W , Wortis M , Mukhopadhyay R .Red Blood Cell Shapes and Shape Transformations: Newtonian Mechanics of a Composite Membrane: Sections 2.1–2.4[M]. 2009.
[64] MESAREC L, GÓŹDŹ W, IGLIČ A, et al. Normal red blood cells’ shape stabilized by membrane’s in-plane ordering[J/OL]. Scientific Reports, 2019, 9(1): 19742.
[65] ABKARIAN M, FAIVRE M, HORTON R, et al. Cellular-scale hydrodynamics[J/OL]. Biomedical Materials, 2008, 3(3): 034011.
[66] GEDDE M, YANG E, HUESTIS W. Shape response of human erythrocytes to altered cell pH[J/OL]. Blood, 1995, 86(4): 1595-1599.
[67] REINHART W, CHIEN S. Red Cell Rheology in Stomatocyte-Echinocyte Transformation: Roles of Cell Geometry and Cell Shape[J/OL]. Blood, 1986, 67: 1110-1118.
[68] SCHWERIN E. Zur Stabilität der dünnwandigen Hohlkugel unter gleichmäßigem Außendruck[J/OL]. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1922, 2(2): 81-91.
[69] MOHANDAS N, EVANS E. Mechanical Properties of the Red Cell Membrane in Relation to Molecular Structure and Genetic Defects[J/OL]. Annual Review of Biophysics, 1994, 23(Volume 23, 1994): 787-818.
[70] EBRAHIM S, FUJITA T, MILLIS B, et al. NMII Forms a Contractile Transcellular Sarcomeric Network to Regulate Apical Cell Junctions and Tissue Geometry[J/OL]. Current biology : CB, 2013, 23.
[71] Human erythrocyte myosin: identification and purification[J]. The Journal of Cell Biology, 1985, 100(1): 47-55.
[72] CANHAM P B. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell[J/OL]. Journal of Theoretical Biology, 1970, 26(1): 61-81.