Modeling biomembranes and red blood cells by coarse-grained particle methods

doi:10.1007/s10483-018-2252-6

Abstract

Abstract:

In this work, the previously developed coarse-grained (CG) particle models for biomembranes and red blood cells (RBCs) are reviewed, and the advantages of the CG particle methods over the continuum and atomistic simulations for modeling biological phenomena are discussed. CG particle models can largely increase the length scale and time scale of atomistic simulations by eliminating the fast degrees of freedom while preserving the mesoscopic structures and properties of the simulated system. Moreover, CG particle models can be used to capture the microstructural alternations in diseased RBCs and simulate the topological changes of biomembranes and RBCs, which are the major challenges to the typical continuum representations of membranes and RBCs. The power and versatility of CG particle methods are demonstrated through simulating the dynamical processes involving significant topological changes, e.g., lipid self-assembly vesicle fusion and membrane budding.

Key words: forming process, numerical simulation, non-incremental algorithm, time-space function, lipid bilayer, red blood cell membrane, membrane fusion, coarse-grained molecular dynamics

2010 MSC Number:

92C05

H. LI, H. Y. CHANG, J. YANG, L. LU, Y. H. TANG, G. LYKOTRAFITIS. Modeling biomembranes and red blood cells by coarse-grained particle methods. Applied Mathematics and Mechanics (English Edition), 2018, 39(1): 3-20.

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References

[1] Alberts, B., Johnson, A., Lewis, J., Ralf, M., Roberts, K., and Walter, P. Molecular Biology of the Cell, Garland, New York (2002)
[2] Boal, D. Mechanics of the Cell, Cambridge University Press, Cambridge (2002)
[3] Sten-Knudsen, O. Biological Membranes:Theory of Transport, Potentials and Electric Impulses, Cambridge University Press, Cambridge (2002)
[4] Agre, P. and Parker, J. C. Red Blood Cell Membranes:Structure, Function, Clinical Implications, Marcel Dekker Inc., New York (1989)
[5] Mohandas, N. and Evans, E. Mechanical properties of the red cell membrane in relation to molecular structure and genetic defects. Annual Review of Biophysics & Biomolecular Structure, 23, 787-818(1994)
[6] Feller, S. E. Molecular dynamics simulations of lipid bilayers. Current Opinion in Colloid & Interface Science, 5, 217-223(2000)
[7] Saiz, L., Bandyopadhyay, S., and Klein, M. L. Towards an understanding of complex biological membranes from atomistic molecular dynamics simulations. Bioscience Reports, 22, 151-173(2002)
[8] Tieleman, D. P., Marrink, S. J., and Berendsen, H. J. C. A computer perspective of membranes:molecular dynamics studies of lipid bilayer systems. Biochimica et Biophysica Acta (BBA)-Reviews, 1331, 235-270(1997)
[9] Tu, K. C., Klein, M. L., and Tobias, D. J. Constant-pressure molecular dynamics investigation of cholesterol effects in a dipalmitoylphosphatidylcholine bilayer. Biophysical Journal, 75, 2147-2156(1998)
[10] Hofsass, C., Lindahl, E., and Edholm, O. Molecular dynamics simulations of phospholipid bilayers with cholesterol. Biophysical Journal, 84, 2192-2206(2003)
[11] Tieleman, D. P., Leontiadou, H., Mark, A. E., and Marrink, S. J. Simulation of pore formation in lipid bilayers by mechanical stress and electric fields. Journal of the American Chemical Society, 125, 6382-6383(2003)
[12] Canham, P. B. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. Journal of Theoretical Biology, 26, 61-81(1970)
[13] Evans, E. Bending resistance and chemically induced moments in membrane bilayers. Biophysical Journal, 14, 923-931(1974)
[14] Helfrich, W. Elastic properties of lipid bilayers:theory and possible experiments. Zeitschrift für Naturforschung. Teil C:Biochemie, Biophysik, Biologie, Virologie, 28, 693-703(1973)
[15] Seifert, U. Configurations of fluid membranes and vesicles. Advances in Physics, 46, 13-137(1997)
[16] Smondyrev, A. M. and Berkowitz, M. L. Molecular dynamics simulation of fluorination effects on a phospholipid bilayer. Journal of Chemical Physics, 111, 9864-9870(1999)
[17] Zhao, H., Isfahani, A. H., Olson, L. N., and Freund, J. B. A spectral boundary integral method for flowing blood cells. Journal of Computational Physics, 229, 3726-3744(2010)
[18] Veerapaneni, S. K., Rahimian, A., Biros, G., and Zorin, D. A fast algorithm for simulating vesicle flows in three dimensions. Journal of Computational Physics, 230, 5610-5634(2011)
[19] Ramanujan, S. and Pozrikidis, C. Deformation of liquid capsules enclosed by elastic membranes in simple shear flow:large deformations and the effect of fluid viscosities. Journal of Fluid Mechanics, 361, 117-143(2000)
[20] Lac, E., Barthes-Biesel, D., Pelekasis, N., and Tsamopoulos, J. Spherical capsules in threedimensional unbounded Stokes flows:effect of the membrane constitutive law and onset of buckling. Journal of Fluid Mechanics, 516, 303-334(2004)
[21] Peskin, C. S. The immersed boundary method. Acta Numerica, 11, 479-517(2002)
[22] Doddi, S. K. and Bagchi, P. Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. Physical Review E, 79, 046318(2009)
[23] Yazdani, A. Z. and Bagchi, P. Phase diagram and breathing dynamics of a single red blood cell and a biconcave capsule in dilute shear flow. Physical Review E, 84, 026314(2011)
[24] Fai, T. G., Griffith, B. E., Mori, Y., and Peskin, C. S. Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers I:numerical method and results. SIAM Journal on Scientific Computing, 35, B1132-B1161(2013)
[25] Yazdani, A. Z., Kalluri, R. M., and Bagchi, P. Tank-treading and tumbling frequencies of capsules and red blood cells. Physical Review E, 83, 046305(2011)
[26] Salehyar, S. and Zhu, Q. Deformation and internal stress in a red blood cell as it is driven through a slit by an incoming flow. Soft Matter, 12, 3156-3164(2016)
[27] Pozrikidis, C. Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press, Cambridge (1992)
[28] Peng, Z., Asaro, R. J., and Zhu, Q. Multiscale modelling of erythrocytes in Stokes flow. Journal of Fluid Mechanics, 686, 299-337(2011)
[29] Venturoli, M., Sperotto, M. M., Kranenburg, M., and Smit, B. Mesoscopic models of biological membranes. Physics Reports, 437, 1-54(2006)
[30] Drouffe, J. M., Maggs, A. C., and Leibler, S. Computer-simulations of self-assembled membranes. Science, 254, 1353-1356(1991)
[31] Goetz, R., Gompper, G., and Lipowsky, R. Mobility and elasticity of self-assembled membranes. Physical Review Letters, 82, 221-224(1999)
[32] Kumar, P. B. S., Gompper, G., and Lipowsky, R. Budding dynamics of multicomponent membranes. Physical Review Letters, 86, 3911-3914(2001)
[33] Noguchi, H. and Takasu, M. Adhesion of nanoparticles to vesicles:A Brownian dynamics simulation. Biophysical Journal, 83, 299-308(2002)
[34] Yamamoto, S., Maruyama, Y., and Hyodo, S. Dissipative particle dynamics study of spontaneous vesicle formation of amphiphilic molecules. Journal of Chemical Physics, 116, 5842-5849(2002)
[35] Farago, O. "Water-free" computer model for fluid bilayer membranes. Journal of Chemical Physics, 119, 596-605(2003)
[36] Marrink, S. J. and Mark, A. E. Molecular dynamics simulation of the formation, structure, and dynamics of small phospholipid vesicles. Journal of the American Chemical Society, 125, 15233-15242(2003)
[37] Marrink, S. J. and Mark, A. E. The mechanism of vesicle fusion as revealed by molecular dynamics simulations. Journal of the American Chemical Society, 125, 11144-11145(2003)
[38] Brannigan, G., Philips, P. F., and Brown, F. L. H. Flexible lipid bilayers in implicit solvent. Physical Review E, 72, 011915(2005)
[39] Cooke, I. R., Kremer, K., and Deserno, M. Tunable generic model for fluid bilayer membranes. Physical Review E, 72, 011506(2005)
[40] Laradji, M. and Kumar, P. B. S. Domain growth, budding, and fission in phase-separating selfassembled fluid bilayers. Journal of Chemical Physics, 123, 224902(2005)
[41] Laradji, M. and Kumar, P. B. S. Dynamics of domain growth in multi-component self-assembled fluid vesicles in explict solvent. Physical Review Letters, 93, 198105(2004)
[42] Markvoort, A. J., Pieterse, K., Steijaert, M. N., Spijker, P., and Hilbers, P. A. J. The bilayervesicle transition is entropy driven. Journal of Physical Chemistry B, 109, 22649-22654(2005)
[43] Wang, Z. J. and Frenkel, D. Modeling flexible amphiphilic bilayers:a solvent-free off-lattice Monte Carlo study. Journal of Chemical Physics, 122, 234711(2005)
[44] Brannigan, G., Lin, L. C. L., and Brown, F. L. H. Implicit solvent simulation models for biomembranes. European Biophysics Journal with Biophysics Letters, 35, 104-124(2006)
[45] Markvoort, A. J., van Santen, R. A., and Hilbers, P. A. J. Vesicle shapes from molecular dynamics simulations. Journal of Physical Chemistry B, 110, 22780-22785(2006)
[46] Noguchi, H. and Gompper, G. Meshless membrane model based on the moving least-squares method. Physical Review E, 73, 021903(2006)
[47] Marrink, S. J., Risselada, H. J., Yefimov, S., Tieleman, D. P., and de Vries, A. H. The MARTINI force field:coarse grained model for biomolecular simulations. Journal of Physical Chemistry B, 111, 7812-7824(2007)
[48] Muller, M., Katsov, K., and Schick, M. Biological and synthetic membranes:what can be learned from a coarse-grained description? Physics Reports, 434, 113-176(2006)
[49] Kohyama, T. Simulations of flexible membranes using a coarse-grained particle-based model with spontaneous curvature variables. Physica A:Statistical Mechanics and Its Applications, 388, 3334-3344(2009)
[50] Muller, M., Katsov, K., and Schick, M. New mechanism of membrane fusion. The Journal of Chemical Physics, 116, 2342-2345(2002)
[51] Ayton, G. and Voth, G. A. Bridging microscopic and mesoscopic simulations of lipid bilayers. Biophysical Journal, 83, 3357-3370(2002)
[52] Yip, S. and Short, M. P. Multiscale materials modelling at the mesoscale. Nature Materials, 12, 774-777(2013)
[53] Chang, H. Y., Sheng, Y. J., and Tsao, H. K. Structural and mechanical characteristics of polymersomes. Soft Matter, 10, 6373-6381(2014)
[54] Li, X., Pivkin, I. V., Liang, H., and Karniadakis, G. E. Shape transformations of membrane vesicles from amphiphilic triblock copolymers:a dissipative particle dynamics simulation study. Macromolecules, 42, 3195-3200(2009)
[55] Li, X., Guo, J., Liu, Y., and Liang, H. Microphase separation of diblock copolymer poly (styreneb-isoprene):a dissipative particle dynamics simulation study. The Journal of Chemical Physics, 130, 074908(2009)
[56] Li, X., Liu, Y., Wang, L., Deng, M., and Liang, H. Fusion and fission pathways of vesicles from amphiphilic triblock copolymers:a dissipative particle dynamics simulation study. Physical Chemistry Chemical Physics, 11, 4051-4059(2009)
[57] Chang, H. Y., Chen, Y. F., Sheng, Y. J., and Tsao, H. K. Blending-induced helical morphologies of confined linear triblock copolymers. Journal of the Taiwan Institute of Chemical Engineers, 56, 196-200(2015)
[58] Lin, Y. L., Chang, H. Y., Sheng, Y. J., and Tsao, H. K. Self-assembled polymersomes formed by symmetric, asymmetric and side-chain-tethered coil-rod-coil triblock copolymers. Soft Matter, 10, 1840-1852(2014)
[59] Lin, Y. L., Chang, H. Y., Sheng, Y. J., and Tsao, H. K. The fusion mechanism of small polymersomes formed by rod-coil diblock copolymers. Soft Matter, 10, 1500-1511(2014)
[60] Li, Z., Bian, X., Yang, X., and Karniadakis, G. E. A comparative study of coarse-graining methods for polymeric fluids:Mori-Zwanzig vs. iterative Boltzmann inversion vs. stochastic parametric optimization. The Journal of Chemical Physics, 145, 044102(2016)
[61] Li, Z., Lee, H. S., Darve, E., and Karniadakis, G. E. Computing the non-Markovian coarsegrained interactions derived from the Mori-Zwanzig formalism in molecular systems:application to polymer melts. The Journal of Chemical Physics, 146, 014104(2017)
[62] Li, H. and Lykotrafitis, G. A coarse-grain molecular dynamics model for sickle hemoglobin fibers. Journal of the Mechanical Behavior of Biomedical Materials, 4, 162-173(2011)
[63] Li, H., Ha, V., and Lykotrafitis, G. Modeling sickle hemoglobin fibers as one chain of coarsegrained particles. Journal of Biomechanics, 45, 1947-1951(2012)
[64] Zhang, Y., Abiraman, K., Li, H., Pierce, D. M., Tzingounis, A. V., and Lykotrafitis, G. Modeling of the axon membrane skeleton structure and implications for its mechanical properties. PLoS Computational Biology, 13, e1005407(2017)
[65] Kim, T., Hwang, W., Lee, H., and Kamm, R. D. Computational analysis of viscoelastic properties of crosslinked actin networks. PLoS Computational Biology, 5, e1000439(2009)
[66] Kim, T., Hwang, W., and Kamm, R. Computational analysis of a cross-linked actin-like network. Experimental Mechanics, 49, 91-104(2009)
[67] Lu, L., Li, X., Vekilov, P. G., and Karniadakis, G. E. Probing the twisted structure of sickle hemoglobin fibers via particle simulations. Biophysical Journal, 110, 2085-2093(2016)
[68] Lu, L., Li, H., Bian, X., Li, X., and Karniadakis, G. E. Mesoscopic adaptive resolution scheme (MARS) toward understanding of interactions between sickle cell fibers. Biophysical Journal, 113, 48-59(2017)
[69] Brannigan, G., Tamboli, A. C., and Brown, F. L. H. The role of molecular shape in bilayer elasticity and phase behavior. Journal of Chemical Physics, 121, 3259-3271(2004)
[70] Yuan, H., Huang, C., Li, J., Lykotrafitis, G., and Zhang, S. One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes. Physical Review E, 82, 011905(2010)
[71] Espanol, P. and Warren, P. Statistical-mechanics of dissipative particle dynamics. Europhysics Letters, 30, 191-196(1995)
[72] Hoogerbrugge, P. J. and Koelman, J. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhysics Letters, 19, 155-160(1992)
[73] Grafmuller, A., Shillcock, J., and Lipowsky, R. Dissipative particle dynamics of tension-induced membrane fusion. Molecular Simulation, 35, 554-560(2009)
[74] Brannigan, G. and Brown, F. L. H. Solvent-free simulations of fluid membrane bilayers. The Journal of Chemical Physics, 120, 1059-1071(2004)
[75] Marrink, S. J., de Vries, A. H., and Tieleman, D. P. Lipids on the move:simulations of membrane pores, domains, stalks and curves. Biochimica et Biophysica Acta (BBA)-Biomembranes, 1788, 149-168(2009)
[76] Lin, C. M., Li, C. S., Sheng, Y. J., Wu, D. T., and Tsao, H. K. Size-dependent properties of small unilamellar vesicles formed by model lipids. Langmuir, 28, 689-700(2011)
[77] Li, X., Tang, Y. H., Liang, H., and Karniadakis, G. E. Large-scale dissipative particle dynamics simulations of self-assembled amphiphilic systems. Chemical Communications, 50, 8306-8308(2014)
[78] Lindahl, E. and Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophysical Journal, 79, 426-433(2000)
[79] Kranenburg, M., Laforge, C., and Smit, B. Mesoscopic simulations of phase transitions in lipid bilayers. Physical Chemistry Chemical Physics, 6, 4531-4534(2004)
[80] Kranenburg, M. and Smit, B. Phase behavior of model lipid bilayers. The Journal of Physical Chemistry B, 109, 6553-6563(2005)
[81] Tristram-Nagle, S. and Nagle, J. F. Lipid bilayers:thermodynamics, structure, fluctuations, and interactions. Chemistry and Physics of Lipids, 127, 3-14(2004)
[82] Lenz, O. and Schmid, F. Structure of symmetric and asymmetric ripple phases in lipid bilayers. Physical Review Letters, 98, 058104(2007)
[83] Rodgers, J. M., Sørensen, J., de Meyer F. J., Schiøtt B., and Smit, B. Understanding the phase behavior of coarse-grained model lipid bilayers through computational calorimetry. The Journal of Physical Chemistry B, 116, 1551-1569(2012)
[84] Wu, H. L., Sheng, Y. J., and Tsao, H. K. Phase behaviors and membrane properties of model liposomes:temperature effect. The Journal of Chemical Physics, 141, 124906(2014)
[85] Venturoli, M., Smit, B., and Sperotto, M. M. Simulation studies of protein-induced bilayer deformations, and lipid-induced protein tilting, on a mesoscopic model for lipid bilayers with embedded proteins. Biophysical Journal, 88, 1778-1798(2005)
[86] Olbrich, K., Rawicz, W., Needham, D., and Evans, E. Water permeability and mechanical strength of polyunsaturated lipid bilayers. Biophysical Journal, 79, 321-327(2000)
[87] Marrink, S. J., de Vries, A. H., and Mark, A. E. Coarse grained model for semiquantitative lipid simulations. The Journal of Physical Chemistry B, 108, 750-760(2004)
[88] Evans, E. and Rawicz, W. Entropy-driven tension and bending elasticity in condensed-fluid membranes. Physical Review Letters, 64, 2094-2097(1990)
[89] Nagle, J. F. and Wilkinson, D. A. Dilatometric studies of the subtransition in dipalmitoylphosphatidylcholine. Biochemistry, 21, 3817-3821(1982)
[90] Tristram-Nagle, S., Wiener, M., Yang, C., and Nagle, J. Kinetics of the subtransition in dipalmitoylphosphatidylcholine. Biochemistry, 26, 4288-4294(1987)
[91] Chernomordik, L. V. and Kozlov, M. M. Protein-lipid interplay in fusion and fission of biological membranes. Annual Review of Biochemistry, 72, 175-207(2003)
[92] Liu, J., Jiang, X., Ashley, C., and Brinker, C. J. Electrostatically mediated liposome fusion and lipid exchange with a nanoparticle-supported bilayer for control of surface charge, drug containment, and delivery. Journal of the American Chemical Society, 131, 7567-7569(2009)
[93] Attwood, S. J., Choi, Y., and Leonenko, Z. Preparation of DOPC and DPPC supported planar lipid bilayers for atomic force microscopy and atomic force spectroscopy. International Journal of Molecular Sciences, 14, 3514-3539(2013)
[94] Wu, H. L., Chen, P. Y., Chi, C. L., Tsao, H. K., and Sheng, Y. J. Vesicle deposition on hydrophilic solid surfaces. Soft Matter, 9, 1908-1919(2013)
[95] Lei, G. and MacDonald, R. C. Lipid bilayer vesicle fusion:intermediates captured by high-speed microfluorescence spectroscopy. Biophysical Journal, 85, 1585-1599(2003)
[96] García, R. A., Pantazatos, S. P., Pantazatos, D. P., and MacDonald, R. C. Cholesterol stabilizes hemifused phospholipid bilayer vesicles. Biochimica et Biophysica Acta (BBA)-Biomembranes, 1511, 264-270(2001)
[97] Stevens, M. J., Hoh, J. H., and Woolf, T. B. Insights into the molecular mechanism of membrane fusion from simulation:evidence for the association of splayed tails. Physical Review Letters, 91, 188102(2003)
[98] Knecht, V. and Marrink, S. J. Molecular dynamics simulations of lipid vesicle fusion in atomic detail. Biophysical Journal, 92, 4254-4261(2007)
[99] Smeijers, A., Markvoort, A., Pieterse, K., and Hilbers, P. A detailed look at vesicle fusion. The Journal of Physical Chemistry B, 110, 13212-13219(2006)
[100] Gao, L., Lipowsky, R., and Shillcock, J. Tension-induced vesicle fusion:pathways and pore dynamics. Soft Matter, 4, 1208-1214(2008)
[101] Wu, S. and Guo, H. Simulation study of protein-mediated vesicle fusion. The Journal of Physical Chemistry B, 113, 589-591(2008)
[102] Kozlovsky, Y., Chernomordik, L. V., and Kozlov, M. M. Lipid intermediates in membrane fusion:formation, structure, and decay of hemifusion diaphragm. Biophysical Journal, 83, 2634-2651(2002)
[103] Lin, C. M., Wu, D. T., Tsao, H. K., and Sheng, Y. J. Membrane properties of swollen vesicles:growth, rupture, and fusion. Soft Matter, 8, 6139-6150(2012)
[104] Kuzmin, P. I., Zimmerberg, J., Chizmadzhev, Y. A., and Cohen, F. S. A quantitative model for membrane fusion based on low-energy intermediates. Proceedings of the National Academy of Sciences, 98, 7235-7240(2001)
[105] Li, H. and Lykotrafitis, G. Two-component coarse-grained molecular-dynamics model for the h0uman erythrocyte membrane. Biophysical Journal, 102, 75-84(2012)
[106] Li, H. and Lykotrafitis, G. Erythrocyte membrane model with explicit description of the lipid bilayer and the spectrin network. Biophysical Journal, 107, 642-653(2014)
[107] Li, J., Lykotrafitis, G., Dao, M., and Suresh, S. Cytoskeletal dynamics of human erythrocyte. Proceedings of the National Academy of Sciences of the United States of America, 104, 4937-4942(2007)
[108] Li, H. and Lykotrafitis, G. Vesiculation of healthy and defective red blood cells. Physical Review E, 92, 012715(2015)
[109] Li, H., Zhang, Y., Ha, V., and Lykotrafitis, G. Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane. Soft Matter, 12, 3643-3653(2016)
[110] Zhang, Y., Huang, C. J., Kim, S., Golkaram, M., Dixon, M. W. A., Tilley, L., Li, J., Zhang, S. L., and Suresh, S. Multiple stiffening effects of nanoscale knobs on human red blood cells infected with Plasmodium falciparum malaria parasite. Proceedings of the National Academy of Sciences, 112, 6068-6073(2015)
[111] Dearnley, M., Chu, T., Zhang, Y., Looker, O., Huang, C. J., Klonis, N., Yeoman, J., Kenny, S., Arora, M., Osborne, J. M., Chandramohanadas, R., Zhang, S. L., Dixon, M. W. A., and Tilley, L. Reversible host cell remodeling underpins deformability changes in malaria parasite sexual blood stages. Proceedings of the National Academy of Sciences, 113, 4800-4805(2016)
[112] Tang, Y. H., Lu, L., Li, H., and Karniadakis, G. E. OpenRBC:a fast simulator of red blood cells at protein resolution. Biophysical Journal, 112, 2030-2037(2017)
[113] Discher, D. E., Boal, D. H., and Boey, S. K. Simulations of the erythrocyte cytoskeleton at large deformation, Ⅱ:micropipette aspiration. Biophysical Journal, 75, 1584-1597(1998)
[114] Li, J., Dao, M., Lim, C. T., and Suresh, S. Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophysical Journal, 88, 3707-3719(2005)
[115] Pivkin, I. V. and Karniadakis, G. E. Accurate coarse-grained modeling of red blood cells. Physical Review Letters, 101, 118105(2008)
[116] Pivkin, I. V., Peng, Z., Karniadakis, G. E., Buffet, P. A., Dao, M., and Suresh, S. Biomechanics of red blood cells in human spleen and consequences for physiology and disease. Proceedings of the National Academy of Sciences, 113, 7804-7809(2016)
[117] Li, X., Caswell, B., and Karniadakis, G. E. Effect of chain chirality on the self-assembly of sickle hemoglobin. Biophysical Journal, 103, 1130-1140(2012)
[118] Fedosov, D. A., Pan, W., Caswell, B., Gompper, G., and Karniadakis, G. E. Predicting human blood viscosity in silico. Proceedings of the National Academy of Sciences, 108, 11772-11777(2011)
[119] Fedosov, D. A., Noguchi, H., and Gompper, G. Multiscale modeling of blood flow:from single cells to blood rheology. Biomechanics and Modeling in Mechanobiology, 13, 239-258(2014)
[120] Blumers, A. L., Tang, Y. H., Li, Z., Li, X., and Karniadakis, G. E. GPU-accelerated red blood cells simulations with transport dissipative particle dynamics. Computer Physics Communications, 217, 171-179(2017)
[121] Rossinelli, D., Tang, Y. H., Lykov, K., Alexeev, D., Bernaschi, M., Hadjidoukas, P., Bisson, M., Joubert, W., Conti, C., Karniadakis, G., Fatica, M., Pivkin, I., and Koumoutsakos, P. The in-silico lab-on-a-chip:petascale and high-throughput simulations of microfluidics at cell resolution. Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Texas (2015)
[122] Peng, Z., Li, X., Pivkin, I. V., Dao, M., Karniadakis, G. E., and Suresh, S. Lipid bilayer and cytoskeletal interactions in a red blood cell. Proceedings of the National Academy of Sciences, 110, 13356-13361(2013)
[123] Li, X., Peng, Z., Lei, H., Dao, M., and Karniadakis, G. E. Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model. Philosophical Transactions of the Royal Society A, 372, 20130389(2014)
[124] Chang, H. Y., Li, X., Li, H., and Karniadakis, G. E. MD/DPD multiscale framework for predicting morphology and stresses of red blood cells in health and disease. PLoS Computational Biology, 12, e1005173(2016)
[125] Chang, H. Y., Li, X., and Karniadakis, G. E. Modeling of biomechanics and biorheology of red blood cells in type-2 diabetes mellitus. Biophysical Journal, 113, 481-490(2017)
[126] Espanol, P. and Revenga, M. Smoothed dissipative particle dynamics. Physical Review E, 67, 026705(2003)
[127] Yang, J. A Smoothed Dissipative Particle Dynamics Methodology for Wall-Bounded Domains, Ph. D. dissertation, Worcester Polytechnic Institute, Worcester (2013)
[128] Gatsonis, N. A., Potami, R., and Yang, J. A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries. Journal of Computational Physics, 256, 441-464(2014)
[129] Fedosov, D. A., Peltomäi, M., and Gompper, G. Deformation and dynamics of red blood cells in flow through cylindrical microchannels. Soft Matter, 10, 4258-4267(2014)
[130] Fedosov, D. A. and Gompper, G. White blood cell margination in microcirculation. Soft Matter, 10, 2961-2970(2014)
[131] Li, X., Li, H., Chang, H. Y., Lykotrafitis, G., and Karniadakis, G. E. Computational biomechanics of human red blood cells in hematological disorders. Journal of Biomechanical Engineering, 139, 021008(2017)
[132] Li, X., Dao, M., Lykotrafitis, G., and Karniadakis, G. E. Biomechanics and biorheology of red blood cells in sickle cell anemia. Journal of Biomechanics, 50, 34-41(2017)
[133] Li, X., Vlahovska, P. M., and Karniadakis, G. E. Continuum-and particle-based modeling of shapes and dynamics of red blood cells in health and disease. Soft Matter, 9, 28-37(2013)