Abstract
As an effective physical method, cell squeezing technology based on microfluidics plays an increasingly promising role in intracellular delivery. To deepen our understanding of microfluidic chip design and optimization, it is essential to explore the underlying physics required in the generation of the appropriate tension for gating capsule membrane. In this investigation, an immersed finite element method (IFEM) has been adopted to simulate the interaction between capsule and fluid fields in microchannel with variable section. Having obtained the numerical results, the gating region on the membrane can be determined by the non-uniform tension distribution based on the critical gating membrane tension during the capsule translocates the microchannel. In addition, the gating integral, which is defined to measure the degree of gating, shows that the setting of driven pressure might be crucial for the design and optimization of the system. The numerical results demonstrate that the occurrence of secondary peak in deformed energy after the capsule passes through the confined microchannel under certain flow condition might be ascribed to the elastic recovery of the membrane. To investigate the effects of initial orientations, the translocation of an ellipsoid capsule through the channel has also been simulated numerically, which indicates that both flow shear force and compressive force due to the constrained solid wall have significant effects on membrane gating. Therefore, to improve the gating efficiency of capsule membrane, it is necessary to optimize various factors to achieve the balance among the compressive force, shear force and the translocation time.
Similar content being viewed by others
Data availability statement
The data that support the findings of this study are available from the corresponding author upon request.
References
Atzberger PJ, Kramer PR, Peskin CS (2007) A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales. J Comput Phys 224:1255–1292
Au SH, Storey BD, Moore JC, Tang Q, Chen YL, Javaid S, Sarioglu AF, Sullivan R, Madden MW, O’Keefe R, Haber DA (2016) Clusters of circulating tumor cells traverse capillary-sized vessels. Proc Natl Acad Sci USA 113:4947–4952
Bao YX, Kaye J, Peskin CS (2016) A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance. J Comput Phys 316:139–144
Bavi N, Nakayama Y, Bavi O, Cox CD, Qin QH, Martinac B (2014) Biophysical implications of lipid bilayer rheometry for mechanosensitive channels. Proc Natl Acad Sci USA 111:13864–13869
Bergert M, Erzberger A, Desai RA, Aspalter IM, Oates AC, Charras G, Salbreux G, Paluch EK (2015) Force transmission during adhesion-independent migration. Nat Cell Bio 17(4):524–9
Bow H, Pivkin IV, Diez-Silva M, Goldfless SJ, Dao M, Niles JC, Suresh S, Han J (2011) A microfabricated deformability-based flow cytometer with application to malaria. Lab Chip 11:1065–1073
Byun H, Hillman TR, Higgins JM, Diez-Silva M, Peng ZL, Dao M, Dasari RR, Suresh S, Park Y (2012) Optical measurement of biomechanical properties of individual erythrocytes from a sickle cell patient. Acta Biomater 8(11):4130–4138
Cao X, Moeendarbary E, Isermann P, Davidson PM, Wang X, Chen MB, Burkart AK, Lammerding J, Kamm RD, Shenoy VB (2016) A chemomechanical model for nuclear morphology and stresses during cell transendothelial migration. Biophys J 111:1541–1552
Chang HY, Li XJ, Karniadakis GE (2017) Modeling of biomechanics and biorheology of red blood cell in type 2 diabetes mellitus. Biophys J 113:481–490
Cordes A, Witt H, Gallemí-Pérez A, Brückner B, Grimm F, Vache M, Oswald T, Bodenschatz J, Flormann D, Lautenschläger F, Tarantola M (2020) Prestress and area compressibility of actin cortices determine the viscoelastic response of living cells. Phys Rev Lett 125(6):068101
Dahl BJ (2015) Microfluidic strategies for understanding the mechanics of cells and cell-mimetic systems. Annu Rev Chem Biomol Eng 6:293–317
Darling EM (2014) High-throughput assessment of cellular mechanical properties. Annu Rev Chem Biomol Eng 17:35–62
Davison J (1999) Genetic exchange between bacteria in the environment. Plasmid 42:73–91
Denais CM, Gilbert RM, Isermann P, McGregor AL, Te Lindert M, Weigelin B, Davidson PM, Friedl P, Wolf K, Lammerding J (2016) Nuclear envelope rupture and repair during cancer cell migration. Science 352:353–358
Dong Z, Jiao Y, Xie B, Hao Y, Wang P, Liu Y, Shi J, Chitrakar C, Black S, Wang YC, Lee LJ (2020) On-chip multiplexed single-cell patterning and controllable intracellular delivery. Microsys Nanoeng 6:1–11
Evans EA, Waugh R, Melnik L (1976) Elastic area compressibility modulus of red cell membrane. Biophys J 16:585–595
Fai TG, Griffith BE, Mori Y, Peskin CS (2013) Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers I: numerical method and results. SIAM J Sci Comput 35(5):B1132–B1161
Fai TG, Griffith BE, Mori Y, Peskin CS (2014) Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers II: theory. SIAM J Sci Comput 36(3):B589–B621
Fan J, Liao H, Ke R, Kucukal E, Gurkan UA, Shen X, Lu J, Li B (2018) A monolithic Lagrangian meshfree scheme for Fluid-Structure Interaction problems within the OTM framework. Comput Methods Appl Mech Eng 337:198–219
Fang J, Hsueh YY, Soto J, Sun W, Wang J, Gu Z, Khademhosseini A, Li S (2020) Engineering biomaterials with Micro/Nanotechnologies for cell reprogramming. ACS Nano 14:1296–1318
Fox MB, Esveld DC, Valero A, Luttge R, Mastwijk HC, Bartels PV, van den Berg A, Boom RM (2006) Electroporation of cells in microfluidic devices: a review. Anal Bioanal Chem 385:474–485
Friedl P, Wolf K, Lammerding J (2011) Nuclear mechanics during cell migration. Curr Opin Cell Biol 23:55–64
Freund JB (2013a) Numerical simulation of flowing blood cells. Annu Rev Fluid Mech 46:67–95
Freund JB (2013b) The flow of red blood cells through a narrow spleen-like slit. Phys Fluids 25:110807–11824
Gong XB, Gong ZX, Huang HX (2014) An immersed boundary method for mass transfer across permeable moving interfaces. J Comput Phys 278:148–168
Gonzalez FG, Tierra G (2018) Unconditionally energy stable numerical schemes for phase-field vesicle membrane model. J Comput Phys 354:67–85
Green AE, Adkins, JE (1970) Large elastic deformations. The Oxford University Press, London, 2nd edition
Griffith BE, Patankar NA (2020) Immersed methods for fluid-structure interaction. Annu Rev Fluid Mech 52:421–448
Gu J, Sakaue M, Takeuchi S, Kajishima T (2018) An immersed lubrication model for the fluid flow in a narrow gap region. Powder Technol 329:445–454
Heitz F, Morris MC, Divita G (2009) Twenty years of cell-penetrating peptides: from molecular mechanisms to therapeutics. Br J Pharmacol 157:195–206
Huang WX, Sung HJ (2009) An immersed boundary method for flow-flexible structure interaction. Comput Methods Appl Mech Eng 198:2650–2661
Hughes TJR, Franca LP, Balestra M (1982) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babu\(\check{s}\)ka-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Engrg 59:85–99
Isermann P, Lammerding J (2013) Nuclear mechanics and mechanotransduction in health and disease. Curr Biol 23:R1113–R1121
Kabacaoǧlu G, Quaife B, Biros G (2018) Low-resolution simulations of vesicle suspensions in 2D. J Comput Phys 357:42–77
Kang G, Carlson DW, Kang TH, Lee S, Haward SJ, Choi I, Shen AQ, Chung AJ (2020) Intracellular nanomaterial delivery via spiral hydroporation. ACS Nano 14:3048–3058
Karabacak NM, Spuhler PS, Fachin F, Lim EJ, Pai V, Ozkumur E, Martel JM, Kojic N, Smith K, Chen PI, Yang J (2014) Microfluidic, marker-free isolation of circulating tumor cells from blood samples. Nat Protoc 9:694–710
Kollmannsperger A, Sharei A, Raulf A, Heilemann M, Langer R, Jensen KF, Wieneke R, Tampé R (2016) Live-cell protein labeling with nanometre precision by cell squeezing. Nat Commun 7:10372–10378
Krüger T (2012) Computer simulation study of collective phenomena in dense suspensions of red blood cells under shear. Spring Sci Business Media 2012:1
Lambert B, Weynans L, Bergmann M (2018) Local lubrication model for spherical particles within incompressible Navier-Stokes flows. Phys Rev E 97:033313–033328
Lee J, Sharei A, Sim WY, Adamo A, Langer R, Jensen KF, Bawendi MG (2012) Non-endocytic delivery of functional engineered nanoparticles into the cytoplasm of live cells using a novel, high through-put microfluidic device. Nano Lett 12:6322–6327
Lee TR, Choi M, Kopacz AM, Yun SH, Liu WK, P. Decuzzi P (2013) On the near-wall accumulation of injectable particles in the microcirculation: smaller is not better. Sci Rep 3:2079–2086
Li H, Chang HY, Yang J, Lu L, Tang YH, Lykotrafitis G (2018) Modeling biomembranes and red blood cells by coarse-grained particle methods. Appl Math Mech 39(1):3–20
Li X, Chen W, Li Z, Li L, Gu H, Fu J (2014) Emerging microengineered tools for functional analysis and phenotyping of blood cells. Trends Biotechnol 32:586–594
Lincoln B, Erickson HM, Schinkinger S, Wottawah F, Mitchell D, Ulvick S, Bilby C, Guck J (2004) Deformability-based flow cytometry. Cytom Part A 59:203–209
Liu F, Wu D, Chen K (2013) Mechanical behavior of cells in microinjection: a minimum potential energy study. J Mech Behav Biomed 24:1–8
Liu L, Luo Q, Sun J, G. Song G (2016) Nucleus and nucleus-cytoskeleton connections in 3D cell migration. Exp Cell Res 348:56–65
Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle method. Int J Numer Meth Fluids 20:1081–1106
Liu WK, Liu Y, Farrell D, Zhang L, Wang XS, Fukui Y, Patankar N, Zhang Y, Bajaj C, Lee J, Hong J (2006a) Immersed finite element method and its applications to biological systems. Comput Methods Appl Mech Eng 195:1722–1749
Liu YL, Liu WK (2006) Rheology of red blood cell aggregation by computer simulation. J Comput Phys 220:139–154
Liu Z, Lee Y, hee Jang J, Li Y, Han X, Yokoi K, Ferrari M, Zhou L, Qin L (2015) Microfluidic cytometric analysis of cancer cell transportability and invasiveness. Sci Rep 5:14272–14283
Lu HJ, Peng ZL (2019) Boundary integral simulations of a red blood cell squeezing through a submicron slit under prescribed inlet and outlet pressures. Phys Fluids 31:031902
Luo ZY, Bai BF (2019) Solute release from an elastic capsule flowing through a microfluidic channel constriction. Phys Fluids 31:121902
Ma JT, Tian FB, Tang X (2014) IB-LBM study on cell sorting by pinched flow fraction. Bio-Med Mater Eng 24:2547–2554
Maas SA, Ellis BJ, Ateshian GA, Weiss JA (2012) FEBio: finite element for biomechanics. J Biomech Eng 134:01100501–01100510
McGregor AL, Hsia CR, Lammerding J (2016) Squish and squeeze-nucleus as a physical barrier during migration in confined environments. Curr Opin Cell Biol 40:32–40
Miller DL, Pislaru SV, Greenleaf JF (2002) Sonoporation: mechanical DNA delivery by ultrasonic cavitation. Somat Cell Mol Genet 27:115–134
Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev Fluid Mech 37:239–261
Moon JY, Tanner RI, Lee JS (2016) A numerical study on the elastic modulus of volume and area dilation for a deformable cell in a microchannel. Biomicrofluidics 10:044110–044124
Nikfar N, Razizadeh M, Paul R, Liu Y (2020) Multiscale modeling of hemolysis during microfiltration. Microfluid Nanofluid 24(5):1–33
Omori T, Ishikawa T, Barthès-Biesel D, Salsac AV, Walter J, Imai Y, Yamaguchi T (2011) Comparison between spring network models and continuum constitutive laws: application to the large deformation of a capsule in shear flow. Phys Rev E 83:041918–041928
Pak OS, Young YN, Marple GR, Veerapaneni S, Stone HA (2015) Gating of a mechanosensitive channel due to cellular flows. Proc Natl Acad Sci USA 112:9822–9827
Peng ZL, Pak OS, Feng Z, Liu AP, Young YN (2016) On the gating of mechanosensitive channels by fluid shear stress. Acta Mech Sin 32:1012–1022
Peskin CS (1997) Numerical analysis of blood flow in the heart. J Comput Phys 25:220–252
Peskin CS (2002) The immersed boundary method. Acta Numer 11:479–517
Phillips R, Kondev J, Theriot J (2012) Physical biology of the cell. Garland Sci 2012:5
Pivkin IV, Peng ZL, Karniadakis GE, Buffet PA, Dao M, Suresh S (2016) Biomechanics of red blood cells in human spleen and consequences for physiology and disease. Proc Natl Acad Sci USA 113:7804–7809
Purcell EM (1997) Life at low Renolds number. AM J Phys 45:3–11
Raab M, Gentili M, de Belly H, Thiam HR, Vargas P, Jimenez AJ, Lautenschlaeger F, Voituriez R, Lennon-Duménil AM, Manel N, Piel M (2016) ESCRT III repairs nuclear envelope ruptures during cell migration to limit DNA damage and cell death. Science 352:359–362
Rahmat A, Barigou M, Alexiadis A (2019) Deformation and rupture of compound cells under shear: a discrete multiphysics study. Phys Fluids 31:051903
Sabass B, Stone HA (2016) Role of the membrane for mechanosensing by tethered channels. Phys Rev Lett 116:258101–258106
Shah P, Wolf K, Lammerding J (2017) Bursting the bubble-nuclear envelope rupture as a path to genomic instability? Trends Cell Biol 27:546–555
Sharei A, Zoldan J, Adamo A, Sim WY, Cho N, Jackson E, Mao S, Schneider S, Han MJ, Lytton-Jean A, Basto PA (2013) A vector-free microfluidic platform for intracellular delivery. Proc Natl Acad Sci USA 110:2082–2087
Shin JW (2018) Squeezing cells through the epigenetic machinery. Proc Natl Acad Sci USA 115:8472–8474
Skalak R, Tozeren A, Zarda RP, Chien S (1973) Strain energy function of red blood cell membrane. Biophys J 13:245–264
Skau CT, Fischer RS, Gurel P, Thiam HR, Tubbs A, Baird MA, Davidson MW, Piel M, Alushin GM, Nussenzweig A, Steeg PS (2016) FMN2 makes perinuclear actin to protect nuclei during confined migration and promote metastasis. Cell 167:1571–1585
Stewart MP, Sharei A, Ding X, Sahay G, Langer R, Jensen KF (2016) In vitro and ex vivo strategies for intracellular delivery. Nature 538:183–192
Stroka KM, Jiang H, Chen SH, Tong Z, Wirtz D, Sun SX, Konstantopoulos K (2014) Water permeation driven tumor cell migration in confined microenvironment. Cell 157:611–623
Szeto GL, Van Egeren D, Worku H, Sharei A, Alejandro B, Park C, Frew K, Brefo M, Mao S, Heimann M, Langer R (2015) Microfluidic squeezing for intracellular antigen loading in polyclonal B-cells as cellular vaccines. Sci Rep 5:10276–10288
Takeuchi S, Fukuoka H, Gu J, Kajishima T (2018) Interaction problem between fluid and membrane by a consistent direct discretisation approach. J Comput Phys 371:1018–1042
Tan J, Sinno TR, Diamond SL (2018) A parallel fluid-solid coupling model Lammps and Palabos based on the immersed boundary method. Comput Sci 25:89–100
Tao S, Chen B, Yang X, Huang S (2018) Second-order accurate immersed boundary-discrete unified gas kinetic scheme for fluid-particle flows. Comput Fluids 165:54–63
Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44
Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8(2):83–130
Thiam HR, Vargas P, Carpi N, Crespo CL, Raab M, Terriac E, King MC, Jacobelli J, Alberts AS, Stradal T, Lennon-Dumenil AM (2015) Perinuclear Arp2/3-driven actin polymerization enables nuclear deformation to facilitate cell migration through complex environments. Nat Commun 7:10997–11010
Thorimbert Y, Marson F, Parmigiani A, Chopard B, Lätt J (2018) Lattice Boltzmann simulation of dense rigid spherical particle suspensions using immersed boundary method. Comput Fluids 166:286–294
Vargas P, Barbier L, Sáez PJ, Piel M (2017) Mechanisms for fast cell migration in complex environments. Curr Opin Cell Biol 48:72–78
Waehler R, Russell SJ, Curiel DT (2007) Engineering targeted viral vectors for gene therapy. Nat Rev Genet 8:573–587
Wang Q, Manmi K, Liu KK (2015) Cell mechanics in biomedical cavitation. Interface Focus 5:20150018–20150030
Wang X, Liu WK (2004) Extended immersed boundary method using FEM and RKPM. Comput Methods Appl Mech Eng 193:1305–1321
Wang Y, Dhong C, Frechette J (2015) Out-of-contact elastohydrodynamic deformation due to lubrication force. Phys Rev Lett 115:248302–248306
Wei Q, Xu YQ, Tian FB, Gao TX, Tang XY, Zu WH (2014) IB-LBM simulation on blood cell sorting with a micro-fence structure. Bio-Med Mater Eng 24:475–481
Wiggins P, Phillips R (2004) Analytic models for mechanotransduction: gating a mechanosensitive channel. Proc Natl Acad Sci USA 101:4071–4076
Wu CH, Fai TG, Atzberger PJ, Peskin CS (2015) Simulation of osmotic swelling by the stochastic immersed boundary method. SIAM J Sci Comput 37(4):B660–B688
Wu YC, Wu TH, Clemens DL, Lee BY, Wen X, Horwitz MA, Teitell MA, Chiou PY (2015) Massively parallel delivery of large cargo into mammalian cells with light pulses. Nat Methods 12:439–444
Yuan WM, Xue CD, Qin KR (2020) The intracellular calcium dynamics in a single vascular endothelial cell being squeezed through a narrow microfluidic channel. Biomech Model Mechanobiol. https://doi.org/10.1007/s10237-020-01368-7
Zhang L, Gerstenberger A, Wang X, Liu WK (2004) Immersed finite element method. Comput Methods Appl Mech Eng 193:2051–2067
Zhang LT, Gay M (2017) Immersed finite element method for fluid-structure interactions. J Fluid Struct 23:839–857
Zhang W, Kai K, Choi DS, Iwamoto T, Nguyen YH, Wong H, Handis MD, Ueno NT, Chang J, Qin L (2012) Microfluidics separation reveals the stem-cell-like deformability of tumor-initiating cells. Proc Natl Acad Sci USA 109:18707–18712
Zhang ZF, Xu J, Drapaca C (2018) Particle squeezing in narrow confinements. Microfluid Nanofluid 22(10):120
Zhao H, Isfahani AH, Olson LN, Freund JB (2010) A spectral boundary integral method for flowing blood cells. J Comput Phys 229:3726–3744
Zhou S, Giannetto M, DeCourcey J, Kang H, Kang N, Li Y, Zheng S, Zhao H, Simmons WR, Wei HS, Bodine DM (2019) Oxygen tension-mediated erythrocyte membrane interactions regulate cerebral capillary hyperemia. Sci Adv 5(5):eaaw4466
Acknowledgements
This research is supported by National Natural Science Foundation of China (Nos. 11772183 and 11832017).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
10404_2020_2415_MOESM1_ESM.pdf
Electronic supplementary material: The online version of this article contains supplementary material, which is available to authorized users.
Rights and permissions
About this article
Cite this article
Xie, J., Hu, GH. Computational modelling of membrane gating in capsule translocation through microchannel with variable section. Microfluid Nanofluid 25, 17 (2021). https://doi.org/10.1007/s10404-020-02415-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10404-020-02415-6