Abstract
Inertial migration of particles to a characteristic lateral equilibrium position in laminar micro-flows has been investigated under various aspects during the last decades. The majority of the studies deal with the equilibrium position of rigid particles and viscous droplets. Here, we compare the equilibrium velocity of viscoelastic cells and rigid polystyrene spheres in flow by applying the method of spatially modulated emission. The technique allows the precise determination of the equilibrium velocity of an object in flow, which has been found to depend on object characteristics like size in earlier studies. Here, we first show that the deformable cells move at higher equilibrium velocity than rigid polystyrene particles, thus revealing that a particle’s equilibrium velocity is related to its deformability—in addition to size. In a second set of experiments, we treat cells with the cytostatic agent colchicine, which results in a systematic decrease of the equilibrium velocity that is attributed to cell stiffening. This study thus provides evidence that the parameter cell deformability can be extracted from the equilibrium velocity based on spatially modulated emission, which opens up an alternative way for high-throughput cell-deformability characterization.
Similar content being viewed by others
References
Amini H, Lee W, Di Carlo D (2014) Inertial microfluidic physics. Lab Chip 2014(14):2739. https://doi.org/10.1039/c4lc00128a
Asmolov ES (1999) The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J Fluid Mech 381:63–87. https://doi.org/10.1017/S0022112098003474
Bai BF, Luo ZY, Wang SQ, He L, Lu TJ, Xu F (2013) Inertia effect on deformation of viscoelastic capsules in microscale flows. Microfluid Nanofluid 14:817–829. https://doi.org/10.1007/s10404-012-1082-8
Boukamp P, Tilgen W, Dzarlieva RT, Breitkreutz D, Haag D, Riehl RK, Bohnert A, Fusenig NE (1982) Phenotypic and genotypic characteristics of a cell line from a squamous cell carcinoma of human skin. J Natl Cancer Inst 68(3):415–427
Casalou C, Cyrne L, Rosa MR, Soares H (2001) Microtubule cytoskeleton perturbation induced by taxol and colchicine affects chaperonin containing TCP-1 (CCT) subunit gene expression inTetrahymena cells. Biochem Biophys Acta 1522:9–21
Di Carlo D (2009) Inertial microfluidics. Lab Chip 9:3038–3046. https://doi.org/10.1039/b912547g
Di Carlo D, Edd JF, Humphry KJ, Stone HA, Toner M (2009) Particle segregation and dynamics in confined flows. Phys Rev Lett 102(9):094503. https://doi.org/10.1103/physrevlett.102.094503
Feng J, Hu HH, Joseph DD (1994) Direct simulation of initial value problems for the motion of solid bodies in a newtonian fluid. Part 2. Couette and Poiseuille flows. J Fluid Mech 277:271–301. https://doi.org/10.1017/S0022112094002764
Gossett DR, Tse HTK, Dudani JS, Goda K, Woods TA, Graves SW, Di Carlo D (2012) Inertial manipulation and transfer of microparticles across laminar fluid streams. Small 8(17):2757–2764. https://doi.org/10.1002/smll.201200588
Ho BP, Leal LG (1974) Inertial migration of rigid spheres in two-dimensional unidirectional flows. J Fluid Mech 65:365–400. https://doi.org/10.1017/s0022112074001431
Hur SC, Henderson-MacLennan NK, McCabe ERB, Di Carlo D (2011) Deformability-based cell classification and enrichment using inertial microfluidics. Lab Chip 11:912. https://doi.org/10.1039/c0lc00595a
Jung H, Shin I, Park YM, Kang KW, Ha KS (1997) Colchicine activates actin polymerization by microtubule depolymerization. Mol Cells 7(3):431–437
Kiesel P, Baßler M, Beck M, Johnson N (2009) Spatially modulated fluorescence emission from moving particles. Appl Phys Lett 94(4):41107. https://doi.org/10.1063/1.3070536
Lee GB, Chang CC, Huang SB, Yang RJ (2006) The hydrodynamic focusing effect inside rectangular microchannels. J Micromech Microeng 16:1024–1032. https://doi.org/10.1088/0960-1317/16/5/020
Liu L, Zhang W, Li L, Zhu X, Liu J, Wang X, Song Z, Xu H, Wang Z (2018) Biomechanical measurement and analysis of colchicine-induced effects on cells by nanoindentation using an atomic force microscope. J Biomech 67:84–90. https://doi.org/10.1016/j.jbiomech.2017.11.018
Panda D, Daijo JE, Jordan MA, Wilson L (1995) Kinetic stabilization of microtubule dynamics at steady state in vitro by substoichiometric concentrations of tubulin—colchicine complex. Biochemistry 34:9921–9929
Prohm C, Stark H (2014) Feedback control of inertial microfluidics using axial control forces. Lab Chip 14:2115. https://doi.org/10.1039/c4lc00145a
Quint S, Wittek J, Spang P, Levanon N, Walther T, Baßler M (2017) Improved signal recovery for flow cytometry based on ‘spatially modulated emission’. Methods Appl Fluoresc 5:035002. https://doi.org/10.1088/2050-6120/aa7916
Ravelli RBG, Gigant B, Curmi PA, Jourdain I, Lachkar S, Sobel A, Knossow M (2004) Insight into tubulin regulation from a complex with colchicine and a stathmin-like domain. Nature 428:198–202. https://doi.org/10.1038/nature02393
Reece AE, Kaastrup K, Sikes HD, Oakey J (2015) Staged inertial microfluidic focusing for complex fluid enrichment. RSC Adv 5:53857–53864. https://doi.org/10.1039/c5ra10634f
Rotsch C, Radmacher M (2000) Drug-induced changes of cytoskeletal structure and mechanics in fibroblasts: an atomic force microscopy study. Biophys J 78(1):520–535. https://doi.org/10.1016/s0006-3495(00)76614-8
Schaaf C, Stark H (2017) Inertial migration and axial control of deformable capsules. Soft Matter 13:3544. https://doi.org/10.1039/c7sm00339k
Schonberg JA, Hinch EJ (1989) Inertial migration of a sphere in Poiseuille flow. J Fluid Mech 203:517–524. https://doi.org/10.1017/s0022112089001564
Segré G, Silberberg A (1961) Radial particle displacements in Poiseuille flow of suspensions. Nature 189(4760):209–210. https://doi.org/10.1038/189209a0
Segré G, Silberberg A (1962a) Behaviourof macroscopic rigid spheres in Poiseuille flow. Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. J Fluid Mech 14(1):115. https://doi.org/10.1017/s002211206200110x
Segré G, Silberberg A (1962b) Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J Fluid Mech 14(1):136. https://doi.org/10.1017/s0022112062001111
Shin SJ, Sung HJ (2011) Inertial migration of an elastic capsule in a Poiseuille flow. Phys Rev E 83:046321. https://doi.org/10.1103/PhysRevE.83.046321
Skoufias DA, Wilson L (1992) Mechanism of inhibition of microtubule polymerization by colchicine: inhibitory potencies of unliganded colchicine and tubulin-colchicine complexes. Biochemistry 31:738–746
Sommer C, Quint S, Spang P, Walther T, Baßler M (2014) The equilibrium velocity of spherical particles in rectangular microfluidic channels for size measurement. Lab Chip 14:2319. https://doi.org/10.1039/c3lc51336j
Tachibana M (1973) On the behaviour of a sphere in the laminar tube flows. Rheol Acta 12:58–69. https://doi.org/10.1007/BF01526901
Yang BH, Wang J, Joseph DD, Hu HH, Pan TW (2005) Migration of a sphere in tube flow. J Fluid Mech 540:109–131. https://doi.org/10.1017/s0022112005005677
Acknowledgements
The authors thank Peter Spang for the manufacturing of the microfluidic device, Christine Paulus for support in the lab and Mareike Bürger, Tobias Schunck and Christian Freese for helpful discussion.
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.
Rights and permissions
About this article
Cite this article
Heinß, N., Alebrand, S., Wittek, J. et al. Equilibrium transport velocity of deformable cells and rigid spheres in micro-channels under laminar flow conditions. Microfluid Nanofluid 24, 3 (2020). https://doi.org/10.1007/s10404-019-2305-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10404-019-2305-z