Computational fluid dynamics is used to investigate the effects of cell deformability and viscoelasticity on receptor-mediated leukocyte adhesion to endothelium or a ligand coated surface in a parallel-plate flow chamber. In the three-dimensional numerical code, a leukocyte is modeled as a compound viscoelastic drop (a nucleus covered by a thick layer of cytoplasm). The nucleus, cytoplasm, and extracellular fluid are considered as Newtonian or viscoelastic liquids of high viscosity. The receptor-ligand interaction is incorporated into the code by using the spring-peeling kinetic model under the assumption that leukocyte receptors are located on the tips of cylindrical microvilli distributed over the leukocyte membrane. The code is based on the volume-of-fluid method, and the Giesekus constitutive equation is implemented in the code to capture viscoelasticity of the cytoplasm and nucleus. Numerical simulations demonstrate the formation and breakup of membrane tethers observed in vitro and suggest that the elasticity of the cytoplasm is responsible for a teardrop shape of rolling leukocytes in vivo. When viewed from the top, as normally occurs during shear flow experiments in vitro, little or no deformation occurs, a side view shows significant deformation in the contact region. We show that the leukocyte membrane can be extended and disrupted under high shear if the receptor-ligand bonds live in a stressed state for a sufficiently long time. If the shear rate is low, the leukocyte rolls along the surface. The rolling velocity of the viscoelastic cell is smaller than that of the Newtonian cell. This is due to the increased deformability of the viscoelastic cell and, as a result, the decreased torque acting on this cell.
REFERENCES
1.
2.
B.
Alberts
, A.
Johnson
, J.
Lewis
, M.
Raff
, K.
Roberts
, and P.
Walter
, Molecular Biology of the Cell
, 4th ed. (Garland
, New York, 2002
).3.
E. C.
Butcher
, “Leukocyte-endothelial cell recognition: Three (or more) steps to specificity and diversity
,” Cell
67
, 1033
(1991
).4.
K.
Ley
, “Molecular mechanisms of leukocyte recruitment in the inflammatory process
,” Cardiovasc. Res.
32
, 733
(1996
).5.
J. J.
Campbell
, J.
Hedrick
, A.
Zlotnik
, M. A.
Siani
, D. A.
Thompson
, and E. C.
Butcher
, “Chemokines and the arrest of lymphocytes rolling under flow conditions
,” Science
279
, 381
(1998
).6.
J. E.
Blanks
, T.
Moll
, R.
Eytner
, and D.
Vestweber
, “Stimulation of P-selectin glycoprotein ligand-1 on mouse neutrophils activates -integrin mediated cell attachment to ICAM-1
,” Eur. J. Immunol.
28
, 433
(1998
).7.
P.
Tandon
and S. L.
Diamond
, “Hydrodynamic effects and receptor interactions of platelets and their aggregates in linear shear flow
,” Biophys. J.
73
, 2819
(1997
).8.
Y.
Zhao
, S.
Chien
, and S.
Weinbaum
, “Dynamic contact forces on leukocyte microvilli and their penetration of the endothelial glycocalyx
,” Biophys. J.
80
, 1124
(2001
).9.
D. A.
Hammer
and D. A.
Lauffenburger
, “A dynamical model for receptor-mediated cell adhesion to surfaces
,” Biophys. J.
52
, 475
(1987
).10.
D. A.
Hammer
and S. M.
Apte
, “Simulation of cell rolling and adhesion on surfaces in shear flow: General results and analysis of selectin-mediated neutrophil adhesion
,” Biophys. J.
63
, 35
(1992
).11.
N. A.
N’Dri
, W.
Shyy
, and R.
Tran-Son-Tay
, “Computational modeling of cell adhesion and movement using a continuum-kinetics approach
,” Biophys. J.
85
, 2273
(2003
).12.
C.
Dong
, J.
Cao
, E. J.
Struble
, and H. H.
Lipowsky
, “Mechanics of leukocyte deformation and adhesion to endothelium in shear flow
,” Ann. Biomed. Eng.
27
, 298
(1999
).13.
M. R.
King
and D. A.
Hammer
, “Multiparticle adhesive dynamics: Hydrodynamic recruitment of rolling leukocytes
,” Proc. Natl. Acad. Sci. U.S.A.
98
, 14919
(2001
).14.
G. I.
Bell
, “Models for the specific adhesion of cells to cells
,” Science
200
, 618
(1978
).15.
M.
Dembo
, D. C.
Torney
, K.
Saxman
, and D. A.
Hammer
, “The reaction-limited kinetics of membrane-to-surface adhesion and detachment
,” Proc. R. Soc. London, Ser. A
234
, 55
(1988
).16.
K.-C.
Chang
, D. F. J.
Tees
, and D. A.
Hammer
, “The state diagram for cell adhesion under flow: Leukocyte rolling and firm adhesion
,” Proc. Natl. Acad. Sci. U.S.A.
97
, 11262
(2000
).17.
J. C.
Firell
and H. H.
Lipowsky
, “Leukocyte margination and deformation in mesenteric venules of rat
,” Am. J. Physiol.
256
, H1667
(1989
).18.
E. R.
Damiano
, J.
Westheider
, A.
Tozeren
, and K.
Ley
, “Variation in the velocity, deformation, and adhesion energy density of leukocytes rolling within venules
,” Circ. Res.
79
, 1122
(1996
).19.
R. M.
Hochmuth
, H. P.
Ting-Beall
, B. B.
Beaty
, D.
Needham
, and R.
Tran-Son-Tay
, “Viscosity of passive human neutrophils undergoing small deformations
,” Biophys. J.
64
, 1596
(1993
).20.
R.
Tran-Son-Tay
, D.
Needham
, A.
Yeung
, and R. M.
Hochmuth
, “Time-dependent recovery of passive neutrophils after large deformation
,” Biophys. J.
60
, 856
(1991
).21.
M. B.
Lawrence
and T. A.
Springer
, “Leukocytes roll on a selectin at physiologic flow rates: Distinction from and prerequisite for adhesion through integrins
,” Cell
65
, 859
(1991
).22.
J.
Cao
, B.
Donell
, D. R.
Deaver
, M. B.
Lawrence
, and C.
Dong
, “In vitro side-view imaging technique and analysis of human T-leukemic cell adhesion to ICAM-1 in shear flow
,” Microvasc. Res.
55
, 124
(1998
).23.
R.
Alon
, S.
Chen
, R.
Fuhlbridge
, K. D.
Puri
, and T. A.
Springer
, “The kinetics and shear threshold of transient and rolling interactions of L-selectin with its ligand on leukocytes
,” Proc. Natl. Acad. Sci. U.S.A.
95
, 11631
(1998
).24.
S.
Chen
and T. A.
Springer
, “An automatic braking system that stabilizes leukocyte rolling by an increase in selectin bond number with shear
,” J. Cell Biol.
144
, 185
(1999
).25.
M. L.
Smith
, M. J.
Smith
, M. B.
Lawrence
, and K.
Ley
, “Viscosity-independent velocity of neutrophils rolling on P-selectin in vitro or in vivo
,” Microcirculation (Philadelphia)
9
, 523
(2002
).26.
K. D.
Rinker
, V.
Prabhakar
, and G. A.
Truskey
, “Effect of contact time and force on monocyte adhesion to vascular endothelium
,” Biophys. J.
80
, 1722
(2001
).27.
C.
Dong
and X. X.
Lei
, “Biomechanics of cell rolling: Shear flow, cell-surface adhesion, and cell deformability
,” J. Biomech.
33
, 35
(2000
).28.
J.-Y.
Shao
, H. P.
Ting-Beall
, and R. M.
Hochmuth
, “Static and dynamic lengths of neutrophil microvilli
,” Proc. Natl. Acad. Sci. U.S.A.
95
, 6797
(1998
).29.
U. H.
von Andrian
, S. R.
Hasslen
, S.
Erlandsen
, and E. C.
Butcher
, “A central role for microvillous receptor presentation in leukocyte adhesion under flow
,” Cell
82
, 989
(1995
).30.
D. V.
Zhelev
, D.
Needham
, and R. M.
Hochmuth
, “Role of the membrane cortex in neutrophil deformation in small pipets
,” Biophys. J.
67
, 696
(1994
).31.
J.-Y.
Shao
and R. M.
Hochmuth
, “Micropipette suction for measuring piconewton forces of adhesion and tether formation from neutrophil membranes
,” Biophys. J.
71
, 2892
(1996
).32.
F. M.
Pavalko
and S. M.
LaRoche
, “Activation of human neutrophils induces an interaction between the integrin -subunit (CD18) and the actin binding protein -actinin
,” J. Immunol.
151
, 3795
(1993
).33.
F. M.
Pavalko
, D. M.
Walker
, L.
Graham
, M.
Goheen
, C. M.
Doerschuk
, and G. S.
Kansas
, “The cytoplasmic domain of L-selectin interacts with cytoskeletal proteins via -actinin: Receptor positioning in microvilli does not require interaction with -actinin
,” J. Cell Biol.
129
, 1155
(1995
).34.
E. B.
Finger
, K. D.
Puri
, R.
Alon
, M. B.
Lawrence
, U. H.
von Andrian
, and T. A.
Springer
, “Adhesion through L-selectin requires a threshold hydrodynamic shear
,” Nature (London)
379
, 266
(1996
).35.
M. B.
Lawrence
, G. S.
Kansas
, E. J.
Kunkel
, and K.
Ley
, “Threshold levels of fluid shear promote leukocyte adhesion through selectins (CD62L,P,E)
,” J. Cell Biol.
136
, 717
(1997
).36.
K.
Konstantopoulos
, W. D.
Hanley
, and D.
Wirtz
, “Receptor-ligand binding: ‘Catch’ bonds finally caught
,” Curr. Biol.
13
, R611
(2003
).37.
B. T.
Marshall
, M.
Long
, J. W.
Piper
, T.
Yago
, R. P.
McEver
, and C.
Zhu
, “Direct observation of catch bonds involving cell-adhesion molecules
,” Nature (London)
423
, 190
(2003
).38.
D. C.
Anderson
, “The role of -integrins and intercellular adhesion molecule type 1 in inflammation
,” in Physiology and Pathophysiology of Leukocyte Adhesion
, edited by D. N.
Granger
and G. W.
Schmid-Schönbein
(Oxford University Press
, New York, 1994
), pp. 3
–42
.39.
M.
Forrest
and J. C.
Paulson
, “Selectin family of adhesion molecules
,” in Physiology and Pathophysiology of Leukocyte Adhesion
, Ref. 38, pp. 43
–80
.40.
J.-Y.
Shao
and R. M.
Hochmuth
, “Mechanical anchoring strength of L-selectin, integrins, and CD45 to neutrophil cytoskeleton and membrane
,” Biophys. J.
77
, 587
(1999
).41.
A.
Hafezi-Moghadam
and K.
Ley
, “Relevance of L-selectin shedding for leukocyte rolling in vivo
,” J. Exp. Med.
189
, 939
(1999
).42.
B. P.
Chan
, W. M.
Reichert
, and G. A.
Truskey
, “Effect of streptavidin-biotin on endothelial vasoregulation and leukocyte adhesion
,” Biomaterials
25
, 3951
(2004
).43.
Y.
Tseng
, T. P.
Kole
, S.-H. J.
Lee
, and D.
Wirtz
, “Local dynamics and viscoelastic properties of cell biological systems
,” Curr. Opin. Colloid Interface Sci.
7
, 210
(2002
).44.
B.
Fabry
, G. N.
Maksym
, J. P.
Butler
, M.
Glogauer
, D.
Navajas
, and J. J.
Fredberg
, “Scaling the microrheology of living cells
,” Phys. Rev. Lett.
87
, 148102
(2001
).45.
A. W. C.
Lau
, B. D.
Hoffman
, A.
Davies
, J. C.
Crocker
, and T. C.
Lubensky
, “Microrheology, stress fluctuations and active behavior of living cells
,” Phys. Rev. Lett.
91
, 198101
(2003
).46.
G. W.
Schmid-Schönbein
, “Rheology of leukocytes
,” in Handbook of Bioengineering
, edited by R.
Skalak
and S.
Chien
(McGraw-Hill
, New York, 1986
), pp. 13
–1
13
–25
.47.
C.
Dong
, R.
Skalak
, K.-L. P.
Sung
, G. W.
Schmid-Schönbein
, and S.
Chien
, “Passive deformation analysis of human leukocytes
,” J. Biomech. Eng.
110
, 27
(1988
).48.
M. A.
Tsai
, R. S.
Frank
, and R. E.
Waugh
, “Passive mechanical behavior of human neutrophils: Power-law fluid
,” Biophys. J.
65
, 2078
(1993
).49.
J. L.
Drury
and M.
Dembo
, “Aspiration of human neutrophils: Effect of shear thinning and cortical dissipation
,” Biophys. J.
81
, 3166
(2001
).50.
R. M.
Hochmuth
, “Micropipette aspiration of living cells
,” J. Biomech.
33
, 15
(2000
).51.
E.
Evans
and B.
Kukan
, “Passive material behavior of granulocytes based on large deformation and recovery after deformation tests
,” Blood
64
, 1028
(1984
).52.
R. E.
Waugh
and M. A.
Tsai
, “Shear rate-dependence of leukocyte cytoplasmic viscosity
,” in Cell Mechanics and Cellular Engineering
, edited by V. C.
Mow
, R.
Tran-Son-Tay
, F.
Guilak
, and R. N.
Hochmuth
(Springer
, New York, 1994
), pp. 33
–45
.53.
R. B.
Bird
, R. C.
Armstrong
, and O.
Hassager
, Dynamics of Polymeric Liquids, Vol. 1: Fluid Mechanics
(Wiley
, New York, 1987
).54.
H.
Giesekus
, “A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility
,” J. Non-Newtonian Fluid Mech.
11
, 69
(1982
).55.
H.
Giesekus
, “Stressing behavior in simple shear flow as predicted by a new constitutive model for polymer fluids
,” J. Non-Newtonian Fluid Mech.
12
, 367
(1983
).56.
H.
Giesekus
, “Constitutive equations for polymer fluids based on the concept of configuration-dependent molecular mobility: A generalized mean-configuration model
,” J. Non-Newtonian Fluid Mech.
17
, 349
(1985
).57.
D.
Gueyffier
, J.
Li
, A.
Nadim
, R.
Scardovelli
, and S.
Zaleski
, “Volume-of-fluid interface tracking and smoothed surface stress methods for three-dimensional flows
,” J. Comput. Phys.
152
, 423
(1999
).58.
R.
Scardovelli
and S.
Zaleski
, “Direct numerical simulation of free surface and interfacial flow
,” Annu. Rev. Fluid Mech.
31
, 567
(1999
).59.
C. W.
Hirt
and B. D.
Nichols
, “Volume of fluid (VOF) method for the dynamics of free boundaries
,” J. Comput. Phys.
39
, 201
(1981
).60.
J.
Li
, “Calcul d’interface affine par morceaux (piecewise linear interface calculation)
,” C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron.
320
, 391
(1995
).61.
J. U.
Brackbill
, D. B.
Kothe
, and C.
Zemach
, “A continuum method for modeling surface tension
,” J. Comput. Phys.
100
, 335
(1992
).62.
I.
Aleinov
and E. G.
Puckett
, “Computing surface tension with high-order kernels
,” in Proceedings of the Sixth International Symposium on Computational Fluid Dynamics
, edited by K.
Oshima
(Lake Tahoe
, NV, 1995
), pp. 13
–18
.63.
A. J.
Chorin
, “A numerical method for solving incompressible viscous flow problems
,” J. Comput. Phys.
2
, 12
(1967
).64.
P. J.
Roache
, Fundamentals of Computational Fluid Dynamics
(Hermosa
, Albuquerque, 1998
).65.
J.
Li
, Y.
Renardy
, and M.
Renardy
, “Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fuid method
,” Phys. Fluids
12
, 269
(2000
).66.
J.
Li
, Y.
Renardy
, and M.
Renardy
, “A numerical study of periodic disturbances on two-layer Couette flow
,” Phys. Fluids
10
, 3056
(1998
).67.
Y.
Zang
, R. L.
Street
, and J. R.
Koseff
, “A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates
,” J. Comput. Phys.
114
, 18
(1994
).68.
B.
Lafaurie
, C.
Nardone
, R.
Scardovelli
, S.
Zaleski
, and G.
Zanetti
, “Modeling merging and fragmentation in multiphase flows with SURFER
,” J. Comput. Phys.
113
, 134
(1994
).69.
M. J.
Crochet
, A. R.
Davies
, and K.
Walters
, Numerical Simulation of Non-Newtonian Flow
(Elsevier
, New York, 1984
).70.
J.
Fritz
, A. G.
Katopodis
, F.
Kolbinger
, and D.
Anselmetti
, “Force-mediated kinetics of single P-selectin/ligand complexes observed by atomic force microscopy
,” Proc. Natl. Acad. Sci. U.S.A.
95
, 12283
(1998
).71.
T. A.
Springer
, “Adhesion receptors of the immune system
,” Nature (London)
346
, 425
(1990
).72.
H. P.
Ting-Beall
, D.
Needham
, and R. M.
Hochmuth
, “Volume and osmotic properties of human neutrophils
,” Blood
81
, 2774
(1993
).73.
H. H.
Lipowsky
, “Mechanics of blood flow in the microcirculation
,” in Handbook of Bioengineering
, edited by R.
Skalak
and S.
Chien
(McGraw-Hill
, New York, 1986
), pp. 18
–1
18
–25
.74.
E. M.
Renkin
, “Microcirculation and exchange
,” in Textbook of Physiology
, edited by H. D.
Patton
, A. F.
Fuchs
, B.
Hille
, A. M.
Scher
, and R.
Steiner
(W. B. Saunders
, Philadelphia, 1989
), pp. 860
–886
.75.
S. E.
Chesla
, P.
Selvaraj
, and C.
Zhu
, “Measuring two-dimensional receptor-ligand binding kinetics by micropipette
,” Biophys. J.
75
, 1553
(1998
).76.
E. Y. H.
Park
, M. J.
Smith
, E. S.
Stropp
, K. R.
Snapp
, J. A.
DiVetro
, W. F.
Walker
, D. W.
Schmidtke
, S. L.
Diamond
, and M. B.
Lawrence
, “Comparison of PSGL-1 microbead and neutrophil rolling: Microvillus elongation stabilizes P-selectin bond clusters
,” Biophys. J.
82
, 1835
(2002
).77.
G.
Kaplanski
, C.
Farnarier
, O.
Tissot
, A.
Pierres
, A.
Benoliel
, M. C.
Alessi
, S.
Kaplanski
, and P.
Bongrand
, “Granulocyte-endothelium initial adhesion: Analysis of transient binding events mediated by E-selectin in a laminar shear flow
,” Biophys. J.
64
, 1922
(1993
).78.
F.
Geissmann
, S.
Jung
, and D. R.
Littman
, “Blood monocytes consist of two principal subsets with distinct migratory properties
,” Immunity
19
, 71
(2003
).79.
R.
Ross
, “Mechanisms of disease: Atherosclerosis—an inflammatory disease
,” N. Engl. J. Med.
340
, 115
(1999
).80.
A. J.
Lusis
, “Atherosclerosis
,” Nature (London)
407
, 233
(2000
).81.
T. W.
Secomb
, R.
Hsu
, and A. R.
Pries
, “Motion of red blood cells in a capillary with an endothelial surface layer: Effect of flow velocity
,” Am. J. Physiol.
281
, H629
(2001
).82.
A.
Nadim
and H. A.
Stone
, “The motion of small particles and droplets in quadratic flows
,” Stud. Appl. Math.
85
, 53
(1991
).83.
D. W.
Schmidtke
and S. L.
Diamond
, “Direct observation of membrane tethers formed during neutrophil attachment to platelets or P-selectin under physiological flow
,” J. Cell Biol.
149
, 719
(2000
).84.
R. M.
Hochmuth
and W. D.
Marcus
, “Membrane tethers formed from blood cells with available area and determination of their adhesion energy
,” Biophys. J.
82
, 2964
(2002
).85.
W. D.
Marcus
and R. M.
Hochmuth
, “Experimental studies of membrane tethers formed from human neutrophils
,” Ann. Biomed. Eng.
30
, 1273
(2002
).86.
M.
Sato
, N.
Ohshima
, and R. M.
Nerem
, “Viscoelastic properties of cultured porcine aortic endothelial cells exposed to shear stress
,” J. Biomech.
29
, 461
(1996
).87.
H.-C.
Kan
, W.
Shyy
, H. S.
Udaykumar
, P.
Vigneron
, and R.
Tran-Son-Tay
, “Effects of nucleus on leukocyte recovery
,” Ann. Biomed. Eng.
27
, 648
(1999
).88.
C.
Migliorini
, Y.-H.
Qian
, E. B.
Brown
, R. K.
Jain
, and L. L.
Munn
, “Red blood cells augment leukocyte rolling in a virtual blood vessel
,” Biophys. J.
83
, 1834
(2002
).89.
G. A.
Truskey
and T. L.
Proulx
, “Relationship between 3T3 cell spreading and the strength of adhesion on glass and silane surfaces
,” Biomaterials
14
, 243
(1993
).90.
A. S.
Goldstein
and P. A.
DiMilla
, “Examination of membrane rupture as a mechanism for mammalian cell detachment from fibronectin-coated biomaterials
,” J. Biomed. Mater. Res.
67
, 658
(2003
).91.
A. J.
Goldman
, R. G.
Cox
, and H.
Brenner
, “Slow viscous motion of a sphere parallel to a plane wall—II. Couette flow
,” Chem. Eng. Sci.
22
, 653
(1967
).92.
L. A.
Olivier
and G. A.
Truskey
, “A numerical analysis of forces exerted by laminar flow on spreading cells in a parallel plate flow chamber assay
,” Biotechnol. Bioeng.
42
, 963
(1993
).93.
A.
Tozeren
and K.
Ley
, “How two selectins mediate rolling in venules
,” Biophys. J.
63
, 700
(1992
).© 2005 American Institute of Physics.
2005
American Institute of Physics
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