Modeling of Cell Aggregation Dynamics Governed by Receptor–Ligand Binding Under Shear Flow

  • Changliang Fu
  • Chunfang Tong
  • Cheng Dong
  • Mian Long
Article

Abstract

Shear-induced cell aggregation and disaggregation, governed by specific receptor–ligand binding, play important roles in many biological and biophysical processes. While a lot of studies have focused on elucidating the shear rate and shear stress dependence of cell aggregation, the majority of existing models based on population balance equation (PBE) has rarely dealt with cell aggregation dynamics upon intrinsic molecular kinetics. Here, a kinetic model was developed for further understanding cell aggregation and disaggregation in a linear shear flow. The novelty of the model is that a set of simple equations was constructed by coupling two-body collision theory with receptor–ligand binding kinetics. Two cases of study were employed to validate the model: one is for the homotypic aggregation dynamics of latex beads cross-linked by protein G-IgG binding, and the other is for the heterotypic aggregation dynamics of neutrophils-tumor cells governed by β2-integrin–ligand interactions. It was found that the model fits the data well and the obtained kinetic parameters are consistent with the previous predictions and experimental measurements. Moreover, the decay factor defined biophysically to account for the chemokine- and shear-induced regulation of receptor and/or ligand expression and conformation was compared at molecular and cellular levels. Our results provided a universal framework to quantify the molecular kinetics of receptor–ligand binding in shear-induced cell aggregation dynamics.

Keywords

Two-dimensional kinetics Cone-plate viscometer Homotypic aggregation Heterotypic aggregation Bell model Protein G-IgG bond β2-Integrin and ICAM-1 bond 

List of Symbols

a

Bond interaction range (nm)

Ac

Contact area between two contact spheres (μm2)

Acmrmlkf, (Acmrmlkf)0

Effective forward rate, value at the moment immediately after PMN stimulation (s−1)

C; C1, C10; C2, C20

Concentration of sphere; value of sphere 1, initial value; value of sphere 2, initial value (m−3)

Cf, 〈Cf

Angle factor (=(sin2 θ1 sin 2ϕ1)max), mean value

CO

Orbit constant

E, E0

Adhesion efficiency, value at the moment immediately after PMN stimulation

fc, fc0

Two-body collision frequency per unit volume per sphere 2, initial value (s−1)

F; FN, FN,max; FS, FS,max

Applied force; normal force, maximum value; shear force, maximum value (pN)

G

Shear rate (s−1)

kB

Boltzmann constant (=1.38 × 10−23 N m K−1)

kf, kfL, kfH

Forward rate, values from low and high shear rate, respectively (μm2 s−1)

kr, kr(n), kr0

Reverse rate, value for dissociation of n-th bond, value at zero force (s−1)

M

Number of data points

n, 〈n

Number of bonds, mean value

N

Maximum number of bonds possibly to link the doublet

pn, pcn

Probability of having n bonds, probability of having n bonds at the end moment of two-body collision (n = 0, 1, 2…)

Pa, Pa30

Probability of adhesion, equilibrium aggregation percentage at 30 min for latex bead homotypic aggregation

Pb

Fraction of doublet break-up

r, r1, r2

Radius of sphere, value of sphere 1, value of sphere 2 (μm)

re

Equivalent axis ratio of doublet

t

Arbitrary time (s)

T

Period of doublet rotation (s)

TK

Absolute temperature (K)

u1, u2, u3

Fluid velocity, u1 = u2 = 0 and u3 = GX2 (μm s−1)

X1, X2, X3

Cartesian coordinates (μm)

yi, y(xi)

Measurement and prediction values at xi

αc, αm

Decay factors at cellular and molecular level, respectively (s−1)

αN, αS

Normal and shear force coefficients, respectively

ε

Two-body collision capture efficiency

η

Medium viscosity (cP, = mPa s = 10−3 N s m−2)

θ1, ϕ1

Polar and azimuthal angles of doublet major axis with respect to X1

θ2

Polar angle of doublet axis respect to X2

ϕ10

Contact angle of two colliding spheres

σi

Standard deviation

τ, \( \bar{\tau } \)

Two-body collision duration, mean value (s)

χ2

Chi-square statistic

Notes

Acknowledgments

This work was supported by National Natural Science Foundation of China grants 30730032, 11072251, 10902117, and 10702075, Chinese Academy of Sciences grants KJCX2-YW-L08 and Y2010030, and National Key Basic Research Foundation of China grant 2011CB710904.

References

  1. 1.
    Adler, P. M. Interaction of unequal spheres. 1. Hydrodynamic interaction—colloidal forces. J. Colloid Interf. Sci. 84(2):461–474, 1981.CrossRefGoogle Scholar
  2. 2.
    Bartok, W., and S. G. Mason. Particle motions in sheared suspensions V. Rigid rods and collision doublets of spheres. J. Colloid Interf. Sci. 12(3):243–262, 1957.Google Scholar
  3. 3.
    Bell, G. I. Models for specific adhesion of cells to cells. Science 200(4342):618–627, 1978.CrossRefGoogle Scholar
  4. 4.
    Capo, C., F. Garrouste, A. M. Benoliel, P. Bongrand, A. Ryter, and G. I. Bell. Concanavalin-A-mediated thymocyte agglutination—a model for a quantitative study of cell-adhesion. J. Cell Sci. 56(1):21–48, 1982.Google Scholar
  5. 5.
    Chesla, S. E., P. Selvaraj, and C. Zhu. Measuring two-dimensional receptor–ligand binding kinetics by micropipette. Biophys. J. 75(3):1553–1572, 1998.CrossRefGoogle Scholar
  6. 6.
    Coussens, L. M., and Z. Werb. Inflammation and cancer. Nature 420(6917):860–867, 2002.CrossRefGoogle Scholar
  7. 7.
    Cozens-Roberts, C., D. A. Lauffenburger, and J. A. Quinn. Receptor-mediated cell attachment and detachment kinetics. 1. Probabilistic model and analysis. Biophys. J. 58(4):841–856, 1990.CrossRefGoogle Scholar
  8. 8.
    Gachet, C. Regulation of platelet functions by P2 receptors. Annu. Rev. Pharmacol. Toxicol. 46:277–300, 2006.CrossRefGoogle Scholar
  9. 9.
    Goldsmith, H. L., T. A. Quinn, G. Drury, C. Spanos, F. A. McIntosh, and S. I. Simon. Dynamics of neutrophil aggregation in Couette flow revealed by videomicroscopy: effect of shear rate on two-body collision efficiency and doublet lifetime. Biophys. J. 81(4):2020–2034, 2001.CrossRefGoogle Scholar
  10. 10.
    Hentzen, E. R., S. Neelamegham, G. S. Kansas, J. A. Benanti, L. V. McIntire, C. W. Smith, and S. I. Simon. Sequential binding of CD11a/CD18 and CD11b/CD18 defines neutrophil capture and stable adhesion to Intercellular adhesion molecule-1. Blood 95(3):911–920, 2000.Google Scholar
  11. 11.
    Hoskins, M. H., and C. Dong. Kinetics analysis of binding between melanoma cells and neutrophils. Mol. Cell. Biomech. 3(2):79–87, 2006.MathSciNetGoogle Scholar
  12. 12.
    Huang, P. Y., and J. D. Hellums. Aggregation and disaggregation kinetics of human blood-platelets. 1. Development and validation of a population balance method. Biophys. J. 65(1):334–343, 1993.CrossRefGoogle Scholar
  13. 13.
    Huang, P. Y., and J. D. Hellums. Aggregation and disaggregation kinetics of human blood-platelets. 2. Shear-induced platelet-aggregation. Biophys. J. 65(1):344–353, 1993.CrossRefGoogle Scholar
  14. 14.
    Huang, P. Y., and J. D. Hellums. Aggregation and disaggregation kinetics of human blood-platelets. 3. The disaggregation under shear-stress of platelet aggregates. Biophys. J. 65(1):354–361, 1993.CrossRefGoogle Scholar
  15. 15.
    Huh, S. J., S. Liang, A. Sharma, C. Dong, and G. P. Robertson. Transiently entrapped circulating tumor cells interact with neutrophils to facilitate lung metastasis development. Cancer Res. 70(14):6071–6082, 2010.CrossRefGoogle Scholar
  16. 16.
    Im, J. H., W. L. Fu, H. Wang, S. K. Bhatia, D. A. Hammer, M. A. Kowalska, and R. J. Muschel. Coagulation facilitates tumor cell spreading in the pulmonary vasculature during early metastatic colony formation. Cancer Res. 64(23):8613–8619, 2004.CrossRefGoogle Scholar
  17. 17.
    Jadhav, S., B. S. Bochner, and K. Konstantopoulos. Hydrodynamic shear regulates the kinetics and receptor specificity of polymorphonuclear leukocyte-colon carcinoma cell adhesive interactions. J. Immunol. 167(10):5986–5993, 2001.Google Scholar
  18. 18.
    Jadhav, S., and K. Konstantopoulos. Fluid shear- and time-dependent modulation of molecular interactions between PMNs and colon carcinomas. Am. J. Physiol. Cell Physiol. 283(4):C1133–C1143, 2002.Google Scholar
  19. 19.
    Konstantopoulos, K., S. Kukreti, and L. V. McIntire. Biomechanics of cell interactions in shear fields. Adv. Drug Deliv. Rev. 33(1–2):141–164, 1998.CrossRefGoogle Scholar
  20. 20.
    Kroll, M. H., J. D. Hellums, L. V. McIntire, A. I. Schafer, and J. L. Moake. Platelets and shear stress. Blood 88(5):1525–1541, 1996.Google Scholar
  21. 21.
    Kwong, D., D. F. J. Tees, and H. L. Goldsmith. Kinetics and locus of failure of receptor–ligand-mediated adhesion between latex spheres. 2. Protein–protein bond. Biophys. J. 71(2):1115–1122, 1996.CrossRefGoogle Scholar
  22. 22.
    Laurenzi, I. J., and S. L. Diamond. Monte Carlo simulation of the heterotypic aggregation kinetics of platelets and neutrophils. Biophys. J. 77(3):1733–1746, 1999.CrossRefGoogle Scholar
  23. 23.
    Liang, S., M. J. Slattery, and C. Dong. Shear stress and shear rate differentially affect the multi-step process of leukocyte-facilitated melanoma adhesion. Exp. Cell Res. 310(2):282–292, 2005.CrossRefGoogle Scholar
  24. 24.
    Liang, S. L., C. L. Fu, D. Wagner, H. G. Guo, D. Y. Zhan, C. Dong, and M. Long. Two-dimensional kinetics of beta(2)-integrin and ICAM-1 bindings between neutrophils and melanoma cells in a shear flow. Am. J. Physiol. Cell Physiol. 294:C743–C753, 2008.CrossRefGoogle Scholar
  25. 25.
    Liang, S. L., A. Sharma, H. H. Peng, G. Robertson, and C. Dong. Targeting mutant (V600E) B-Raf in melanoma interrupts immunoediting of leukocyte functions and melanoma extravasation. Cancer Res. 67(12):5814–5820, 2007.CrossRefGoogle Scholar
  26. 26.
    Lomakina, E. B., and R. E. Waugh. Micromechanical tests of adhesion dynamics between neutrophils and immobilized ICAM-1. Biophys. J. 86(2):1223–1233, 2004.CrossRefGoogle Scholar
  27. 27.
    Long, M., H. L. Goldsmith, D. F. J. Tees, and C. Zhu. Probabilistic modeling of shear-induced formation and breakage of doublets cross-linked by receptor–ligand bonds. Biophys. J. 76(2):1112–1128, 1999.CrossRefGoogle Scholar
  28. 28.
    McCarty, O. J. T., S. Jadhav, M. M. Burdick, W. R. Bell, and K. Konstantopoulos. Fluid shear regulates the kinetics and molecular mechanisms of activation-dependent platelet binding to colon carcinoma cells. Biophys. J. 83(2):836–848, 2002.CrossRefGoogle Scholar
  29. 29.
    McQuarrie, D. A. Kinetics of small systems. I. J. Chem. Phys. 38(2):433–436, 1963.CrossRefGoogle Scholar
  30. 30.
    Merkel, R. Force spectroscopy on single passive biomolecules and single biomolecular bonds. Phys. Rep. 346(5):344–385, 2001.CrossRefGoogle Scholar
  31. 31.
    Neelamegham, S., A. D. Taylor, A. R. Burns, C. W. Smith, and S. I. Simon. Hydrodynamic shear shows distinct roles for LFA-1 and Mac-1 in neutrophil adhesion to intercellular adhesion molecule-1. Blood 92(2):1626–1638, 1998.Google Scholar
  32. 32.
    Neelamegham, S., A. D. Taylor, J. D. Hellums, M. Dembo, C. W. Smith, and S. I. Simon. Modeling the reversible kinetics of neutrophil aggregation under hydrodynamic shear. Biophys. J. 72(4):1527–1540, 1997.CrossRefGoogle Scholar
  33. 33.
    Neelamegham, S., A. D. Taylor, H. Shankaran, C. W. Smith, and S. I. Simon. Shear and time-dependent changes in Mac-1, LFA-1, and ICAM-3 binding regulate neutrophil homotypic adhesion. J. Immunol. 164(7):3798–3805, 2000.Google Scholar
  34. 34.
    Neumann, F. J., N. Marx, M. Gawaz, K. Brand, I. Ott, C. Rokitta, C. Sticherling, C. Meinl, A. May, and A. Schomig. Induction of cytokine expression in leukocytes by binding of thrombin-stimulated platelets. Circulation 95(10):2387–2394, 1997.Google Scholar
  35. 35.
    Ott, I., F. J. Neumann, M. Gawaz, M. Schmitt, and A. Schomig. Increased neutrophil–platelet adhesion in patients with unstable angina. Circulation 94(6):1239–1246, 1996.Google Scholar
  36. 36.
    Palabrica, T., R. Lobb, B. C. Furie, M. Aronovitz, C. Benjamin, Y. M. Hsu, S. A. Sajer, and B. Furie. Leukocyte accumulation promoting fibrin deposition is mediated invivo by P-selectin on adherent platelets. Nature 359(6398):848–851, 1992.CrossRefGoogle Scholar
  37. 37.
    Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in Fortran 77: The Art of Scientific Computing (2nd ed.). Cambridge: Cambridge University Press, pp. 675–683, 1992.Google Scholar
  38. 38.
    Sahai, E. Illuminating the metastatic process. Nat. Rev. Cancer 7(10):737–749, 2007.CrossRefGoogle Scholar
  39. 39.
    Shankaran, H., and S. Neelamegham. Hydrodynamic forces applied on intercellular bonds, soluble molecules, and cell-surface receptors. Biophys. J. 86(1):576–588, 2004.CrossRefGoogle Scholar
  40. 40.
    Simon, S. I., J. D. Chambers, and L. A. Sklar. Flow cytometric analysis and modeling of cell–cell adhesive interactions—the neutrophil as a model. J. Cell Biol. 111(6):2747–2756, 1990.CrossRefGoogle Scholar
  41. 41.
    Simon, S. I., and C. E. Green. Molecular mechanics and dynamics of leukocyte recruitment during inflammation. Annu. Rev. Biomed. Eng. 7:151–185, 2005.CrossRefGoogle Scholar
  42. 42.
    Simson, D. A., M. Strigl, M. Hohenadl, and R. Merkel. Statistical breakage of single protein A-IgG bonds reveals crossover from spontaneous to force-induced bond dissociation. Phys. Rev. Lett. 83(3):652–655, 1999.CrossRefGoogle Scholar
  43. 43.
    Slattery, M. J., S. Liang, and C. Dong. Distinct role of hydrodynamic shear in leukocyte-facilitated tumor cell extravasation. Am. J. Physiol. Cell Physiol. 288(4):C831–C839, 2005.CrossRefGoogle Scholar
  44. 44.
    Smoluchowski, M. V. Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Losungen. Z. Phys. Chem. 92:129–168, 1917.Google Scholar
  45. 45.
    Tandon, P., and S. L. Diamond. Hydrodynamic effects and receptor interactions of platelets and their aggregates in linear shear flow. Biophys. J. 73(5):2819–2835, 1997.CrossRefGoogle Scholar
  46. 46.
    Tandon, P., and S. L. Diamond. Kinetics of beta(2)-integrin and L-selectin bonding during neutrophil aggregation in shear flow. Biophys. J. 75(6):3163–3178, 1998.CrossRefGoogle Scholar
  47. 47.
    Taylor, A. D., S. Neelamegham, J. D. Hellums, C. W. Smith, and S. I. Simon. Molecular dynamics of the transition from L-selectin- to beta(2)-integrin-dependent neutrophil adhesion under defined hydrodynamic shear. Biophys. J. 71(6):3488–3500, 1996.CrossRefGoogle Scholar
  48. 48.
    Tees, D. F. J., O. Coenen, and H. L. Goldsmith. Interaction forces between red-cells agglutinated by antibody. 4. Time and force dependence of break-up. Biophys. J. 65(3):1318–1334, 1993.CrossRefGoogle Scholar
  49. 49.
    Tees, D. F. J., and H. L. Goldsmith. Kinetics and locus of failure of receptor–ligand-mediated adhesion between latex spheres. 1. Protein–carbohydrate bond. Biophys. J. 71(2):1102–1114, 1996.CrossRefGoogle Scholar
  50. 50.
    van de Ven, T. G. M., and S. G. Mason. Microrheology of colloidal dispersions. 4. Pairs of interacting spheres in shear-flow. J. Colloid Interf. Sci. 57(3):505–516, 1976.CrossRefGoogle Scholar
  51. 51.
    Zhang, P., T. Ozdemir, C. Y. Chung, G. P. Robertson, and C. Dong. Sequential binding of alphaVbeta3 and ICAM-1 determines fibrin-mediated melanoma capture and stable adhesion to CD11b/CD18 on neutrophils. J. Immunol. 186(1):242–254, 2011.CrossRefGoogle Scholar
  52. 52.
    Zhu, C. Kinetics and mechanics of cell adhesion. J. Biomech. 33(1):23–33, 2000.CrossRefGoogle Scholar
  53. 53.
    Zhu, C., M. Long, S. E. Chesla, and P. Bongrand. Measuring receptor/ligand interaction at the single-bond level: Experimental and interpretative issues. Ann. Biomed. Eng. 30(3):305–314, 2002.CrossRefGoogle Scholar
  54. 54.
    Zwartz, G., A. Chigaev, T. Foutz, R. S. Larson, R. Posner, and L. A. Sklar. Relationship between molecular and cellular dissociation rates for VLA-4/VCAM-1 interaction in the absence of shear stress. Biophys. J. 86(2):1243–1252, 2004.CrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2011

Authors and Affiliations

  • Changliang Fu
    • 1
    • 2
    • 3
  • Chunfang Tong
    • 1
    • 2
    • 3
  • Cheng Dong
    • 4
  • Mian Long
    • 1
    • 2
    • 3
  1. 1.Key Laboratory of MicrogravityInstitute of Mechanics, Chinese Academy of SciencesBeijingPeople’s Republic of China
  2. 2.National Microgravity LaboratoryInstitute of Mechanics, Chinese Academy of SciencesBeijingPeople’s Republic of China
  3. 3.Center of Biomechanics and BioengineeringInstitute of Mechanics, Chinese Academy of SciencesBeijingPeople’s Republic of China
  4. 4.Department of BioengineeringThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations