Skip to main content
SpringerLink
Log in
Book cover

Molecular and Cellular Biology of Phagocytosis pp 55–70Cite as

Receptor Models of Phagocytosis: The Effect of Target Shape

  • Chapter
  • First Online:

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 1246))

Abstract

Phagocytosis is a remarkably complex process, requiring simultaneous organisation of the cell membrane, the cytoskeleton, receptors and various signalling molecules. As can often be the case, mathematical modelling is able to penetrate some of this complexity, identifying the key biophysical components and generating understanding that would take far longer with a purely experimental approach. This chapter will review a particularly important class of phagocytosis model, championed in recent years, that primarily focuses on the role of receptors during the engulfment process. These models are pertinent to a host of unsolved questions in the subject, including the rate of cup growth during uptake, the role of both intra- and extracellular noise, and the precise differences between phagocytosis and other forms of endocytosis. In particular, this chapter will focus on the effect of target shape and orientation, including how these influence the rate and final outcome of phagocytic engulfment.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Allen LA, Aderem A (1996) Molecular definition of distinct cytoskeletal structures involved in complement- and Fc receptor-mediated phagocytosis in macrophages. J Exp Med 184:627–637

    Article  CAS  PubMed  Google Scholar 

  • An G, Fitzpatrick BG, Christley S, Federico P, Kanarek A, Neilan RM, Oremland M, Salinas R, Laubenbacher R, Lenhart S (2017) Optimization and control of agent-based models in biology: a perspective. Bull Math Biol 79(1):63–87

    Article  CAS  PubMed  Google Scholar 

  • Axline SG, Reaven EP (1974) Inhibition of phagocytosis and plasma membrane mobility of the cultivated macrophage by cytochalasin B. Role of subplasmalemmal microfilaments. J Cell Biol 62:647–659

    Article  CAS  PubMed  Google Scholar 

  • Bahrami AH, Raatz M, Agudo-Canalejo J, Michel R, Curtis EM, Hall CK, Gradzielski M, Lipowsky R, Weikl TR (2014) Wrapping of nanoparticles by membranes. Adv Colloid Interface Sci 208:214–224

    Article  CAS  PubMed  Google Scholar 

  • Bahrami AH, Lipowsky R, Weikl TR (2016) The role of membrane curvature for the wrapping of nanoparticles. Soft Matter 12(2):581–7

    Article  CAS  PubMed  Google Scholar 

  • Beningo KA, Wang Y-L (2002) Fc-receptor-mediated phagocytosis is regulated by mechanical properties of the target. J Cell Sci 115:849–856

    CAS  PubMed  Google Scholar 

  • Berg HC (1993) Random walks in biology. Princeton University Press, Princeton. ISBN: 978-0-69100-064-0

    Google Scholar 

  • Cannon GJ, Swanson JA (1992) The macrophage capacity for phagocytosis. J Cell Sci 101(Pt 4):907–913

    PubMed  Google Scholar 

  • Carrera J, Covert MW (2015) Why build whole-cell models? Trends Cell Biol 25(12):719–722

    Article  PubMed  PubMed Central  Google Scholar 

  • Champion JA, Mitragotri S (2006) Role of target geometry in phagocytosis. Proc Natl Acad Sci USA 103(13):4930–4934

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Champion JA, Mitragotri S (2009) Shape induced inhibition of phagocytosis of polymer particles. Pharm Res 26(1):244–249

    Article  CAS  PubMed  Google Scholar 

  • Champion JA, Walker A, Mitragotri S (2008) Role of particle size in phagocytosis of polymeric microspheres. Pharm Res 25(8):1815–1821

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Clarke M, Engel U, Giorgione J, Müller-Taubenberger A, Prassler J, Veltman D, Gerisch G (2010) Curvature recognition and force generation in phagocytosis. BMC Biol 8:154

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Codling EA, Plank MJ, Benhamou S (2008) Random walk models in biology. J R Soc Interface 5(25):813–834

    Article  PubMed  PubMed Central  Google Scholar 

  • Deuling H, Helfrich W (1976) The curvature elasticity of fluid membranes: a catalogue of vesicle shapes. Journal de Physique 37(11):1335–1345

    Article  CAS  Google Scholar 

  • Dieckmann R, von Heyden Y, Kistler C, Gopaldass N, Hausherr S, Crawley SW, Schwarz EC, Diensthuber RP, Côté GP, Tsiavaliaris G, Soldati T (2010) A myosin IK-Abp1-PakB circuit acts as a switch to regulate phagocytosis efficiency. Mol Biol Cell 21:1505–18

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Dorn M, E Silva MB, Buriol LS, Lamb LC (2014) Three-dimensional protein structure prediction: Methods and computational strategies. Comput Biol Chem 53:251–276

    Google Scholar 

  • Feig M, Sugita Y (2019) Whole-cell models and simulations in molecular detail. Annu Rev Cell Dev Biol 35:191–211

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Flannagan RS, Jaumouillé V, Grinstein S (2012) The cell biology of phagocytosis. Annu Rev Pathol Mech Dis 7:61–98

    Article  CAS  Google Scholar 

  • Freund LB, Lin Y (2004) The role of binder mobility in spontaneous adhesive contact and implications for cell adhesion. J Mech Phys Solids 52:2455–2472

    Article  Google Scholar 

  • Gao H, Shi W, Freund L (2005) Mechanics of receptor-mediated endocytosis. Proc Natl Acad Sci USA 102(27):9469–9474

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • García-García E, Rosales C (2005) Adding complexity to phagocytic signaling: phagocytosis-associated cell responses and phagocytic efficiency. In: Molecular mechanisms of phagocytosis. Springer, pp 58–71, ISBN 978-0-387-25419-7

    Google Scholar 

  • Geng Y, Dalhaimer P, Cai S, Tsai R, Tewari M, Minko T, Discher DE (2007) Shape effects of filaments versus spherical particles in flow and drug delivery. Nat Nanotechnol 2(4):249–255

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Goldberg AP, Szigeti B, Chew YH, Sekar JA, Roth YD, Karr JR (2018) Emerging whole-cell modeling principles and methods. Curr Opin Biotechnol 51:97–102

    Article  CAS  PubMed  Google Scholar 

  • Goosney DL, de Grado M, Finlay BB (1999) Putting E. coli on a pedestal: a unique system to study signal transduction and the actin cytoskeleton. Trends Cell Biol 9(1):11–14

    Article  CAS  PubMed  Google Scholar 

  • Greenberg S (2001) Diversity in phagocytic signalling. J Cell Sci 114:1039–1040

    CAS  PubMed  Google Scholar 

  • Gupta SC (2003) The classical Stefan problem: basic concepts, modelling and analysis. North-Holland series in Applied mathematics and mechanics (Book 45). JAI Press. ISBN: 978-0-44451-086-0

    Google Scholar 

  • Heinrich V (2015) Controlled one-on-one encounters between immune cells and microbes reveal mechanisms of phagocytosis. Biophys J 109:469–476

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Heinrich V, Lee C-Y (2011) Blurred line between chemotactic chase and phagocytic consumption: an immunophysical single-cell perspective. J Cell Sci 124:3041–3051

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Helfrich W (1973) Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch 28:693–703

    Article  CAS  Google Scholar 

  • Herant M, Heinrich V, Dembo M (2005) Mechanics of neutrophil phagocytosis: behavior of the cortical tension. J Cell Sci 118:1789–1797

    Article  CAS  PubMed  Google Scholar 

  • Herant M, Heinrich V, Dembo M (2006) Mechanics of neutrophil phagocytosis: experiments and quantitative models. J Cell Sci 119:1903–1913

    Article  CAS  PubMed  Google Scholar 

  • Herant M, Lee C-Y, Dembo M, Heinrich V (2011) Protrusive push versus enveloping embrace: computational model of phagocytosis predicts key regulatory role of cytoskeletal membrane anchors. PLoS Comput Biol 7:e1001068

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its applications to conduction and excitation in nerve. J Physiol (Lond) 117:500–544

    Article  CAS  Google Scholar 

  • Hollingsworth SA, Dror RO (2018) Molecular dynamics simulation for all. Neuron 99(6):1129–1143

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Horwitz MA (1984) Phagocytosis of the Legionnaires’ disease bacterium (Legionella pneumophila) occurs by a novel mechanism: engulfment within a pseudopod coil. Cell 36(1):27–33

    Article  CAS  PubMed  Google Scholar 

  • Hospital A, Goñi JM, Orozco M Gelpí JL (2015) Molecular dynamics simulations: advances and applications. Adv Appl Bioinforma Chem 8:37–47

    Google Scholar 

  • Kaper JB, Nataro JP, Mobley HL (2004) Pathogenic Escherichia coli. Nat Rev Microbiol 2(2):123–140

    Article  CAS  PubMed  Google Scholar 

  • Kaplan G (1977) Differences in the mode of phagocytosis with Fc and C3 receptors in macrophages. Scand J Immunol 6:797–807

    Article  CAS  PubMed  Google Scholar 

  • Koval M, Preiter K, Adles C, Stahl PD, Steinberg TH (1998) Size of IgG-opsonized particles determines macrophage response during internalization. Exp Cell Res 242(1):265–273

    Article  CAS  PubMed  Google Scholar 

  • Kress H, Stelzer EHK, Holzer D, Buss F, Griffiths G, Rohrbach A (2007) Filopodia act as phagocytic tentacles and pull with discrete steps and a load-dependent velocity. Proc Natl Acad Sci USA 104:11633–11638

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kwiatkowska K, Sobota A (1999) Signaling pathways in phagocytosis. Bioessays 21(5):422–431

    Article  CAS  PubMed  Google Scholar 

  • Lengerová A, Lenger VJ, Esslová M, Tuscany R, Volfová M (1957) The influence of the shape of dust particles on the rate of phagocytosis in vitro. Br J Ind Med 14(1):43–46

    PubMed  PubMed Central  Google Scholar 

  • Lu Z, Qiao Y, Zheng XT, Chan-Park MB, Li CM (2010) Effect of particle shape on phagocytosis of CdTe quantum dot-cystine composites. MedChemComm 1:84–86

    Article  CAS  Google Scholar 

  • Möller J, Luehmann T, Hall H, Vogel V (2012) The race to the pole: how high-aspect ratio shape and heterogeneous environments limit phagocytosis of filamentous Escherichia coli bacteria by macrophages. Nano Lett 12(6):2901–2905

    Article  PubMed  CAS  Google Scholar 

  • Mackey MC, Maini PK (2015) What has mathematics done for biology? Bull Math Biol 77(5):735–738

    Article  PubMed  Google Scholar 

  • Meirmanov AM (1992) The Stefan problem. De Gruyter expositions in mathematics. Walter de Gruyter, Berlin. ISBN: 3-11-011479-8

    Google Scholar 

  • Niedergang F, Di Bartolo V, Alcover A (2016) Comparative anatomy of phagocytic and immunological synapses. Front Immunol 7:18

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Nowak MA (2006) Evolutionary dynamics: exploring the equations of life. Harvard University Press, Cambridge. ISBN: 978-0-67402-338-3

    Book  Google Scholar 

  • Ojkic N, López-Garrido J, Pogliano K, Endres RG (2014) Bistable forespore engulfment in Bacillus subtilis by a zipper mechanism in absence of the cell wall. PLoS Comput Biol 10(10):e1003912

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Ojkic N, López-Garrido J, Pogliano K, Endres RG (2016) Cell-wall remodeling drives engulfment during Bacillus subtilis sporulation. Elife 5:e18657

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Pacheco P, White D, Sulchek T (2013) Effects of microparticle size and Fc density on macrophage phagocytosis. PLoS One 8:e60989

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Paul D, Achouri S, Yoon Y-Z, Herre J, Bryant CE, Cicuta P (2013) Phagocytosis dynamics depends on target shape. Biophys J 105(5):1143–1150

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Pratten MK, Lloyd JB (1986) Pinocytosis and phagocytosis: the effect of size of a particulate substrate on its mode of capture by rat peritoneal macrophages cultured in vitro. Biochim Biophys Acta 881(3):307–313

    Article  CAS  PubMed  Google Scholar 

  • Reed MC (2004) Why is mathematical biology so hard? Notices Am Math Soc 51(3):338–342

    Google Scholar 

  • Richards DM, Endres RG (2014) The mechanism of phagocytosis: two stages of engulfment. Biophys J 107:1542–1553

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Richards DM, Endres RG (2016) Target shape dependence in a simple model of receptor-mediated endocytosis and phagocytosis. Proc Natl Acad Sci USA 113:6113–6118

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Richards DM, Endres RG (2017) How cells engulf: a review of theoretical approaches to phagocytosis. Rep Prog Phys 80(12):126601

    Article  PubMed  CAS  Google Scholar 

  • Rittig MG, Krause A, Häupl T, Schaible UE, Modolell M, Kramer MD, Lütjen-Drecoll E, Simon MM, Burmester GR (1992) Coiling phagocytosis is the preferential phagocytic mechanism for Borrelia burgdorferi. Infect Immun 60:4205–4212

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Sharma G, Valenta DT, Altman Y, Harvey S, Xie H, Mitragotri S, Smith JW (2010) Polymer particle shape independently influences binding and internalization by macrophages. J Control Release 147(3):408–412

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Stefan J (1891) On the theory of ice formation, particularly in the polar seas (Über die Theorie der Eisbildung, insbesondere über die Eisbildung im Polarmeere). Annalen der Physik und Chemie 42:269–286

    Article  Google Scholar 

  • Swanson JA (2008) Shaping cups into phagosomes and macropinosomes. Nat Rev Mol Cell Biol 9(8):639–649

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Tabata Y, Ikada Y (1988) Effect of the size and surface charge of polymer microspheres on their phagocytosis by macrophage. Biomaterials 9(4):356–362

    Article  CAS  PubMed  Google Scholar 

  • The Human Brain Project (2013) https://www.humanbrain project.eu/en/

  • Tindall MJ, Porter SL, Maini PK, Gaglia G, Armitage JP (2008) Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell. Bull Math Biol 70(6):1525–1569

    Article  CAS  PubMed  Google Scholar 

  • Tindall MJ, Maini PK, Porter SL, Armitage JP (2008) Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations. Bull Math Biol 70(6):1570–1607

    Article  CAS  PubMed  Google Scholar 

  • Tollis S, Dart AE, Tzircotis G, Endres RG (2010) The zipper mechanism in phagocytosis: energetic requirements and variability in phagocytic cup shape. BMC Syst Biol 4:149–165

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Underhill DM, Ozinsky A (2002) Phagocytosis of microbes: Complexity in action. Annu Rev Immunol 20:825–852

    Article  CAS  PubMed  Google Scholar 

  • van Zon JS, Tzircotis G, Caron E, Howard M (2009) A mechanical bottleneck explains the variation in cup growth during FcγR phagocytosis. Mol Syst Biol 5:298–309

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Voit EO, Martens HA, Omholt SW (2015) 150 years of the mass action law. PLoS Comput Biol 11(1):e1004012

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Vonna L, Wiedemann A, Aepfelbacher M, Sackmann E (2007) Micromechanics of filopodia mediated capture of pathogens by macrophages. Eur Biophys J 36:145–151

    Article  CAS  PubMed  Google Scholar 

  • Zhang Y, Hoppe AD, Swanson JA (2010) Coordination of Fc receptor signaling regulates cellular commitment to phagocytosis. Proc Natl Acad Sci USA 107(45):19332–19337

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Zigmond SH, Hirsch JG (1972) Effects of cytochalasin B on polymorphonuclear leucocyte locomotion, phagocytosis and glycolysis. Exp Cell Res 73:383–393

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Living Systems Institute, University of Exeter, Exeter, UK

    David M. Richards

Authors
  1. David M. Richards
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David M. Richards .

Editor information

Editors and Affiliations

  1. School of Medicine, Cardiff University, Cardiff, UK

    Maurice B. Hallett

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Richards, D.M. (2020). Receptor Models of Phagocytosis: The Effect of Target Shape. In: Hallett, M. (eds) Molecular and Cellular Biology of Phagocytosis . Advances in Experimental Medicine and Biology, vol 1246. Springer, Cham. https://doi.org/10.1007/978-3-030-40406-2_4

Download citation

Publish with us

Policies and ethics

Search

Navigation