European Biophysics Journal

, Volume 18, Issue 6, pp 334–346 | Cite as

Galvanotaxis of human granulocytes: electric field jump studies

  • K. Franke
  • H. Gruler


The static and dynamic responses of human granulocytes to an electric field were investigated. The trajectories of the cells were determined from digitized pictures (phase contrast). The basic results are: (i) The track velocity is a constant as shown by means of the velocity autocorrelation function. (ii) The chemokinetic signal transduction/response mechanism is described in analogy to enzyme kinetics. The model predicts a single gaussian for the track velocity distribution density as measured. (iii) The mean drift velocity induced by an electric field, is the product of the mean track velocity and the polar order parameter. (iv) The galvanotactic dose-response curve was determined and described by using a generating function. This function is linear in E for E < E0 = 0.78 V/mm with a galvanotaxis coefficient K G of (−0.22 V/mm)−1 at 2.5 mM Ca++. For E > E0 the galvanotactic response is diminished. This inhibition is described by a second term in the generating function (−K G · K I (EE0)) with an inhibition coefficient K I of 3.5 (v) The characteristic time involved in directed movement is a function of the applied electric field strength: about 30 s at low field strengths and below 10 s at high field strengths. The characteristic time is 32.4 s if the cells have to make a large change in direction of movement even at large field strength (E jump). (vi) The lag-time between signal recognition and cellular response was 8.3 s. (vii) The galvanotactic response is Ca++ dependent. The granulocytes move towards the anode at 2.5 mM Ca++ towards the cathode at 0.1 mM Ca++. (viii) The directed movement of granulocytes can be described by a proportional-integral controler.

Key words

Chemokinesis Galvanotaxis Dose-response curve E-jump Granulocytes 


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  1. Alt W, Hoffmann G (eds) (1990) Biological motion. Springer, Berlin Heidelberg New YorkGoogle Scholar
  2. Becker EL, Showell HJ, Naccache PH, Sha'afi R (1978) Enzymes in granulocytes movement: preliminary evidence for the involvement of Na+ and K+ ATPase. In: Gallin JI, Quie PG (eds) Leukocyte chemotaxis. Raven Press, New York, pp 113–121Google Scholar
  3. Becker EL, Kanaho Y, Kermode JC (1987) Nature and functioning of the pertussis toxin-sensitive G-protein of neutrophils. Biomed Pharmacol 41:289–297Google Scholar
  4. de Boisfleury-Chevance A, Rapp B, Gruler H (1989). Locomotion of white blood cells: a biophysical analysis. Blood Cells 15:315–333Google Scholar
  5. Cooke E, Al-Mohanna FA, Hallett MB (1989) Calcium-dependent and independent mechanisms of cellular control within neutrophils: the roles of kinase C, diacylglycerol, and unidentified intracellular messengers. In: Hallett MB (ed) The neutrophil: cellular biochemistry and physiology. CRC Press, Boca Raton, pp 219–241Google Scholar
  6. Erickson CA, Nuccitelli R (1984) Embryonic fibroblast motility and orientation can be influenced by physiological electric fields. J Cell Biol 98:296–307Google Scholar
  7. Ferguson JL (1968) Liquid crystals in nondestructive testing. Appl Opt 7:1729–1737Google Scholar
  8. Fukushima K, Senda N, Innnui H, Tamai Y, Murakami Y (1953) Studies of galvanotaxis of leukocytes. Med J Osaka Univ 4:195–208Google Scholar
  9. Fukushima K, Senda N, Ishigami S, Murakami Y, Nishian K (1954) Dynamic pattern in the movement of leukocyte II. The behaviour of neutrophil immediately after commencement and removal of stimulation. Med J Osaka Univ 5:47–56Google Scholar
  10. Gallin EK, McKinney LC (1989) Ion transport in phagocytes. In: Hallett MB (ed) The neutrophil: cellular biochemistry and physiology. CRC Press, Boca Raton, pp 243–259Google Scholar
  11. Gerish G, Keller H-H (1981) Chemotactic reorientation of granulocytes stimulated with micropipettes containing f-Met-Leu-Phe. J Cell Sci 52:1–10Google Scholar
  12. Gruler H (1984) Cell movement analysis in a necrotactic assay. Blood Cells 10:107–121Google Scholar
  13. Gruler H (1988) Cell movement and symmetry of the cellular environment. Z Naturforsch 43c:754–764Google Scholar
  14. Gruler H (1989) Biophysics of leukocytes: neutrophil chemotaxis, characteristics and mechanisms. In: Hallett MB (ed) The cellular biochemistry and physiology of neutrophil. CRC Press, Boca Raton, pp 63–95Google Scholar
  15. Gruler H (1990) Chemokinesis, chemotaxis and galvanotaxis. In: Alt W Hoffmann G (eds) Lecture notes in biomathematics. Springer, Berlin Heidelberg New YorkGoogle Scholar
  16. Gruler H, de Boisfleury-Chevance A (1987) Chemokinesis and necrotaxis of human granulocytes: the important cellular organelles. Z Naturforsch 42c:1126–1134Google Scholar
  17. Gruler H, Bültmann BD (1984) Virus-induced order-disorder transition of moving human leukocytes. Il Nuovo Cimento 3D:152–173Google Scholar
  18. Gruler H, Franke K (1990) Automatic control and directed cell movement: (to be published)Google Scholar
  19. Gruler H, Gow NAR (1990) Directed growth of fungal hyphae in an electric field. A biophysical analysis. Z Naturforsch 45c:306–313Google Scholar
  20. Gruler H, Nuccitelli R (1986) New insights into galvanotaxis and other directed cell movements: an analysis of the translocation distribution function. In: Nuccitelli R (ed) Ionic currents in development. Liss, New York, pp 337–347Google Scholar
  21. Haken H (1983) Synergetics. Springer, Berlin Heidelberg New York, pp 146–189Google Scholar
  22. Hallett MB (1989) The significance of stimulus-response coupling in the neutrophil for physiology and pathology. In: Hallett MB (ed) The neutrophil: Cellular biochemistry and physiology. CRC Press, Boca Raton, pp 1–22Google Scholar
  23. Jäger U, Gruler H, Bültmann BD (1988) Morphological changes and membrane potential of human granulocytes under influence of chemotactic peptide and/or echo-virus, type 9. Klin Wochenschr 66:434–436Google Scholar
  24. Matthes T, Gruler H (1988) Analysis of cell locomotion. Contact guidance of human polymorphonuclear leukocytes. Eur Biophys J 15:343–357Google Scholar
  25. McGillivray AM, Gow NAR (1986) Applied electric fields polarize the growth of mycelial fungi. J Gen Microbiol 132:2515–2525Google Scholar
  26. Müller-Enoch D, Churchill P, Fleischer S, Guengerich FP (1984) Interaction of liver microsomal cytochrome P-450 and NADPH-cytochrome P-450 reductase in the presence and absence of lipid. J Biol Chem 259:8174–8182Google Scholar
  27. Naccache PH, Sha'afi RI, Borgeat P (1989) Mobilization, metabolism, and biological effects of eicosanoids in polymorphonuclear leukocytes. In: Hallett MB (ed) The neutrophil: cellular biochemistry and physiology. CRC Press, Boca Raton, pp 113–139Google Scholar
  28. Ramsey WS (1972) Analysis of individual leucocyte behavior during chemotaxis. Exp Cell Res 70:129–139Google Scholar
  29. Rapp B, de Boisfleury-Chevance A, Gruler H (1988) Galvanotaxis of human granulocytes. Dose-respone curve. Eur Biophys J 16:313–319Google Scholar
  30. Risken H (1984) The Fokker-Planck equation. Springer, Berlin Heidelberg New YorkGoogle Scholar
  31. Scharstein H, Alt W (1990) Discretization problems. In: Alt W, Hoffmann G (eds) Biological motion. Springer, Berlin Heidelberg New YorkGoogle Scholar
  32. Tranquillo RT (1990) Models of chemical gradient sensing cells. In: Alt W, Hoffmann G (eds) Biological motion. Springer, Berlin Heidelberg New YorkGoogle Scholar
  33. Tranquillo RT, Lauffenburger DA (1987) Stochastic model of leukocyte chemosensory movement. J Math Biol 25:229–262Google Scholar
  34. Tranquillo RT, Lauffenburger DA, Zigmond SH (1988a) A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations. J Cell Biol 106:303–309Google Scholar
  35. Tranquillo RT, Zigmond SH, Lauffenburger DA (1988b) Measurement of the chemotaxis coefficient for human neutrophils in the under-agarose migration assay. Cell Motil Cytoskelet 11:1–15Google Scholar
  36. Van Laere AJ (1988) Effect of electrical fields on polar growth of Phycomyces blakesleeanus FEMS Microbiol Lett 49:111–116Google Scholar
  37. Wiener N (1961) Cybernetics: or control and communication in the animal and the machine. MIT Press, CambridgeGoogle Scholar
  38. Wilkinson PC (1982) Chemotaxis and inflammation. Churchill Livingstone, Edinburgh London MelbourneGoogle Scholar
  39. Zigmond SH, Sullivan SJ (1981) Receptor modulation and its consequences for the response to chemotactic peptides. In: Lackie JM, Wilkinson PC (eds) Biology of chemotactic response. University Press, Cambridge London, pp 73–88Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • K. Franke
    • 1
  • H. Gruler
    • 1
  1. 1.Abteilung für BiophysikUniversität UlmUlmFederal Republic of Germany

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