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Chaotic behavior in the locomotion ofamoeba proteus

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Summary

The locomotion ofAmoeba proteus has been investigated by algorithms evaluating correlation dimension and Lyapunov spectrum developed in the field of nonlinear science. It is presumed by these parameters whether the random behavior of the system is stochastic or deterministic. For the analysis of the nonlinear parameters, n-dimensional time-delayed vectors have been reconstructed from a time series of periphery and area ofA. proteus images captured with a charge-coupled-device camera, which characterize its random motion. The correlation dimension analyzed has shown the random motion ofA. proteus is subjected only to 3–4 macrovariables, though the system is a complex system composed of many degrees of freedom. Furthermore, the analysis of the Lyapunov spectrum has shown its largest exponent takes positive values. These results indicate the random behavior ofA. proteus is chaotic and deterministic motion on an attractor with low dimension. It may be important for the elucidation of the cell locomotion to take account of nonlinear interactions among a small number of dynamics such as the sol-gel transformation, the cytoplasmic streaming, and the relating chemical reaction occurring in the cell.

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References

  • Allen RD, Francis D, Zeh R (1971) Direct test of the positive pressure gradient theory of pseudopod extension and retraction in Amoebae. Science 174:1237–240

    Article  PubMed  CAS  Google Scholar 

  • Babloyants A, Destexhe A (1986) Low-dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci USA 83: 3513–3517

    Article  Google Scholar 

  • — Salazer JM (1985) Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys Lett 111 A: 152–156

    Google Scholar 

  • Cunningham CC, Stossel TP, Kwiatkowski DJ (1991) Enhanced motility in NIH 3T3 fibroblasts that overexpress gelsolin. Science 251:1233–1236

    Article  PubMed  CAS  Google Scholar 

  • Essex C, Lookman T, Nerenberg MAH (1987) The climate attractor over short timescales. Nature 326: 64–66

    Article  Google Scholar 

  • Fukui Y (1993) Toward a new concept of cell motility: cytoskeletal dynamics in amoeboid movement and cell division. Int Rev Cytol 144: 85–127

    PubMed  CAS  Google Scholar 

  • — Lynch TJ, Brzesca H, Korn ED (1989) Myosin I is located at the leading edges of locomoting Dictyostelium amoebae. Nature 341: 328–331

    Article  PubMed  CAS  Google Scholar 

  • Gaulitta W, Stockem W (1980) Organization and arrangement of fluorescein-labeled native actin microinjected into normal locomoting and experimentally influencedAmoeba proteus. Cell Tissue Res 206:181–191

    Google Scholar 

  • Grassberger P, Procaccia I (1983) Characterization of strange attractors. Phys Rev Lett 31: 346–349

    Article  Google Scholar 

  • Harris AS, Morrow JS (1990) Calmodulin and calcium-dependent protease I coordinately regulate the interaction of fodrin with actin. Proc Natl Acad Sci USA 87: 3009–3013

    Article  PubMed  CAS  Google Scholar 

  • John THM, Ghosh RN, Maxfield FR (1995) Intracellular calcium levels correlate with speed and persistent forward motion in migrating neutrophils. Biophys J 68:1207–1217

    Google Scholar 

  • Killich T, Plath PJ, Xiang W, Bultmann H, Rensing L, Vicker MG (1993) The locomotion, shape and pseudopodial dynamics of unstimulatedDictyostelium cells are not random. J Cell Sci 106: 1005–1013

    PubMed  Google Scholar 

  • Korohoda W, Golda J, Sroka J, Wojnarowicz A, Jochym P, Madeja Z (1997) Chemotaxis ofAmoeba proteus in the developing pH gradient within a pocket-like chamber studied with the computer assisted method. Cell Motil Cytoskeleton 38: 38–53

    Article  PubMed  CAS  Google Scholar 

  • Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20: 130–141

    Article  Google Scholar 

  • Mattfeldt T (1997) Nonlinear deterministic analysis of tissue texture: a stereological study on mastopathic and mammary cancer tissue using chaos theory. J Micros 185: 47–66

    Article  CAS  Google Scholar 

  • Peterson SC, Noble PB (1972) A two-dimensional random walk analysis of human granulocyte movement. Biophys J 12: 1048–1055

    Article  PubMed  CAS  Google Scholar 

  • Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. Wiley, London

  • Potel MJ, McKay SA (1979) Preaggregative cell motion inDictyostelium. J Cell Sci 36:281–309

    PubMed  CAS  Google Scholar 

  • Rosenstein MT, Collins JJ, DeLuca CJ (1994) Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica D 73: 82–98

    Article  Google Scholar 

  • Sano M, Sawada Y (1985) Measurement of the Lyapunov spectrum from a chaotic time series. Phys Rev Lett 55:1082–1085

    Article  PubMed  Google Scholar 

  • Sato S, Sano M, Sawada Y (1987) Practical methods of measuring the generalized dimension and the largest Lyapunov exponent in high dimensional chaotic systems. Prog Theor Phys 77:1–5

    Article  Google Scholar 

  • Satoh H, Ueda T, Kobatake Y (1985) Oscillations in cell shape and size during locomotion and in contractile activities ofPhysarum polycephalum, Dictyostelium discoideum, Amoeba proteus and macrophages. Exp Cell Res 156:79–90

    Article  PubMed  CAS  Google Scholar 

  • Shimada I, Nagashima T (1979) A numerical approach to ergodic problem of dissipative dynamical systems. Prog Theor Phys 61: 1605–1616

    Article  Google Scholar 

  • Singer SJ, Kupfer A (1986) The directed migration of eukaryotic cells. Annu Rev Cell Biol 2: 337–365

    Article  PubMed  CAS  Google Scholar 

  • Stockem W, Hoffmann HU, Wolfgang G (1982) Spatial organization and fine structure of the cortical filament layer in normal locomotingAmoeba proteus. Cell Tissue Res 221: 505–519

    Article  PubMed  CAS  Google Scholar 

  • Takens F (1981) Detecting strange attractors in turbulence. Lecture Notes Math 898: 366–381

    Article  Google Scholar 

  • Tatsuka M, Jinno S, Owada MK, Kakunaga T (1989) A digital image processing system for quantitating dynamic morphology in cultured mammalian cells. Exp Cell Res 185: 342–352

    Article  PubMed  CAS  Google Scholar 

  • Taylor DL, Moore PL, Condeelis JS, Allen RD (1976) The mechanical basis of amoeboid movement I: ionic requirements for maintaining viscoelasticity and contractility of amoeba cytoplasm. Exp Cell Res 101:127–133

    Article  PubMed  CAS  Google Scholar 

  • Ueda T, Kobatake Y (1983) Quantitative analysis of changes in cell shape ofAmoeba proteus during locomotion and upon responses to salt stimuli. Exp Cell Res 147:466–472

    Article  PubMed  CAS  Google Scholar 

  • Wagner CD, Persson PB (1995) Nonlinear chaotic dynamics of arterial blood pressure and renal blood flow. Am J Physiol 268: H621-H627

    PubMed  CAS  Google Scholar 

  • Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Deterministic Lyapunov exponents from a time series. Physica D 16: 285–317

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Biological Sciences, Faculty of Bioscience and Biotechnology, Tokyo Instiof Technology, Midoriku, Yokohama

    Hiromi Miyoshi & Yuki Kagawa

  2. Department of Biological Sciences, Faculty of Bioscience and Biotechnology, Tokyo Institute of Technology, Nagatsuta 4259, Midoriku, 226-8501, Yokohama, Japan

    Yoshimi Tsuchiya

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  1. Hiromi Miyoshi
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  2. Yuki Kagawa
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  3. Yoshimi Tsuchiya
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Miyoshi, H., Kagawa, Y. & Tsuchiya, Y. Chaotic behavior in the locomotion ofamoeba proteus . Protoplasma 216, 66–70 (2001). https://doi.org/10.1007/BF02680132

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  • DOI: https://doi.org/10.1007/BF02680132

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