Stochastic models for cell motion and taxis

Journal of Mathematical Biology

Volumn 48, Issue 1, 2004, Pages 23-37

  Ionides, Edward L ^a   Fang, Kathy S ^c   Isseroff, R Rivkah ^c   Oster, George F ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b University of California Berkeley   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Cell migration; Chemotaxis; Galvanotaxis; Nonlinear diffusion; Stochastic model

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL MOTION; CHEMOTAXIS; ELECTROPHYSIOLOGY; HUMAN; KINETICS; NONLINEAR SYSTEM; ORIENTATION; PHYSIOLOGY; STATISTICAL ANALYSIS; STATISTICAL MODEL; STATISTICS;

ALGORITHMS; ANIMALS; CELL MOVEMENT; CHEMOTAXIS; DATA INTERPRETATION, STATISTICAL; ELECTROPHYSIOLOGY; HUMANS; KINESIS; KINETICS; LINEAR MODELS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; STOCHASTIC PROCESSES;

EID: 6044249273     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00285-003-0220-z     Document Type: Article

References (54)

1. Alt, W.: Biased random walk models for chemotaxis and related diffusion approximations. J. Math. Biol. 9, 147-177 (1980)
2. Alt, W., Deutsch, A., Dunn, G.: Dynamics of Cell and Tissue Motion. Birkhäuser, Basel, 1997
3. Alt, W., Hoffmann, G.: Biological Motion. Springer, Berlin, 1990
4. Bailly, M., Condeelis, J.S., Segall, J.E.: Chemoattractant-induced lamellipod extension. Microsc. Res. Tech. 43, 433-443 (1998)
5. Box, G.E.P., Jenkins, G.M.: Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco, 1970
6. Bray, D.: Cell Movements. Garland Publishing, New York, 1992
7. Brillinger, D.R.: A particle migrating randomly on a sphere. J. Theoret. Probab. 10, 429-443 (1997)
8. Brillinger, D.R., Preisler, H.K., Ager, A.A., Kie, J.G.: An exploratory data analysis (EDA) of the paths of moving animals. J. Stat. Plan. Infer., submitted, 2001
9. Brillinger, D.R., Stewart, B.S.: Elephant-seal movements: Modelling migration. Canadian J. Statist. 26, 431-443 (1998)
10. Byrne, H.M., Cave, G., McElwain, D.: The effect of chemotaxis and chemokinesis on leukocyte locomotion: A new interpretation of experimental results. IMA J. Math. Appl. in Medic, and Biol. 15, 235-256 (1998)
11. Dembo, M.: Field theorems of the cytoplasm. Comments Theor. Biol. 1, 159-177 (1989)
12. Dickinson, R.B., Tranquillo, R.J.: Optimal estimation of cell movement indices from the statistical analysis of cell tracking data. AIChE J. 39, 1995-2010 (1993)
13. Dickinson, R.B., Tranquillo, R.J.: A stochastic model for adhesion-mediated cell random motility and haptotaxis. J. Math. Biol. 31, 563-600 (1993)
14. Dickinson, R.B., Tranquillo, R.T.: Transport equations and indices for random and biased cell migration based on single cell properties. SIAM J. Appl. Math. 55, 1419-1454 (1995)
15. DiMilla, P.A., Quinn, J.A., Albelda, S.M., Lauffenburger, D.A.: Measurement of individual cell migration parameters for human tissue cells. AIChE J. 38, 1092-1104 (1992)
16. Doucet, A., de Freitas, N., Gordon, N.J. : Sequential Monte Carlo methods in practice. Springer, New York, 2001
17. Doucet, P.G., Dunn, G.A.: Distintion between kinesis and taxis in terms of system theory. In: Alt, W., Hoffmann, G., (eds) Biological Motion, pp. 498-509. Springer, Berlin, 1990
18. Dunn, G.A.: Characterising a kinesis response: Time averaged measures of cell speed and directional persistence. Agents Actions Suppl. 12, 14-33 (1983)
19. Dunn, G.A., Brown, A.F.: A unified approach to analyzing cell motility. J. Cell Sci. Suppl. 8, 81-102 (1987)
20. Durbin, J., Koopman, S.J.: Time series analysis by state space models. Oxford University Press, 2001
21. Fang, K.S., Ionides, E., Oster, G., Nuccitelli, R., Isseroff, R.R.: Epidermal growth factor receptor relocalization and kinase activity are necessary for directional migration of keratinocytes in dc electric fields. J. Cell Sci. 112, 1967-1978 (1999)
22. Farrell, B.E., Daniele, R.P., Lauffenburger, D.A.: Quantitative relationships between sin-gle-cell and cell-population model parameters for chemosensory migration responses of alveolar macrophages to C5a. Cell Motil. Cytoskel. 16, 279-293 (1990)
23. Ford, R.M., Lauffenburger, D.A.: Measurement of bacterial random motility and chemotaxis coefficients: II. Application of single-cell-based mathematical model. Biotechnology and Bioengineering 37, 661-672 (1991)
24. Ford, R.M., Phillips, B.R., Quinn, I.A., Lauffenberger, D.A.: Measurement of bacterial random motility and chemotaxis coefficients: I. Stopped-flow diffusion chamber assay. Biotechnology and Bioengineering 37, 647-660 (1991)
25. Gardiner, C.W.: Handbook of Stochastic Methods. Springer, New York, second edition, 1985
26. Giardini, P.A., Theriot, J.A.: Effects of intermediate filaments on actin-based motility of listeria monocytogenes. Biophys. J. 81, 3193-3203 (2001)
27. Gruler, H., Nuccitelli, R.: The galvanotaxis response mechanism of keratinocytes can be modeled as a proportional controler. Cell Biochem. Biophys. 33, 33-51 (2000)
28. Harvey, A.C.: Forecasting, structural time series models and the Kalman filter. Cambridge University Press, 1989
29. Huttenlocher, A., Sandborg, R.R., Horwitz, A.F.: Adhesion in cell migration. Curr. Opin. Cell Biol. 7, 697-706 (1995)
30. Ionides, E.L.: Statistical analysis of cell motion. PhD thesis, University of California, Berkeley, 2001
31. Karlin, S., Taylor, H.M.: A Second Course in Stochastic Processes. Academic Press, New York, 1981
32. Kauermann, G., Carroll, R.J.: A note on the efficiency of sandwich covariance matrix estimation. J. Amer. Statist. Assoc. 96, 1387-1496 (2001)
33. Keller, E.F., Segel, L.A.: Model for chemotaxis. J. Theor. Biol. 30, 225-235 (1971)
34. Kendall, D.G.: Pole-seeking Brownian motion and bird navigation. J. Roy. Statist. Soc. Ser. B 36, 365-417 (1974)
35. Kitagawa, G.: Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J. Comput. Graph. Statist. 5, 1-25 (1996)
36. Kloeden, P.E., Platen, E.: Numerical Soluion of Stochastic Differential Equations. Springer, New York, 1992
37. Langer, R.S., Vacanti, J.P.: Tissue engineering: The challenges ahead. Scientific American. 280(4), 86-89 (1999)
38. Lauffenburger, D.A., Linderman, J.J.: Receptors: Models for Binding, Tracking and Signalling. Oxford University Press, New York, 1993
39. Maheshwari, G., Lauffenburger, D.A.: Deconstructing (and reconstructing) cell migration. Microscopy Res. Technique. 43, 358-368 (1998)
40. Mogilner, A., Oster, G.: The physics of lamellipodial protrusion. Eur. Biophys. J. 25, 47-53 (1996)
41. Mooney, D.J., Mikos, A.G.: Growing new organs. Scientific American. 280(4), 60-65 (1999)
42. Nishimura, K.Y., Isseroff, R.R., Nuccitelli, R.: Human keratinocytes migrate to the negative pole in DC electric fields comparable to those measured in mammalian wounds. J. Cell Sci. 109, 199-207 (1996)
43. Oksendal, B.: Stochastic Differential Equations. Springer, New York, 1998
44. Parenteau, N.: Skin: The first tissue-engineered products. Scientific American 280(4), 83-84 (1999)
45. Preisler, H.K., Brillinger, D.R., Ager, A.A., Kie, J.: Analysis of animal movement using telemetry and gis data. In: Proc. ASA Section on Statistics and the Environment, pp. 100-105, 1999
46. Rao, C.R.: Linear Statistical Inference and Its Applications. Wiley, New York, 2nd edition, 1973
47. Roberts, G.O., Stramer, O.: On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm. Biometrika. 88, 603-621 (2001)
48. Saxton, M.J.: Single-particle tracking: The distribution of diffusion coefficients. Biophys. J. 72, 1744-1753 (1997)
49. Shenderov, A.D., Sheetz, M.P.: Inversely correlated cycles in speed and turning in an amoeba: An oscillatory model of cell locomotion. Biophys. J. 72, 2382-2389 (1997)
50. Shephard, N., Pitt, M.K.: Likelihood analysis of non-Gaussian measurement time series. Biometrika. 84, 653-667 (1997)
51. Stokes, C.L., Lauffenbuger, D.A., Williams, S.K.: Migration of individual microvessel endothelial cells; stochastic model and parmeter measurement. J. Cell Sci. 99, 419-430 (1991)
52. Stroock, D.W.: Some stochastic processes which arise from a model of the motion of a bacterium. Z. Wahrscheinlichkeitstheorie verw. Geb. 28, 305-315 (1974)
53. Tranquillo, R.T., Alt, W.: Stochastic model of receptor-mediated cytomechanics and dynamic morphology of leukocytes. J. Math. Biol. 54, 361-412 (1996)
54. White, H.: Maximum likelihood estimation of mis-specified models. Econometrica. 50, 1-26 (1982)