×

Biased random walk models for chemotaxis and related diffusion approximations. (English) Zbl 0434.92001


MSC:

92B05 General biology and biomathematics
92Cxx Physiological, cellular and medical topics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Albrecht-Buehler, G.: Phagokinetic tracks of 3T3 cells: Parallels between the orientation of track segments and of cellular structures which contain actin or tubulin. Cell 12, 333-339 (1977)
[2] Albrecht-Buehler, G.: The angular distribution of directional changes of guided 3T3 cells. J. Cell Biol. 80, 53-60 (1979)
[3] Allan, R. B., Wilkinson, P. C.: A visual analysis of chemotactic and chemokinetic locomotion of human neutrophil leukocytes. Exp. Cell Res. 111, 191-203 (1978)
[4] Alt, W.: Orientation of cells migrating in a chemotactic gradient. In: Proc. Conf. on Models of Biological Growth and Spread, Heidelberg, 1979 (to appear) · Zbl 0445.92009
[5] Alt, W.: Singular perturbation of differential integral equations describing biased random walks. Crelle J. Reine Angew. Math. (submitted) · Zbl 0437.60059
[6] Berg, H. C., Brown, D. A.: Chemotaxis in Escherichia coli analyzed by three-dimensional tracking. In: Antibiotics and Chemotherapy, Vol. 19, pp. 55-78. Basel: Karger, 1974
[7] Berg, H. C., Tedesco, P. M.: Transient response to chemotactic stimuli in Escherichia coli. Proc. Nat. Acad. Sci. USA 72, 3235-3239 (1975)
[8] Brown, D. A., Berg H. C.: Temporal stimulation of chemotaxis in Escherichia coli. Proc. Nat. Acad. Sci. USA 71, 1388-1392 (1974)
[9] Boyarsky, A., Noble, P. B.: A Markov chain characterization of human neutrophil locomotion under neutral and chemotactic conditions. Can. J. Physiol. Pharmacology 55, 1-6 (1977)
[10] Dipasquale, A.: Locomotory activity of epithelial cells in culture. Exp. Cell Res. 94, 191-215 (1975)
[11] Gallin, J. I., Gallin, E. K., Malech, H. L., Cramer, E. B.: Structural and ionic events during leukocyte chemotaxis. In: Leukocyte chemotaxis (J. I. Gallin, P. G. Quie, eds.) pp. 123-141. New York: Raven Press, 1978
[12] Gerisch, G., Hess, B., Malchow, D.: Cell communication and cyclic-AMP regulation during aggregation of the slime mold dictyostelium discoideum. In: Biochemistry of sensory functions (L. Jaenicke, ed.) pp. 279-298. Berlin, Heidelberg, New York: Springer Verlag, 1974
[13] Hall, R. L.: Amoeboid movement as a correlated walk. J. math. Biol. 4, 327-335 (1977) · Zbl 0375.92009
[14] Hall, R. L., Peterson, S. C.: Trajectories of human granulocytes. Biophys. J. 25, 365-372 (1979)
[15] Jungi, T. W.: Different concentrations of chemotactic factors can produce attraction or migration inhibition of leukocytes. Int. Archs. Allergy appl. Immun. 53, 29-36 (1977)
[16] Keller, E. F.: Mathematical aspects of bacterial chemotaxis. In: Antibiotics and Chemotherapy, Vol. 19, pp. 79-93. Basel: Karger, 1974
[17] Keller, E. F., Segel, L. A.: Model for chemotaxis. J. theor. Biol. 30, 225-234 (1971). · Zbl 1170.92307
[18] Koshland, D. E., jr.: A response regulator model in a simple sensory system. Science 196, 1055-1063 (1977)
[19] Kurtz, Th. G.: A limit theorem for perturbed operator semigroups with applications to random evolutions. J. Funct. Anal. 12, 55-67 (1973) · Zbl 0246.47053
[20] Lauffenburger, D., Keller, K. H.: Effects of leukocyte random motility and chemotaxis in tissue inflammatory response. J. theor. Biol. 81, 475-503 (1979)
[21] Lovely, P. S., Dahlquist, F. W.: Statistical measures of bacterial motility and chemotaxis. J. theor. Biol. 50, 477-496 (1975)
[22] MacNab, R., Koshland, D. E., jr.: The gradient-sensing mechanism in bacterial chemotaxis. Proc. Nat. Acad. Sci. USA 69, 2509-2512 (1972)
[23] MacNab, R., Koshland, D. E., jr.: Persistence as a concept in the motility of chemotactic bacteria. J. Mechanochem. Cell Motility 2, 141-148 (1973)
[24] Maderazo, E. G., Woronick, Ch. L.: A modified micropore filter assay of human granulocyte leukotaxis. In: Leukocyte chemotaxis (J. I. Gallin, P. G. Quie, eds.) pp. 43-55. New York: Raven Press, 1978
[25] Nishida, T.: Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation. Commun. math. Phys. 61, 119-148 (1978) · Zbl 0381.76060
[26] Nossal, R.: Directed cell locomotion arising from strongly biased turn angles. Math. Biosc. 31, 121-129 (1976) · Zbl 0333.92005
[27] Nossal, R.: Mathematical theories of topotaxis. In: Proc. Conf. on Models of Biological Growth and Spread. Heidelberg, 1979 (to appear) · Zbl 0445.92010
[28] Nossal, R., Weiss, G. H.: Analysis of a densiometric assay for bacterial chemotaxis. J. theor. Biol. 41, 143-147 (1973)
[29] Nossal, R., Weiss, G. H.: A descriptive theory of cell migration on surfaces. J. theor. Biol. 47, 103-113 (1974)
[30] Nossal, R., Zigmond, S. H.: Chemotropism indices for polymorphonuclear leukocytes. Biophys. J. 16, 1171-1182 (1976)
[31] Ordal, G. W., Fields, R. B.: A biochemical mechanism for bacterial chemotaxis. J. theor. Biol. 68, 491-500 (1977)
[32] Papanicolaou, G. C.: Some probabilistic problems and methods in singular perturbations. Rocky Mount. J. Math. 6, 653-674 (1976) · Zbl 0365.60049
[33] Papanicolaou, G. C.: Introduction to the asymptotic analysis of stochastic equations. In: Modern modeling of continuum phenomena. AMS Lectures in Appl. Math., Vol. 16 (R. C. DiPrima, ed.) pp. 109-147. Providence, 1977
[34] Patlak, C. S.: Random walk with persistence and external bias. Bull. math. Biophys. 15, 311-338 (1953) · Zbl 1296.82044
[35] Peterson, S. C., Noble, P. B.: A two-dimensional random-walk analysis of human granulocyte movement. Biophys. J. 12, 1048-1055 (1972)
[36] Ramsey, W. S.: Analysis of individual leukocyte behaviour during chemotaxis. Exp. Cell Res. 70, 129-139 (1972)
[37] Segel, L. A.: A theoretical study of receptor mechanisms in bacterial chemotaxis. SIAM J. Appl. Math. 32, 653-665 (1977) · Zbl 0356.92009
[38] Segel, L. A.: Mathematical models for cellular behavior. In: A study in mathematical biology. MAA Studies in Math. Vol. 15 (S. Levin, ed.) pp. 156-190. Washington, 1978
[39] Stossel, Th. P.: The mechanism of leukocyte locomotion. In: Leukocyte chemotaxis (J. I. Gallin, P. G. Quie, eds.) pp. 143-160. New York: Raven Press, 1978
[40] Stroock, D. W.: Some stochastic processes which arise from a model of the motion of a bacterium. Zeitschr. Wahrsch.th. 28, 305-315 (1974) · Zbl 0282.60047
[41] Zigmond, S. H.: Mechanisms of sensing chemical gradients by polymorphonuclear leukocytes. Nature 249, 450-452 (1974)
[42] Zigmond, S. H.: Ability of polymorphonuclear leukocytes to orient in gradients of chemotactic factors. J. Cell Biol. 75, 606-616 (1977)
[43] Zigmond, S. H.: Chemotaxis by polymorphonuclear leukocytes. J. Cell Biol. 77, 269-287 (1978)
[44] Zigmond, S. H., Hirsch, J. G.: Leukocyte locomotion and chemotaxis. J. Exp. Medicine 137, 387-410 (1973)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.