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Mathematics and the Life-Sciences: A Personal Point of View

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Abstract

Four classical examples on mathematical modeling in the life-sciences are summarized. These include Turing’s diffusion-reaction systems in morphogenesis, Hodkin’s and Huxley’s model on the initiation and propagation of action potentials in a nerve fibre, first rigorous chemotaxis models, and the mathematical analysis of molecular sequence characteristics.

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References

  1. Childress, S., Percus, J.K.: Nonlinear aspects of chemotaxis. Math. Biosci. 56(3–4), 217–237 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dembo, A., Karlin, S.: Strong limit theorems of empirical functionals for large exceedances of partial sums of i.i.d. variables. Ann. Probab. 19(4), 1737–1755 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dembo, A., Karlin, S.: Strong limit theorems of empirical distributions for large segmental exceedances of partial sums of Markov variables. Ann. Probab. 19(4), 1756–1767 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dembo, A., Karlin, S., Zeitouni, O.: Critical phenomena for sequence matching with scoring. Ann. Probab. 22(4), 1993–2021 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dembo, A., Karlin, S., Zeitouni, O.: Limit distribution of maximal non-aligned two-sequence segmental score. Ann. Probab. 22(4), 2022–2039 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. Karlin, S., Dembo, A., Kawabata, T.: Statistical composition of high-scoring segments from molecular sequences. Ann. Stat. 18(2), 571–581 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hodkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)

    Article  Google Scholar 

  8. Horstmann, D.: From 1970 until present: the Keller-Segel model in chemotaxis and its consequences I. Jahresber. Dtsch. Math.-Ver. 105(3), 103–165 (2003)

    MathSciNet  MATH  Google Scholar 

  9. Horstmann, D.: From 1970 until present: the Keller-Segel model in chemotaxis and its consequences II. Jahresber. Dtsch. Math.-Ver. 106(2), 51–69 (2004)

    MathSciNet  MATH  Google Scholar 

  10. Jäger, W., Luckhaus, S.: On explosions of solutions to a system on partial differential equations modelling chemotaxis. Trans. Am. Math. Soc. 329(2), 819–824 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. Karlin, S., Altschul, S.F.: Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes. Proc. Natl. Acad. Sci. USA 87, 2264–2268 (1990)

    Article  MATH  Google Scholar 

  12. Keller, E.F., Segel, L.A.: Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26(26), 399–415 (1970)

    Article  MATH  Google Scholar 

  13. Nanjundiah, V.: Chemotaxis, signal relaying and aggregation morphology. J. Theor. Biol. 42(1), 63–105 (1973)

    Article  Google Scholar 

  14. Schaaf, R.: Stationary solutions of chemotaxis systems. Trans. Am. Math. Soc. 292(2), 531–556 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  15. Turing, A.M.: The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond., Ser. B 237(641), 37–72 (1952)

    Article  MathSciNet  Google Scholar 

  16. Turing, A.M.: In: Saunders, P.T. (ed.) Collected Works of A.M. Turing: Morphogenesis. North Holland, Amsterdam (1992)

    Google Scholar 

  17. Wolansky, G.: On steady distributions of self-attracting clusters under friction and fluctuations. Arch. Ration. Mech. Anal. 119(4), 355–391 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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Stevens, A. Mathematics and the Life-Sciences: A Personal Point of View. Jahresber. Dtsch. Math. Ver. 119, 143–168 (2017). https://doi.org/10.1365/s13291-017-0165-6

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