Optimisations and evolution of the mammalian respiratory system

A suggestion of possible gene sharing in evolution
Regular Article
Part of the following topical collections:
  1. Physical constraints of morphogenesis and evolution

Abstract

The respiratory system of mammalians is made of two successive branched structures with different physiological functions. The upper structure, or bronchial tree, is a fluid transportation system made of approximately 15 generations of bifurcations leading to the order of about 215 = 30, 000 terminal bronchioles with a diameter of approximately 0.5mm in the human lung. The branching pattern continues up to generation 23 but the structure and function of each of the subsequent structures, called acini, is different. Each acinus consists in a branched system of ducts surrounded by alveoli and plays the role of a diffusion cell where oxygen and carbon dioxide are exchanged with blood across the alveolar membrane. We show here that the bronchial tree simultaneously presents several different optimal properties. It is first energy efficient, second, it is space filling and third it is also “rapid”. This physically based multi-optimality suggests that, in the course of evolution, an organ selected against one criterion could have been used later for a totally different purpose. For example, once selected for its energetic efficiency for the transport of a viscous fluid like blood, the same genetic material could have been used for its optimized rapidity. This would have allowed the emergence of atmospheric respiration made of inspiration-expiration cycles. For this phenomenon to exist, rapidity is essential as fresh air has to reach the gas exchange organs, the pulmonary acini, before the beginning of expiration. We finally show that the pulmonary acinus is optimized in the sense that the acinus morphology is directly related to the notion of a “best possible” extraction of entropic energy by a diffusion exchanger that has to feed oxygen efficiently from air to blood across a membrane of finite permeability.

Graphical abstract

Keywords

Topical issue: Physical constraints of morphogenesis and evolution 

References

  1. 1.
    T. Young, Philos. Trans. R. Soc. London 99, 1 (1809).CrossRefGoogle Scholar
  2. 2.
    W.R. Hess, Archiv. Anat. Physiol: Physiol. Abt. 1/2, 1 (1914).Google Scholar
  3. 3.
    C.D. Murray, Proc. Natl. Acad. Sci. U.S.A. 12, 207 (1926).ADSCrossRefGoogle Scholar
  4. 4.
    L.D. Cohn, Bull. Math. Biophys. 16, 59 (1954).CrossRefGoogle Scholar
  5. 5.
    T.F. Sherman, J. Gen. Physiol. 78, 431 (1981) and references therein.CrossRefGoogle Scholar
  6. 6.
    G.B. West, J.H. Brown, B.J. Enquist, Science 276, 122 (1997).CrossRefGoogle Scholar
  7. 7.
    A. Bejan, Shape and Structure, From Engineering to Nature (Cambridge University Press, 2000).Google Scholar
  8. 8.
    B. Mauroy, M. Filoche, E.R. Weibel, B. Sapoval, Nature 427, 633 (2004).ADSCrossRefGoogle Scholar
  9. 9.
    J.B. Grotberg, Annu. Rev. Biomed. Eng. 3, 421 (2001).CrossRefGoogle Scholar
  10. 10.
    B.B. Mandelbrot, The Fractal Geometry of Nature (W.H. Freeman and Co, 1982).Google Scholar
  11. 11.
    M. Bernot, V. Caselles, J.-M. Morel, Optimal Transportation Networks: Models and Theory (Springer, 2008).Google Scholar
  12. 12.
    M. Canals, F.F. Novoa, M.M. Rosenmann, Acta Biotheor. 52, 1 (2004).CrossRefGoogle Scholar
  13. 13.
    E.R. Weibel, Morphometry of the Human Lung (Springer Verlag and Academic Press, Heidelberg-New York, 1963).Google Scholar
  14. 14.
    E.R. Weibel, The Pathway for Oxygen (Harvard University Press, Cambridge, 1984).Google Scholar
  15. 15.
    A. Tsuda, J.J. Fredberg, J. Appl. Physiol. 69, 553 (1990).Google Scholar
  16. 16.
    J.S. Andrade jr. et al., Phys. Rev. Lett. 81, 926 (1998).ADSCrossRefGoogle Scholar
  17. 17.
    T.B. Martonen, X. Guan, R.M. Schreck, Inhal. Toxicol. 13, 261 (2001).CrossRefGoogle Scholar
  18. 18.
    J.K. Comer, C. Kleinstreuer, Z. Zhang, J. Fluid Mech. 435, 25 (2001).ADSMATHGoogle Scholar
  19. 19.
    B. Mauroy, M. Filoche, J.S. Andrade jr., B. Sapoval, Phys. Rev. Lett. 90, 148101 (2003).ADSCrossRefGoogle Scholar
  20. 20.
    M. Zamir, The Physics of Pulsatile Flow (Springer, New York, 2000).Google Scholar
  21. 21.
    M. Florens, B. Sapoval, M. Filoche, J. Appl. Physiol. 110, 756 (2011).CrossRefGoogle Scholar
  22. 22.
    K. Horsfield, G. Cumming, J. Appl. Physiol. 24, 373 (1968).Google Scholar
  23. 23.
    K. Horsfield, G. Dart, D.E. Olson, G.F. Filley, G. Cumming, J. Appl. Physiol. 31, 207 (1971).Google Scholar
  24. 24.
    A. Majumdar, A.M. Alencar, S.V. Buldyrev, Z. Hantos, K.R. Lutchen, H.E. Stanley, B. Suki, Phys. Rev. Lett. 95, 168101 (2005).ADSCrossRefGoogle Scholar
  25. 25.
    E.R. Weibel, The Lung: Scientific Foundations, Vol. 1, edited by R.G. Crystal, J.B. West, E.R. Weibel, P.J. Barnes, 2nd edition (Lippincott-Raven Publishers, Philadelphia, 1997) pp. 1061-1071.Google Scholar
  26. 26.
    K.A. McCulloh, J.S. Sperry, F.R. Adler, Nature 421, 939 (2003).ADSCrossRefGoogle Scholar
  27. 27.
    J. Feder, Fractals (Plenum Press, New York, 1988).Google Scholar
  28. 28.
    B. Sapoval, Universalités et Fractales (Flammarion, Paris, 1997).Google Scholar
  29. 29.
    M. Florens, B. Sapoval, M. Filoche, Phys. Rev. Lett. 106, 178104 (2011).ADSCrossRefGoogle Scholar
  30. 30.
    B. Sapoval, M. Filoche, Fund. Clin. Pharmacol. 26, 57 (2012).Google Scholar
  31. 31.
    J.B. West, O. Mathieu-Costello, Annu. Rev. Physiol. 61, 543 (1999).CrossRefGoogle Scholar
  32. 32.
    B. Sapoval, M. Filoche, E.R. Weibel, Proc. Natl. Acad. Sci. U.S.A. 99, 10411 (2002) and references therein.ADSCrossRefGoogle Scholar
  33. 33.
    B. Sapoval, Phys. Rev. Lett. 73, 3314 (1994).ADSCrossRefGoogle Scholar
  34. 34.
    B. Sapoval, M. Filoche, E.R. Weibel, Branching in Nature, edited by V. Fleury, J.F. Gouyet, M. Leonetti (EDP Sciences/Springer Verlag, 2001) pp. 225-242.Google Scholar
  35. 35.
    A. Beaumont, P. Cassier, Biologie Animale (Dunod Université, Paris, 1978).Google Scholar
  36. 36.
    F. Jacob, Science, New Series 196, 1161 (1977).ADSGoogle Scholar
  37. 37.
    H. Ashida, A. Danchin, A. Yokota, Res. Microbiol. 156, 611 (2005).CrossRefGoogle Scholar
  38. 38.
    J. Piatigorsky, J. Struct. Funct. Genomics. 3, 131 (2003).CrossRefGoogle Scholar
  39. 39.
    G. Reddy Bhanuprakash, P. Anil Kumar, M. Satish Kumar, Life 58, 632 (2006).Google Scholar
  40. 40.
    A. Danchin, The Delphic Boat (Harvard University Press, Cambridge, 2002).Google Scholar
  41. 41.
    J. Piatigorsky, Gene Sharing and Evolution (Harvard University Press, Cambridge, 2007).Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Physique de la Matière Condensée, Ecole PolytechniqueCNRSPalaiseauFrance
  2. 2.CMLA, ENS CachanCNRSCachanFrance

Personalised recommendations