Skip to main content
SpringerLink
Log in
Book cover

Advances in Biochemical Engineering, Volume 11 pp 49–83Cite as

Mass and energy balances for microbial growth kinetics

  • Conference paper
  • First Online:

Part of the book series: Advances in Biochemical Engineering ((ABE,volume 11))

Abstract

First, quantitative aspects on the problems of any sort of microbial growth are depicted starting from the most general term of growth yield, YX/S, followed by more meaningful parameters, i.e., growth yields based on total energy available in the medium, Ykcal and based on catabolic activity, Y X/C involved physicochemical features, and in addition growth yield based on ATP generation, YATP being connected with physiological features. Second, quantitative relationships with respect to stoichiometry, and mass and energy balances in the growth reactions are discussed to establish kinetic equations, including growth, substrate consumption, respiration, heat evolution and noncellular product formation applicable to process control in microbial cultivations.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Abbreviations

A:

amount of oxygen required for the combustion of substrate, mole · mole −1

B:

amount of oxygen required for the combustion of dry cell, mole · g− 1

C:

amount of oxygen required for the combustion of noncellular product, mole · mole−1

Cp :

concentration of noncellular product in culture medium, mole · 1 −1

D:

dilution rate, h−1

DO:

dissolved oxygen concentration in culture medium, mole · l−1

DO*:

saturation concentration of DO, mole · l−1

ΔHa :

heat of combustion of dry cells, kcal · g−1

ΔhC :

heat generation by catabolism, kcal · l−1

ΔHO :

heat generation based on oxygen consumed, kcal · mole− 1

ΔHP :

heat of combustion of noncellular product, kcal · mole−1

ΔHS :

heat of combustion of substrate, kcal · mole−1

\(I_{CO_2 }\) :

rate of carbon dioxide evolution, mole · 1−1 · h−1

\(I_{O_2 }\) :

rate of oxygen consumption, mole · l−1 · h−1

\(k_{L^a }\) :

volumetric oxygen-transfer coefficient, h−1

m:

maintenance coefficient for substrate, mole · g−1 · h−1

m′:

maintenance coefficient based on heat generation, kcal · g−1 · h−1

mA :

maintenance coefficient for ATP generation, mole · g−1 · h −1

mO :

maintenance coefficient for oxygen, mole · g−1 · h−1

P:

total pressure in gas phase, atm

Pc :

partial pressure of carbon dioxide in gas phase, atm

PO :

partial pressure of oxygen in gas phase, atm

PW :

partial pressure of water in gas phase, atm

QATP :

specific rate of ATP generation, mole · g−1 · h−1

\(Q_{CO_2 }\) :

specific rate of carbon dioxide evolution, mole · g−1 · h −1

\(Q_{O_2 }\) :

specific rate of oxygen uptake, mole · g−1 · h−1

Qp :

specific rate of noncellular product formation, mole · g−1 · h−1

RQ:

respiratory quotient = \({{I_{CO_2 } } \mathord{\left/{\vphantom {{I_{CO_2 } } {I_{O_2 } }}} \right.\kern-\nulldelimiterspace} {I_{O_2 } }}\), mole · mole−1

S:

substrate concentration in culture medium, mole · l−1

So :

substrate concentration in fresh medium, mole · l−1

t:

culture time, h

V:

culture volume, 1

X:

biomass concentration in culture medium, g · l−1

Yav e/S :

total electron available from substrate, av e · mole−1

Yav e :

growth yield based on electron available, g · av e−1

YATP :

growth yield based on ATP generation, g · mole−1

Y MAXATP :

maximum growth yield based on ATP generation, g · mole−1

YA/S :

ATP yield from substrate catabolized, mole · mole−1

YG :

true growth yield from substrate, g · mole−1

YGO :

true growth yield based on oxygen consumed, g · mole−1

Ykcal :

growth yield based on total energy available, g · kcal−1

YP/S :

noncellular-product yield from substrate, mole · mole−1

YX/C :

growth yield based on catabolic activity, g · kcal−1

YX/O :

growth yield based on oxygen consumed, g · mole−1

YX/S :

growth yield from substrate, g · mole−1

YW :

substrate catabolized for true biosynthesis, mole · g−1

α 1 :

carbon content of substrate, g · mole−1

α 2 :

carbon content of cells, g · g−1

α 3 :

carbon content of carbon dioxide, g · mole−1

α 4 :

carbon content of noncellular product, g · mole−1

μ:

specific growth rate, h−1

ν:

specific rate of substrate consumption, mole · g−1 · h− 1

7 References

  1. Aiba, S., Humphrey, A. E., Millis, N.: Biochem. Eng. 2nd Edit., University of Tokyo Press 1973

    Google Scholar 

  2. Blanch, H. W., Dunn, I. J.: In: Adv. Biochem. Eng., Ghose, T. K., Fiechter, A., Blakebrough, N. (Eds.), Vol. 3, p. 127. Springer-Verlag 1974

    Google Scholar 

  3. Nyiii, L. K.: In: Adv. Biochem. Eng., Ghose, T. K., Fiechter, A., Blakebrough, N. (Eds.), Vol. 2, p. 49. Springer-Verlag 1972

    Google Scholar 

  4. Calam, C. T, Ellis, S. H., McCann, M. J.: J. Appl. Chem. Biotechnol. 21, 181 (1971)

    Google Scholar 

  5. Gyllenberg, H. G., Koskenniemi, E., Rauramaa, V.: Biotech. Bioeng. 11, 757 (1969)

    Article  Google Scholar 

  6. Yamashita, S., Hoshi, H., Inagaki, T.: In: Fermentation Adv., Perlman, D. (Ed.), p. 441. Academic Press 1969

    Google Scholar 

  7. Constantinides, A., Spencer, J. L., Gaden, E. L. Jr.: Biotech. Bioeng. 12, 803, 1081 (1970)

    Article  Google Scholar 

  8. Ramkrishna, D., Fredrikson, A. G., Tsuchiya, H. M.: Biotech. Bioeng. 9, 129 (1967)

    Article  Google Scholar 

  9. Kono, T., Asai, T.: Biotech. Bioeng. 11, 293 (1969)

    Article  Google Scholar 

  10. Luedeking, R., Piiet, E. L.: J. Biochem. Microbiol. Technol. Eng. 1, 393 (1959)

    Article  Google Scholar 

  11. Nagai, S., Nishizawa, Y., Aiba, S.: J. Gen. Appl. Microbiol. 19, 221 (1973)

    Google Scholar 

  12. Shoda, M., Nagai, S., Aiba, S.: J. Appl. Chem. Biotech. 25, 305 (1975)

    Google Scholar 

  13. Koga, S., Kagami, I., Kao, I. C: In: Fermentation Adv., Perlman, D. (Ed.), p. 369. Academic Press 1969

    Google Scholar 

  14. Imanaka, T., Kaieda, T., Sato, K., Taguchi, H.: J. Ferment. Technol. 50, 633 (1972)

    Google Scholar 

  15. Imanaka, T, Aiba, S.: Biotech. Bioeng. 19, 757 (1977)

    Article  Google Scholar 

  16. Monod, J.: Recherches sur la Croissance des Cultures Bacteriennes. Hermann et Cie., Paris 1942

    Google Scholar 

  17. DeMoss, R. D., Bard, R. C, Gunsalus, I. C: J. Bacteriol. 62, 499 (1951)

    PubMed  Google Scholar 

  18. Bauchop, T., Elsden, S. R.: J. Gen. Microbiol. 23, 457 (1960)

    PubMed  Google Scholar 

  19. Pirt, S. J.: Principles of Microbe and Cell Cultivation. Blackwell Scientific Publications, p. 64 1975

    Google Scholar 

  20. Mayberry, W. R., Prochazka, G. J., Payne, W. J.: Appl. Microbiol. 15, 1332 (1967)

    Google Scholar 

  21. Pirt, S. J., Callow, D. S.: J. Appl. Bacteriol. 23, 87 (1960)

    Google Scholar 

  22. Johnson, M. J.: Science. 155, 1515 (1967)

    PubMed  Google Scholar 

  23. Payne, W. J.: Ann. Rev. Microbiol. 24, 17 (1970)

    Article  Google Scholar 

  24. Nagai, S., Nishizawa, Y., Doin, P. A., Aiba, S.: J. Gen. Appl. Microbiol. 18, 201 (1972)

    Google Scholar 

  25. Hadjipetrou, L. P., Gerrits, J. P., Teulings, F. A. C, Stouthamer, A. H.: J. Gen. Microbiol. 36, 139(1964)

    Google Scholar 

  26. Hernadez, E., Johnson, M. J.: J. Bacteriol. 94, 996 (1967)

    PubMed  Google Scholar 

  27. Nishizawa, Y., Nagai, S., Aiba, S.: J. Ferment. Technol. 52, 526 (1974)

    Google Scholar 

  28. von Meyenberg, H. K.: Arch. Microbiol. 66, 289 (1969)

    Google Scholar 

  29. Nishio, N., Tsuchiya, Y., Hayashi, M., Nagai, S.: J. Ferment. Technol. 55, 151 (1977)

    Google Scholar 

  30. Dostalek, M., Molin, N.: In: Single-Cell Protein II. Tannenbaum, S. R., Wang, D. I. C. (Eds.), p. 385. The MIT Press 1975

    Google Scholar 

  31. Harrison, D. E. F., Topiwala, H. H., Hamer, G.: In: Fermentation Technology Today. Terui, G. (Ed.), p. 491. Society of Fermentation Technology, Japan 1972

    Google Scholar 

  32. Harwood, J. H., Pirt, S. J.: J. Appl. Bacteriol. 35, 597 (1972)

    PubMed  Google Scholar 

  33. Nagai, S., Mori, T, Aiba, S.: J. Appl. Chem. Biotechnol. 23, 549 (1973)

    Google Scholar 

  34. Dawes, E. A., Ribbons, D. W., Rees, D. A.: Biochem. J. 98, 804 (1966)

    PubMed  Google Scholar 

  35. Okunuki, K.: Fermentation Chemistry. Kyoritsu Shuppan Co., Tokyo 1951

    Google Scholar 

  36. Experimental Chemistry-Handbook. Kyoritsu Shuppan Co., Tokyo 1975

    Google Scholar 

  37. Mickelson, M. N.: J. Bacteriol. 109, 96 (1972)

    PubMed  Google Scholar 

  38. Minkevich, I. G., Eroshin, V. K.: Folia Microbiol. 18, 376 (1973)

    Google Scholar 

  39. Gunsalus, I. C, Shuster, C. W.: In: The Bacteria. Gunsalus, I. C, Stanier, R. Y. (Eds.). Vol. II Metabolism, p. 46. Academic Press 1961

    Google Scholar 

  40. de Vries, W., Kapteijn, W. M. C, van der Beek, E. G., Stouthamer, A. H.: J. Gen. Microbiol. 63, 333 (1970)

    PubMed  Google Scholar 

  41. Stouthamer, A. H.: Biochim. Biophys. AcU 56, 19 (1962)

    Article  Google Scholar 

  42. Mickelson, M. N.: J. Bacteriol. 100, 895 (1969)

    PubMed  Google Scholar 

  43. Stouthamer, A. H.: In: Methods in Microbiology. Norris, J. R., Ribbons, D. W. (Eds.). Vol. 1, p. 629. Academic Press, 1969

    Google Scholar 

  44. Smalley, A. J., Jahrling, P., van Demark, P. J.: J. Bacteriol. 96, 1595 (1968)

    PubMed  Google Scholar 

  45. Stouthamer, A. H., Bettenhaussen, C. W.: Biochim. Biophys. Acta. 301, 53 (1973)

    PubMed  Google Scholar 

  46. Rogers, P. J., Stewart, P. R.: Arch. Microbiol. 99, 25 (1974)

    Article  PubMed  Google Scholar 

  47. Stouthamer, A. H., Bettenhaussen, C. W.: Arch. Microbiol. 102, 187 (1975)

    Article  PubMed  Google Scholar 

  48. Hadjipetrou, L. P., Stouthamer, A. H.: J. Gen. Microbiol. 38, 29 (1965)

    PubMed  Google Scholar 

  49. Hernandez, E., Johnson, M. J.: J. Bacteriol. 94, 991 (1967)

    PubMed  Google Scholar 

  50. Buchanan, B. B., Pine, L.: J. Gen. Microbiol. 46, 225 (1967)

    PubMed  Google Scholar 

  51. de Vries, W., Stouthamer, A. H.: J. Bacteriol. 96, 472 (1968)

    PubMed  Google Scholar 

  52. Twarog, R., Wolfe, R. S.: J. Bacteriol. 86, 112 (1963)

    PubMed  Google Scholar 

  53. Ljungdahl, L. G., Wood, H. G.: Ann. Rev. Microbiol. 23, 515 (1969)

    Article  Google Scholar 

  54. Senez, J. C: Bacteriol. Rev. 26, 95 (1962)

    PubMed  Google Scholar 

  55. Oxenburgh, M. S., SnosweU, A. M.: J. Bacteriol. 89, 913 (1965)

    PubMed  Google Scholar 

  56. Belaich, J. P., Senez, J. C: J. Bacteriol. 89, 1195 (1965)

    PubMed  Google Scholar 

  57. Belaich, J. P., Belaich, A., Simonpietri, P.: J. Gen. Microbiol. 70, 179 (1972)

    Google Scholar 

  58. Lazdunski, A., Belaich, J. P.: J. Gen. Microbiol. 70, 187 (1972)

    Google Scholar 

  59. Nagai, S., Aiba, S.: J. Gen. Microbiol. 73, 531 (1972)

    PubMed  Google Scholar 

  60. Cooney, C. L., Wang, H. Y., Wang, D. I. C: Biotech. Bioeng. 19, 55 (1977)

    Article  Google Scholar 

  61. Wang, H. Y., Cooney, C. L., Wang, D. I. C: Biotech. Bioeng. 19, 69 (1977)

    Article  Google Scholar 

  62. Mor, J. R., Fiechter, A.: Biotech. Bioeng. 10, 159 (1968)

    Article  Google Scholar 

  63. Johnson, M. J.: Chem. Ind. Sept. 1532 (1964)

    Google Scholar 

  64. Pirt, S. J.: Proc. Roy. Soc. B. 163, 224 (1965)

    Google Scholar 

  65. Herbert, D.: Symp. International Congress of Microbiology, No. 6, 381 (1958)

    Google Scholar 

  66. Schultze, K. L., Lipe, R. S.: Arch. Microbiol. 48, 1 (1964)

    Google Scholar 

  67. van Uden, N.: Arch. Microbiol. 62, 34 (1968)

    Google Scholar 

  68. Battley, E. H.: Physiol. Plant. 13, 628 (1960)

    Google Scholar 

  69. Shibasaki, I.: Doctor Thesis. Faculty of Engineering, Osaka University, Japan (1959)

    Google Scholar 

  70. Terui, G., Shibasaki, I., Mochizuki, T.: J. Ferment. Technol. 37, 479 (1959)

    Google Scholar 

  71. Guenther, K. R.: Biotech. Bioeng. 7, 445 (1965)

    Article  Google Scholar 

  72. Wang, D. I. C: Chem. Eng. Aug. 26, 99 (1968)

    Google Scholar 

  73. Cooney, C. L., Wang, D. I. C, Mateles, R. I.: Biotech. Bioeng. 11, 269 (1968)

    Article  Google Scholar 

  74. Imanaka, T., Aiba, S.: J. Appl. Chem. Biotechnol. 26, 559 (1976)

    Google Scholar 

  75. Nagai, S.: The 5th International Conference. Global Impacts of Appl. Microbiology (GIAM), Bangkok 1977

    Google Scholar 

  76. Nakamura, Y., Yamada, S.: J. Soc. Brewing, Japan. 52, 582 (1957)

    Google Scholar 

  77. Aiba, S., Nagai, S., Nishizawa, Y.: Biotech. Bioeng. 18, 1001 (1976)

    Article  Google Scholar 

  78. Hobson, P. N., Summers, R.: J. Gen. Microbiol. 47, 53 (1967)

    PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Fermentation Technology, Faculty of Engineering, Hiroshima University, Hiroshima, Japan

    S. Nagai

Authors
  1. S. Nagai
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag

About this paper

Cite this paper

Nagai, S. (1979). Mass and energy balances for microbial growth kinetics. In: Advances in Biochemical Engineering, Volume 11. Advances in Biochemical Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08990-X_22

Download citation

  • DOI: https://doi.org/10.1007/3-540-08990-X_22

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08990-2

  • Online ISBN: 978-3-540-35678-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation