A theoretical and empirical investigation of delayed growth response in the continuous culture of bacteria

Journal of Theoretical Biology

Volumn 222, Issue 4, 2003, Pages 485-494

  Ellermeyer, Sean ^a   Hendrix, Jerald ^a   Ghoochan, Nariman ^a  

^a KENNESAW STATE UNIVERSITY   (United States)

Author keywords

Chemostat; Continuous culture; Delayed growth response; Microbial growth

Indexed keywords

GLUCOSE;

BACTERIUM; CHEMOSTAT; GROWTH; MICROBIOLOGY; NUTRIENT LIMITATION;

ARTICLE; BACTERIAL GROWTH; BACTERIAL STRAIN; BACTERIUM CULTURE; CHEMOSTAT; COMPARATIVE STUDY; CONCENTRATION (PARAMETERS); CONTINUOUS CULTURE; DATA ANALYSIS; EMPIRICISM; ESCHERICHIA COLI; EXPERIMENTAL MODEL; GROWTH RATE; GROWTH REGULATION; GROWTH RETARDATION; MEASUREMENT; NONHUMAN; NUTRIENT LIMITATION; NUTRIENT SUPPLY; PARAMETER; PREDICTION; PRIORITY JOURNAL; SPECIES EXTINCTION; STEADY STATE; THEORETICAL MODEL; THEORY;

BACTERIA (MICROORGANISMS); ESCHERICHIA COLI;

EID: 0038778266     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5193(03)00063-8     Document Type: Article

References (20)

1. Bush A.W., Cook A.E. The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater. J. theor. Biol. 63:1975;385-396.
2. Butler G.J., Wolkowicz G.S.K. A mathematical model of the chemostat with a general class of functions describing nutrient uptake. SIAM J. Appl. Math. 45:1985;138-151.
3. Caperon J. Time lag in population growth response of Isochrysis galbana to a variable nitrate environment. Ecology. 50:1969;188-192.
4. Cooke K.L., Yorke J.A. Some equations modelling growth processes and gonorrhea epidemics. Math. Biosci. 16:1973;75-101.
5. Ellermeyer S.F. Competition in the chemostat. asymptotic behavior of a model with delayed response in growth SIAM J. Appl. Math. 54:1994;456-465.
6. Gyllenberg M. Does time lag of nutrient utilization justify Monod's model of bacterial growth? Bull. Math. Biol. 55:1993;487-489.
7. Hansen S.R., Hubbell S.P. Single-nutrient microbial competition. qualitative agreement between experimental and theoretically forecast outcomes Science. 207:1980;1491-1493.
8. Herbert D., Elsworth R., Telling R.C. The continuous culture of bacteria. a theoretical and experimental study J. Gen. Microbiol. 14:1956;601-622.
9. Hsu S.B., Hubbell S., Waltman P. A mathematical theory for single-nutrient competition in continuous cultures of microorganisms. SIAM J. Appl. Math. 32:1977;366-383.
10. Kunnst, A., Draeger, B., Ziegenhorn, J., 1984. In: Bergmeyer, H.U. (Ed.), Methods of Enzymatic Analysis, 3rd Edition, Vol. 2, Academic Press, New York, pp. 163-172.
11. MacDonald N. Time delays in chemostat models. Bazin M.J. Microbial Population Dynamics. 1982;33-53 CRC Press, Boca Raton.
12. Makay, G., 1994. DifEqu - Differential Equation Presentation V.1.1.
13. Monod J. La technique de culture continue; theorie et applications. Ann. Inst. Pasteur. 79:1950;390-410.
14. Novick A., Szilard L. Description of the chemostat. Science. 112:1950;715-716.
15. Pirt S.J. The dynamics of microbial processes: a personal view. Poole R.K., Bazin M.J., Keevil W. Microbial Growth Dynamics. 1990;1-16 IRL Press, Oxford.
16. Smith H.L., Waltman P. The Theory of the Chemostat: Dynamics of Microbial Competition. 1995;Cambridge University Press, Cambridge, UK.
17. Thingstad T.F., Langeland T.I. Dynamics of chemostat culture. the effect of a delay in cell response J. theor. Biol. 48:1974;149-159.
18. Wolkowicz G.S.K., Xia H. Global asymptotic behavior of a chemostat model with discrete delays. SIAM J. Appl. Math. 57:1997;1019-1043.
19. Wolkowicz G.S.K., Xia H., Ruan S. Competition in the chemostat. a distributed delay model and its global asymptotic behavior SIAM J. Appl. Math. 57:1997;1281-1310.
20. Wolkowicz G.S.K., Xia H., Wu J. Global dynamics of a chemostat competition model with distributed delay. J. Math. Biol. 38:1999;285-316.