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Mathematical and statistical analysis of the Trypanosoma brucei slender to stumpy transition

Published online by Cambridge University Press:  19 January 2004

N. J. SAVILL  and
J. R. SEED
N. J. SAVILL
Affiliation:
Department of Zoology, Cambridge University, Downing Street, Cambridge CB2 3EJ, UK
J. R. SEED
Affiliation:
Department of Epidemiology, School of Public Health, University of North Carolina, Chapel Hill, North Carolina 27599–7435, USA
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Abstract

We propose a new model for the Stumpy Induction Factor-induced slender to stumpy transformation of Trypanosoma brucei gambiense cells in immunosuppressed mice. The model is a set of delay differential equations that describe the time-course of the infection. We fit the model, using a maximum-likelihood method, to previously published data on parasitaemia in four mice. The model is shown to be a good fit and parameter estimates and confidence intervals are derived. Our estimated parameter values are consistent with estimates from previous experimental studies. The model predicts the following. Slender cells can be classified as uncommitted, committed and dividing, and committed and non-dividing. A committed slender cell undergoes about 5 divisions before exiting the cell-cycle. Committed slender cells must produce SIF, and stumpy cells must not produce SIF. There are two mechanisms for differentiation, a background differentiation rate, and a SIF-concentration-dependent differentiation rate, which is proportional to SIF concentration. SIF has a half-life of about 1·4 h in mice. We also show, with suitable changes in the parameter values, that the model reflects behaviours seen in other host species and trypanosome strains.

Keywords

SIFdifferentiationdelay differential equation
Type
Research Article
Information
Parasitology , Volume 128 , Issue 1 , January 2004 , pp. 53 - 67
Copyright
2004 Cambridge University Press

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References

REFERENCES

BARRY, J. D. & TURNER, C. M. R. (1991). The dynamics of antigenic variation and growth of African Trypanosomes. Parasitology Today 7, 207–211.CrossRefGoogle Scholar
BLACK, S. J., HEWETT, R. S. & SENDASHONGA, C. N. (1982). Trypanosoma brucei variable surface antigen is released by degenerating parasites but not by actively dividing parasites. Parasite Immunology 4, 233–244.CrossRefGoogle Scholar
BLACK, S. J., SENDASHONGA, C. N., O'BRIAN, C., BOROWY, N. K., NAESSENS, M., WEBSTER, P. & MURRAY, M. (1985). Regulation of parasitemia in mice infected with Trypanosoma brucei. Current Topics in Microbiology and Immunology 117, 93–118.Google Scholar
HESSE, F., SELZER, P. M., MÜHLSTÄDT, K. & DUSZENKO, M. (1995). A novel cultivation technique for long-term maintenance of bloodstream form trypanosomes in vitro. Molecular and Biochemical Parasitology 70, 157–166.CrossRefGoogle Scholar
PRESS, W. H., TEUKOLSKY, S. A., VETTERLING, W. T. & FLANNERY, B. P. (1992). Numerical Recipies in C: The Art of Scientific Computing, 2nd Edn. Cambridge University Press, Cambridge.
REUNER, B., VASSELLA, E., YUTZY, B. & BOSHART, M. (1997). Cell density triggers to stumpy differentiation of Trypanosoma brucei bloodstream forms in culture. Molecular and Biochemical Parasitology 90, 269–280.CrossRefGoogle Scholar
SEED, J. R. & BLACK, S. J. (1997). A proposed density-dependent model of long slender to short stumpy transformation in the African trypanosomes. Journal of Parasitology 83, 656–662.CrossRefGoogle Scholar
SEED, J. R. & BLACK, S. J. (1999). A revised arithmetic model of long slender to short stumpy transformation in the African trypanosomes. Journal of Parasitology 85, 850–854.CrossRefGoogle Scholar
SEED, J. R. & SECHELSKI, J. B. (1988). Growth of pleomorphic Trypanosoma brucei rhodesiense in irradiated inbred mice. Journal of Parasitology 74, 781–789.CrossRefGoogle Scholar
SEED, J. R. & SECHELSKI, J. B. (1989 a). African trypanosomes: Inheritance of factors in resistance to the African trypanosomes. Experimental Parasitology 69, 1–8.Google Scholar
SEED, J. R. & SECHELSKI, J. B. (1989 b). Mechanism of long slender (LS) to short stumpy (SS) transformation in the African trypanosomes. Journal of Protozoology 36, 572–577.Google Scholar
SQUIRES, G. L. (1985). Practical Physics, 3rd Edn. Cambridge University Press, Cambridge.
TURNER, C. M. R., ASLAM, N. & DYE, C. (1995). Replication, differentiation, growth and the virulence of Trypanosoma brucei infections. Parasitology 111, 289–300.CrossRefGoogle Scholar
TYLER, K. M., HIGGS, P. G., MATTHEWS, K. R. & GULL, K. (2001). Limitation of Trypanosoma brucei parasitemia results from density-dependent parasite differentiation and parasite killing by the host immune response. Proceedings of the Royal Society London, B 268, 2235–2243.CrossRefGoogle Scholar
TYLER, K. M., MATTHEWS, K. R. & GULL, K. (1997). The bloodstream differentiation-division of Trypanosoma brucei studied using mitochondrial markers. Proceedings of the Royal Society London, B 264, 1481–1490.CrossRefGoogle Scholar
VASSELLA, E., REUNER, B., YUTZY, B. & BOSHART, M. (1997). Differentiation of African trypanosomes is controlled by a density sensing mechanism which signals cell cycle arrest via the cAMP pathway. Journal of Cell Science 110, 2661–2671.Google Scholar