Modelling conjugation with stochastic differential equations

Journal of Theoretical Biology

Volumn 263, Issue 1, 2010, Pages 134-142

  Philipsen, K R ^a   Christiansen, L E ^a   Hasman, H ^a   Madsen, H ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

AIC; CTSM; Enterococcus faecium; Hidden Markov model; Horizontal gene transfer; Likelihood ratio test; Mathematical modelling; Resistance; SDE

Indexed keywords

AGAR;

BACTERIUM; GENE TRANSFER; MARKOV CHAIN; MAXIMUM LIKELIHOOD ANALYSIS; NUMERICAL MODEL; STOCHASTICITY;

ARTICLE; BACTERIAL STRAIN; BACTERIUM CONJUGATION; BACTERIUM CULTURE; CONTROLLED STUDY; CULTURE MEDIUM; ENTEROCOCCUS FAECIUM; HIDDEN MARKOV MODEL; HORIZONTAL GENE TRANSFER; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MAXIMUM LIKELIHOOD METHOD; NONHUMAN; PRIORITY JOURNAL; SIGNAL NOISE RATIO; STOCHASTIC MODEL;

AGAR; ALGORITHMS; CONJUGATION, GENETIC; DRUG RESISTANCE, BACTERIAL; ENTEROCOCCUS FAECALIS; GENETIC TECHNIQUES; HUMANS; LIKELIHOOD FUNCTIONS; MARKOV CHAINS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MODELS, THEORETICAL; STOCHASTIC PROCESSES; TIME FACTORS;

ENTEROCOCCUS FAECIUM;

EID: 77649341401     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2009.11.011     Document Type: Article

References (26)

1. Andrup L., Andersen K. A comparison of the kinetics of plasmid transfer in the conjugation systems encoded by the f plasmid from Escherichia coli and plasmid pcf10 from Enterococcus faecalis. Microbiology 1999, 145(8):2001-2009.
2. Andrup L., Smidt L., Andersen K., Boe L. Kinetics of conjugative transfer: a study of the plasmid pxo16 from Bacillus thuringiensis subsp. israelensis. Plasmid 1998, 40(1):30-43.
3. Clewlow L.J., Cresswell N., Wellington E.M.H. Mathematical model of plasmid transfer between strains of streptomycetes in soil microcosms. Appl. Environ. Microbiol. 1990, 56(10):3139-3145.
4. De Gelder L., Ponciano J.M., Abdo Z., Joyce P., Forney L.J., Top E.M. Combining mathematical models and statistical methods to understand and predict the dynamics of antibiotic-sensitive mutants in a population of resistant bacteria during experimental evolution. Genetics 2004, 168(3):1131-1144.
5. De Gelder L., Ponciano J.M., Joyce P., Top E.M. Stability of a promiscuous plasmid in different hosts: no guarantee for a long-term relationship. Microbiology (Reading, Engl.) 2007, 153(Part 2):452-463.
6. Dennis B., Ponciano J.M., Lele S.R. Estimating density dependence, process noise, and observation error. Ecol. Monogr. 2006, 76(3):323.
7. Freter R., Freter R.R., Brickner H. Experimental and mathematical models of Escherichia coli plasmid transfer in vitro and in vivo. Infect. Immun. 1983, 39(1):60-84.
8. Hasman H., Aarestrup F.M. Mechanisms of resistance-tcrB, a gene conferring transferable copper resistance in Enterococcus faecium: occurrence, transferability, and linkage to macrolide and glycopeptide resistance. Antimicrob. Agents Chemother. 2002, 46(5):1410.
9. Higham D.J. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 2001, 43(3):525-546.
10. Ionides E.L., Bretó C., King A.A. Inference for nonlinear dynamical systems. Proc. Natl. Acad. Sci. USA 2006, 103(49):18438-18443.
11. Joyce P., Abdo Z., Ponciano J.M., Gelder L.D., Forney L.J., Top E.M. Modeling the impact of periodic bottlenecks, unidirectional mutation, and observational error in experimental evolution. J. Math. Biol. 2005, 50(6):645-662.
12. King A.A., Ionides E.L., Pascual M., Bouma M.J. Inapparent infections and cholera dynamics. Nature 2008, 454(7206):877-880.
13. Klim S., Mortensen S., Kristensen N., Overgaard R., Madsen H. Population stochastic modelling (psm)-an R package for mixed-effects models based on stochastic differential equations. Comput. Methods Programs Biomed. 2009, 94(3):279-289.
14. Knudsen G.R., Walter M.V., Porteous L.A., Prince V.J., Armstrong J.L., Seidler R.J. Predictive model of conjugative plasmid transfer in the rhizosphere and phyllosphere. Appl. Environ. Microbiol. 1988, 54(2):343-347.
15. Kristensen N.R., Madsen H., Jørgensen S.B. A method for systematic improvement of stochastic grey-box models. Comput. Chem. Eng. 2004, 28:1431-1449.
16. Kristensen N.R., Madsen H., Jørgensen S.B. Parameter estimation in stochastic gray-box models. Automatica 2004, 40(40):225-237.
17. Levin B.R., Stewart F.M., Rice V.A. The kinetics of conjugative plasmid transmission: fit of a simple mass action model. Plasmid 1979, 2(2):247-260.
18. Levin B.R., Stewart F.M. The population biology of bacterial plasmids: a priori conditions for the existence of mobilizable nonconjugative factors. Genetics 1980, 94(2):425-443.
19. MacDonald J.A., Smets B.F., Rittmann B.E. Effects of energy availability on the conjugative-transfer kinetics of plasmid rp4. Water Res. 1992, 26(4):461-468.
20. Monod J. The growth of bacterial cultures. Annu. Rev. Microbiol. 1949, 3:371-394.
21. Ponciano J.M., Gelder L.D., Top E.M., Joyce P. The population biology of bacterial plasmids: a hidden Markov model approach. Genetics 2007, 176(2):957.
22. Slater F.R., Bailey M.J., Tett A.J., Turner S.L. Progress towards understanding the fate of plasmids in bacterial communities. FEMS Microbiol. Ecol. 2008, 66(1):3-13.
23. Sudarshana P., Knudsen G.R. Quantification and modeling of plasmid mobilization on seeds and roots. Curr. Microbiol. 2006, 52(6):455-459.
24. Tier C., Floyd H. Persistence in density dependent stochastic populations. Math. Biosci. 1981, 53:89-117.
25. Top E., Vanrolleghem P., Mergeay M., Verstraete W. Determination of the mechanism of retrotransfer by mechanistic mathematical modeling. J. Bacteriol. 1992, 174(18):5953-5960.
26. Willms A., Roughan P., Heinemann J. Static recipient cells as reservoirs of antibiotic resistance during antibiotic therapy. Theor. Popul. Biol. 2006, 70(4):436-451.