Population Dynamics Approach for the Study of Synergetic Coupling between Antibiotic and Helper Compounds

Christian T. Veje, Morten Willatzen, Oliver Hendricks, Jean-Marie Pagès, Jette Kristiansen

Aix-Marseille University, UMR-MD-1, IRBA, Marseille, France.
Department of Research, King Christian X’s Rheumatism Hospital, University of Southern Denmark, Odense, Denmark.
Institute of Physics and Chemistry, University of Southern Denmark, Denmark.
Mads Clausen Institute, University of Southern Denmark, S?nderborg, Denmark.

DOI: 10.4236/cmb.2012.21001                

Abstract

Non-antibiotics affect bacterial susceptibility towards antibiotics in a multifactorial manner, including perturbation of membrane energetic and a possibly direct interaction with drug efflux transporters themselves. Thus, efflux inhibiting compounds affect susceptibilities to antibiotics that act either intracellular or at the bacterial wall. Therefore they may be applied as helper compounds to conventional antibiotic treatments. A valid definition of the effect of these compounds is crucial. Conventional microbiological quotations such as checkerboard or MIC definition do not discriminate the complexity of a system where several compounds interact with several targets both on the bacterial membrane and soma. We presume the fact, that certain resistance mechanisms, such as efflux, are neither adequately nor precisely monitored, utilizing the established microbiologic screening tools, such as agar- or microdilution techniques. In this context this paper may contribute as an innovative step, utilizing mathematic modeling in order to describe interactions on the surface of microorganisms. Thus, mathematical modeling might be a tool which can be adopted to optimize the description of certain forms of bacterial resistance, as well as the influence of antibacterial drugs on such targets which interact with bacterial outer-membrane transport mechanisms. This paper presents modeling of bacterial population dynamics as an attempt to precise complex compound target interaction. Furthermore, the importance of a synergetic coupling term in the model is exemplified by comparison with experimental data of Kumar et al. [1]. A specific procedure for extraction of model coefficients is devised for further experimental studies of the coupling between an antibiotics and a helper compound. In particular, it is found that the scarce experimental data of Kumar et al. [1] can be fitted to the mathematical model demonstrating synergetic effects of non-antibiotics.

Keywords

Reversal of Resistance; Non-Antibiotic; Mathematical Model

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. K. Kumar, K. Mazumdar, N. K. Dutta, P. Karak, S. G. Dastidar and R. Ray, “Evaluation of Synergism between the Aminoglycoside Antibiotic Streptomycin and the Cardiovascular Agent Amlodipine,” Biological and Pharmaceutical Bulletin, Vol. 27, No. 7, 2004, pp. 1116-1120. doi:10.1248/bpb.27.1116
[2]	D. A. Stopher, A. P. Beresford, P. V. Macrae and M. J. Humphrey, “The Metabolism and Pharmacokinetics of Amlopidine in Humans and Animals,” Journal of Cardiovascular Pharmacology, Vol. 12, Suppl. 7, 1988, pp. 55-59. doi:10.1097/00005344-198812007-00012
[3]	W. R. Byrne, S. L. Welkos, M. L. Pitt, K. J. Davis, R. P. Brueckner, J. W. Ezzell, G. O. Nelson, J. R. Vaccaro, L. C. Battersby and A. M. Friedlander, “Antibiotic Treatment of Experimental Pneumonic Plague in Mice,” Antimicrobial Agents and Chemotherapy, Vol. 42, No. 3, 1998, pp. 675-681.
[4]	S. Blot, P. Depuydt, K. Vandewoude and D. De Bacquer, “Measuring the Impact of Multidrug Resistance in Nosocomial Infection,” Current Opinion in Infectious Diseases, Vol. 20, No. 4, 2007, pp. 391-396. doi:10.1097/QCO.0b013e32818be6f7
[5]	I. Chopra, C. Schofield, M. Everett, A. O’Neill, K. Miller, M. Wilcox, J. M. Frère, M. Dawson, L. Czaplewski, U. Urleb and P. Courvalin, “Treatment of Health-Care-Associated Infections Caused by Gram-Negative Bacteria: A Consensus Statement,” The Lancet Infectious Diseases, Vol. 8, No. 2, 2008, pp. 133-139. doi:10.1016/S1473-3099(08)70018-5
[6]	M. E. Falagas and I. A. Bliziotis, “Pandrug-Resistant Pandrug-Resistant Gram-Negative Bacteria: The Dawn of the Post-Antibiotic Era?” International Journal of Antimicrobial Agents, Vol. 29, No. 6, 2007, pp. 630-636. doi:10.1016/j.ijantimicag.2006.12.012
[7]	A. Davin-Regli, J. M. Bolla, C. E. James, J. P. Lavigne, J. Chevalier, E. Garnotel, A. Molitor and J.-M. Pagès, “Membrane Permeability and Regulation of Drug ‘Influx and Efflux’ in Enterobacterial Pathogens,” Current Drug Targets, Vol. 9, No. 9, 2008, pp. 750-759. doi:10.2174/138945008785747824
[8]	M. Lipsitch and B. R. Levin, “The Population Dynamics of Antimicrobial Chemotherapy,” Antimicrobial Agents and Chemotherapy, Vol. 41, No. 2, 1997, pp. 363-373.
[9]	A. Handel, E. Margolis and B. R. Levin, “Exploring the Role of the Immune Response in Preventing Antibiotic Resistance,” Journal of Theoretical Biology, Vol. 256, No. 4, 2009, pp. 655-662. doi:10.1016/j.jtbi.2008.10.025
[10]	J. M. Pagès and L. Amaral, “Mechanisms of Drug Efflux and Strategies to Combat Them: Challenging the Efflux Pump of Gram-Negative Bacteria,” Biochimica et Biophysica Acta, Vol. 1794, No. 5, 2009, pp. 826-833.
[11]	K. I. Udekwu, N. Parrish, P. Ankomah, F. Baquero and B. R. Levin, “Functional Relationship between Bacterial Cell Density and the Efficacy of Antibiotics,” Journal of Antimicrobial Chemotherapy, Vol. 63, No. 4, 2009, pp. 745-757. doi:10.1093/jac/dkn554
[12]	J. J. Campion, P. J. McNamara and M. E. Evans, “Pharmacodynamic Modeling of Ciprofloxacin Resistance in Staphylococcus Aureus,” Antimicrobial Agents and Chemotherapy, Vol. 49, No. 1, 2005, pp. 209-219. doi:10.1128/AAC.49.1.209-219.2005
[13]	P. Chung, P. J. McNamara, J. J. Campion and M. E. Evans, “Mechanism-Based Pharmacodynamic Models of Fluoroquinolone Resistance in Staphylococcus aureus,” Antimicrobial Agents and Chemotherapy, Vol. 50, No. 9, 2006, pp. 2957-2965. doi:10.1128/AAC.00736-05
[14]	J. E. Kristiansen, “Antimicrobial Activity of Non-Antibiotics,” ASM News, Vol. 57, 1991, p. 135.
[15]	J. E. Kristiansen, “Chlorpromazine Non-Antibiotics with Antimicrobial Activity-New Insight in Managing Resistance?” Current Opinion in Investigational Drugs, Vol. 2, 1993, pp. 587-591.
[16]	J. E. Kristiansen and L. Amaral, “The Potential Management of Resistant Infections with Non-Antibiotics,” Journal of Antimicrobial Chemotherapy, Vol. 40, No. 3, 1997, pp. 319-327. doi:10.1093/jac/40.3.319
[17]	J. E. Kristiansen, O. Hendricks, T. Delvin, T. S. Butterworth, L. Aagaard, J. B. Christensen, V. C. Flores and H. Keyzer, “Reversal of Resistance in Microorganisms by Help of Non-Antibiotic,” Journal of Antimicrobial Chemotherapy; Vol. 59, No. 6, 2007, pp. 1271-1279. doi:10.1093/jac/dkm071
[18]	G. W. Kaatz, V. V. Moudgal, S. M. Seo and J. E. Kristiansen, “Phenothiazines and Thioxanthenes Inhibit Multidrug Efflux Pump Activity in Staphylococcus aureus,” Antimicrobial Agents and Chemotherapy, Vol. 47, No. 2, 2003, pp. 719-726. doi:10.1128/AAC.47.2.719-726.2003
[19]	O. Lomovskaya, M. S. Warren, A. Lee, J. Galazzo, R. Fronko, M. Lee, J. Blais, D. Cho, S. Chamberland, T. Renau, R. Leger, S. Hecker, W. Watkins, K. Hoshino, H. Ishida and V. J. Lee, “Identification and Characterization of Inhibitors of Multidrug Resistance Efflux Pumps in Pseudomonas aeruginosa: Novel Agents for Combination Therapy,” Antimicrobial Agents and Chemotherapy, Vol. 45, No. 1, 2001, pp. 105-116. doi:10.1128/AAC.45.1.105-116.2001
[20]	H. Nikaido and H. I. Zgurskaya, “AcrAB and Related Multidrug Efflux Pumps of Escherichia coli,” Journal of Molecular Microbiology and Biotechnology, Vol. 3, No. 2, 2001, pp. 215-218.
[21]	F. Van Bambeke, Y. Glupczynski, P. Plésiat, J. C. Pechère and P. M. Tulkens, “Antibiotic Efflux Pumps in Prokaryotic Cells: Occurrence, Impact on Resistance and Strategies for the Future of Antimicrobial Therapy,” Journal of Antimicrobial Chemotherapy, Vol. 51, No. 5, 2003, pp. 1055-1065. doi:10.1093/jac/dkg224
[22]	W. J. Gooderham and R. E. Hancock, “Regulation of Virulence and Antibiotic Resistance by Two-Component Regulatory Systems in Pseudomonas aeruginosa,” FEMS Microbiology Reviews, Vol. 33, No. 2, 2009, pp. 279-294. doi:10.1111/j.1574-6976.2008.00135.x
[23]	K. Nishino, E. Nikaido and A. Yamaguchi, “Regulation and Physiological Function of Multidrug Efflux Pumps in Escherichia coli and Salmonella,” Biochimica et Biophysica Acta, Vol. 1794, No. 5, 2009, pp. 834-843.
[24]	L. Sandegren and D. I. Andersson, “Bacterial Gene Amplification: Implications for the Evolution of Antibiotic Resistance,” Nature Reviews Microbiology, Vol. 7, No. 8, 2009, pp. 578-588. doi:10.1038/nrmicro2174
[25]	J. L. Martinez, A. Fajardo, L. Garmendia, A. Hernandez, J. F. Linares, L. Martínez-Solano and M. B. Sánchez, “A Global View of Antibiotic Resistance,” FEMS Microbiology Reviews, Vol. 33, No. 1, 2009, pp. 44-65. doi:10.1111/j.1574-6976.2008.00142.x
[26]	M. Martins, S. G. Dastidar, S. Fanning, J. E. Kristiansen, J. Molnar, J. M. Pagès, Z. Schelz, G. Spengler, M. Viveiros and L. Amaral, “Potential Role of Non-Antibiotics (Helper Compounds) in the Treatment of Multidrug-Resistant Gram-Negative Infections: Mechanisms for Their Direct and Indirect Activities,” International Journal of Antimicrobial Agents, Vol. 31, No. 3, 2008, pp. 198-208. doi:10.1016/j.ijantimicag.2007.10.025
[27]	J. E. Kristiansen, O. Sebbesen, N. Frimodt-M?ller, T. Aaes-J?rgensen and E. F. Hvidberg, “Synergy between a Non-Neuroleptic Thioxanthene Stereo-Isomer and Penicillin in Vivo,” Acta Pathologica, Microbiologica et Immunologica Scandinavica, Vol. 96, No. 12, 1988, pp. 1079-1084. doi:10.1111/j.1699-0463.1988.tb00984.x
[28]	J. Molnár, I. Haszon, T. Bodrogi, E. Martonyi, and S. Turi, “Synergistic Effect of Promethazine with Gentamycin in Frequently Recurring Pyelonephrotis,” International Urology and Nephrology, Vol. 22, No. 5, 1990, pp. 405-411. doi:10.1007/BF02549770
[29]	J. M. Bolla, S. Alibert-Franco, J. Handzlik, J. Chevalier, A. Mahamoud, G. Boyer, K. Kiec-Kononowicz and J.-M. Pages, “Strategies for Bypassing the Membrane Barrier in Multidrug Resistant Gram-Negative Bacteria,” FEBS Letters, Vol. 585, No. 11, 2011, pp. 1682-1690. doi:10.1016/j.febslet.2011.04.054