Geodesic
Optimal multiplicative control of bacterial quorum sensing under external enzyme impact
Anna Maslovskaya1 ; Christina Kuttler2 ; Alexander Chebotarev3 ; Andrey Kovtanyuk4, 5
1 Department of Mathematics and Computer Science, Amur State University, Ignatievskoe shosse 21, 675027 Blagoveshchensk, Russia
2 Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
3 Institute for Applied Mathematics FEB RAS, Radio st. 7, 690041 Vladivostok, Russia
4 Klinikum rechts der Isar, Technische Universität München, Ismaningerstr. 22, 81675 München, Germany
5 Far Eastern Federal University, Far Eastern Center for Research and Education in Mathematics, Ajax Bay 10, Russky Island, 690922 Vladivostok, Russia
Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 29.

Voir la notice de l'article provenant de la source EDP Sciences

The use of external enzymes provides an alternative way of reducing communication in pathogenic bacteria that may lead to the degradation of their signal and the loss of their pathogeneity. The present study considers an optimal control problem for the semilinear reaction-diffusion model of bacterial quorum sensing under the impact of external enzymes. Estimates of the solution of the controlled system are obtained, on the basis of which the solvability of the extremal problem is proved and the necessary optimality conditions of the first-order are derived. A numerical algorithm to find a solution of the optimal control problem is constructed and implemented. The conducted numerical experiments demonstrate an opportunity to build an effective strategy of the enzymes impact for treatment.
DOI : 10.1051/mmnp/2022031

Anna Maslovskaya 1 ; Christina Kuttler 2 ; Alexander Chebotarev 3 ; Andrey Kovtanyuk 4, 5

1 Department of Mathematics and Computer Science, Amur State University, Ignatievskoe shosse 21, 675027 Blagoveshchensk, Russia
2 Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany
3 Institute for Applied Mathematics FEB RAS, Radio st. 7, 690041 Vladivostok, Russia
4 Klinikum rechts der Isar, Technische Universität München, Ismaningerstr. 22, 81675 München, Germany
5 Far Eastern Federal University, Far Eastern Center for Research and Education in Mathematics, Ajax Bay 10, Russky Island, 690922 Vladivostok, Russia 
@article{MMNP_2022_17_a33,
     author = {Anna Maslovskaya and Christina Kuttler and Alexander Chebotarev and Andrey Kovtanyuk},
     title = {Optimal multiplicative control of bacterial quorum sensing under external enzyme impact},
     journal = {Mathematical modelling of natural phenomena},
     eid = {29},
     publisher = {mathdoc},
     volume = {17},
     year = {2022},
     doi = {10.1051/mmnp/2022031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2022031/}
}
TY  - JOUR
AU  - Anna Maslovskaya
AU  - Christina Kuttler
AU  - Alexander Chebotarev
AU  - Andrey Kovtanyuk
TI  - Optimal multiplicative control of bacterial quorum sensing under external enzyme impact
JO  - Mathematical modelling of natural phenomena
PY  - 2022
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2022031/
DO  - 10.1051/mmnp/2022031
LA  - en
ID  - MMNP_2022_17_a33
ER  - 
%0 Journal Article
%A Anna Maslovskaya
%A Christina Kuttler
%A Alexander Chebotarev
%A Andrey Kovtanyuk
%T Optimal multiplicative control of bacterial quorum sensing under external enzyme impact
%J Mathematical modelling of natural phenomena
%D 2022
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2022031/
%R 10.1051/mmnp/2022031
%G en
%F MMNP_2022_17_a33
Anna Maslovskaya; Christina Kuttler; Alexander Chebotarev; Andrey Kovtanyuk. Optimal multiplicative control of bacterial quorum sensing under external enzyme impact. Mathematical modelling of natural phenomena, Tome 17 (2022), article  no. 29. doi : 10.1051/mmnp/2022031. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2022031/

[1] G.V. Alekseev, R.V. Brizitskii, Z.Y. Saritskaya Stability estimates of extremum problem’s solutions for nonlinear convection-diffusion-reaction equation Sib. J. Ind. Math. 2016 155 167

[2] M. Ananda, I. Rusmana, A. Akhdiya Quorum quenching of Bacillus cereus INT1c against Pseudomonas syringae J. Phys.: Conf. Series 2019 012010

[3] K. Anguige, J.R. King, J.P. Ward, P. Williams Mathematical modelling of therapies targeted at bacterial quorum sensing Math. Biosci. 2004 39 83

[4] A.K. Bhardwaj, K. Vinothkumar, N. Rajpara Bacterial quorum sensing inhibitors: attractive alternatives for control of infectious pathogens showing multiple drug resistance Recent Pat. Antiinfect. Drug Discov. 2013 68 83

[5] R.V. Brizitskii, Z.Y. Saritskaya Optimization analysis of the inverse coefficient problem for the nonlinear convectiondiffusion-reaction equation J. Inv. Ill-Posed Probl. 2018 821 834

[6] A.Y. Chebotarev, A.E. Kovtanyuk, G.V. Grenkin, N.D. Botkin, K.-H. Hoffmann Nondegeneracy of optimality conditions in control problems for a radiative-conductive heat transfer model Appl. Math. Comput. 2016 371 380

[7] J.D. Dockery, J.P. Keener A mathematical model for quorum sensing in Pseudomonas aeruginosa Bull. Math. Biol. 2001 95 116

[8] M.G. Fagerlind, P. Nilsson, M. Harlen, S. Karlsson, S.A. Rice, S. Kjelleberg Modeling the effect of acylated homoserine lactone antagonists in Pseudomonas aeruginosa Biosystems 2005 201 213

[9] A. Fekete, C. Kuttler, M. Rothballer, B.A. Hense, D. Fischer, K. Buddrus-Schiemann, M. Lucio, J. Muller, P. Schmitt-Kopplin, A. Hartmann Dynamic regulation of N-acyl-homoserine lactone production and degradation in Pseudomonas putida IsoF FEMS Microbiol. Ecol. 2010 22 34

[10] M. Fernandez, M. Porcel, J. De La Torre, M.A. Molina-Henares, A. Daddaoua, M.A. Llamas, A. Roca, V. Carriel, I. Garzon, J.L. Ramos, M. Alaminos, E. Duque Analysis of the pathogenic potential of nosocomial Pseudomonas putida strains Front. Microbiol. 2015 71

[11] A.V. Fursikov, Optimal Control of Distributed Systems. Theory and Applications. American Math. Soc. (2000).

[12] A.B. Goryachev Understanding bacterial cell-cell communication with computational modeling Chem. Rev. 2011 238 250

[13] A.D. Ioffe and V.M. Tikhomirov, Theory of Extremal Problems. North-Holland, Amsterdam (1979).

[14] S. James, P. Nilsson, G. James, S. Kjelleberg, T. Fagersötrm Luminescence control in the marine bacterium Vibrio fischeri: an analysis of the dynamics of lux regulation J. Mol. Biol. 2000 1127 1137

[15] Q. Jiang, J. Chen, C. Yang, Y. Yin, K. Yao Quorum Sensing: a prospective therapeutic target for bacterial diseases BioMed. Res. Int. 2019 2015978

[16] A. Koerber, J. King, J. Ward, P. Williams, J. Croft, R. Sockett A mathematical model of partial-thickness burn-wound infection by Pseudomonas aeruginosa: quorum sensing and the build-up to invasion Bull. Math. Biol. 2002 239 259

[17] A.E. Kovtanyuk, A.Y. Chebotarev, A.A. Astrakhantseva Inverse extremum problem for a model of endovenous laser ablation J. Inv. Ill-Posed Probl. 2021 467 476

[18] C. Kuttler, Reaction—diffusion equations and their application on bacterial communication. Handbook of Statistics (Chapter 4) (2017) 55–91.

[19] C. Kuttler, A. Maslovskaya Computer simulation of communication in bacterial populations under external impact of signal-degrading enzymes CEUR Workshop Proc. 2020 163 179

[20] C. Kuttler and A. Maslovskaya, Wave effects in stochastic time lagging reaction-diffusion model of quorum-sensing in bacterial populations. Proc. Int. Conf. Days on Diffraction 2020 (2020) 62–67.

[21] C. Kuttler, A. Maslovskaya Hybrid stochastic fractional-based approach to modeling bacterial quorum sensing Appl. Math. Model. 2021 360 375

[22] C. Kuttler, A. Maslovskaya and L. Moroz, Numerical simulation of time-fractional diffusion-wave processes applied to communication in bacterial populations. Proc. of the IEEE, “Days on Diffraction” (2021) 114–119.

[23] J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Springer-Verlag (1972).

[24] L. Molina, Z. Udaondo, E. Duque, M. Fernandez, C. Molina-Santiago, A. Roca, M. Porcel, J. De La Torre, A. Segura, P. Plesiat, K. Jeannot, J.-L. Ramos Antibiotic resistance determinants in a Pseudomonas putida strain isolated from a hospital PLoS ONE 2014 e81604

[25] J. Perez-Velazquez, M. Gölgeli, R. Garcia-Contreras Mathematical modelling of bacterial quorum sensing: a review Bull. Math. Biol. 2016 1585 1639

[26] S. Peter, P. Oberhettinger, L. Schuele, A. Dinkelacker, W. Vogel, D. Dorfel, D. Bezdan, S. Ossowski, M. Marschal, J. Liese, M. Willmann Genomic characterization of clinical and environmental Pseudomonas putida group strains and determination of their role in the transfer of antimicrobial resistance genes to Pseudomonas aeruginosa BMC Genomics 2017 859

[27] S.T. Rutherford, B.L. Bassler Bacterial quorum sensing: its role in virulence and possibilities for its control Cold Spring Harb. Perspect. Med. 2012 a012427

[28] K. Saurav, R. Bar-Shalom, M. Haber, I. Burgsdorf, G. Oliviero, V. Costantino, D. Morgenstern, L. Steindler In search of alternative antibiotic drugs: Quorum-quenching activity in sponges and their bacterial isolates Front. Microbiol. 2016 416

[29] A. Steidle, M. Allesen-Holm, K. Riedel, G. Berg, M. Givskov, S. Molin, L. Eberl Identification and characterization of an N-Acylhomoserine lactone-dependent quorum-sensing system in Pseudomonas putida Strain IsoF Appl. Environ. Microbiol. 2002 6371 6382

[30] J.P. Ward, J.R. King, A.J. Koerber, P. Williams, J.M. Croft, R.E. Sockett Mathematical modelling of quorum sensing in bacteria Math. Med. Biol. 2001 263 292

[31] J. Ward, Mathematical modeling of quorum-sensing control in biofilms. Control of biofilm infections by signal manipulation, edited by N. Balaban. Springer, Berlin (2008) 79–108.

[32] A. Weimer, M. Kohlstedt, D.C. Volke, P.I. Nikel, C. Wittmannet Industrial biotechnology of Pseudomonas putida: advances and prospects Appl. Microbiol. Biotechnol. 2020 7745 7766

[33] N.A. Whitehead, A.M.L. Barnard, H. Slater, N.J.L. Simpson, G.P.C. Salmond Quorum-sensing in Gram-negative bacteria FEMS Microbiol. Rev. 2001 365 404

[34] A. Yajima Recent progress in the chemistry and chemical biology of microbial signaling molecules: quorum-sensing pheromones and microbial hormones Tetrahedr. Lett. 2014 2773 2780

Cité par Sources :