Robust Observer to estimate states and parameters of Nonlinear Quorum Sensing Dynamics with Time Delay

https://doi.org/10.58571/CNCA.AMCA.2022.045

Resumen: Quorum sensing (QS) is a self organization process in bacteria colonies where certain collective action is performed blue when a population density threshold is reached. Some medically relevant behaviors of bacteria are known to be described by QS dynamics such as virulence or antibiotics resistance. Estimation of states and parameters in QS model is important to address such medical issues but difficult in scenarios where measurements are limited and internal activation delay times are considered. In this paper an exteded Kalman filter is applied to estimate two unknown states and a nonlinear parameter of a time delay QS (TDQS) system. To the author’s knowledge this is the first extended Kalman filter applied to estimate state variables of QS in its delayed version. In this work it is shown how, by measuring only one of the states of the TDQS, the rest of the variables can be estimated, as well one nonlinear parameter.

¿Cómo citar?

Flores-Pérez, A., Breña-Medina, V. & González-Olvera M. Robust Observer to estimate states and parameters of Nonlinear Quorum Sensing Dynamics with Time Delay. Memorias del Congreso Nacional de Control Automático, pp. 312-317, 2022. https://doi.org/10.58571/CNCA.AMCA.2022.045

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Procesos Biológicos; Procesos Biotecnológicos; Otros Tópicos Afines

• Batmani, Y. and Khaloozadeh, H. (2014). On the design of observer for nonlinear time-delay systems. Asian Journal of Control, 16(4), 1191–1201.
• Chen, M., Liu, H., and Yan, F. (2019). Oscillatory dynamics mechanism induced by protein synthesis time delay in quorum-sensing system. Physical Review E, 99(6).
• Chen, M., Ji, J., Liu, H., and Yan, F. (2020). Periodic Oscillations in the Quorum-Sensing System with Time Delay. International Journal of Bifurcation and Chaos, 30(9). doi:10.1142/S0218127420501278.
• Flores Pérez, A. and Breña -Medina, V. (2020). Fenómeno de autoinducción con retraso en una población de bacterias. Congreso de la Sociedad Matemática Mexicana.
• Harris-Heredia, M. (2019). Mathematical Modelling of Quorum Sensing Dynamics. Autonomous Technological Institute of Mexico. Bachelor tesis.
• Hugues-Salas, O. and Shore, K.A. (2010). An extended kalman filtering approach to nonlinear time-delay systems: Application to chaotic secure communications. IEEE Transactions on Circuits and Systems I: Regular Papers, 57(9), 2520–2530.
• Hutchinson, G.E. et al. (1948). Circular causal systems in ecology. Ann. NY Acad. Sci, 50(4), 221–246.
• Jiang, W., He, X., Luo, Y., Mu, Y., Gu, F., Liang, Q., and Qi, Q. (2020). Two completely orthogonal quorum sensing systems with selfproduced autoinducers enable automatic delayed cascade control. ACS Synth. Biol., 9, 2588–2599.
• Karafyllis, I., Malisoff, M., Mazenc, F., and Pepe, P. (2016). Recent results on nonlinear delay control systems. Springer.
• Marquez-Martinez, L., Moog, C., and Velasco-Villa, M. (2000). Observability and observers for nonlinear systems with time delays. IFAC Proceedings Volumes, 33(23), 109–114.
• McClean, K.H., Winson, M.K., Fish, L., Taylor, A., Chhabra, S.R., Camara, M., Daykin, M., Lamb, J.H., Swift, S., Bycroft, B.W., et al. (1997). Quorum sensing and chromobacterium violaceum: exploitation of violacein production and inhibition for the detection of nacylhomoserine lactones. Microbiology, 143(12), 3703–3711.
• Miller, M.B. and Bassler, B.L. (2001). Quorum sensing in bacteria. Annual Reviews in Microbiology, 55(1), 165–199.
• Monk, N. (2020). “oscillatory expression of hes1, p53, and nf-kappab driven by transcriptional time delays. Curr. Biol., 13, 1409–1413.
• Nadell, C.D., Xavier, J.B., Levin, S.A., and Foster, K.R. (2008). The evolution of quorum sensing in bacterial biofilms. PLoS biology, 6(1), e14.
• Nealson, K.H., Platt, T., and Hastings, J.W. (1970). Cellular control of the synthesis and activity of the bacterial luminescent system. Journal of bacteriology, 104(1), 313–322.
• Perez-Velazquez, J., Gölgeli, M., and Garcia-Contreras, R. (2016). Mathematical modelling of bacterial quorum sensing: a review. Bulletin of mathematical biology, 78(8), 1585–1639.
• Raff, T. and Allgower, F. (2006). An ekf-based observer for nonlinear time-delay systems. In 2006 American control conference, 4–pp. IEEE.
• Reif, K., Sonnemann, F., and Unbehauen, R. (1998). An ekf-based nonlinear observer with a prescribed degree of stability. Automatica, 34(9), 1119–1123.
• Richard, J.P. (2003). Time-delay systems: an overview of some recent advances and open problems. automatica, 39(10), 1667–1694.
• Santillan, M. (2014). Chemical kinetics, stochastic processes, and irreversible thermodynamics, volume 2014. Springer.
• Ward, J.P., King, J.R., Koerber, A., Williams, P., Croft, J., and Sockett, R. (2001). Mathematical modelling of quorum sensing in bacteria. Mathematical Medicine and Biology, 18(3), 263–292.
• Waters, C.M. and Bassler, B.L. (2005). Quorum sensing: cell-to-cell communication in bacteria. Annu. Rev. Cell Dev. Biol., 21, 319–346.
• Zhang, Y., Liu, H., and Zhou, J. (2016). Oscillatory expression in escherichia coli mediated by micrornas with transcriptional and translational time delays. IET Systems Biology, 10(6), 203–209.