Research article Special Issues

Optimal bacterial resource allocation: metabolite production in continuous bioreactors

  • Received: 07 June 2020 Accepted: 22 September 2020 Published: 20 October 2020
  • We show novel results addressing the problem of synthesizing a metabolite of interest in continuous bioreactors through resource allocation control. Our approach is based on a coarse-grained self-replicator dynamical model that accounts for microbial culture growth inside the bioreactor, and incorporates a synthetic growth switch that allows to externally modify the RNA polymerase concentration of the bacterial population, thus disrupting the natural process of allocation of available resources in bacteria. Further on, we study its asymptotic behavior using dynamical systems theory, and we provide conditions for the persistence of the bacterial population. We aim to maximize the synthesis of the metabolite of interest during a fixed interval of time in terms of the resource allocation decision. The latter is formulated as an Optimal Control Problem which is then explored using Pontryagin's Maximum Principle. We analyze the solution of the problem and propose a sub-optimal control strategy given by a constant allocation decision, which eventually takes the system to the optimal steady-state production regime. On this basis, we study and compare the two most significant steadystate production objectives in continuous bioreactors: biomass production and metabolite production. For this last purpose, and in addition to the allocation parameter, we control the dilution rate of the bioreactor, and we analyze the results through a numerical approach. The resulting two-dimensional optimization problem is defined in terms of Michaelis-Menten kinetics, and takes into account the constraints for the existence of the equilibrium of interest.

    Citation: Agustín Gabriel Yabo, Jean-Baptiste Caillau, Jean-Luc Gouzé. Optimal bacterial resource allocation: metabolite production in continuous bioreactors[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7074-7100. doi: 10.3934/mbe.2020364

    Related Papers:

  • We show novel results addressing the problem of synthesizing a metabolite of interest in continuous bioreactors through resource allocation control. Our approach is based on a coarse-grained self-replicator dynamical model that accounts for microbial culture growth inside the bioreactor, and incorporates a synthetic growth switch that allows to externally modify the RNA polymerase concentration of the bacterial population, thus disrupting the natural process of allocation of available resources in bacteria. Further on, we study its asymptotic behavior using dynamical systems theory, and we provide conditions for the persistence of the bacterial population. We aim to maximize the synthesis of the metabolite of interest during a fixed interval of time in terms of the resource allocation decision. The latter is formulated as an Optimal Control Problem which is then explored using Pontryagin's Maximum Principle. We analyze the solution of the problem and propose a sub-optimal control strategy given by a constant allocation decision, which eventually takes the system to the optimal steady-state production regime. On this basis, we study and compare the two most significant steadystate production objectives in continuous bioreactors: biomass production and metabolite production. For this last purpose, and in addition to the allocation parameter, we control the dilution rate of the bioreactor, and we analyze the results through a numerical approach. The resulting two-dimensional optimization problem is defined in terms of Michaelis-Menten kinetics, and takes into account the constraints for the existence of the equilibrium of interest.


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    [1] R. U. Ibarra, J. S. Edwards, B. O. Palsson, Escherichia coli k-12 undergoes adaptive evolution to achieve in silico predicted optimal growth, Nature, 420 (2002), 186.
    [2] E. Bosdriesz, D. Molenaar, B. Teusink, F. J. Bruggeman, How fast-growing bacteria robustly tune their ribosome concentration to approximate growth-rate maximization, FEBS J., 282 (2015), 2029-2044. doi: 10.1111/febs.13258
    [3] J. D. Van Elsas, A. V. Semenov, R. Costa, J. T. Trevors, Survival of escherichia coli in the environment: fundamental and public health aspects, ISME J., 5 (2011), 173-183. doi: 10.1038/ismej.2010.80
    [4] N. Giordano, F. Mairet, J.-L. Gouzé, J. Geiselmann, H. De Jong, Dynamical allocation of cellular resources as an optimal control problem: novel insights into microbial growth strategies, PLoS Comput. Biol., 12 (2016), e1004802.
    [5] H. De Jong, S. Casagranda, N. Giordano, E. Cinquemani, D. Ropers, J. Geiselmann, et al., Mathematical modelling of microbes: metabolism, gene expression and growth, J. R. Soc. Interface, 14 (2017), 20170502.
    [6] A. L. Koch, Why can't a cell grow infinitely fast?, Can. J. Microbiol., 34 (1988), 421-426.
    [7] J. Shu, M. Shuler, A mathematical model for the growth of a single cell of E. coli on a glucose/glutamine/ammonium medium, Biotechnol. Bioeng., 33 (1989), 1117-1126. doi: 10.1002/bit.260330907
    [8] D. V. Goeddel, D. G. Kleid, F. Bolivar, H. L. Heyneker, D. G. Yansura, R. Crea, et al., Expression in escherichia coli of chemically synthesized genes for human insulin, Proc. Natl. Acad. Sci., 76 (1979), 106-110.
    [9] L. Huo, J. J. Hug, C. Fu, X. Bian, Y. Zhang, R. Müller, Heterologous expression of bacterial natural product biosynthetic pathways, Nat. Product Rep., 36 (2019), 1412-1436. doi: 10.1039/C8NP00091C
    [10] I. Yegorov, F. Mairet, H. De Jong, J.-L. Gouzé, Optimal control of bacterial growth for the maximization of metabolite production, J. Math. Biol., 78 (2019), 985-1032.
    [11] E. Cinquemani, F. Mairet, I. Yegorov, H. de Jong, J.-L. Gouzé, Optimal control of bacterial growth for metabolite production: the role of timing and costs of control, in 2019 18th European Control Conference (ECC), IEEE, 2019, 2657-2662.
    [12] A. G. Yabo, J.-B. Caillau, J.-L. Gouzé, Singular regimes for the maximization of metabolite production, in 2019 IEEE 58th Conference on Decision and Control (CDC), IEEE, 2019, 31-36.
    [13] J. Izard, C. D. G. Balderas, D. Ropers, S. Lacour, X. Song, Y. Yang, et al., A synthetic growth switch based on controlled expression of rna polymerase, Mol. Syst. Biol., 11 (2015), 840.
    [14] I. Otero-Muras, A. A. Mannan, J. R. Banga, D. A. Oyarzún, Multiobjective optimization of gene circuits for metabolic engineering, IFAC-PapersOnLine, 52 (2019), 13-16.
    [15] D. Molenaar, R. Van Berlo, D. De Ridder, B. Teusink, Shifts in growth strategies reflect tradeoffs in cellular economics, Mol. Syst. Biol., 5 (2009), 323.
    [16] M. T. Wortel, E. Bosdriesz, B. Teusink, F. J. Bruggeman, Evolutionary pressures on microbial metabolic strategies in the chemostat, Sci. Rep., 6 (2016), 29503.
    [17] D. W. Spitzer, Maximization of steady-state bacterial production in a chemostat with ph and substrate control, Biotechnol. Bioeng., 18 (1976), 167-178. doi: 10.1002/bit.260180203
    [18] R. R. Lichtl, M. J. Bazin, D. O. Hall, The biotechnology of hydrogen production by nostoc flagelliforme grown under chemostat conditions, Appl. Microbiol. Biotechnol., 47 (1997), 701-707. doi: 10.1007/s002530050998
    [19] M. C. D'anjou, A. J. Daugulis, A rational approach to improving productivity in recombinant pichia pastoris fermentation, Biotechnol. Bioeng., 72 (2001), 1-11. doi: 10.1002/1097-0290(20010105)72:1<1::AID-BIT1>3.0.CO;2-T
    [20] T. Bayen, F. Mairet, Optimization of the separation of two species in a chemostat, Automatica, 50 (2014), 1243-1248. doi: 10.1016/j.automatica.2014.02.024
    [21] C. Martínez, O. Bernard, F. Mairet, Maximizing microalgae productivity in a light-limited chemostat, IFAC-PapersOnLine, 51 (2018), 735-740. doi: 10.1016/j.ifacol.2018.05.070
    [22] H. R. Thieme, Convergence results and a PoincaréBendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), 755-763.
    [23] L. S. Pontryagin, Mathematical Theory of Optimal Processes, Routledge, 2018.
    [24] H. L. Smith, P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, 1995.
    [25] H. Bremer, P. P. Dennis, Modulation of chemical composition and other parameters of the cell by growth rate, in Escherichia coli and Salmonella: Cellular and Molecular Biology, ASM Press, Washington, (1996), 1553-1569.
    [26] S. Goutelle, M. Maurin, F. Rougier, X. Barbaut, L. Bourguignon, M. Ducher, et al., The hill equation: a review of its capabilities in pharmacological modelling, Fundam. Clin. Pharmacol., 22 (2008), 633-648.
    [27] K. A. Johnson, R. S. Goody, The original Michaelis constant: translation of the 1913 Michaelis-Menten paper, Biochemistry, 50 (2011), 8264-8269. doi: 10.1021/bi201284u
    [28] A. A. Agrachev, Y. Sachkov, Control Theory from the Geometric Viewpoint, Springer Science & Business Media, 2013.
    [29] M. I. Zelikin, V. F. Borisov, Theory of Chattering Control: With Applications to Astronautics, Robotics, Economics, and Engineering, Springer Science & Business Media, 2012.
    [30] A. Van der Schaft, Symmetries in optimal control, SIAM J. Control Optim., 25 (1987), 245-259.
    [31] E. Trélat, E. Zuazua, The turnpike property in finite-dimensional nonlinear optimal control, J. Differ. Equations, 258 (2015), 81-114. doi: 10.1016/j.jde.2014.09.005
    [32] W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Turnpike features in optimal selection of species represented by quota models, Submitted.
    [33] I. S. Team Commands, Bocop: an open source toolbox for optimal control, 2017. Available from: http://bocop.org.
    [34] H. Robbins, A generalized Legendre-Clebsch condition for the singular cases of optimal control, IBM J. Res. Dev., 11 (1967), 361-372. doi: 10.1147/rd.114.0361
    [35] M. Scott, C. W. Gunderson, E. M. Mateescu, Z. Zhang, T. Hwa, Interdependence of cell growth and gene expression: origins and consequences, Science, 330 (2010), 1099-1102. doi: 10.1126/science.1192588
    [36] I. Yegorov, F. Mairet, J.-L. Gouzé, Optimal feedback strategies for bacterial growth with degradation, recycling, and effect of temperature, Optim. Control Appl. Methods, 39 (2018), 1084-1109.
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