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Autonomous and Adaptive Control of Populations of Bacteria Through Environment Regulation

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Computational Methods in Systems Biology (CMSB 2016)

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Abstract

The proliferation of antibiotic-resistant bacteria poses a significant threat to humans health and welfare. To reduce the bacterial pathogenesis and growth, we propose an autonomous biological controller that can adaptively generate quorum sensing inhibitors and control the iron availability in the environment. As the main theoretical contribution, we provide a detailed analysis of our proposed controller that includes model calibration, system response, and inhibitor effectiveness. We also formulate a constrained optimization problem to choose the values of the biological parameters of the proposed controller under given environment constraints. Finally, we validate our results via detailed population-level simulations and demonstrate that bacteria virulence can be significantly reduced without developing drug resistance or inducing selective pressure among bacteria wild type and mutants. This work represents a first step towards a paradigm change in reducing bacterial pathogenesis via controlling the dynamics of the cell-cell communication through environment regulation.

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Notes

  1. 1.

    Denoted as AI in this paper.

  2. 2.

    Since the number of bacteria is proportional to the biomass, we use biomass and the number of bacteria to account for the total virulence interchangeably.

  3. 3.

    We discuss a design example for the biological parameters in subsequent sections.

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Appendix

Appendix

General form of a dynamic constrained optimization problem. A general dynamic optimization problem can be formulated as follows:

$$\begin{aligned} \begin{aligned}&\underset{p}{\text {min}} \qquad \qquad J(x_{t},p) \\&\text {subject to} \quad ~\quad \dot{x}_t = f(x_t,p) \ \forall t \in [t_0, t_{FL}] \\&\qquad \qquad \quad ~~ x_{t_0}(p) = x_0(p) \\&\qquad \qquad \quad ~~ p^L \le p \le p^U \\ \end{aligned} \end{aligned}$$

where \(t \in R\) is time, \(t_0, t_f\) are the initial and final time, respectively, \(t_i \in [t_0, t_{FL}],\) x and \(\dot{x} \in R^n\) are the state variables and their time derivatives, respectively, and \(p \in R^r\) are the time-invariant parameters and is subjected to the lower constraints \(p^L\) and upper constraints \(p^U\). The function J is the objective that we want to minimize. f describes the system dynamics. \(x_0\) is the initial conditions of the state variables.

Control problem formulation. Consider a general control system which consists of a plant and a controller (see Fig. 1(c)). The plant (process) takes in the input variable (d(t)) and control variable (CV) (u(t)) generating the process variable (PV) (y(t)). The controller calculates an error (e(t)) signal as the difference between a measured process variable and a desired setpoint (SP) (r(t)). The controller aims at minimizing the error by adjusting the process through the control variable (u(t)). The control system can be characterized by the following equations:

$$\begin{aligned} \dot{x}(t)&= f(x(t),u(t),d(t)), \dot{u}(t) = h(e(t),u(t)) \end{aligned}$$
(31)
$$\begin{aligned} y(t)&= g(x(t)), e(t) = y(t) - r(t) \end{aligned}$$
(32)

where f, g and h are arbitrary functions. The controller, in this case, can be viewed as an integral controller since the control signal is proportional to the integral of the error signal.

Simulation Environment Configuration. We model bacterial growth in a 3D microfluidic environment (\(100 \mu m\) x \(100 \mu m\) x \(100 \mu m\)) that is initialized and inoculated with 1000 wild-type cells, all of which are non-overlapping and randomly attached to the substrate. We set up the simulation time up to 150 h in order to observe the evolution dynamics of bacteria growth.

Table 2. Table with numerical values of model parameters from [8, 13]
Table 3. Table with numerical values of model parameters calibrated in this paper as explained below.

Model Calibration. We calibrate the model parameters of the pqs QS system shown in Table 3. We first use similar values from [8, 13] as our initial values. Next, we tune the model parameters to capture the behavior of the QS system. More precisely, we tune the model parameters based on the relative concentration change of the LasR protein under different iron concentration levels.

As shown in Fig. 2, when we change the iron concentration from 0.01 (a.u.) to 1 (a.u.), the LasR concentration changes from 2 (a.u.) to 0.5 (a.u.) which preserves the fold changes reported in Fig. 4 of reference [12].

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Lo, C., Marculescu, R. (2016). Autonomous and Adaptive Control of Populations of Bacteria Through Environment Regulation. In: Bartocci, E., Lio, P., Paoletti, N. (eds) Computational Methods in Systems Biology. CMSB 2016. Lecture Notes in Computer Science(), vol 9859. Springer, Cham. https://doi.org/10.1007/978-3-319-45177-0_11

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  • DOI: https://doi.org/10.1007/978-3-319-45177-0_11

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