A central challenge in industrial microbiological applications is engineering of genetic networks to achieve a target yield or steady state concentration. This is a particularly challenging problem when optimizing under novel reaction conditions where canonical models of metabolic pathways are no longer valid. In these scenarios, the biological systems are entirely represented by data for which no direct methods exist to optimize the reaction output. We introduce a datadriven model discovery approach that leverages Koopman operator theory and time-series expression measurements to discover models that predict untested reaction outcomes. These Koopman models allow us to design control strategies to achieve target steady state concentrations for products of interest. We develop a model of the trypotophan pathway and illustrate this steady stateprogramming framework on this pathway. Tryptophan is an essential amino acid and is a valuable product in industrial microbiology. We show how Koopman operator theory can thus be used program the steady state of a genetic network in a data-driven context .
This paper describes the optimal selection of a control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are common (along with limit cycles), and the aim is to program cells to perform both digital and analog computation, though developing genetic digital computation has been the main focus. We frame the analog computing challenge of generating a steady state input-output function inside living cells. To program the steady state, a data-driven approach is taken wherein an approximation of the Koopman operator, identified via deep dynamic mode decomposition, is used to describe the dynamics of the system linearly. The new representation of the dynamics are then used to solve an optimization problem for the input which maximizes a direction in state space. Some added structure on the Koopman operator learning process for controlled systems is given for dynamics that are separable in the state and input. Finally, the methods are demonstrated on simulation examples of an incoherent feedforward loop and a combinatorial promoter system, two common network architectures seen in the field of synthetic biology .
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A central challenge in industrial microbiological applications is engineering of genetic networks to achieve a target yield or steady state concentration. This is a particularly challenging problem when optimizing under novel reaction conditions where canonical models of metabolic pathways are no longer valid. In these scenarios, the biological systems are entirely represented by data for which no direct methods exist to optimize the reaction output. We introduce a datadriven model discovery approach that leverages Koopman operator theory and time-series expression measurements to discover models that predict untested reaction outcomes. These Koopman models allow us to design control strategies to achieve target steady state concentrations for products of interest. We develop a model of the trypotophan pathway and illustrate this steady stateprogramming framework on this pathway. Tryptophan is an essential amino acid and is
This paper describes the optimal selection of
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valuable product in industrial microbiology. We show how Koopman operator theory can thus be used program the steady state of a genetic network in a
control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are common (along with limit cycles), and the aim is to program cells to perform both digital and analog computation, though developing genetic digital computation has been the main focus. We frame the analog computing challenge of generating a steady state input-output function inside living cells. To program the steady state, a
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context
approach is taken wherein an approximation of the Koopman operator, identified via deep dynamic mode decomposition, is used to describe the dynamics of the system linearly. The new representation of the dynamics are then used to solve an optimization problem for the input which maximizes a direction in state space. Some added structure on the Koopman operator learning process for controlled systems is given for dynamics that are separable in the state and input. Finally, the methods are demonstrated on simulation examples of an incoherent feedforward loop and a combinatorial promoter system, two common network architectures seen in the field of synthetic biology