Using optimal control to understand complex metabolic pathways

Optimal control of ribosome population for gene expression under periodic nutrient intake

Translation of proteins is a fundamental part of gene expression that is mediated by ribosomes. As ribosomes significantly contribute to both cellular mass and energy consumption, achieving efficient management of the ribosome population is also crucial to metabolism and growth. Inspired by biological evidence for nutrient-dependent mechanisms that control both ribosome-active degradation and genesis, we introduce a dynamical model of protein production, that includes the dynamics of resources and control over the ribosome population. Under the hypothesis that active degradation and biogenesis are optimal for maximizing and maintaining protein production, we aim to qualitatively reproduce empirical observations of the ribosome population dynamics. Upon formulating the associated optimization problem, we first analytically study the stability and global behaviour of solutions under constant resource input, and characterize the extent of oscillations and convergence rate to a global equilibrium. We further use these results to simplify and solve the problem under a quasi-static approximation. Using biophysical parameter values, we find that optimal control solutions lead to both control mechanisms and the ribosome population switching between periods of feeding and fasting, suggesting that the intense regulation of ribosome population observed in experiments allows to maximize and maintain protein production. Finally, we find some range for the control values over which such a regime can be observed, depending on the intensity of fasting.

Understanding cellular growth strategies via optimal control

Evolutionary prediction and control are increasingly interesting research topics that are expanding to new areas of application. Unravelling and anticipating successful adaptations to different selection pressures becomes crucial when steering rapidly evolving cancer or microbial populations towards a chosen target. Here we introduce and apply a rich theoretical framework of optimal control to understand adaptive use of traits, which in turn allows eco-evolutionarily informed population control. Using adaptive metabolism and microbial experimental evolution as a case study, we show how demographic stochasticity alone can lead to lag time evolution, which appears as an emergent property in our model. We further show that the cycle length used in serial transfer experiments has practical importance as it may cause unintentional selection for specific growth strategies and lag times. Finally, we show how frequency-dependent selection can be incorporated to the state-dependent optimal control framework allowing the modelling of complex eco-evolutionary dynamics. Our study demonstrates the utility of optimal control theory in elucidating organismal adaptations and the intrinsic decision making of cellular communities with high adaptive potential.

Nonlinear optimal control of a mean-field model of neural population dynamics

We apply the framework of nonlinear optimal control to a biophysically realistic neural mass model, which consists of two mutually coupled populations of deterministic excitatory and inhibitory neurons. External control signals are realized by time-dependent inputs to both populations. Optimality is defined by two alternative cost functions that trade the deviation of the controlled variable from its target value against the “strength” of the control, which is quantified by the integrated 1- and 2-norms of the control signal. We focus on a bistable region in state space where one low- (“down state”) and one high-activity (“up state”) stable fixed points coexist. With methods of nonlinear optimal control, we search for the most cost-efficient control function to switch between both activity states. For a broad range of parameters, we find that cost-efficient control strategies consist of a pulse of finite duration to push the state variables only minimally into the basin of attraction of the target state. This strategy only breaks down once we impose time constraints that force the system to switch on a time scale comparable to the duration of the control pulse. Penalizing control strength via the integrated 1-norm (2-norm) yields control inputs targeting one or both populations. However, whether control inputs to the excitatory or the inhibitory population dominate, depends on the location in state space relative to the bifurcation lines. Our study highlights the applicability of nonlinear optimal control to understand neuronal processing under constraints better.

Modeling and Optimization of a Molecular Biocontroller for the Regulation of Complex Metabolic Pathways

Achieving optimal production in microbial cell factories, robustness against changing intracellular and environmental perturbations requires the dynamic feedback regulation of the pathway of interest. Here, we consider a merging metabolic pathway motif, which appears in a wide range of metabolic engineering applications, including the production of phenylpropanoids among others. We present an approach to use a realistic model that accounts for in vivo implementation and then propose a methodology based on multiobjective optimization for the optimal tuning of the gene circuit parts composing the biomolecular controller and biosensor devices for a dynamic regulation strategy. We show how this approach can deal with the trade-offs between the performance of the regulated pathway, robustness to perturbations, and stability of the feedback loop. Using realistic models, our results suggest that the strategies for fine-tuning the trade-offs among performance, robustness, and stability in dynamic pathway regulation are complex. It is not always possible to infer them by simple inspection. This renders the use of the multiobjective optimization methodology valuable and necessary.

Optimization and feedback control system of dilution rate for 1,3-propanediol in two-stage fermentation: A theoretical study

In utilizing glycerol to produce 1,3-propanediol by microbial fermentation, the problems of low utilization rate and poor production performance need to be addressed. Based on the analysis of a mathematical model for 1,3-propanediol production from glycerol by Klebsiella pneumoniae, this study theoretically investigated the effects of the dilution rate and the initial glycerol concentration in a two-stage fermentation process and the feasibility of applying the feedback control methods. First, the optimal operation conditions of initial glycerol concentration and dilution rate were obtained. Through the use of feedback control theory, a control strategy for dilution rate was designed and optimized to shorten the settling time (time required for fermentation to reach stability) from 60.92 to 36.68 h for the first reactor, and from 53.66 to 22.68 h for the second reactor. In addition, the yield of 1,3-propanediol in both two reactors reached up to 0.5 g·g^-1 . The simulation results indicated that the feedback control strategy for dilution rate increased the product concentration, reduced the residual glycerol in the fermentation broth, and greatly improved the performance of the fermentation. A feeding strategy of automatic control for dilution rate has been established and will be applied as an effective guiding scheme in automatic continuous fermentations for production of 1,3-propanediol.

Yeast synthetic biology advances biofuel production

Increasing concerns of environmental impacts and global warming calls for urgent need to switch from use of fossil fuels to renewable technologies. Biofuels represent attractive alternatives of fossil fuels and have gained continuous attentions. Through the use of synthetic biology it has become possible to engineer microbial cell factories for efficient biofuel production in a more precise and efficient manner. Here, we review advances on yeast-based biofuel production. Following an overview of synthetic biology impacts on biofuel production, we review recent advancements on the design, build, test, learn steps of yeast-based biofuel production, and end with discussion of challenges associated with use of synthetic biology for developing novel processes for biofuel production.

Implementation and acceleration of optimal control for systems biology

Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.

Enhancing in silico strain design predictions through next generation metabolic modeling approaches

The reconstruction and analysis of metabolic models has garnered increasing attention due to the multitude of applications in which these have proven to be practical. The growing number of generated metabolic models has been accompanied by an exponentially expanding arsenal of tools used to analyze them. In this work, we discussed the biological relevance of a number of promising modeling frameworks, focusing on the questions and hypotheses each method is equipped to address. To this end, we critically analyzed the steady-state modeling approaches focusing on resource allocation and incorporation of thermodynamic considerations which produce promising results and aid in the generation and experimental validation of numerous predictions. For smaller networks involving more complex regulation, we addressed kinetic modeling techniques which show encouraging results in addressing questions outside the scope of steady-state modeling. Finally, we discussed the potential application of the discussed frameworks within the field of strain design. Adoption of such methodologies is believed to significantly enhance the accuracy of in silico predictions and hence decrease the number of design-build-test cycles required.

Automated engineering of synthetic metabolic pathways for efficient biomanufacturing

Metabolic engineering involves the engineering and optimization of processes from single-cell to fermentation in order to increase production of valuable chemicals for health, food, energy, materials and others. A systems approach to metabolic engineering has gained traction in recent years thanks to advances in strain engineering, leading to an accelerated scaling from rapid prototyping to industrial production. Metabolic engineering is nowadays on track towards a truly manufacturing technology, with reduced times from conception to production enabled by automated protocols for DNA assembly of metabolic pathways in engineered producer strains. In this review, we discuss how the success of the metabolic engineering pipeline often relies on retrobiosynthetic protocols able to identify promising production routes and dynamic regulation strategies through automated biodesign algorithms, which are subsequently assembled as embedded integrated genetic circuits in the host strain. Those approaches are orchestrated by an experimental design strategy that provides optimal scheduling planning of the DNA assembly, rapid prototyping and, ultimately, brings forward an accelerated Design-Build-Test-Learn cycle and the overall optimization of the biomanufacturing process. Achieving such a vision will address the increasingly compelling demand in our society for delivering valuable biomolecules in an affordable, inclusive and sustainable bioeconomy.