Using optimal control to understand complex metabolic pathways

Abstract

Background Optimality principles have been used to explain the structure and behavior of living matter at different levels of organization, from basic phenomena at the molecular level, up to complex dynamics in whole populations. Most of these studies have assumed a single-criteria approach. Such optimality principles have been justified from an evolutionary perspective. In the context of the cell, previous studies have shown how dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point, and a single objective for the optimality criteria. Results Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework which has been designed with scalability and efficiency in mind, including mechanisms to avoid the most common pitfalls. Third, we illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments. Conclusions We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we also show how to consider general cost/benefit trade-offs. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction or gene regulatory networks.

Implementation and acceleration of optimal control for systems biology

“…Further challenges can be introduced; either through the formulation of the control problem, or as a result of the behaviour of the underlying system. Examples of such challenges include control problems with singular arcs, path constraints, multiple local solutions, discontinuous dynamics and sensitivity to the initial guess of the control [35]. These challenges can introduce numerical difficulties, and complications in terms of the optimal control theory; for example, control problems with singular arcs typically require additional necessary conditions for optimality beyond those obtained from the PMP [38].…”

“…Interface 18: 20210241 principles that may guide the system [33]. Optimality principles have been employed to investigate mechanisms in metabolism; for example, in [34], where optimal control techniques provide rationalization for experimentally and numerically observed sequential activation of metabolic pathways; in [35] where optimal control techniques predict enzyme activation times and metabolite concentrations; and in other work reviewed in [36], where further insights are gained regarding metabolic pathway activation and regulation. Optimal control has also provided insight into the emergence of persister cells in the presence of environmental volatility [37].…”

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

“…Dynamic network models, from grey-box to black-box ones, of scales ranging from a subset of pathways to genome-scale, have been used to this end ( Otero-Muras and Banga, 2017 ; Li et al, 2018 ; Yang et al, 2019 ; Lo-Thong et al, 2020 ). The optimal intervention points and intervention strategies (required up- or down-regulation) can be assessed using sensitivity analysis methods like metabolic control analysis ( Lo-Thong et al, 2020 ) dynamic optimization ( Otero-Muras and Banga, 2017 ; Li et al, 2018 ; Yang et al, 2019 ) and optimal control principles ( Tsiantis and Banga, 2020 ). Thus, these methods address the fundamental problem of determining the structure of (optimal) control intervention points in complex metabolic networks.…”

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

“…In an “analytic” application scenario, it can help us understand the way in which a natural dynamical system is designed and offers explanations of its workings in terms of optimization principles. In the past, OCT has been applied successfully in biology and biomedicine with applications to cellular systems, metabolic networks, and the development of effective treatments against pathogens (see, e.g., Ewald et al, 2017 ; Tsiantis and Banga, 2020 for recent reviews).…”