Reconciling periodic rhythms of large-scale biological networks by optimal control

Periodic rhythms are ubiquitous phenomena that illuminate the underlying mechanism of cyclic activities in biological systems, which can be represented by cyclic attractors of the related biological network. Disorders of periodic rhythms are detrimental to the natural behaviours of living organisms. Previous studies have shown that the state transition from one to another attractor can be accomplished by regulating external signals. However, most of these studies until now have mainly focused on point attractors while ignoring cyclic ones. The aim of this study is to investigate an approach for reconciling abnormal periodic rhythms, such as diminished circadian amplitude and phase delay, to the regular rhythms of complex biological networks. For this purpose, we formulate and solve a mixed-integer nonlinear dynamic optimization problem simultaneously to identify regulation variables and to determine optimal control strategies for state transition and adjustment of periodic rhythms. Numerical experiments are implemented in three examples including a chaotic system, a mammalian circadian rhythm system and a gastric cancer gene regulatory network. The results show that regulating a small number of biochemical molecules in the network is sufficient to successfully drive the system to the target cyclic attractor by implementing an optimal control strategy.

Identification of regulatory variables for state transition of biological networks

Attractors represent steady states of biological networks. Recent studies have shown that regulatory variables can be used to steer a network state transition from an undesired attractor, such as a cancerous state, to a desired healthy one. Therefore, it is important to identify the regulatory variables and determine their time-dependent profile for state transition of a given network. However, this is a challenging task since regulatory variables have to be identified among numerous candidates in a large-scale biological network. In this study, we developed a new method for identifying regulatory variables in large-scale biological networks for the purpose of state transition. As a result, a set of optimal regulatory variables can be determined based on formulating and solving a mixed-integer nonlinear dynamic optimization problem. A relaxation scheme is used to overcome the difficulties in solving this complex problem containing a large number of binary variables. The solution to this problem simultaneously identifies the optimal regulatory variables, provides strength of regulatory interactions, and obtains the minimal control time to realize the required state transition. In addition, by adjusting the objective function, various combinations of the strength of regulatory interactions and the transition time can be achieved according to the requirement for disease therapy. Results of three case studies (a myeloid differentiation regulatory network, a cancer gene regulatory network, and a T-LGL signaling network) demonstrate the efficacy of the proposed approach. Therefore, this study establishes an appropriate framework for identifying the regulatory variables for state transition of complex biological networks.

A Survey of Real-Time Optimal Power Flow

There has been a strong increase of penetration of renewable energies into power systems. However, the renewables pose new challenges for the operation of the networks. Particularly, wind power is intermittently fluctuating, and, therefore, the network operator has to fast update the operations correspondingly. This task should be performed by an online optimization. Therefore, real-time optimal power flow (RT-OPF) has become an attractive topic in recent years. This paper presents an overview of recent studies on RT-OPF under wind energy penetration, offering a critical review of the major advancements in RT-OPF. It describes the challenges in the realization of the RT-OPF and presents available approaches to address these challenges. The paper focuses on a number of topics which are reviewed in chronological order of appearance: offline energy management systems (EMSs) (deterministic and stochastic approaches) and real-time EMSs (constraint satisfaction-based and OPF-based methods). The particular challenges associated with the incorporation of battery storage systems in the networks are explored, and it is concluded that the current research on RT-OPF is not sufficient, and new solution approaches are needed.

Production optimization for concentration and volume-limited fed-batch reactors in biochemical processes

Since a very slight violation of constraint could cause process safety and product quality problems in biochemical processes, an adaptive approach of fed-batch reactor production optimization that can strictly satisfy constraints over the entire operating time is presented. In this approach, an improved smooth function is proposed such that the inequality constraints can be transformed into smooth constraints. Based on this, only an auxiliary state is needed to monitor violations in the augmented performance index. Combined with control variable parameterization (CVP), the dynamic optimization is executed and constraint violations are examined by calculating the sensitivities of states to ensure that the inequality constraints are satisfied everywhere inside the time interval. Three biochemical production optimization problems, including the manufacturing of ethanol, penicillin and protein, are tested as illustrations. Meanwhile, comparisons with pure penalty CVP method, famous dynamic optimization toolbox DOTcvp and literature results are carried out. Research results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost.

Deciphering the regulation of metabolism with dynamic optimization: an overview of recent advances

Understanding optimality principles shaping the evolution of regulatory networks controlling metabolism is crucial for deriving a holistic picture of how metabolism is integrated into key cellular processes such as growth, adaptation and pathogenicity. While in the past the focus of research in pathway regulation was mainly based on stationary states, more recently dynamic optimization has proved to be an ideal tool to decipher regulatory strategies for metabolic pathways in response to environmental cues. In this short review, we summarize recent advances in the elucidation of optimal regulatory strategies and identification of optimal control points in metabolic pathways. We discuss biological implications of the discovered optimality principles on genome organization and provide examples how the derived knowledge can be used to identify new treatment strategies against pathogens. Furthermore, we briefly discuss the variety of approaches for solving dynamic optimization problems and emphasize whole-cell resource allocation models as an important emerging area of research that will allow us to study the regulation of metabolism on the whole-cell level.

Identification of optimal strategies for state transition of complex biological networks

Complex biological networks typically contain numerous parameters, and determining feasible strategies for state transition by parameter perturbation is not a trivial task. In the present study, based on dynamical and structural analyses of the biological network, we optimized strategies for controlling variables in a two-node gene regulatory network and a T-cell large granular lymphocyte signaling network associated with blood cancer by using an efficient dynamic optimization method. Optimization revealed the critical value for each decision variable to steer the system from an undesired state into a desired attractor. In addition, the minimum time for the state transition was determined by defining and solving a time-optimal control problem. Moreover, time-dependent variable profiles for state transitions were achieved rather than constant values commonly adopted in previous studies. Furthermore, the optimization method allows multiple controls to be simultaneously adjusted to drive the system out of an undesired attractor. Optimization improved the results of the parameter perturbation method, thus providing a valuable guidance for experimental design.

Dynamic optimization identifies optimal programmes for pathway regulation in prokaryotes

To survive in fluctuating environmental conditions, microorganisms must be able to quickly react to environmental challenges by upregulating the expression of genes encoding metabolic pathways. Here we show that protein abundance and protein synthesis capacity are key factors that determine the optimal strategy for the activation of a metabolic pathway. If protein abundance relative to protein synthesis capacity increases, the strategies shift from the simultaneous activation of all enzymes to the sequential activation of groups of enzymes and finally to a sequential activation of individual enzymes along the pathway. In the case of pathways with large differences in protein abundance, even more complex pathway activation strategies with a delayed activation of low abundance enzymes and an accelerated activation of high abundance enzymes are optimal. We confirm the existence of these pathway activation strategies as well as their dependence on our proposed constraints for a large number of metabolic pathways in several hundred prokaryotes.

Glucose-insulin regulation model with subcutaneous insulin injection and evaluation using diabetic inpatients data

Closed-loop insulin delivery systems often implement glucose measurement and insulin administration in the subcutis. However some existing models for glucose-insulin system ignored the dynamics of subcutaneous glucose and subcutaneously-injected insulin. This paper reports a two-compartment model that includes glucose and insulin dynamics in subcutis, and its evaluation using patient data. Clinical information such as glucose level, insulin dosage, insulin injection time and meals of anonymous diabetes inpatients was collected. Measured glucose level of the diabetic inpatients agrees with that of computer simulation. Due to the lack of glucose-insulin model with subcutaneously-injected insulin for type 2 diabetic patients, our model was compared with existing model for type 1 subjects. The new glucose-insulin model can mimic dynamics of glucose and insulin under the disturbance of insulin injections and meals. Model parameters were estimated using nonlinear least square method and their effect on pathology and physiology of diabetes were analyzed.

Optimal regulatory strategies for metabolic pathways in Escherichia coli depending on protein costs

While previous studies have shed light on the link between the structure of metabolism and its transcriptional regulation, the extent to which transcriptional regulation controls metabolism has not yet been fully explored. In this work, we address this problem by integrating a large number of experimental data sets with a model of the metabolism of Escherichia coli. Using a combination of computational tools including the concept of elementary flux patterns, methods from network inference and dynamic optimization, we find that transcriptional regulation of pathways reflects the protein investment into these pathways. While pathways that are associated to a high protein cost are controlled by fine-tuned transcriptional programs, pathways that only require a small protein cost are transcriptionally controlled in a few key reactions. As a reason for the occurrence of these different regulatory strategies, we identify an evolutionary trade-off between the conflicting requirements to reduce protein investment and the requirement to be able to respond rapidly to changes in environmental conditions.

Modeling the physiological glucose-insulin system on normal and diabetic subjects

This paper aims to present a mathematical model to describe the plasma glucose and insulin daily variations on normal and diabetic subjects. The proposed model consists of two delay differential equations (DDEs) where five adjustable parameters are used to characterize the respective dynamics and oscillation behavior of normal and diabetic subjects. Several clinical data tests demonstrate that the suggested model is practical to approach the daily-life glucose dynamics on normal, diabetic Type 1 and Type 2 subjects. Moreover, the corresponding parameters are fairly persuasive to identify the patients' conditions of physiological functions.