Multi-objective optimization of enzyme manipulations in metabolic networks considering resilience effects

Principles of Endocrine Regulation: Reconciling Tensions Between Robustness in Performance and Adaptation to Change

Endocrine regulation in the hypothalamic-pituitary-thyroid (HPT) axis is orchestrated by physiological circuits which integrate multiple internal and external influences. Essentially, it provides either of the two responses to overt biological challenges: to defend the homeostatic range of a target hormone or adapt it to changing environmental conditions. Under certain conditions, such flexibility may exceed the capability of a simple feedback control loop, rather requiring more intricate networks of communication between the system's components. A new minimal mathematical model, in the form of a parametrized nonlinear dynamical system, is here formulated as a proof-of-concept to elucidate the principles of the HPT axis regulation. In particular, it allows uncovering mechanisms for the homeostasis of the key biologically active hormone free triiodothyronine (FT3). One mechanism supports the preservation of FT3 homeostasis, whilst the other is responsible for the adaptation of the homeostatic state to a new level. Together these allow optimum resilience in stressful situations. Preservation of FT3 homeostasis, despite changes in FT4 and TSH levels, is found to be an achievable system goal by joining elements of top-down and bottom-up regulation in a cascade of targeted feedforward and feedback loops. Simultaneously, the model accounts for the combination of properties regarded as essential to endocrine regulation, namely sensitivity, the anticipation of an adverse event, robustness, and adaptation. The model therefore offers fundamental theoretical insights into the effective system control of the HPT axis.

Tryptophan Production Maximization in a Fed-Batch Bioreactor with Modified E. coli Cells, by Optimizing Its Operating Policy Based on an Extended Structured Cell Kinetic Model

Hybrid kinetic models, linking structured cell metabolic processes to the dynamics of macroscopic variables of the bioreactor, are more and more used in engineering evaluations to derive more precise predictions of the process dynamics under variable operating conditions. Depending on the cell model complexity, such a math tool can be used to evaluate the metabolic fluxes in relation to the bioreactor operating conditions, thus suggesting ways to genetically modify the microorganism for certain purposes. Even if development of such an extended dynamic model requires more experimental and computational efforts, its use is advantageous. The approached probative example refers to a model simulating the dynamics of nanoscale variables from several pathways of the central carbon metabolism (CCM) of Escherichia coli cells, linked to the macroscopic state variables of a fed-batch bioreactor (FBR) used for the tryptophan (TRP) production. The used E. coli strain was modified to replace the PTS system for glucose (GLC) uptake with a more efficient one. The study presents multiple elements of novelty: (i) the experimentally validated modular model itself, and (ii) its efficiency in computationally deriving an optimal operation policy of the FBR.

MOMO - multi-objective metabolic mixed integer optimization: application to yeast strain engineering

BACKGROUND

In this paper, we explore the concept of multi-objective optimization in the field of metabolic engineering when both continuous and integer decision variables are involved in the model. In particular, we propose a multi-objective model that may be used to suggest reaction deletions that maximize and/or minimize several functions simultaneously. The applications may include, among others, the concurrent maximization of a bioproduct and of biomass, or maximization of a bioproduct while minimizing the formation of a given by-product, two common requirements in microbial metabolic engineering.

RESULTS

Production of ethanol by the widely used cell factory Saccharomyces cerevisiae was adopted as a case study to demonstrate the usefulness of the proposed approach in identifying genetic manipulations that improve productivity and yield of this economically highly relevant bioproduct. We did an in vivo validation and we could show that some of the predicted deletions exhibit increased ethanol levels in comparison with the wild-type strain.

CONCLUSIONS

The multi-objective programming framework we developed, called MOMO, is open-source and uses POLYSCIP (Available at http://polyscip.zib.de/). as underlying multi-objective solver. MOMO is available at http://momo-sysbio.gforge.inria.fr.

Fuzzy Decision Making Approach to Identify Optimum Enzyme Targets and Drug Dosage for Remedying Presynaptic Dopamine Deficiency

Model-based optimization approaches are valuable in developing new drugs for human metabolic disorders. The core objective in most optimal drug designs is positive therapeutic effects. In this study, we considered the effects of therapeutic, adverse, and target variation simultaneously. A fuzzy optimization method was applied to formulate a multiobjective drug design problem for detecting enzyme targets in the presynaptic dopamine metabolic network to remedy two types of enzymopathies caused by deficiencies of vesicular monoamine transporter 2 (VMAT2) and tyrosine hydroxylase (TH). The fuzzy membership approach transforms a two-stage drug discovery problem into a unified decision-making problem. We developed a nested hybrid differential evolution algorithm to efficiently identify a set of potential drug targets. Furthermore, we also simulated the effects of current clinical drugs for Parkinson’s disease (PD) in this model and tried to clarify the possible causes of neurotoxic and neuroprotective effects. The optimal drug design could yield 100% satisfaction grade when both therapeutic effect and the number of targets were considered in the objective. This scenario required regulating one to three and one or two enzyme targets for 50%–95% and 50%–100% VMAT2 and TH deficiencies, respectively. However, their corresponding adverse and target variation effect grades were less satisfactory. For the most severe deficiencies of VMAT2 and TH, a compromise design could be obtained when the effects of therapeutic, adverse, and target variation were simultaneously applied to the optimal drug discovery problem. Such a trade-off design followed the no free lunch theorem for optimization; that is, a more serious dopamine deficiency required more enzyme targets and lower satisfaction grade. In addition, the therapeutic effects of current clinical medications for PD could be enhanced in combination with new enzyme targets. The increase of toxic metabolites after treatment might be the cause of neurotoxic effects of some current PD medications.

A Multi-State Optimization Framework for Parameter Estimation in Biological Systems

Parameter estimation is a key concern for reliable and predictive models of biological systems. In this paper, we propose a multi-objective, multi-state optimization framework that allows multiple data sources to be incorporated into the parameter estimation process. This enables the model to better represent a diverse range of data from both within and outwith the training set; and to determine more biologically relevant parameter values for the model parameters. The framework is based on a multi-objective PSwarm implementation (MoPSwarm) and is validated via a case study on the ERK signalling pathway, in which significant advantages over the conventional single-state approach are demonstrated. Several variants of the framework are analyzed to determine the optimal configuration for convergence and solution quality.

Fuzzy optimization for detecting enzyme targets of human uric acid metabolism

MOTIVATION

Mathematical modeling and optimization have been used for detecting enzyme targets in human metabolic disorders. Such optimal drug design methods are generally differentiated as two stages, identification and decision-making, to find optimal targets. We developed a unified method named fuzzy equal metabolic adjustment to formulate an optimal enzyme target design problem for drug discovery. The optimization framework combines the identification of enzyme targets and a decision-making strategy simultaneously. The objectives of this algorithm include evaluations of the therapeutic effect of target enzymes, the adverse effects of drugs and the minimum effective dose (MED).

RESULTS

An existing generalized mass action system model of human uric acid (UA) metabolism was used to formulate the fuzzy optimization method for detecting two types of enzymopathies: hyperuricemia caused by phosphoribosylpyrophosphate synthetase (PRPPS) overactivity and Lesch-Nyhan syndrome. The fuzzy objectives were set so that the concentrations of the metabolites were as close as possible to the healthy levels. The target design included a diet control of ribose-5-phospahate (R5P). The diet control of R5P served as an extra remedy to reduce phosphate uptake entering the purine metabolic pathway, so that we could obtain a more satisfactory treatment than obtained for those without a diet control. Moreover, enhancing UA excretion resulted in an effective treatment of hyperuricemia caused by PRPPS overactivity. This result correlates with using probenecid and benbromazone, which are uricosuric agents present in current clinical medications. By contrast, the Lesch-Nyhan syndrome required at least three enzyme targets to cure hyperuricemia.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and Pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.