Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data

From observational to actionable: rethinking omics in biologics production

As the era of omics continues to expand with increasing ubiquity and success in both academia and industry, omics-based experiments are becoming commonplace in industrial biotechnology, including efforts to develop novel solutions in bioprocess optimization and cell line development. Omic technologies provide particularly valuable 'observational' insights for discovery science, especially in academic research and industrial R&D; however, biomanufacturing requires a different paradigm to unlock 'actionable' insights from omics. Here, we argue the value of omic experiments in biotechnology can be maximized with deliberate selection of omic approaches and forethought about analysis techniques. We describe important considerations when designing and implementing omic-based experiments and discuss how systems biology analysis strategies can enhance efforts to obtain actionable insights in mammalian-based biologics production.

Evaluation of Lung Cancer Patient Response to First-Line Chemotherapy by Integration of Tumor Core Biopsy Metabolomics with Multiscale Modeling

The standard of care for intermediate (Stage II) and advanced (Stages III and IV) non-small cell lung cancer (NSCLC) involves chemotherapy with taxane/platinum derivatives, with or without radiation. Ideally, patients would be screened a priori to allow non-responders to be initially treated with second-line therapies. This evaluation is non-trivial, however, since tumors behave as complex multiscale systems. To address this need, this study employs a multiscale modeling approach to evaluate first-line chemotherapy response of individual patient tumors based on metabolomic analysis of tumor core biopsies obtained during routine clinical evaluation. Model parameters were calculated for a patient cohort as a function of these metabolomic profiles, previously obtained from high-resolution 2DLC-MS/MS analysis. Evaluation metrics were defined to classify patients as Disease-Control (DC) [encompassing complete-response (CR), partial-response (PR), and stable-disease (SD)] and Progressive-Disease (PD) following first-line chemotherapy. Response was simulated for each patient and compared to actual response. The results show that patient classifications were significantly separated from each other, and also when grouped as DC vs. PD and as CR/PR vs. SD/PD, by fraction of initial tumor radius metric at 6 days post simulated bolus drug injection. This study shows that patient first-line chemotherapy response can in principle be evaluated from multiscale modeling integrated with tumor tissue metabolomic data, offering a first step towards individualized lung cancer treatment prognosis.

Metabolic Fingerprinting of Fabry Disease: Diagnostic and Prognostic Aspects

Fabry disease (FD) is an X-linked lysosomal disease due to a deficiency in the activity of the lysosomal-galactosidase A (GalA), a key enzyme in the glycosphingolipid degradation pathway. FD is a complex disease with a poor genotype–phenotype correlation. In the early stages, FD could involve the peripheral nervous system (acroparesthesias and dysautonomia) and the ski (angiokeratoma), but later kidney, heart or central nervous system impairment may significantly decrease life expectancy. The advent of omics technologies offers the possibility of a global, integrated and systemic approach well-suited for the exploration of this complex disease. In this narrative review, we will focus on the main metabolomic studies, which have underscored the importance of detecting biomarkers for a diagnostic and prognostic purpose in FD. These investigations are potentially useful to explain the wide clinical, biochemical and molecular heterogeneity found in FD patients. Moreover, the quantitative mass spectrometry methods developed to evaluate concentrations of these biomarkers in urine and plasma will be described. Finally, the complex metabolic biomarker profile depicted in FD patients will be reported, which varies according to gender, types of mutations, and therapeutic treatment.

Modeling of Tumor Growth with Input from Patient-Specific Metabolomic Data

Advances in omic technologies have provided insight into cancer progression and treatment response. However, the nonlinear characteristics of cancer growth present a challenge to bridge from the molecular- to the tissue-scale, as tumor behavior cannot be encapsulated by the sum of the individual molecular details gleaned experimentally. Mathematical modeling and computational simulation have been traditionally employed to facilitate analysis of nonlinear systems. In this study, for the first time tumor metabolomic data are linked via mathematical modeling to the tumor tissue-scale behavior, showing the capability to mechanistically simulate cancer progression personalized to omic information obtainable from patient tumor core biopsy analysis. Generally, a higher degree of metabolic dysregulation has been correlated with more aggressive tumor behavior. Accordingly, key parameters influenced by metabolomic data in this model include tumor proliferation, vascularization, aggressiveness, lactic acid production, monocyte infiltration and macrophage polarization, and drug effect. The model enables evaluating interactions of interest between these parameters which drive tumor growth based on the metabolomic data. The results show that the model can group patients consistently with the clinically observed outcomes of response/non-response to chemotherapy. This modeling approach provides a first step towards evaluation of tumor growth based on tumor-specific metabolomic data.

Improving the performance of machine learning models for biotechnology: The quest for deus ex machina

Machine learning is becoming an integral part of the Design-Build-Test-Learn cycle in biotechnology. Machine learning models learn from collected datasets such as omics data and predict a defined outcome, which has led to both production improvements and predictive tools in the field. Robust prediction of the behavior of microbial cell factories and production processes not only greatly increases our understanding of the function of such systems, but also provides significant savings of development time. However, many pitfalls when modeling biological data - bad fit, noisy data, model instability, low data quantity and imbalances in the data - cause models to suffer in their performance. Here we provide an accessible, in-depth analysis on the problems created by these pitfalls, as well as means of their detection and mediation, with a focus on supervised learning. Assessing the state of the art, we show that, currently, in-depth analyses of model performance are often absent and must be improved. This review provides a toolbox for the analysis of model robustness and performance, and simultaneously proposes a standard for the community to facilitate future work. It is further accompanied by an interactive online tutorial on the discussed issues.

Root locus-based stability analysis for biological systems

Background: The first objective for realizing and handling biological systems is to choose a suitable model prototype and then perform structure and parameter identification. Afterwards, a theoretical analysis is needed to understand the characteristics, abilities, and limitations of the underlying systems. Generalized Michaelis-Menten kinetics (MM) and S-systems are two well-known biochemical system theory-based models. Research on steady-state estimation of generalized MM systems is difficult because of their complex structure. Further, theoretical analysis of S-systems is still difficult because of the power-law structure, and even the estimation of steady states can be easily achieved via algebraic equations. Aim: We focus on how to flexibly use control technologies to perform deeper biological system analysis. Methods: For generalized MM systems, the root locus method (proposed by Walter R. Evans) is used to predict the direction and rate (flux) limitations of the reaction and to estimate the steady states and stability margins (relative stability). Mode analysis is additionally introduced to discuss the transient behavior and the setting time. For S-systems, the concept of root locus, mode analysis, and the converse theorem are used to predict the dynamic behavior, to estimate the setting time and to analyze the relative stability of systems. Theoretical results were examined via simulation in a Simulink/MATLAB environment. Results: Four kinds of small functional modules (a system with reversible MM kinetics, a system with a singular or nearly singular system matrix and systems with cascade or branch pathways) are used to describe the proposed strategies clearly. For the reversible MM kinetics system, we successfully predict the direction and the rate (flux) limitations of reactions and obtain the values of steady state and net flux. We observe that theoretically derived results are consistent with simulation results. Good prediction is observed ([Formula: see text]% accuracy). For the system with a (nearly) singular matrix, we demonstrate that the system is neither globally exponentially stable nor globally asymptotically stable but globally semistable. The system possesses an infinite gain margin (GM denoting how much the gain can increase before the system becomes unstable) regardless of how large or how small the values of independent variables are, but the setting time decreases and then increases or always decreases as the values of independent variables increase. For S-systems, we first demonstrate that the stability of S-systems can be determined by linearized systems via root loci, mode analysis, and block diagram-based simulation. The relevant S-systems possess infinite GM for the values of independent variables varying from zero to infinity, and the setting time increases as the values of independent variables increase. Furthermore, the branch pathway maintains oscillation until a steady state is reached, but the oscillation phenomenon does not exist in the cascade pathway because in this system, all of the root loci are located on real lines. The theoretical predictions of dynamic behavior for these two systems are consistent with the simulation results. This study provides a guideline describing how to choose suitable independent variables such that systems possess satisfactory performance for stability margins, setting time and dynamic behavior. Conclusion: The proposed root locus-based analysis can be applied to any kind of differential equation-based biological system. This research initiates a method to examine system dynamic behavior and to discuss operating principles.

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

Biosystems Design by Machine Learning

Biosystems such as enzymes, pathways, and whole cells have been increasingly explored for biotechnological applications. However, the intricate connectivity and resulting complexity of biosystems poses a major hurdle in designing biosystems with desirable features. As -omics and other high throughput technologies have been rapidly developed, the promise of applying machine learning (ML) techniques in biosystems design has started to become a reality. ML models enable the identification of patterns within complicated biological data across multiple scales of analysis and can augment biosystems design applications by predicting new candidates for optimized performance. ML is being used at every stage of biosystems design to help find nonobvious engineering solutions with fewer design iterations. In this review, we first describe commonly used models and modeling paradigms within ML. We then discuss some applications of these models that have already shown success in biotechnological applications. Moreover, we discuss successful applications at all scales of biosystems design, including nucleic acids, genetic circuits, proteins, pathways, genomes, and bioprocesses. Finally, we discuss some limitations of these methods and potential solutions as well as prospects of the combination of ML and biosystems design.

Machine and deep learning meet genome-scale metabolic modeling

Omic data analysis is steadily growing as a driver of basic and applied molecular biology research. Core to the interpretation of complex and heterogeneous biological phenotypes are computational approaches in the fields of statistics and machine learning. In parallel, constraint-based metabolic modeling has established itself as the main tool to investigate large-scale relationships between genotype, phenotype, and environment. The development and application of these methodological frameworks have occurred independently for the most part, whereas the potential of their integration for biological, biomedical, and biotechnological research is less known. Here, we describe how machine learning and constraint-based modeling can be combined, reviewing recent works at the intersection of both domains and discussing the mathematical and practical aspects involved. We overlap systematic classifications from both frameworks, making them accessible to nonexperts. Finally, we delineate potential future scenarios, propose new joint theoretical frameworks, and suggest concrete points of investigation for this joint subfield. A multiview approach merging experimental and knowledge-driven omic data through machine learning methods can incorporate key mechanistic information in an otherwise biologically-agnostic learning process.

Nutrimetabolomics: An Integrative Action for Metabolomic Analyses in Human Nutritional Studies

The life sciences are currently being transformed by an unprecedented wave of developments in molecular analysis, which include important advances in instrumental analysis as well as biocomputing. In light of the central role played by metabolism in nutrition, metabolomics is rapidly being established as a key analytical tool in human nutritional studies. Consequently, an increasing number of nutritionists integrate metabolomics into their study designs. Within this dynamic landscape, the potential of nutritional metabolomics (nutrimetabolomics) to be translated into a science, which can impact on health policies, still needs to be realized. A key element to reach this goal is the ability of the research community to join, to collectively make the best use of the potential offered by nutritional metabolomics. This article, therefore, provides a methodological description of nutritional metabolomics that reflects on the state-of-the-art techniques used in the laboratories of the Food Biomarker Alliance (funded by the European Joint Programming Initiative "A Healthy Diet for a Healthy Life" (JPI HDHL)) as well as points of reflections to harmonize this field. It is not intended to be exhaustive but rather to present a pragmatic guidance on metabolomic methodologies, providing readers with useful "tips and tricks" along the analytical workflow.

Using metabolome data for mathematical modeling of plant metabolic systems

Plant metabolism is characterized by a wide diversity of metabolites, with systems far more complicated than those of microorganisms. Mathematical modeling is useful for understanding dynamic behaviors of plant metabolic systems for metabolic engineering. Time-series metabolome data has great potential for estimating kinetic model parameters to construct a genome-wide metabolic network model. However, data obtained by current metabolomics techniques does not meet the requirement for constructing accurate models. In this article, we highlight novel strategies and algorithms to handle the underlying difficulties and construct dynamic in vivo models for large-scale plant metabolic systems. The coarse but efficient modeling enables the prediction of unknown mechanisms regulating plant metabolism.

Machine Learning Methods for Analysis of Metabolic Data and Metabolic Pathway Modeling

Machine learning uses experimental data to optimize clustering or classification of samples or features, or to develop, augment or verify models that can be used to predict behavior or properties of systems. It is expected that machine learning will help provide actionable knowledge from a variety of big data including metabolomics data, as well as results of metabolism models. A variety of machine learning methods has been applied in bioinformatics and metabolism analyses including self-organizing maps, support vector machines, the kernel machine, Bayesian networks or fuzzy logic. To a lesser extent, machine learning has also been utilized to take advantage of the increasing availability of genomics and metabolomics data for the optimization of metabolic network models and their analysis. In this context, machine learning has aided the development of metabolic networks, the calculation of parameters for stoichiometric and kinetic models, as well as the analysis of major features in the model for the optimal application of bioreactors. Examples of this very interesting, albeit highly complex, application of machine learning for metabolism modeling will be the primary focus of this review presenting several different types of applications for model optimization, parameter determination or system analysis using models, as well as the utilization of several different types of machine learning technologies.

Effects of Storage Time on Glycolysis in Donated Human Blood Units

Background: Donated blood is typically stored before transfusions. During storage, the metabolism of red blood cells changes, possibly causing storage lesions. The changes are storage time dependent and exhibit donor-specific variations. It is necessary to uncover and characterize the responsible molecular mechanisms accounting for such biochemical changes, qualitatively and quantitatively; Study Design and Methods: Based on the integration of metabolic time series data, kinetic models, and a stoichiometric model of the glycolytic pathway, a customized inference method was developed and used to quantify the dynamic changes in glycolytic fluxes during the storage of donated blood units. The method provides a proof of principle for the feasibility of inferences regarding flux characteristics from metabolomics data; Results: Several glycolytic reaction steps change substantially during storage time and vary among different fluxes and donors. The quantification of these storage time effects, which are possibly irreversible, allows for predictions of the transfusion outcome of individual blood units; Conclusion: The improved mechanistic understanding of blood storage, obtained from this computational study, may aid the identification of blood units that age quickly or more slowly during storage, and may ultimately improve transfusion management in clinics.