Kinetic modeling of cell metabolism for microbial production

Structural and practical identifiability analysis in bioengineering: a beginner's guide

Advancements in digital technology have brought modelling to the forefront in many disciplines from healthcare to architecture. Mathematical models, often represented using parametrised sets of ordinary differential equations, can be used to characterise different processes. To infer possible estimates for the unknown parameters, these models are usually calibrated using associated experimental data. Structural and practical identifiability analyses are a key component that should be assessed prior to parameter estimation. This is because identifiability analyses can provide insights as to whether or not a parameter can take on single, multiple, or even infinitely or countably many values which will ultimately have an impact on the reliability of the parameter estimates. Also, identifiability analyses can help to determine whether the data collected are sufficient or of good enough quality to truly estimate the parameters or if more data or even reparameterization of the model is necessary to proceed with the parameter estimation process. Thus, such analyses also provide an important role in terms of model design (structural identifiability analysis) and the collection of experimental data (practical identifiability analysis). Despite the popularity of using data to estimate the values of unknown parameters, structural and practical identifiability analyses of these models are often overlooked. Possible reasons for non-consideration of application of such analyses may be lack of awareness, accessibility, and usability issues, especially for more complicated models and methods of analysis. The aim of this study is to introduce and perform both structural and practical identifiability analyses in an accessible and informative manner via application to well established and commonly accepted bioengineering models. This will help to improve awareness of the importance of this stage of the modelling process and provide bioengineering researchers with an understanding of how to utilise the insights gained from such analyses in future model development.

Community-scale models of microbiomes: Articulating metabolic modelling and metagenome sequencing

Building models is essential for understanding the functions and dynamics of microbial communities. Metabolic models built on genome-scale metabolic network reconstructions (GENREs) are especially relevant as a means to decipher the complex interactions occurring among species. Model reconstruction increasingly relies on metagenomics, which permits direct characterisation of naturally occurring communities that may contain organisms that cannot be isolated or cultured. In this review, we provide an overview of the field of metabolic modelling and its increasing reliance on and synergy with metagenomics and bioinformatics. We survey the means of assigning functions and reconstructing metabolic networks from (meta-)genomes, and present the variety and mathematical fundamentals of metabolic models that foster the understanding of microbial dynamics. We emphasise the characterisation of interactions and the scaling of model construction to large communities, two important bottlenecks in the applicability of these models. We give an overview of the current state of the art in metagenome sequencing and bioinformatics analysis, focusing on the reconstruction of genomes in microbial communities. Metagenomics benefits tremendously from third-generation sequencing, and we discuss the opportunities of long-read sequencing, strain-level characterisation and eukaryotic metagenomics. We aim at providing algorithmic and mathematical support, together with tool and application resources, that permit bridging the gap between metagenomics and metabolic modelling.

Flux balance analysis-based metabolic modeling of microbial secondary metabolism: Current status and outlook

In microorganisms, different from primary metabolism for cellular growth, secondary metabolism is for ecological interactions and stress responses and an important source of natural products widely used in various areas such as pharmaceutics and food additives. With advancements of sequencing technologies and bioinformatics tools, a large number of biosynthetic gene clusters of secondary metabolites have been discovered from microbial genomes. However, due to challenges from the difficulty of genome-scale pathway reconstruction and the limitation of conventional flux balance analysis (FBA) on secondary metabolism, the quantitative modeling of secondary metabolism is poorly established, in contrast to that of primary metabolism. This review first discusses current efforts on the reconstruction of secondary metabolic pathways in genome-scale metabolic models (GSMMs), as well as related FBA-based modeling techniques. Additionally, potential extensions of FBA are suggested to improve the prediction accuracy of secondary metabolite production. As this review posits, biosynthetic pathway reconstruction for various secondary metabolites will become automated and a modeling framework capturing secondary metabolism onset will enhance the predictive power. Expectedly, an improved FBA-based modeling workflow will facilitate quantitative study of secondary metabolism and in silico design of engineering strategies for natural product production.

From Spatial-Temporal Multiscale Modeling to Application: Bridging the Valley of Death in Industrial Biotechnology

The Valley of Death confronts industrial biotechnology with a significant challenge to the commercialization of products. Fortunately, with the integration of computation, automation and artificial intelligence (AI) technology, the industrial biotechnology accelerates to cross the Valley of Death. The Fourth Industrial Revolution (Industry 4.0) has spurred advanced development of intelligent biomanufacturing, which has evolved the industrial structures in line with the worldwide trend. To achieve this, intelligent biomanufacturing can be structured into three main parts that comprise digitalization, modeling and intellectualization, with modeling forming a crucial link between the other two components. This paper provides an overview of mechanistic models, data-driven models and their applications in bioprocess development. We provide a detailed elaboration of the hybrid model and its applications in bioprocess engineering, including strain design, process control and optimization, as well as bioreactor scale-up. Finally, the challenges and opportunities of biomanufacturing towards Industry 4.0 are also discussed.

A dynamic kinetic model captures cell-free metabolism for improved butanol production

Cell-free systems are useful tools for prototyping metabolic pathways and optimizing the production of various bioproducts. Mechanistically-based kinetic models are uniquely suited to analyze dynamic experimental data collected from cell-free systems and provide vital qualitative insight. However, to date, dynamic kinetic models have not been applied with rigorous biological constraints or trained on adequate experimental data to the degree that they would give high confidence in predictions and broadly demonstrate the potential for widespread use of such kinetic models. In this work, we construct a large-scale dynamic model of cell-free metabolism with the goal of understanding and optimizing butanol production in a cell-free system. Using a combination of parameterization methods, the resultant model captures experimental metabolite measurements across two experimental conditions for nine metabolites at timepoints between 0 and 24 h. We present analysis of the model predictions, provide recommendations for butanol optimization, and identify the aldehyde/alcohol dehydrogenase as the primary bottleneck in butanol production. Sensitivity analysis further reveals the extent to which various parameters are constrained, and our approach for probing valid parameter ranges can be applied to other modeling efforts.

Predicting plant growth response under fluctuating temperature by carbon balance modelling

Quantification of system dynamics is a central aim of mathematical modelling in biology. Defining experimentally supported functional relationships between molecular entities by mathematical terms enables the application of computational routines to simulate and analyse the underlying molecular system. In many fields of natural sciences and engineering, trigonometric functions are applied to describe oscillatory processes. As biochemical oscillations occur in many aspects of biochemistry and biophysics, Fourier analysis of metabolic functions promises to quantify, describe and analyse metabolism and its reaction towards environmental fluctuations. Here, Fourier polynomials were developed from experimental time-series data and combined with block diagram simulation of plant metabolism to study heat shock response of photosynthetic CO₂ assimilation and carbohydrate metabolism in Arabidopsis thaliana. Simulations predicted a stabilising effect of reduced sucrose biosynthesis capacity and increased capacity of starch biosynthesis on carbon assimilation under transient heat stress. Model predictions were experimentally validated by quantifying plant growth under such stress conditions. In conclusion, this suggests that Fourier polynomials represent a predictive mathematical approach to study dynamic plant-environment interactions.

Synergisms of machine learning and constraint-based modeling of metabolism for analysis and optimization of fermentation parameters

Recent noteworthy advances in the development of high-performing microbial and mammalian strains have enabled the sustainable production of bio-economically valuable substances such as bio-compounds, biofuels, and biopharmaceuticals. However, to obtain an industrially viable mass-production scheme, much time and effort are required. The robust and rational design of fermentation processes requires analysis and optimization of different extracellular conditions and medium components, which have a massive effect on growth and productivity. In this regard, knowledge- and data-driven modeling methods have received much attention. Constraint-based modeling (CBM) is a knowledge-driven mathematical approach that has been widely used in fermentation analysis and optimization due to its capabilities of predicting the cellular phenotype from genotype through high-throughput means. On the other hand, machine learning (ML) is a data-driven statistical method that identifies the data patterns within sophisticated biological systems and processes, where there is inadequate knowledge to represent underlying mechanisms. Furthermore, ML models are becoming a viable complement to constraint-based models in a reciprocal manner when one is used as a pre-step of another. As a result, more predictable model is produced. This review highlights the applications of CBM and ML independently and the combination of these two approaches for analyzing and optimizing fermentation parameters. This article is protected by copyright. All rights reserved.

Integrating systemic and molecular levels to infer key drivers sustaining metabolic adaptations

Metabolic adaptations to complex perturbations, like the response to pharmacological treatments in multifactorial diseases such as cancer, can be described through measurements of part of the fluxes and concentrations at the systemic level and individual transporter and enzyme activities at the molecular level. In the framework of Metabolic Control Analysis (MCA), ensembles of linear constraints can be built integrating these measurements at both systemic and molecular levels, which are expressed as relative differences or changes produced in the metabolic adaptation. Here, combining MCA with Linear Programming, an efficient computational strategy is developed to infer additional non-measured changes at the molecular level that are required to satisfy these constraints. An application of this strategy is illustrated by using a set of fluxes, concentrations, and differentially expressed genes that characterize the response to cyclin-dependent kinases 4 and 6 inhibition in colon cancer cells. Decreases and increases in transporter and enzyme individual activities required to reprogram the measured changes in fluxes and concentrations are compared with down-regulated and up-regulated metabolic genes to unveil those that are key molecular drivers of the metabolic response.

Deciphering the essential events in the reprogramming of metabolic networks subjected to complex perturbations, including the response to pharmacological treatments in multifactorial diseases like cancer, is crucial for the design of efficient therapies. Yet, tools to infer the molecular drivers sustaining such metabolic responses remain elusive for large metabolic networks. Here we develop an efficient computational strategy that integrates measured changes at systemic and molecular levels and combines metabolic control analysis with linear programming tools to infer key molecular drivers sustaining the metabolic adaptations to complex perturbations, such as an antitumoral drug therapy. The collective behavior is approximated using linear expressions where the adaptation of systemic concentrations and fluxes to a perturbation is described as a function of the molecular reprogramming of transport and enzyme activities. Starting from measured changes in fluxes and concentrations, we identify changes in the reprogramming of transporter and enzyme activities that are required to orchestrate the metabolic adaptation of colon cancer cells to a cell cycle inhibitor.

Constraint-based metabolic control analysis for rational strain engineering

The advancements in genome editing techniques over the past years have rekindled interest in rational metabolic engineering strategies. While Metabolic Control Analysis (MCA) is a well-established method for quantifying the effects of metabolic engineering interventions on flows in metabolic networks and metabolite concentrations, it does not consider the physiological limitations of the cellular environment and metabolic engineering design constraints. We report here a constraint-based framework, Network Response Analysis (NRA), for rational genetic strain design. NRA is cast as a Mixed-Integer Linear Programming problem that integrates MCA, Thermodynamically-based Flux Analysis (TFA), biologically relevant constraints, as well as genome editing restrictions into a comprehensive platform for identifying metabolic engineering targets. We show that the NRA formulation and its core constraints are equivalent to the ones of Flux Balance Analysis (FBA) and TFA, which allows it to be used for a wide range of optimization criteria and with various physiological constraints. We also show how the parametrization and introduction of biological constraints enhance the NRA formulation compared to the classical MCA approach, and we demonstrate its features and its ability to generate multiple alternative optimal strategies given several user-defined boundaries and objectives. In summary, NRA is a sophisticated alternative to classical MCA for rational metabolic engineering that accommodates the incorporation of physiological data at metabolic flux, metabolite concentration, and enzyme expression levels.

Atlas: automatic modeling of regulation of bacterial gene expression and metabolism using rule-based languages

MOTIVATION

Cells are complex systems composed of hundreds of genes whose products interact to produce elaborated behaviors. To control such behaviors, cells rely on transcription factors to regulate gene expression, and gene regulatory networks (GRNs) are employed to describe and understand such behavior. However, GRNs are static models, and dynamic models are difficult to obtain due to their size, complexity, stochastic dynamics and interactions with other cell processes.

RESULTS

We developed Atlas, a Python software that converts genome graphs and gene regulatory, interaction and metabolic networks into dynamic models. The software employs these biological networks to write rule-based models for the PySB framework. The underlying method is a divide-and-conquer strategy to obtain sub-models and combine them later into an ensemble model. To exemplify the utility of Atlas, we used networks of varying size and complexity of Escherichia coli and evaluated in silico modifications, such as gene knockouts and the insertion of promoters and terminators. Moreover, the methodology could be applied to the dynamic modeling of natural and synthetic networks of any bacteria.

AVAILABILITY AND IMPLEMENTATION

Code, models and tutorials are available online (https://github.com/networkbiolab/atlas).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Model Parameterization with Quantitative Proteomics: Case Study with Trehalose Metabolism in Saccharomyces cerevisiae

When Saccharomyces cerevisiae undergoes heat stress it stimulates several changes that are necessary for its survival, notably in carbon metabolism. Notable changes include increase in trehalose production and glycolytic flux. The increase in glycolytic flux has been postulated to be due to the regulatory effects in upper glycolysis, but this has not been confirmed. Additionally, trehalose is a useful industrial compound for its protective properties. A model of trehalose metabolism in S. cerevisiae was constructed using Convenient Modeller, a software that uses a combination of convenience kinetics and a genetic algorithm. The model was parameterized with quantitative omics under standard conditions and validated using data collected under heat stress conditions. The completed model was used to show that feedforward activation of pyruvate kinase by fructose 1,6-bisphosphate during heat stress contributes to the increase in metabolic flux. We were also able to demonstrate in silico that overexpression of enzymes involved in production and degradation of trehalose can lead to higher trehalose yield in the cell. By integrating quantitative proteomics with metabolic modelling, we were able to confirm that the flux increase in trehalose metabolic pathways during heat stress is due to regulatory effects and not purely changes in enzyme expression. The overexpression of enzymes involved in trehalose metabolism is a potential approach to be exploited for trehalose production without need for increasing temperature.

KiMoSys 2.0: an upgraded database for submitting, storing and accessing experimental data for kinetic modeling

The KiMoSys (https://kimosys.org), launched in 2014, is a public repository of published experimental data, which contains concentration data of metabolites, protein abundances and flux data. It offers a web-based interface and upload facility to share data, making it accessible in structured formats, while also integrating associated kinetic models related to the data. In addition, it also supplies tools to simplify the construction process of ODE (Ordinary Differential Equations)-based models of metabolic networks. In this release, we present an update of KiMoSys with new data and several new features, including (i) an improved web interface, (ii) a new multi-filter mechanism, (iii) introduction of data visualization tools, (iv) the addition of downloadable data in machine-readable formats, (v) an improved data submission tool, (vi) the integration of a kinetic model simulation environment and (vii) the introduction of a unique persistent identifier system. We believe that this new version will improve its role as a valuable resource for the systems biology community. Database URL:  www.kimosys.org.

Identification of flux checkpoints in a metabolic pathway through white-box, grey-box and black-box modeling approaches

Metabolic pathway modeling plays an increasing role in drug design by allowing better understanding of the underlying regulation and controlling networks in the metabolism of living organisms. However, despite rapid progress in this area, pathway modeling can become a real nightmare for researchers, notably when few experimental data are available or when the pathway is highly complex. Here, three different approaches were developed to model the second part of glycolysis of E. histolytica as an application example, and have succeeded in predicting the final pathway flux: one including detailed kinetic information (white-box), another with an added adjustment term (grey-box) and the last one using an artificial neural network method (black-box). Afterwards, each model was used for metabolic control analysis and flux control coefficient determination. The first two enzymes of this pathway are identified as the key enzymes playing a role in flux control. This study revealed the significance of the three methods for building suitable models adjusted to the available data in the field of metabolic pathway modeling, and could be useful to biologists and modelers.

Metabolic Modelling as a Framework for Metabolomics Data Integration and Analysis

Metabolic networks are regulated to ensure the dynamic adaptation of biochemical reaction fluxes to maintain cell homeostasis and optimal metabolic fitness in response to endogenous and exogenous perturbations. To this end, metabolism is tightly controlled by dynamic and intricate regulatory mechanisms involving allostery, enzyme abundance and post-translational modifications. The study of the molecular entities involved in these complex mechanisms has been boosted by the advent of high-throughput technologies. The so-called omics enable the quantification of the different molecular entities at different system layers, connecting the genotype with the phenotype. Therefore, the study of the overall behavior of a metabolic network and the omics data integration and analysis must be approached from a holistic perspective. Due to the close relationship between metabolism and cellular phenotype, metabolic modelling has emerged as a valuable tool to decipher the underlying mechanisms governing cell phenotype. Constraint-based modelling and kinetic modelling are among the most widely used methods to study cell metabolism at different scales, ranging from cells to tissues and organisms. These approaches enable integrating metabolomic data, among others, to enhance model predictive capabilities. In this review, we describe the current state of the art in metabolic modelling and discuss future perspectives and current challenges in the field.

Kinetic model optimization and its application to mitigating the Warburg effect through multiple enzyme alterations

Pathway engineering is a powerful tool in biotechnological and clinical applications. However, many phenomena cannot be rewired with a single enzyme change, and in a complex network like energy metabolism, the selection of combinations of targets to engineer is a daunting task. To facilitate this process, we have developed an optimization framework and applied it to a mechanistic kinetic model of energy metabolism. We then identified combinations of enzyme alternations that led to the elimination of the Warburg effect seen in the metabolism of cancer cells and cell lines, a phenomenon coupling rapid proliferation to lactate production. Typically, optimization approaches use integer variables to achieve the desired flux redistribution with a minimum number of altered genes. This framework uses convex penalty terms to replace these integer variables and improve computational tractability. Optimal solutions are identified which substantially reduce or eliminate lactate production while maintaining the requirements for cellular proliferation using three or more enzymes.

Kinetic modeling of Stickland reactions-coupled methanogenesis for a methanogenic culture

Studying amino acid catabolism-coupled methanogenesis is the important standpoints to decipher the metabolic behavior of a methanogenic culture. l-Glycine and l-alanine are acted as sole carbon and nitrogen sources for acidogenic bacteria. One amino acid is oxidized and another one is reduced for acetate production via pyruvate by oxidative deamination process in the Stickland reactions. Herein, we have developed a kinetic model for the Stickland reactions-coupled methanogenesis (SRCM) and simulated objectively to maximize the rate of methane production. We collected the metabolic information from enzyme kinetic parameters for amino acid catabolism of Clostridium acetobutylicum ATCC 824 and methanogenesis of Methanosarcina acetivorans C2A. The SRCM model of this study consisted of 18 reactions and 61 metabolites with enzyme kinetic parameters derived experimental data. The internal or external metabolic flux rate of this system found to control the acidogenesis and methanogenesis in a methanogenic culture. Using the SRCM model, flux distributions were calculated for each reaction and metabolite in order to maximize the methane production rate from the glycine–alanine pair. Results of this study, we demonstrated the metabolic behavior, metabolite pairing while mutually interact, and advantages of syntrophic metabolism of amino acid-directed methane production in a methanogenic starter culture.

Comprehensive analysis of a metabolic model for lipid production in Rhodosporidium toruloides

The yeast Rhodosporidium toruloides has been extensively studied for its application in biolipid production. The knowledge of its metabolism capabilities and the application of constraint-based flux analysis methodology provide useful information for process prediction and optimization. The accuracy of the resulting predictions is highly dependent on metabolic models. A metabolic reconstruction for R. toruloides metabolism has been recently published. On the basis of this model, we developed a curated version that unblocks the central nitrogen metabolism and, in addition, completes charge and mass balances in some reactions neglected in the former model. Then, a comprehensive analysis of network capability was performed with the curated model and compared with the published metabolic reconstruction. The flux distribution obtained by lipid optimization with flux balance analysis was able to replicate the internal biochemical changes that lead to lipogenesis in oleaginous microorganisms. These results motivate the development of a genome-scale model for complete elucidation of R. toruloides metabolism.

Fermentation of Saccharomyces cerevisiae - Combining kinetic modeling and optimization techniques points out avenues to effective process design

A combined experimental/theoretical approach is presented, for improving the predictability of Saccharomyces cerevisiae fermentations. In particular, a mathematical model was developed explicitly taking into account the main mechanisms of the fermentation process, allowing for continuous computation of key process variables, including the biomass concentration and the respiratory quotient (RQ). For model calibration and experimental validation, batch and fed-batch fermentations were carried out. Comparison of the model-predicted biomass concentrations and RQ developments with the corresponding experimentally recorded values shows a remarkably good agreement for both batch and fed-batch processes, confirming the adequacy of the model. Furthermore, sensitivity studies were performed, in order to identify model parameters whose variations have significant effects on the model predictions: our model responds with significant sensitivity to the variations of only six parameters. These studies provide a valuable basis for model reduction, as also demonstrated in this paper. Finally, optimization-based parametric studies demonstrate how our model can be utilized for improving the efficiency of Saccharomyces cerevisiae fermentations.

Acceleration Strategies to Enhance Metabolic Ensemble Modeling Performance

Developing reliable, predictive kinetic models of metabolism is a difficult, yet necessary, priority toward understanding and deliberately altering cellular behavior. Constraint-based modeling has enabled the fields of metabolic engineering and systems biology to make great strides in interrogating cellular metabolism but does not provide sufficient insight into regulation or kinetic limitations of metabolic pathways. Moreover, the growth-optimized assumptions that constraint-based models often rely on do not hold when studying stationary or persistor cell populations. However, developing kinetic models provides many unique challenges, as many of the kinetic parameters and rate laws governing individual enzymes are unknown. Ensemble modeling (EM) was developed to circumnavigate this challenge and effectively sample the large kinetic parameter solution space using consistent experimental datasets. Unfortunately, EM, in its base form, requires long solve times to complete and often leads to unstable kinetic model predictions. Furthermore, these limitations scale prohibitively with increasing model size. As larger metabolic models are developed with increasing genetic information and experimental validation, the demand to incorporate kinetic information increases. Therefore, in this work, we have begun to tackle the challenges of EM by introducing additional steps to the existing method framework specifically through reducing computation time and optimizing parameter sampling. We first reduce the structural complexity of the network by removing dependent species, and second, we sample locally stable parameter sets to reflect realistic biological states of cells. Lastly, we presort the screening data to eliminate the most incorrect predictions in the earliest screening stages, saving further calculations in later stages. Our complementary improvements to this EM framework are easily incorporated into concurrent EM efforts and broaden the application opportunities and accessibility of kinetic modeling across the field.

Robust Parameter Identification to Perform the Modeling of pta and poxB Genes Deletion Effect on Escherichia Coli

The aim of this study was to design a robust parameter identification algorithm to characterize the effect of gene deletion on Escherichia coli (E. coli) MG1655. Two genes (pta and poxB) in the competitive pathways were deleted from this microorganism to inhibit pyruvate consumption. This condition deviated the E. coli metabolism toward the Krebs cycle. As a consequence, the biomass, substrate (glucose), lactic, and acetate acids as well as ethanol concentrations were modified. A hybrid model was proposed to consider the effect of gene deletion on the metabolism of E. coli. The model parameters were estimated by the application of a least mean square method based on the instrument variable technique. To evaluate the parametric identifier method, a set of robust exact differentiators, based on the super-twisting algorithm, was implemented. The hybrid model was successfully characterized by the parameters obtained from experimental information of E. coli MG1655. The significant difference between parameters obtained with wild-type strain and the modified (with deleted genes) justifies the application of the parametric identification algorithm. This characterization can be used to optimize the production of different byproducts of commercial interest.

N-Glycosylation Design and Control of Therapeutic Monoclonal Antibodies

The N-linked glycan profiles on recombinant monoclonal antibody therapeutics significantly affect antibody biological functions and are largely determined by host cell genotypes and culture conditions. A key step in bioprocess development for monoclonal antibodies (mAbs) involves optimization and control of N-glycan profiles. With pressure from pricing and biosimilars looming, more efficient and effective approaches are sought in the field of glycoengineering. Metabolic studies and mathematical modeling are two such approaches that optimize bioprocesses by better understanding and predicting glycosylation. In this review, we summarize a group of strategies currently used for glycan profile modulation and control. Metabolic analysis and mathematical modeling are then explored with an emphasis on how these two techniques can be utilized to advance glycoengineering.