Dynamic genome-scale modeling of Saccharomyces cerevisiae unravels mechanisms for ester formation during alcoholic fermentation.

Fermentation employing Saccharomyces cerevisiae has produced alcoholic beverages and bread for millennia. More recently, S. cerevisiae has been used to manufacture specific metabolites for the food, pharmaceutical, and cosmetic industries. Among the most important of these metabolites are compounds associated with desirable aromas and flavors, including higher alcohols and esters. Although the physiology of yeast has been well-studied, its metabolic modulation leading to aroma production in relevant industrial scenarios such as winemaking is still unclear. Here we ask what are the underlying metabolic mechanisms that explain the conserved and varying behavior of different yeasts regarding aroma formation under enological conditions? We employed dynamic flux balance analysis (dFBA) to answer this key question using the latest genome-scale metabolic model (GEM) of S. cerevisiae. The model revealed several conserved mechanisms among wine yeasts, for example, acetate ester formation is dependent on intracellular metabolic acetyl-CoA/CoA levels, and the formation of ethyl esters facilitates the removal of toxic fatty acids from cells using CoA. Species-specific mechanisms were also found, such as a preference for the shikimate pathway leading to more 2-phenylethanol production in the Opale strain as well as strain behavior varying notably during the carbohydrate accumulation phase and carbohydrate accumulation inducing redox restrictions during a later cell growth phase for strain Uvaferm. In conclusion, our new metabolic model of yeast under enological conditions revealed key metabolic mechanisms in wine yeasts, which will aid future research strategies to optimize their behavior in industrial settings.

Mechanisms of Listeria monocytogenes Disinfection with Benzalkonium Chloride: From Molecular Dynamics to Kinetics of Time-Kill Curves.

Unravelling the mechanisms of action of disinfectants is essential to optimise dosing regimes and minimise the emergence of antimicrobial resistance. In this work, we examined the mechanisms of action of a commonly used disinfectant-benzalkonium chloride (BAC)-over a significant pathogen-L. monocytogenes-in the food industry. For that purpose, we used modelling at multiple scales, from the cell membrane to cell population inactivation. Molecular modelling revealed that the integration of the BAC into the membrane requires three phases: (1) the approaching of BAC to the cellular membrane, (2) the absorption of BAC to its surface, and (3) the integration of the compound into the lipid bilayer, where it remains at least for several nanoseconds, probably destabilising the membrane. We hypothesised that the equilibrium of adsorption, although fast, was limiting for sufficiently large BAC concentrations, and a kinetic model was derived to describe time-kill curves of a large population of cells. The model was tested and validated with time series data of free BAC decay and time-kill curves of L. monocytogenes at different inocula and BAC dose concentrations. The knowledge gained from the molecular simulation plus the proposed kinetic model offers the means to design novel disinfection processes rationally.

The Monod Model Is Insufficient To Explain Biomass Growth in Nitrogen-Limited Yeast Fermentation.

The yeast Saccharomyces cerevisiae is an essential microorganism in food biotechnology, particularly in wine- and beermaking. During wine fermentation, yeasts transform sugars present in grape juice into ethanol and carbon dioxide. The process occurs under batch conditions and is, for the most part, an anaerobic process. Previous studies linked nitrogen-limited conditions with problematic fermentations, with negative consequences for the performance of the process and the quality of the final product. It is therefore of the highest interest to anticipate such problems through mathematical models. Here, we propose a model to explain fermentations under nitrogen-limited anaerobic conditions. We separated biomass formation into two phases: growth and carbohydrate accumulation. Growth was modeled using the well-known Monod equation, while carbohydrate accumulation was modeled by an empirical function analogous to a proportional controller activated by the limitation of available nitrogen. We also proposed to formulate the fermentation rate as a function of the total protein content when relevant data are available. The final model was used to successfully explain experiments taken from the literature, performed under normal and nitrogen-limited conditions. Our results revealed that the Monod model is insufficient to explain biomass formation kinetics in nitrogen-limited fermentations of S. cerevisiae. The goodness of fit of the model proposed here is superior to that of previously published models, offering the means to predict and, thus, control fermentations. IMPORTANCE Problematic fermentations still occur in the industrial winemaking practice. Problems include low rates of fermentation, which have been linked to insufficient levels of assimilable nitrogen. Data and relevant models can help anticipate poor fermentation performance. In this work, we propose a model to predict biomass growth and fermentation rates under nitrogen-limited conditions and tested its performance with previously published experimental data. Our results show that the well-known Monod equation does not suffice to explain biomass formation.

Optimality and identification of dynamic models in systems biology: an inverse optimal control framework.

Motivation: Optimality principles have been used to explain many biological processes and systems. However, the functions being optimized are in general unknown a priori. Here we present an inverse optimal control framework for modeling dynamics in systems biology. The objective is to identify the underlying optimality principle from observed time-series data and simultaneously estimate unmeasured time-dependent inputs and time-invariant model parameters. As a special case, we also consider the problem of optimal simultaneous estimation of inputs and parameters from noisy data. After presenting a general statement of the inverse optimal control problem, and discussing special cases of interest, we outline numerical strategies which are scalable and robust. Results: We discuss the existence, relevance and implications of identifiability issues in the above problems. We present a robust computational approach based on regularized cost functions and the use of suitable direct numerical methods based on the control-vector parameterization approach. To avoid convergence to local solutions, we make use of hybrid global-local methods. We illustrate the performance and capabilities of this approach with several challenging case studies, including simulated and real data. We pay particular attention to the computational scalability of our approach (with the objective of considering large numbers of inputs and states). We provide a software implementation of both the methods and the case studies. Availability and implementation: The code used to obtain the results reported here is available at https://zenodo.org/record/1009541. Supplementary information: Supplementary data are available at Bioinformatics online.

GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models.

Motivation: Mathematical modeling using ordinary differential equations is used in systems biology to improve the understanding of dynamic biological processes. The parameters of ordinary differential equation models are usually estimated from experimental data. To analyze a priori the uniqueness of the solution of the estimation problem, structural identifiability analysis methods have been developed. Results: We introduce GenSSI 2.0, an advancement of the software toolbox GenSSI (Generating Series for testing Structural Identifiability). GenSSI 2.0 is the first toolbox for structural identifiability analysis to implement Systems Biology Markup Language import, state/parameter transformations and multi-experiment structural identifiability analysis. In addition, GenSSI 2.0 supports a range of MATLAB versions and is computationally more efficient than its previous version, enabling the analysis of more complex models. Availability and implementation: GenSSI 2.0 is an open-source MATLAB toolbox and available at https://github.com/genssi-developer/GenSSI. Contact: thomas.ligon@physik.uni-muenchen.de or jan.hasenauer@helmholtz-muenchen.de. Supplementary information: Supplementary data are available at Bioinformatics online.

Development of a PBPK Model for Silver Accumulation in Chub Infected with Acanthocephalan Parasites.

Simultaneous presence of metals and parasites in fish might lead to potential risks to human health. Parasites might influence metal accumulation and disturb detoxification in fish, thereby affecting biomarkers of fish responses as well as metal biomagnification in humans. It is, therefore, of importance to take into account parasite infection when investigating metal accumulation in fish. However, mechanisms of metal accumulation and distribution in fish-parasite systems are not integrated into current approaches. The present study proposes a new physiologically based pharmacokinetic model for mechanistic simulation of metal partitioning between intestinal parasites and their hosts. As a particular case, Ag accumulation in the system of chub Squalius cephalus and the acanthocephalan Pomphorhynchus tereticollis was investigated. As a novelty, fish cardiac output and organ-specific blood flow distribution were incorporated in our model. This approach distinguishes the current model from the ones developed previously. It also facilitates model extrapolation and application to varying conditions. In general, the model explained Ag accumulation in the system well, especially in chub gill, storage (including skin, muscle, and carcass), and liver. The highest concentration of Ag was found in the liver. The accumulation of Ag in the storage, liver, and gill compartments followed a similar pattern, i.e., increasing during the exposure and decreasing during the depuration. The model also generated this observed trend. However, the model had a weaker performance for simulating Ag accumulation in the intestine and the kidney. Silver accumulation in these organs was less evident with considerable variations.

AMIGO2, a toolbox for dynamic modeling, optimization and control in systems biology.

MOTIVATION: Many problems of interest in dynamic modeling and control of biological systems can be posed as non-linear optimization problems subject to algebraic and dynamic constraints. In the context of modeling, this is the case of, e.g. parameter estimation, optimal experimental design and dynamic flux balance analysis. In the context of control, model-based metabolic engineering or drug dose optimization problems can be formulated as (multi-objective) optimal control problems. Finding a solution to those problems is a very challenging task which requires advanced numerical methods. RESULTS: This work presents the AMIGO2 toolbox: the first multiplatform software tool that automatizes the solution of all those problems, offering a suite of state-of-the-art (multi-objective) global optimizers and advanced simulation approaches. AVAILABILITY AND IMPLEMENTATION: The toolbox and its documentation are available at: sites.google.com/site/amigo2toolbox CONTACT: ebalsa@iim.csic.esSupplementary information: Supplementary data are available at Bioinformatics online.

Optimal programs of pathway control: dissecting the influence of pathway topology and feedback inhibition on pathway regulation.

BACKGROUND: Adjusting the capacity of metabolic pathways in response to rapidly changing environmental conditions is an important component of microbial adaptation strategies to stochastic environments. In this work, we use advanced dynamic optimization techniques combined with theoretical models to study which reactions in pathways are optimally targeted by regulatory interactions in order to minimize the regulatory effort that is required to adjust the flux through a complex metabolic network. Moreover, we analyze how constraints in the speed at which an organism can respond on a proteomic level influences these optimal targets of pathway control. RESULTS: We find that limitations in protein biosynthetic rates have a strong influence. With increasing protein biosynthetic rates the regulatory effort targeting the initial enzyme in a pathway is reduced while the regulatory effort in the terminal enzyme is increased. Studying the impact of allosteric regulation for different pathway topologies, we find that the presence of feedback inhibition by products of metabolic pathways allows organisms to reduce the regulatory effort that is required to control a metabolic pathway in all cases. In a linear pathway this even leads to the case where the sole transcriptional regulatory control of the terminal enzyme is sufficient to control flux through the entire pathway. We confirm the utilization of these pathway regulation strategies through the large-scale analysis of transcriptional regulation in several hundred prokaryotes. CONCLUSIONS: This work expands our knowledge about optimal programs of pathway control. Optimal targets of pathway control strongly depend on the speed at which proteins can be synthesized. Moreover, post-translational regulation such as allosteric regulation allows to strongly reduce the number of transcriptional regulatory interactions required to control a metabolic pathway across different pathway topologies.

Reverse-engineering post-transcriptional regulation of gap genes in Drosophila melanogaster.

Systems biology proceeds through repeated cycles of experiment and modeling. One way to implement this is reverse engineering, where models are fit to data to infer and analyse regulatory mechanisms. This requires rigorous methods to determine whether model parameters can be properly identified. Applying such methods in a complex biological context remains challenging. We use reverse engineering to study post-transcriptional regulation in pattern formation. As a case study, we analyse expression of the gap genes Krüppel, knirps, and giant in Drosophila melanogaster. We use detailed, quantitative datasets of gap gene mRNA and protein expression to solve and fit a model of post-transcriptional regulation, and establish its structural and practical identifiability. Our results demonstrate that post-transcriptional regulation is not required for patterning in this system, but is necessary for proper control of protein levels. Our work demonstrates that the uniqueness and specificity of a fitted model can be rigorously determined in the context of spatio-temporal pattern formation. This greatly increases the potential of reverse engineering for the study of development and other, similarly complex, biological processes.

Modelling the physiological status of yeast during wine fermentation enables the prediction of secondary metabolism.

Saccharomyces non-cerevisiae yeasts are gaining momentum in wine fermentation due to their potential to reduce ethanol content and achieve attractive aroma profiles. However, the design of the fermentation process for new species requires intensive experimentation. The use of mechanistic models could automate process design, yet to date, most fermentation models have focused on primary metabolism. Therefore, these models do not provide insight into the production of secondary metabolites essential for wine quality, such as aromas. In this work, we formulate a continuous model that accounts for the physiological status of yeast, that is, exponential growth, growth under nitrogen starvation and transition to stationary or decay phases. To do so, we assumed that nitrogen starvation is associated with carbohydrate accumulation and the induction of a set of transcriptional changes associated with the stationary phase. The model accurately described the dynamics of time series data for biomass and primary and secondary metabolites obtained for various yeast species in single culture fermentations. We also used the proposed model to explore different process designs, showing how the addition of nitrogen could affect the aromatic profile of wine. This study underlines the potential of incorporating yeast physiology into batch fermentation modelling and provides a new means of automating process design.

A Dynamic Genome-Scale Model Identifies Metabolic Pathways Associated with Cold Tolerance in Saccharomyces kudriavzevii.

Saccharomyces kudriavzevii is a cold-tolerant species identified as a good alternative for industrial winemaking. Although S. kudriavzevii has never been found in winemaking, its co-occurrence with Saccharomyces cerevisiae in Mediterranean oaks is well documented. This sympatric association is believed to be possible due to the different growth temperatures of the two yeast species. However, the mechanisms behind the cold tolerance of S. kudriavzevii are not well understood. In this work, we propose the use of a dynamic genome-scale model to compare the metabolic routes used by S. kudriavzevii at two temperatures, 25°C and 12°C, to decipher pathways relevant to cold tolerance. The model successfully recovered the dynamics of biomass and external metabolites and allowed us to link the observed phenotype with exact intracellular pathways. The model predicted fluxes that are consistent with previous findings, but it also led to novel results which we further confirmed with intracellular metabolomics and transcriptomic data. The proposed model (along with the corresponding code) provides a comprehensive picture of the mechanisms of cold tolerance that occur within S. kudriavzevii. The proposed strategy offers a systematic approach to explore microbial diversity from extracellular fermentation data at low temperatures. IMPORTANCE Nonconventional yeasts promise to provide new metabolic pathways for producing industrially relevant compounds and tolerating specific stressors such as cold temperatures. The mechanisms behind the cold tolerance of S. kudriavzevii or its sympatric relationship with S. cerevisiae in Mediterranean oaks are not well understood. This study proposes a dynamic genome-scale model to investigate metabolic pathways relevant to cold tolerance. The predictions of the model would indicate the ability of S. kudriavzevii to produce assimilable nitrogen sources from extracellular proteins present in its natural niche. These predictions were further confirmed with metabolomics and transcriptomic data. This finding suggests that not only the different growth temperature preferences but also this proteolytic activity may contribute to the sympatric association with S. cerevisiae. Further exploration of these natural adaptations could lead to novel engineering targets for the biotechnological industry.

AMIGO, a toolbox for advanced model identification in systems biology using global optimization.

MOTIVATION: Mathematical models of complex biological systems usually consist of sets of differential equations which depend on several parameters which are not accessible to experimentation. These parameters must be estimated by fitting the model to experimental data. This estimation problem is very challenging due to the non-linear character of the dynamics, the large number of parameters and the frequently poor information content of the experimental data (poor practical identifiability). The design of optimal (more informative) experiments is an associated problem of the highest interest. RESULTS: This work presents AMIGO, a toolbox which facilitates parametric identification by means of advanced numerical techniques which cover the full iterative identification procedure putting especial emphasis on robust methods for parameter estimation and practical identifiability analyses, plus flexible capabilities for optimal experimental design. AVAILABILITY: The toolbox and the corresponding documentation may be downloaded from: http://www.iim.csic.es/~amigo CONTACT: ebalsa@iim.csic.es.

GenSSI: a software toolbox for structural identifiability analysis of biological models.

SUMMARY: Mathematical modeling has a key role in systems biology. Model building is often regarded as an iterative loop involving several tasks, among which the estimation of unknown parameters of the model from a certain set of experimental data is of central importance. This problem of parameter estimation has many possible pitfalls, and modelers should be very careful to avoid them. Many of such difficulties arise from a fundamental (yet often overlooked) property: the so-called structural (or a priori) identifiability, which considers the uniqueness of the estimated parameters. Obviously, the structural identifiability of any tentative model should be checked at the beginning of the model building loop. However, checking this property for arbitrary non-linear dynamic models is not an easy task. Here we present a software toolbox, GenSSI (Generating Series for testing Structural Identifiability), which enables non-expert users to carry out such analysis. The toolbox runs under the popular MATLAB environment and is accompanied by detailed documentation and relevant examples. AVAILABILITY: The GenSSI toolbox and the related documentation are available at http://www.iim.csic.es/%7Egenssi. CONTACT: ebalsa@iim.csic.es.

Global optimization in systems biology: stochastic methods and their applications.

Mathematical optimization is at the core of many problems in systems biology: (1) as the underlying hypothesis for model development, (2) in model identification, or (3) in the computation of optimal stimulation procedures to synthetically achieve a desired biological behavior. These problems are usually formulated as nonlinear programing problems (NLPs) with dynamic and algebraic constraints. However the nonlinear and highly constrained nature of systems biology models, together with the usually large number of decision variables, can make their solution a daunting task, therefore calling for efficient and robust optimization techniques. Here, we present novel global optimization methods and software tools such as cooperative enhanced scatter search (eSS), AMIGO, or DOTcvpSB, and illustrate their possibilities in the context of modeling including model identification and stimulation design in systems biology.

Use of a generalized fisher equation for global optimization in chemical kinetics.

A new approach for parameter estimation in chemical kinetics has been recently proposed (Ross et al. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 12777). It makes use of an optimization criterion based on a Generalized Fisher Equation (GFE). Its utility has been demonstrated with two reaction mechanisms, the chlorite-iodide and Oregonator, which are computationally stiff systems. In this Article, the performance of the GFE-based algorithm is compared to that obtained from minimization of the squared distances between the observed and predicted concentrations obtained by solving the corresponding initial value problem (we call this latter approach "traditional" for simplicity). Comparison of the proposed GFE-based optimization method with the "traditional" one has revealed their differences in performance. This difference can be seen as a trade-off between speed (which favors GFE) and accuracy (which favors the traditional method). The chlorite-iodide and Oregonator systems are again chosen as case studies. An identifiability analysis is performed for both of them, followed by an optimal experimental design based on the Fisher Information Matrix (FIM). This allows to identify and overcome most of the previously encountered identifiability issues, improving the estimation accuracy. With the new data, obtained from optimally designed experiments, it is now possible to estimate effectively more parameters than with the previous data. This result, which holds for both GFE-based and traditional methods, stresses the importance of an appropriate experimental design. Finally, a new hybrid method that combines advantages from the GFE and traditional approaches is presented.

Optimal Experimental Design for Systems and Synthetic Biology Using AMIGO2.

Dynamic modeling in systems and synthetic biology is still quite a challenge-the complex nature of the interactions results in nonlinear models, which include unknown parameters (or functions). Ideally, time-series data support the estimation of model unknowns through data fitting. Goodness-of-fit measures would lead to the best model among a set of candidates. However, even when state-of-the-art measuring techniques allow for an unprecedented amount of data, not all data suit dynamic modeling.Model-based optimal experimental design (OED) is intended to improve model predictive capabilities. OED can be used to define the set of experiments that would (a) identify the best model or (b) improve the identifiability of unknown parameters. In this chapter, we present a detailed practical procedure to compute optimal experiments using the AMIGO2 toolbox.

A Cyber-Physical Platform for Model Calibration.

Synthetic biology has so far made limited use of mathematical models, mostly because their inference has been traditionally perceived as expensive and/or difficult. We have recently demonstrated how in silico simulations and in vitro/vivo experiments can be integrated to develop a cyber-physical platform that automates model calibration and leads to saving 60-80% of the effort. In this book chapter, we illustrate the protocol used to attain such results. By providing a comprehensive list of steps and pointing the reader to the code we use to operate our platform, we aim at providing synthetic biologists with an additional tool to accelerate the pace at which the field progresses toward applications.

A Multiphase Multiobjective Dynamic Genome-Scale Model Shows Different Redox Balancing among Yeast Species of the Saccharomyces Genus in Fermentation.

Yeasts constitute over 1,500 species with great potential for biotechnology. Still, the yeast Saccharomyces cerevisiae dominates industrial applications, and many alternative physiological capabilities of lesser-known yeasts are not being fully exploited. While comparative genomics receives substantial attention, little is known about yeasts' metabolic specificity in batch cultures. Here, we propose a multiphase multiobjective dynamic genome-scale model of yeast batch cultures that describes the uptake of carbon and nitrogen sources and the production of primary and secondary metabolites. The model integrates a specific metabolic reconstruction, based on the consensus Yeast8, and a kinetic model describing the time-varying culture environment. In addition, we proposed a multiphase multiobjective flux balance analysis to compute the dynamics of intracellular fluxes. We then compared the metabolism of S. cerevisiae and Saccharomyces uvarum strains in a rich medium fermentation. The model successfully explained the experimental data and brought novel insights into how cryotolerant strains achieve redox balance. The proposed model (along with the corresponding code) provides a comprehensive picture of the main steps occurring inside the cell during batch cultures and offers a systematic approach to prospect or metabolically engineering novel yeast cell factories. IMPORTANCE Nonconventional yeast species hold the promise to provide novel metabolic routes to produce industrially relevant compounds and tolerate specific stressors, such as cold temperatures. This work validated the first multiphase multiobjective genome-scale dynamic model to describe carbon and nitrogen metabolism throughout batch fermentation. To test and illustrate its performance, we considered the comparative metabolism of three yeast strains of the Saccharomyces genus in rich medium fermentation. The study revealed that cryotolerant Saccharomyces species might use the γ-aminobutyric acid (GABA) shunt and the production of reducing equivalents as alternative routes to achieve redox balance, a novel biological insight worth being explored further. The proposed model (along with the provided code) can be applied to a wide range of batch processes started with different yeast species and media, offering a systematic and rational approach to prospect nonconventional yeast species metabolism and engineering novel cell factories.