Full-scale model of glycolysis in Saccharomyces cerevisiae

Kinetic modelling of glycolytic oscillations

Glycolytic oscillations have been studied for well over 60 years, but aspects of their function, and mechanisms of regulation and synchronisation remain unclear. Glycolysis is amenable to mechanistic mathematical modelling, as its components have been well characterised, and the system can be studied at many organisational levels: in vitro reconstituted enzymes, cell free extracts, individual cells, and cell populations. In recent years, the emergence of individual cell analysis has opened new ways of studying this intriguing system.

Data integration strategies for whole-cell modeling

Data makes the world go round-and high quality data is a prerequisite for precise models, especially for whole-cell models (WCM). Data for WCM must be reusable, contain information about the exact experimental background, and should-in its entirety-cover all relevant processes in the cell. Here, we review basic requirements to data for WCM and strategies how to combine them. As a species-specific resource, we introduce the Yeast Cell Model Data Base (YCMDB) to illustrate requirements and solutions. We discuss recent standards for data as well as for computational models including the modeling process as data to be reported. We outline strategies for constructions of WCM despite their inherent complexity.

Chemical Memory with Discrete Turing Patterns Appearing in the Glycolytic Reaction

Memory is an essential element in information processing devices. We investigated a network formed by just three interacting nodes representing continuously stirred tank reactors (CSTRs) in which the glycolytic reaction proceeds as a potential realization of a chemical memory unit. Our study is based on the 2-variable computational model of the reaction. The model parameters were selected such that the system has a stable limit cycle and several distinct, discrete Turing patterns characterized by stationary concentrations at the nodes. In our interpretation, oscillations represent a blank memory unit, and Turing patterns code information. The considered memory can preserve information on one of six different symbols. The time evolution of the nodes was individually controlled by the inflow of ATP. We demonstrate that information can be written with a simple and short perturbation of the inflow. The perturbation applies to only one or two nodes, and it is symbol specific. The memory can be erased with identical inflow perturbation applied to all nodes. The presented idea of pattern-coded memory applies to other reaction networks that allow for discrete Turing patterns. Moreover, it hints at the experimental realization of memory in a simple system with the glycolytic reaction.

Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions

An inhomogeneous profile of chemostatted species generates a rich variety of patterns in glycolytic waves depicted in a Selkov reaction-diffusion framework here. A key role played by diffusion amplitude and symmetry in the chemostatted species profile in dictating the fate of local spatial dynamics involving periodic, quasiperiodic, and chaotic patterns and transitions among them are investigated systematically. More importantly, various dynamic transitions, including wave propagation direction changes, are illustrated in interesting situations. Besides numerical results, our analytical formulation of the amplitude equation connecting complex Ginzburg-Landau and Lambda-omega representation shed light on the phase dynamics of the system. This systematic study of the glycolytic reaction-diffusion wave is in line with previous experimental results in open spatial reactor and will provide a knowledge about the dynamics that shape and control biological information processing and related phenomena.

Towards inferring absolute concentrations from relative abundance in time-course GC-MS metabolomics data

Metabolomics, the large-scale study of metabolites, has significant appeal as a source of information for metabolic modeling and other scientific applications. One common approach for measuring metabolomics data is gas chromatography-mass spectrometry (GC-MS). However, GC-MS metabolomics data are typically reported as relative abundances, precluding their use with approaches and tools where absolute concentrations are necessary. While chemical standards can be used to help provide quantification, their use is time-consuming, expensive, or even impossible due to their limited availability. The ability to infer absolute concentrations from GC-MS metabolomics data without chemical standards would have significant value. We hypothesized that when analyzing time-course metabolomics datasets, the mass balances of metabolism and other biological information could provide sufficient information towards inference of absolute concentrations. To demonstrate this, we developed and characterized MetaboPAC, a computational framework that uses two approaches-one based on kinetic equations and another using biological heuristics-to predict the most likely response factors that allow translation between relative abundances and absolute concentrations. When used to analyze noiseless synthetic data generated from multiple types of kinetic rate laws, MetaboPAC performs significantly better than negative control approaches when 20% of kinetic terms are known a priori. Under conditions of lower sampling frequency and high noise, MetaboPAC is still able to provide significant inference of concentrations in 3 of 4 models studied. This provides a starting point for leveraging biological knowledge to extract concentration information from time-course intracellular GC-MS metabolomics datasets, particularly for systems that are well-studied and have partially known kinetic structures.

Diverse classes of constraints enable broader applicability of a linear programming-based dynamic metabolic modeling framework

Current metabolic modeling tools suffer from a variety of limitations, from scalability to simplifying assumptions, that preclude their use in many applications. We recently created a modeling framework, Linear Kinetics-Dynamic Flux Balance Analysis (LK-DFBA), that addresses a key gap: capturing metabolite dynamics and regulation while retaining a potentially scalable linear programming structure. Key to this framework's success are the linear kinetics and regulatory constraints imposed on the system. However, while the linearity of these constraints reduces computational complexity, it may not accurately capture the behavior of many biochemical systems. Here, we developed three new classes of LK-DFBA constraints to better model interactions between metabolites and the reactions they regulate. We tested these new approaches on several synthetic and biological systems, and also performed the first-ever comparison of LK-DFBA predictions to experimental data. We found that no single constraint approach was optimal across all systems examined, and systems with the same topological structure but different parameters were often best modeled by different types of constraints. However, we did find that when genetic perturbations were implemented in the systems, the optimal constraint approach typically remained the same as for the wild-type regardless of the model topology or parameterization, indicating that just a single wild-type dataset could allow identification of the ideal constraint to enable model predictivity for a given system. These results suggest that the availability of multiple constraint approaches will allow LK-DFBA to model a wider range of metabolic systems.

Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: Achievements, Limitations, and Opportunities

Central carbon metabolism comprises the metabolic pathways in the cell that process nutrients into energy, building blocks and byproducts. To unravel the regulation of this network upon glucose perturbation, several metabolic models have been developed for the microorganism Saccharomyces cerevisiae. These dynamic representations have focused on glycolysis and answered multiple research questions, but no commonly applicable model has been presented. This review systematically evaluates the literature to describe the current advances, limitations, and opportunities. Different kinetic models have unraveled key kinetic glycolytic mechanisms. Nevertheless, some uncertainties regarding model topology and parameter values still limit the application to specific cases. Progressive improvements in experimental measurement technologies as well as advances in computational tools create new opportunities to further extend the model scale. Notably, models need to be made more complex to consider the multiple layers of glycolytic regulation and external physiological variables regulating the bioprocess, opening new possibilities for extrapolation and validation. Finally, the onset of new data representative of individual cells will cause these models to evolve from depicting an average cell in an industrial fermenter, to characterizing the heterogeneity of the population, opening new and unseen possibilities for industrial fermentation improvement.

Synchronisation of glycolytic activity in yeast cells

Glycolysis is the central metabolic pathway of almost every cell and organism. Under appropriate conditions, glycolytic oscillations may occur in individual cells as well as in entire cell populations or tissues. In many biological systems, glycolytic oscillations drive coherent oscillations of other metabolites, for instance in cardiomyocytes near anorexia, or in pancreas where they lead to a pulsatile release of insulin. Oscillations at the population or tissue level require the cells to synchronize their metabolism. We review the progress achieved in studying a model organism for glycolytic oscillations, namely yeast. Oscillations may occur on the level of individual cells as well as on the level of the cell population. In yeast, the cell-to-cell interaction is realized by diffusion-mediated intercellular communication via a messenger molecule. The present mini-review focuses on the synchronisation of glycolytic oscillations in yeast. Synchronisation is a quorum-sensing phenomenon because the collective oscillatory behaviour of a yeast cell population ceases when the cell density falls below a threshold. We review the question, under which conditions individual cells in a sparse population continue or cease to oscillate. Furthermore, we provide an overview of the pathway leading to the onset of synchronized oscillations. We also address the effects of spatial inhomogeneities (e.g., the formation of spatial clusters) on the collective dynamics, and also review the emergence of travelling waves of glycolytic activity. Finally, we briefly review the approaches used in numerical modelling of synchronized cell populations.

Performance of Yeast Microbial Fuel Cell Integrated with Sugarcane Bagasse Fermentation for COD Reduction and Electricity Generation

The purpose of this analysis is to evaluate the efficiency of the Microbial Fuel Cell (MFC) system incorporated with the fermentation process, with the aim of reducing COD and generating electricity, using sugarcane bagasse extract as a substrate, in the presence and absence of sugarcane fibers. There is a possibility of turning bagasse extract into renewable bioenergy to promote the sustainability of the environment and energy. As a result, the integration of liquid fermentation (LF) with MFC has improved efficiency compared to semi-solid state fermentation (S-SSF). The maximum power generated was 14.88 mW/m2, with an average COD removal of 39.68% per cycle. The variation margin of the liquid fermentation pH readings remained slightly decrease, with a slight deflection of +0.14 occurring from 4.33. With the absence of bagasse fibers, biofilm can grow freely on the anode surface so that the transfer of electrons is fast and produces a relatively high current. Experimental data showed a positive potential after an effective integration of the LF and MFC systems in the handling of waste. The product is then simultaneously converted into electrical energy. Copyright © 2021 by Authors, Published by BCREC Group. This is an open access article under the CC BY-SA License (https://creativecommons.org/licenses/by-sa/4.0). 

VANESA: An open-source hybrid functional Petri net modeling and simulation environment in systems biology

Petri nets are a common method for modeling and simulation of systems biology application cases. Usually different Petri net concepts (e.g. discrete, hybrid, functional) are demanded depending on the purpose of the application cases. Modeling complex application cases requires a unification of those concepts, e.g. hybrid functional Petri nets (HFPN) and extended hybrid Petri nets (xHPN). Existing tools have certain limitations which motivated the extension of VANESA, an existing open-source editor for biological networks. The extension can be used to model, simulate, and visualize Petri nets based on the xHPN formalism. Moreover, it comprises additional functionality to support and help the user. Complex (kinetic) functions are syntactically analyzed and mathematically rendered. Based on syntax and given physical unit information, modeling errors are revealed. The numerical simulation is seamlessly integrated and executed in the background by the open-source simulation environment OpenModelica utilizing the Modelica library PNlib. Visualization of simulation results for places, transitions, and arcs are useful to investigate and understand the model and its dynamic behavior. The impact of single parameters can be revealed by comparing multiple simulation results. Simulation results, charts, and entire specification of the Petri net model as Latex file can be exported. All these features are shown in the demonstration case. The utilized Petri net formalism xHPN is fully specified and implemented in PNlib. This assures transparency, reliability, and comprehensible simulation results. Thus, the combination of VANESA and OpenModelica shape a unique open-source Petri net environment focusing on systems biology application cases. VANESA is available at: http://agbi.techfak.uni-bielefeld.de/vanesa.

Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability

Evolution of the nonequilibrium thermodynamic entities corresponding to dynamics of the Hopf instabilities and traveling waves at a nonequilibrium steady state of a spatially extended glycolysis model is assessed here by implementing an analytically tractable scheme incorporating a complex Ginzburg-Landau equation (CGLE). In the presence of self and cross diffusion, a more general amplitude equation exploiting the multiscale Krylov-Bogoliubov averaging method serves as an essential tool to reveal the various dynamical instability criteria, especially Benjamin-Feir (BF) instability, to estimate the corresponding nonlinear dispersion relation of the traveling wave pattern. The critical control parameter, wave-number selection criteria, and magnitude of the complex amplitude for traveling waves are modified by self- and cross-diffusion coefficients within the oscillatory regime, and their variabilities are exhibited against the amplitude equation. Unlike the traveling waves, a low-amplitude broad region appears for the Hopf instability in the concentration dynamics as the system phase passes through minima during its variation with the control parameter. The total entropy production rate of the uniform Hopf oscillation and glycolysis wave not only qualitatively reflects the global dynamics of concentrations of intermediate species but almost quantitatively. Despite the crucial role of diffusion in generating and shaping the traveling waves, the diffusive part of the entropy production rate has a negligible contribution to the system's total entropy production rate. The Hopf instability shows a more complex and colossal change in the energy profile of the open nonlinear system than in the traveling waves. A detailed analysis of BF instability shows a contrary nature of the semigrand Gibbs free energy with discrete and continuous wave numbers for the traveling wave. We hope the Hopf and traveling wave pattern around the BF instability in terms of energetics and dissipation will open up new applications of such dynamical phenomena.

SCOUR: a stepwise machine learning framework for predicting metabolite-dependent regulatory interactions

BACKGROUND

The topology of metabolic networks is both well-studied and remarkably well-conserved across many species. The regulation of these networks, however, is much more poorly characterized, though it is known to be divergent across organisms-two characteristics that make it difficult to model metabolic networks accurately. While many computational methods have been built to unravel transcriptional regulation, there have been few approaches developed for systems-scale analysis and study of metabolic regulation. Here, we present a stepwise machine learning framework that applies established algorithms to identify regulatory interactions in metabolic systems based on metabolic data: stepwise classification of unknown regulation, or SCOUR.

RESULTS

We evaluated our framework on both noiseless and noisy data, using several models of varying sizes and topologies to show that our approach is generalizable. We found that, when testing on data under the most realistic conditions (low sampling frequency and high noise), SCOUR could identify reaction fluxes controlled only by the concentration of a single metabolite (its primary substrate) with high accuracy. The positive predictive value (PPV) for identifying reactions controlled by the concentration of two metabolites ranged from 32 to 88% for noiseless data, 9.2 to 49% for either low sampling frequency/low noise or high sampling frequency/high noise data, and 6.6-27% for low sampling frequency/high noise data, with results typically sufficiently high for lab validation to be a practical endeavor. While the PPVs for reactions controlled by three metabolites were lower, they were still in most cases significantly better than random classification.

CONCLUSIONS

SCOUR uses a novel approach to synthetically generate the training data needed to identify regulators of reaction fluxes in a given metabolic system, enabling metabolomics and fluxomics data to be leveraged for regulatory structure inference. By identifying and triaging the most likely candidate regulatory interactions, SCOUR can drastically reduce the amount of time needed to identify and experimentally validate metabolic regulatory interactions. As high-throughput experimental methods for testing these interactions are further developed, SCOUR will provide critical impact in the development of predictive metabolic models in new organisms and pathways.

Intercellular communication induces glycolytic synchronization waves between individually oscillating cells

Many organs have internal structures with spatially differentiated and sometimes temporally synchronized groups of cells. The mechanisms leading to such differentiation and coordination are not well understood. Here we design a diffusion-limited microfluidic system to mimic a multicellular organ structure with peripheral blood flow and test whether a group of individually oscillating yeast cells could form subpopulations of spatially differentiated and temporally synchronized cells. Upon substrate addition, the dynamic response at single-cell level shows glycolytic oscillations, leading to wave fronts traveling through the monolayered population and to synchronized communities at well-defined positions in the cell chamber. A detailed mechanistic model with the architectural structure of the flow chamber incorporated successfully predicts the spatial-temporal experimental data, and allows for a molecular understanding of the observed phenomena. The intricate interplay of intracellular biochemical reaction networks leading to the oscillations, combined with intercellular communication via metabolic intermediates and fluid dynamics of the reaction chamber, is responsible for the generation of the subpopulations of synchronized cells. This mechanism, as analyzed from the model simulations, is experimentally tested using different concentrations of cyanide stress solutions. The results are reproducible and stable, despite cellular heterogeneity, and the spontaneous community development is reminiscent of a zoned cell differentiation often observed in multicellular organs.

The Emergence of the Bilateral Symmetry in Animals: A Review and a New Hypothesis

Most biological organisms exhibit different kinds of symmetry; an Animal (Metazoa), which is our Darwinist ancestor, has bilateral symmetry, and many plants exhibit rotational symmetry. It raises some questions: I. How can the evolution from an undifferentiated cell without bilateral symmetry to a complex biological organism with symmetry, which is based on asymmetric DNA and enzymes, lead to the bilateral symmetry? II. Is this evolution to an organism with bilateral symmetry obtained by other factors than DNA and enzymatic reactions? The existing literature about the evolution of the bilateral symmetry has been reviewed, and a new hypothesis has been formulated based on these reviews. The hypothesis is that the morphogenesis of biosystems is connected with the metabolism and that the oscillating kinetics in the Glycolysis have played a role in the polarity of the biological cells and in the establishment of the bilateral symmetry in Animals.

Population-Based Parameter Identification for Dynamical Models of Biological Networks with an Application to Saccharomyces cerevisiae

One of the central elements in systems biology is the interaction between mathematical modeling and measured quantities. Typically, biological phenomena are represented as dynamical systems, and they are further analyzed and comprehended by identifying model parameters using experimental data. However, all model parameters cannot be found by gradient-based optimization methods by fitting the model to the experimental data due to the non-differentiable character of the problem. Here, we present POPI4SB, a Python-based framework for population-based parameter identification of dynamic models in systems biology. The code is built on top of PySCeS that provides an engine to run dynamic simulations. The idea behind the methodology is to provide a set of derivative-free optimization methods that utilize a population of candidate solutions to find a better solution iteratively. Additionally, we propose two surrogate-assisted population-based methods, namely, a combination of a k-nearest-neighbor regressor with the Reversible Differential Evolution and the Evolution of Distribution Algorithm, that speeds up convergence. We present the optimization framework on the example of the well-studied glycolytic pathway in Saccharomyces cerevisiae.

Advanced Chemical Computing Using Discrete Turing Patterns in Arrays of Coupled Cells

We examine dynamical switching among discrete Turing patterns that enable chemical computing performed by mass-coupled reaction cells arranged as arrays with various topological configurations: three coupled cells in a cyclic array, four coupled cells in a linear array, four coupled cells in a cyclic array, and four coupled cells in a branched array. Each cell is operating as a continuous stirred tank reactor, within which the glycolytic reaction takes place, represented by a skeleton inhibitor-activator model where ADP plays the role of activator and ATP is the inhibitor. The mass coupling between cells is assumed to be operating in three possible transport regimes: (i) equal transport coefficients of the inhibitor and activator (ii) slightly faster transport of the activator, and (iii) strongly faster transport of the inhibitor. Each cellular array is characterized by two pairs of tunable parameters, the rate coefficients of the autocatalytic and inhibitory steps, and the transport coefficients of the coupling. Using stability and bifurcation analysis we identified conditions for occurrence of discrete Turing patterns associated with non-uniform stationary states. We found stable symmetric and/or asymmetric discrete Turing patterns coexisting with stable uniform periodic oscillations. To switch from one of the coexisting stable regimes to another we use carefully targeted perturbations, which allows us to build systems of logic gates specific to each topological type of the array, which in turn enables to perform advanced modes of chemical computing. By combining chemical computing techniques in the arrays with glycolytic excitable channels, we propose a cellular assemblage design for advanced chemical computing.

Cellular metabolism and colloids: Realistically linking physiology and biological physical chemistry

Important concepts from colloidal physical chemistry such as coacervation, phase transitions, emergent properties and ionic association, are currently emerging in the lexicon of cellular biology, prompted mostly by recent experimental observations of liquid phase coexistence in the cell cytosol. Nevertheless, from an historical point of view, the application of these concepts in cell biology is not new. They were key concepts into the so-called protoplasmic doctrine, an alternative (and largely forgotten) approach to cell physiology. The most complete theory originating from this line of thinking was the Association-Induction Hypothesis (AIH), introduced by Gilbert N. Ling in 1962. The AIH, which envisions living cells as complex dynamical colloidal systems, provides ample theory and experimental evidence to call into question the now dominant view of living cells as fluid-filled vesicles. This review attempts to present and discuss the usefulness of the AIH to understand a series of experimental observations from our laboratory from living suspensions of the yeast Saccharomyces cerevisiae exhibiting glycolytic oscillations. Particularly, the AIH helped us integrate, in a mechanistic sense, the basis of a strong temporal coupling observed between ATP and a series of cellular properties such as intracellular water dipolar relaxation, intracellular K⁺ concentration, among many others, where the colloidal physical chemistry of the cell interior plays a fundamental role.

A predictive dynamic yeast model based on component, energy, and electron carrier balances

The present study describes a novel yeast model for the prediction of yeast fermentation. The proposed model considers the possible metabolic pathways of yeast. For each pathway, the time evolution of components, energy (ATP/ADP), and electron carriers (NAD⁺ /NADH) are expressed with limitation factors for all quantities consumed by each respective pathway. In this manner, the model can predict the partition of these pathways based on the growth conditions and their evolution over time. Several biological pathways and their stoichiometric coefficients are well known from literature. It is important to note that most of the kinetic parameters have no effect as the actual kinetics are controlled by the balance of limiting factors. The few remaining parameters were adjusted and compared with the literature when the data set was available. The model fits our experimental data from yeast fermentation on glucose in a nonaerated batch system. The predictive ability of the model and its capacity to represent the intensity of each pathway over time facilitate an improved understanding of the interactions between the pathways. The key role of energy (ATP) and electron carrier (NAD⁺ ) to trigger the different metabolic pathways during yeast growth is highlighted, whereas the involvement of mitochondrial respiration not being associated with the TCA cycle is also shown.

Effect of macromolecular crowding on the kinetics of glycolytic enzymes and the behaviour of glycolysis in yeast

Water is involved in all aspects of biological activity, both as a solvent and as a reactant. It is hypothesized that intracellular water is in a highly structured state due to the high concentrations of macromolecules in the cell and that this may change the activity of intracellular enzymes due to altered binding affinities and allosteric regulations. Here we first investigate the kinetics of two glycolytic enzymes in artificially crowded aqueous solutions and show that crowding does indeed change their kinetics. Based on our kinetic measurements we propose a new model of oscillating glycolysis that instead of Michaelis-Menten or Monod-Wyman-Changeux kinetics uses the Yang-Ling adsorption isotherm introduced by G. Ling in the frame of the Association-Induction (AI) hypothesis. Using this model, we can reproduce previous experimental observations of the coupling of glycolytic oscillations and intracellular water dynamics, e.g., (i) during the metabolic oscillations, the latter variable oscillates in phase with ATP activity, and (ii) the emergence of glycolytic oscillations largely depends on the extent of intracellular water dipolar relaxation in cells in the resting state. Our results support the view that the extent of intracellular water dipolar relaxation is regulated by the ability of cytoplasmic proteins to polarize intracellular water with the assistance of ATP, as suggested in the AI hypothesis. This hypothesis may be relevant to the interpretation of many other biological oscillators, including cell signalling processes.

Misinterpretation risks of global stochastic optimisation of kinetic models revealed by multiple optimisation runs

One of use cases for metabolic network optimisation of biotechnologically applied microorganisms is the in silico design of new strains with an improved distribution of metabolic fluxes. Global stochastic optimisation methods (genetic algorithms, evolutionary programing, particle swarm and others) can optimise complicated nonlinear kinetic models and are friendly for unexperienced user: they can return optimisation results with default method settings (population size, number of generations and others) and without adaptation of the model. Drawbacks of these methods (stochastic behaviour, undefined duration of optimisation, possible stagnation and no guaranty of reaching optima) cause optimisation result misinterpretation risks considering the very diverse educational background of the systems biology and synthetic biology research community. Different methods implemented in the COPASI software package are tested in this study to determine their ability to find feasible solutions and assess the convergence speed to the best value of the objective function. Special attention is paid to the potential misinterpretation of results. Optimisation methods are tested with additional constraints that can be introduced to ensure the biological feasibility of the resulting optimised design: (1) total enzyme activity constraint (called also amino acid pool constraint) to limit the sum of enzyme concentrations and (2) homeostatic constraint limiting steady state metabolite concentration corridor around the steady state concentrations of metabolites in the original model. Impact of additional constraints on the performance of optimisation methods and misinterpretation risks is analysed.

Modeling and Simulating the Aerobic Carbon Metabolism of a Green Microalga Using Petri Nets and New Concepts of VANESA

In this work we present new concepts of VANESA, a tool for modeling and simulation in systems biology. We provide a convenient way to handle mathematical expressions and take physical units into account. Simulation and result management has been improved, and syntax and consistency checks, based on physical units, reduce modeling errors. As a proof of concept, essential components of the aerobic carbon metabolism of the green microalga Chlamydomonas reinhardtii are modeled and simulated. The modeling process is based on xHPN Petri net formalism and simulation is performed with OpenModelica, a powerful environment and compiler for Modelica. VANESA, as well as OpenModelica, is open source, free-of-charge for non-commercial use, and is available at: http://agbi.techfak.uni-bielefeld.de/vanesa.

A mechanism for bistability in glycosylation

Glycosyltransferases are a class of enzymes that catalyse the posttranslational modification of proteins to produce a large number of glycoconjugate acceptors from a limited number of nucleotide-sugar donors. The products of one glycosyltransferase can be the substrates of several other enzymes, causing a combinatorial explosion in the number of possible glycan products. The kinetic behaviour of systems where multiple acceptor substrates compete for a single enzyme is presented, and the case in which high concentrations of an acceptor substrate are inhibitory as a result of abortive complex formation, is shown to result in non-Michaelian kinetics that can lead to bistability in an open system. A kinetic mechanism is proposed that is consistent with the available experimental evidence and provides a possible explanation for conflicting observations on the β-1,4-galactosyltransferases. Abrupt switching between steady states in networks of glycosyltransferase-catalysed reactions may account for the observed changes in glycosyl-epitopes in cancer cells.

Constrained stoichiometric network analysis

Stoichiometric network analysis (SNA) is a method for studying the stability of steady states of stoichiometric systems by decomposing the corresponding network into elementary subnetworks (also known as extreme currents) and identifying those that may cause loss of a network's stability via interplay of positive and negative feedback. Experimentally studied complex (bio)chemical reactions often display dynamical instabilities leading to oscillations or bistable switches. When modelling such systems, a frequently met case is that an assumed detailed mechanism in terms of power law kinetics is available, but some of the rate coefficients are unknown and obtaining them by traditional kinetic methods based on a least-square fit is cumbersome or unfeasible. We propose a method combining the SNA and experimental data at the point of instability, which provides an estimate of the unknown rate coefficients along with unknown steady state concentrations. The core of the method rests in using constrained linear optimization to find a combination of the elementary subnetworks such that the dominant instability-causing subnetwork is just counter-balanced by stabilizing effects of all other subnetworks to obtain the instability threshold, and at the same time, the experimentally available data (inflow constraints, measured steady state concentrations of some species, frequency of emerging oscillations, etc.) are exactly matched. We illustrate this approach by examining two classical chemical oscillators: the Brusselator chosen as the simplest model for illustration of our methods and the Belousov-Zhabotinsky reaction and its mechanism represented by the Oregonator model as a more advanced example.

Model-based metabolism design: constraints for kinetic and stoichiometric models

The implementation of model-based designs in metabolic engineering and synthetic biology may fail. One of the reasons for this failure is that only a part of the real-world complexity is included in models. Still, some knowledge can be simplified and taken into account in the form of optimization constraints to improve the feasibility of model-based designs of metabolic pathways in organisms. Some constraints (mass balance, energy balance, and steady-state assumption) serve as a basis for many modelling approaches. There are others (total enzyme activity constraint and homeostatic constraint) proposed decades ago, but which are frequently ignored in design development. Several new approaches of cellular analysis have made possible the application of constraints like cell size, surface, and resource balance. Constraints for kinetic and stoichiometric models are grouped according to their applicability preconditions in (1) general constraints, (2) organism-level constraints, and (3) experiment-level constraints. General constraints are universal and are applicable for any system. Organism-level constraints are applicable for biological systems and usually are organism-specific, but these constraints can be applied without information about experimental conditions. To apply experimental-level constraints, peculiarities of the organism and the experimental set-up have to be taken into account to calculate the values of constraints. The limitations of applicability of particular constraints for kinetic and stoichiometric models are addressed.

Understanding start-up problems in yeast glycolysis

Yeast glycolysis has been the focus of research for decades, yet a number of dynamical aspects of yeast glycolysis remain poorly understood at present. If nutrients are scarce, yeast will provide its catabolic and energetic needs with other pathways, but the enzymes catalysing upper glycolytic fluxes are still expressed. We conjecture that this overexpression facilitates the rapid transition to glycolysis in case of a sudden increase in nutrient concentration. However, if starved yeast is presented with abundant glucose, it can enter into an imbalanced state where glycolytic intermediates keep accumulating, leading to arrested growth and cell death. The bistability between regularly functioning and imbalanced phenotypes has been shown to depend on redox balance. We shed new light on these phenomena with a mathematical analysis of an ordinary differential equation model, including NADH to account for the redox balance. In order to gain qualitative insight, most of the analysis is parameter-free, i.e., without assigning a numerical value to any of the parameters. The model has a subtle bifurcation at the switch between an inviable equilibrium state and stable flux through glycolysis. This switch occurs if the ratio between the flux through upper glycolysis and ATP consumption rate of the cell exceeds a fixed threshold. If the enzymes of upper glycolysis would be barely expressed, our model predicts that there will be no glycolytic flux, even if external glucose would be at growth-permissable levels. The existence of the imbalanced state can be found for certain parameter conditions independent of the mentioned bifurcation. The parameter-free analysis proved too complex to directly gain insight into the imbalanced states, but the starting point of a branch of imbalanced states can be shown to exist in detail. Moreover, the analysis offers the key ingredients necessary for successful numerical continuation, which highlight the existence of this bistability and the influence of the redox balance.

Parameters Estimation in Phase-Space Landscape Reconstruction of Cell Fate: A Systems Biology Approach

The thermodynamical formalism of irreversible processes offers a theoretical framework appropriate to explain the complexity observed at the macroscopic level of dynamic systems. In this context, together with the theory of complex systems and systems biology, the thermodynamical formalism establishes an appropriate conceptual framework to address the study of biological systems, in particular cancer.The Chapter is organized as follows: In Subheading 1, an integrative view of these disciplines is offered, for the characterization of the emergence and evolution of cancer, seen as a self-organized dynamic system far from the thermodynamic equilibrium. Development of a thermodynamic framework, based on the entropy production rate, is presented in Subheading 2. Subheading 3 is dedicated to all tumor growth, as seen through a "phase transitions" far from equilibrium. Subheading 4 is devoted to complexity of cancer glycolysis. Finally, some concluding remarks are presented in Subheading 5.

The dynamics of intracellular water constrains glycolytic oscillations in Saccharomyces cerevisiae

We explored the dynamic coupling of intracellular water with metabolism in yeast cells. Using the polarity-sensitive probe 6-acetyl-2-dimethylaminonaphthalene (ACDAN), we show that glycolytic oscillations in the yeast S. cerevisiae BY4743 wild-type strain are coupled to the generalized polarization (GP) function of ACDAN, which measures the physical state of intracellular water. We analysed the oscillatory dynamics in wild type and 24 mutant strains with mutations in many different enzymes and proteins. Using fluorescence spectroscopy, we measured the amplitude and frequency of the metabolic oscillations and ACDAN GP in the resting state of all 25 strains. The results showed that there is a lower and an upper threshold of ACDAN GP, beyond which oscillations do not occur. This critical GP range is also phenomenologically linked to the occurrence of oscillations when cells are grown at different temperatures. Furthermore, the link between glycolytic oscillations and the ACDAN GP value also holds when ATP synthesis or the integrity of the cell cytoskeleton is perturbed. Our results represent the first demonstration that the dynamic behaviour of a metabolic process can be regulated by a cell-wide physical property: the dynamic state of intracellular water, which represents an emergent property.

Live Cell Imaging Reveals pH Oscillations in Saccharomyces cerevisiae During Metabolic Transitions

Addition of glucose to starved Saccharomyces cerevisiae initiates collective NADH dynamics termed glycolytic oscillations. Numerous questions remain about the extent to which single cells can oscillate, if oscillations occur in natural conditions, and potential physiological consequences of oscillations. In this paper, we report sustained glycolytic oscillations in single cells without the need for cyanide. Glucose addition to immobilized cells induced pH oscillations that could be imaged with fluorescent sensors. A population of cells had oscillations that were heterogeneous in frequency, start time, stop time, duration and amplitude. These changes in cytoplasmic pH were necessary and sufficient to drive changes in NADH. Oscillators had lower mitochondrial membrane potentials and budded more slowly than non-oscillators. We also uncovered a new type of oscillation during recovery from H₂O₂ challenge. Our data show that pH in S. cerevisiae changes over several time scales, and that imaging pH offers a new way to measure glycolytic oscillations on individual cells.

Dissipative structures and biological rhythms

Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca⁺⁺ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.

Mathematical model of chaotic oscillations and oscillatory entrainment in glycolysis originated from periodic substrate supply

We study the influence of periodic influx on a character of glycolytic oscillations within the forced Selkov system. We demonstrate that such a simple system demonstrates a rich variety of dynamical regimes (domains of entrainment of different order (Arnold tongues), quasiperiodic oscillations, and chaos), which can be qualitatively collated with the known experimental data. We determine detailed dynamical regimes exploring the map of Lyapunov characteristic exponents obtained in numerical simulations of the Selkov system with periodic influx. In addition, a special study of the chaotic regime and the scenario of its origin in this system was evaluated and discussed.

Search for a Minimal Set of Parameters by Assessing the Total Optimization Potential for a Dynamic Model of a Biochemical Network

Selecting an efficient small set of adjustable parameters to improve metabolic features of an organism is important for a reduction of implementation costs and risks of unpredicted side effects. In practice, to avoid the analysis of a huge combinatorial space for the possible sets of adjustable parameters, experience-, and intuition-based subsets of parameters are often chosen, possibly leaving some interesting counter-intuitive combinations of parameters unrevealed. The combinatorial scan of possible adjustable parameter combinations at the model optimization level is possible; however, the number of analyzed combinations is still limited. The total optimization potential (TOP) approach is proposed to assess the full potential for increasing the value of the objective function by optimizing all possible adjustable parameters. This seemingly unpractical combination of adjustable parameters allows assessing the maximum attainable value of the objective function and stopping the combinatorial space scanning when the desired fraction of TOP is reached and any further increase in the number of adjustable parameters cannot bring any reasonable improvement. The relation between the number of adjustable parameters and the reachable fraction of TOP is a valuable guideline in choosing a rational solution for industrial implementation. The TOP approach is demonstrated on the basis of two case studies.

A systemic approach to explore the flexibility of energy stores at the cellular scale: Examples from muscle cells

Variations in energy storage and expenditure are key elements for animals adaptation to rapidly changing environments. Because of the multiplicity of metabolic pathways, metabolic crossroads and interactions between anabolic and catabolic processes within and between different cells, the flexibility of energy stores in animal cells is difficult to describe by simple verbal, textual or graphic terms. We propose a mathematical model to study the influence of internal and external challenges on the dynamic behavior of energy stores and its consequence on cell energy status. The role of the flexibility of energy stores on the energy equilibrium at the cellular level is illustrated through three case studies: variation in eating frequency (i.e., glucose input), level of physical activity (i.e., ATP requirement), and changes in cell characteristics (i.e., maximum capacity of glycogen storage). Sensitivity analysis has been performed to highlight the most relevant parameters of the model; model simulations have then been performed to illustrate how variation in these key parameters affects cellular energy balance. According to this analysis, glycogen maximum accumulation capacity and homeostatic energy demand are among the most important parameters regulating muscle cell metabolism to ensure its energy equilibrium.

Adenosine diphosphate restricts the protein remodeling activity of the Hsp104 chaperone to Hsp70 assisted disaggregation

Hsp104 disaggregase provides thermotolerance in yeast by recovering proteins from aggregates in cooperation with the Hsp70 chaperone. Protein disaggregation involves polypeptide extraction from aggregates and its translocation through the central channel of the Hsp104 hexamer. This process relies on adenosine triphosphate (ATP) hydrolysis. Considering that Hsp104 is characterized by low affinity towards ATP and is strongly inhibited by adenosine diphosphate (ADP), we asked how Hsp104 functions at the physiological levels of adenine nucleotides. We demonstrate that physiological levels of ADP highly limit Hsp104 activity. This inhibition, however, is moderated by the Hsp70 chaperone, which allows efficient disaggregation by supporting Hsp104 binding to aggregates but not to non-aggregated, disordered protein substrates. Our results point to an additional level of Hsp104 regulation by Hsp70, which restricts the potentially toxic protein unfolding activity of Hsp104 to the disaggregation process, providing the yeast protein-recovery system with substrate specificity and efficiency in ATP consumption.

DOI:http://dx.doi.org/10.7554/eLife.15159.001

Under stressful conditions, such as high temperatures, many proteins lose their proper structure and clump together to form large irregular aggregates. To combat this effect, living organisms exposed to stress produce specialized proteins called chaperones, which can rescue the damaged proteins from aggregates.

Studies into this “disaggregation” process often use budding yeast as a model organism. The protein-recovery machinery in this yeast is composed of a ring-shaped enzyme called Hsp104, together with a chaperone called Hsp70 and its partner Hsp40. The Hsp104 enzyme converts molecules of ATP into ADP and uses the energy released from the reaction to move, or “translocate”, damaged proteins through its central channel and release them from the aggregates.

Previous studies had reported that ADP negatively affects Hsp104. Now, Kłosowska et al show that Hsp104 is almost inactive in a test-tube if the concentration of ADP is as high as that found inside a cell. This raises a question: how can Hsp104 efficiently remove proteins from aggregates in cells if the conditions are so unfavorable?

Using purified proteins, Kłosowska et al. go on to show that Hsp104 is able to tolerate the level of ADP found inside cells thanks to the Hsp70 chaperone. The experiments show that ADP weakens Hsp104’s ability to bind proteins while Hsp70 supports this ability and counteracts the negative effect of ADP. Further experiments demonstrate that Hsp104 is less affected by ADP, and binds more readily to ATP, when it is translocating proteins. These findings explain how the yeast disaggregating machinery can work even at relatively high concentrations of ADP, and reveal a new control mechanism in the disaggregation process.

Many important proteins have poorly organized fragments that can be recognized by Hsp104, and if Hsp104 was to bind to and translocate these proteins it could harm the cell. The findings of Kłosowska et al. suggest that Hsp70 helps Hsp104 to specifically bind to and act upon proteins in aggregates, while binding to partly unstructured proteins is limited by the high ADP concentration. Further studies are now needed to understand how the protein-recovery machinery can discriminate between aggregated and non-aggregated proteins.

DOI:http://dx.doi.org/10.7554/eLife.15159.002

Dynamic metabolic models in context: biomass backtracking

Mathematical modeling has proven to be a powerful tool to understand and predict functional and regulatory properties of metabolic processes. High accuracy dynamic modeling of individual pathways is thereby opposed by simplified but genome scale constraint based approaches. A method that links these two powerful techniques would greatly enhance predictive power but is so far lacking. We present biomass backtracking, a workflow that integrates the cellular context in existing dynamic metabolic models via stoichiometrically exact drain reactions based on a genome scale metabolic model. With comprehensive examples, for different species and environmental contexts, we show the importance and scope of applications and highlight the improvement compared to common boundary formulations in existing metabolic models. Our method allows for the contextualization of dynamic metabolic models based on all available information. We anticipate this to greatly increase their accuracy and predictive power for basic research and also for drug development and industrial applications.

Flux Control in Glycolysis Varies Across the Tree of Life

Biochemical thought posits that rate-limiting steps (defined here as points of flux control) are strongly selected as points of pathway regulation and control and are thus expected to be evolutionarily conserved. Conversely, population genetic thought based upon the concepts of mutation-selection-drift balance at the pathway level might suggest variation in flux controlling steps over evolutionary time. Glycolysis, as one of the most conserved and best characterized pathways, was studied to evaluate its evolutionary conservation. The flux controlling step in glycolysis was found to vary over the tree of life. Further, phylogenetic analysis suggested at least 60 events of gene duplication and additional events of putative positive selection that might alter pathway kinetic properties. Together, these results suggest that even with presumed largely negative selection on pathway output on glycolysis, the co-evolutionary process under the hood is dynamic.

Improved metabolite profile smoothing for flux estimation

As genome-scale metabolic models become more sophisticated and dynamic, one significant challenge in using these models is to effectively integrate increasingly prevalent systems-scale metabolite profiling data into them. One common data processing step when integrating metabolite data is to smooth experimental time course measurements: the smoothed profiles can be used to estimate metabolite accumulation (derivatives), and thus the flux distribution of the metabolic model. However, this smoothing step is susceptible to the (often significant) noise in experimental measurements, limiting the accuracy of downstream model predictions. Here, we present several improvements to current approaches for smoothing metabolite time course data using defined functions. First, we use a biologically-inspired mathematical model function taken from transcriptional profiling and clustering literature that captures the dynamics of many biologically relevant transient processes. We demonstrate that it is competitive with, and often superior to, previously described fitting schemas, and may serve as an effective single option for data smoothing in metabolic flux applications. We also implement a resampling-based approach to buffer out sensitivity to specific data sets and allow for more accurate fitting of noisy data. We found that this method, as well as the addition of parameter space constraints, yielded improved estimates of concentrations and derivatives (fluxes) in previously described fitting functions. These methods have the potential to improve the accuracy of existing and future dynamic metabolic models by allowing for the more effective integration of metabolite profiling data.

Collective and individual glycolytic oscillations in yeast cells encapsulated in alginate microparticles

Yeast cells were encapsulated into alginate microparticles of a few hundred micrometers diameter using a centrifuge-based droplet shooting device. We demonstrate the first experimental results of glycolytic oscillations in individual yeast cells immobilized in this way. We investigated both the individual and collective oscillatory behaviors at different cell densities. As the cell density increased, the amplitude of the individual oscillations increased while their period decreased, and the collective oscillations became more synchronized, with an order parameter close to 1 (indicating high synchrony). We also synthesized biphasic-Janus microparticles encapsulating yeast cells of different densities in each hemisphere. The cellular oscillations between the two hemispheres were entrained at both the individual and population levels. Such systems of cells encapsulated into microparticles are useful for investigating how cell-to-cell communication depends on the density and spatial distribution of cells.

Quantification of Interactions between Dynamic Cellular Network Functionalities by Cascaded Layering

Large, naturally evolved biomolecular networks typically fulfil multiple functions. When modelling or redesigning such systems, functional subsystems are often analysed independently first, before subsequent integration into larger-scale computational models. In the design and analysis process, it is therefore important to quantitatively analyse and predict the dynamics of the interactions between integrated subsystems; in particular, how the incremental effect of integrating a subsystem into a network depends on the existing dynamics of that network. In this paper we present a framework for simulating the contribution of any given functional subsystem when integrated together with one or more other subsystems. This is achieved through a cascaded layering of a network into functional subsystems, where each layer is defined by an appropriate subset of the reactions. We exploit symmetries in our formulation to exhaustively quantify each subsystem's incremental effects with minimal computational effort. When combining subsystems, their isolated behaviour may be amplified, attenuated, or be subject to more complicated effects. We propose the concept of mutual dynamics to quantify such nonlinear phenomena, thereby defining the incompatibility and cooperativity between all pairs of subsystems when integrated into any larger network. We exemplify our theoretical framework by analysing diverse behaviours in three dynamic models of signalling and metabolic pathways: the effect of crosstalk mechanisms on the dynamics of parallel signal transduction pathways; reciprocal side-effects between several integral feedback mechanisms and the subsystems they stabilise; and consequences of nonlinear interactions between elementary flux modes in glycolysis for metabolic engineering strategies. Our analysis shows that it is not sufficient to just specify subsystems and analyse their pairwise interactions; the environment in which the interaction takes place must also be explicitly defined. Our framework provides a natural representation of nonlinear interaction phenomena, and will therefore be an important tool for modelling large-scale evolved or synthetic biomolecular networks.

Discerning mechanistically rewired biological pathways by cumulative interaction heterogeneity statistics

Changes in response of a biological pathway could be a consequence of either pathway rewiring, changed input, or a combination of both. Most pathway analysis methods are not designed for mechanistic rewiring such as regulatory element variations. This limits our understanding of biological pathway evolution. Here we present a Q-method to discern whether changed pathway response is caused by mechanistic rewiring of pathways due to evolution. The main innovation is a cumulative pathway interaction heterogeneity statistic accounting for rewiring-specific effects on the rate of change of each molecular variable across conditions. The Q-method remarkably outperformed differential-correlation based approaches on data from diverse biological processes. Strikingly, it also worked well in differentiating rewired chaotic systems, whose dynamics are notoriously difficult to predict. Applying the Q-method on transcriptome data of four yeasts, we show that pathway interaction heterogeneity for known metabolic and signaling pathways is indeed a predictor of interspecies genetic rewiring due to unbalanced TATA box-containing genes among the yeasts. The demonstrated effectiveness of the Q-method paves the way to understanding network evolution at the resolution of functional biological pathways.

Cyanohydrin reactions enhance glycolytic oscillations in yeast

Synchronous metabolic oscillations can be induced in yeast by addition of glucose and removal of extracellular acetaldehyde (ACAx). Compared to other means of ACAx removal, cyanide robustly induces oscillations, indicating additional cyanide reactions besides ACA to lactonitrile conversion. Here, (13)C NMR is used to confirm our previous hypothesis, that cyanide directly affects glycolytic fluxes through reaction with carbonyl-containing compounds. Intracellularly, at least 3 cyanohydrins were identified. Extracellularly, all signals could be identified and lactonitrile was found to account for ~66% of total cyanide removal. Simulations of our updated computational model show that intracellular cyanide reactions increase the amplitude of oscillations and that cyanide addition lowers [ACA] instantaneously. We conclude that cyanide provides the following means of inducing global oscillations: a) by reducing [ACAx] relative to oscillation amplitude, b) by targeting multiple intracellular carbonyl compounds during fermentation, and c) by acting as a phase resetting stimulus.

Entrainment of heterogeneous glycolytic oscillations in single cells

Cell signaling, gene expression, and metabolism are affected by cell-cell heterogeneity and random changes in the environment. The effects of such fluctuations on cell signaling and gene expression have recently been studied intensively using single-cell experiments. In metabolism heterogeneity may be particularly important because it may affect synchronisation of metabolic oscillations, an important example of cell-cell communication. This synchronisation is notoriously difficult to describe theoretically as the example of glycolytic oscillations shows: neither is the mechanism of glycolytic synchronisation understood nor the role of cell-cell heterogeneity. To pin down the mechanism and to assess its robustness and universality we have experimentally investigated the entrainment of glycolytic oscillations in individual yeast cells by periodic external perturbations. We find that oscillatory cells synchronise through phase shifts and that the mechanism is insensitive to cell heterogeneity (robustness) and similar for different types of external perturbations (universality).

Construction and validation of a detailed kinetic model of glycolysis in Plasmodium falciparum

The enzymes in the Embden-Meyerhof-Parnas pathway of Plasmodium falciparum trophozoites were kinetically characterized and their integrated activities analyzed in a mathematical model. For validation of the model, we compared model predictions for steady-state fluxes and metabolite concentrations of the hexose phosphates with experimental values for intact parasites. The model, which is completely based on kinetic parameters that were measured for the individual enzymes, gives an accurate prediction of the steady-state fluxes and intermediate concentrations. This is the first detailed kinetic model for glucose metabolism in P. falciparum, one of the most prolific malaria-causing protozoa, and the high predictive power of the model makes it a strong tool for future drug target identification studies. The modelling workflow is transparent and reproducible, and completely documented in the SEEK platform, where all experimental data and model files are available for download.

DATABASE

The mathematical models described in the present study have been submitted to the JWS Online Cellular Systems Modelling Database (http://jjj.bio.vu.nl/database/penkler). The investigation and complete experimental data set is available on SEEK (10.15490/seek.1.

INVESTIGATION

56).

Applications of computational modeling in metabolic engineering of yeast

Generally, a microorganism's phenotype can be described by its pattern of metabolic fluxes. Although fluxes cannot be measured directly, inference of fluxes is well established. In biotechnology the aim is often to increase the capacity of specific fluxes. For this, metabolic engineering methods have been developed and applied extensively. Many of these rely on balancing of intracellular metabolites, redox, and energy fluxes, using genome-scale models (GEMs) that in combination with appropriate objective functions and constraints can be used to predict potential gene targets for obtaining a preferred flux distribution. These methods point to strategies for altering gene expression; however, fluxes are often controlled by post-transcriptional events. Moreover, GEMs are usually not taking into account metabolic regulation, thermodynamics and enzyme kinetics. To facilitate metabolic engineering, tools from synthetic biology have emerged, enabling integration and assembly of naturally nonexistent, but well-characterized components into a living organism. To describe these systems kinetic models are often used and to integrate these systems with the standard metabolic engineering approach, it is necessary to expand the modeling of metabolism to consider kinetics of individual processes. This review will give an overview about models available for metabolic engineering of yeast and discusses their applications.