Investigating the dynamic behavior of biochemical networks using model families

Rethinking 13C-metabolic flux analysis - The Bayesian way of flux inference

Metabolic reaction rates (fluxes) play a crucial role in comprehending cellular phenotypes and are essential in areas such as metabolic engineering, biotechnology, and biomedical research. The state-of-the-art technique for estimating fluxes is metabolic flux analysis using isotopic labelling (13C-MFA), which uses a dataset-model combination to determine the fluxes. Bayesian statistical methods are gaining popularity in the field of life sciences, but the use of 13C-MFA is still dominated by conventional best-fit approaches. The slow take-up of Bayesian approaches is, at least partly, due to the unfamiliarity of Bayesian methods to metabolic engineering researchers. To address this unfamiliarity, we here outline similarities and differences between the two approaches and highlight particular advantages of the Bayesian way of flux analysis. With a real-life example, re-analysing a moderately informative labelling dataset of E. coli, we identify situations in which Bayesian methods are advantageous and more informative, pointing to potential pitfalls of current 13C-MFA evaluation approaches. We propose the use of Bayesian model averaging (BMA) for flux inference as a means of overcoming the problem of model uncertainty through its tendency to assign low probabilities to both, models that are unsupported by data, and models that are overly complex. In this capacity, BMA resembles a tempered Ockham's razor. With the tempered razor as a guide, BMA-based 13C-MFA alleviates the problem of model selection uncertainty and is thereby capable of becoming a game changer for metabolic engineering by uncovering new insights and inspiring novel approaches.

Integrating a dynamic central metabolism model of cancer cells with a hybrid 3D multiscale model for vascular hepatocellular carcinoma growth

We develop here a novel modelling approach with the aim of closing the conceptual gap between tumour-level metabolic processes and the metabolic processes occurring in individual cancer cells. In particular, the metabolism in hepatocellular carcinoma derived cell lines (HEPG2 cells) has been well characterized but implementations of multiscale models integrating this known metabolism have not been previously reported. We therefore extend a previously published multiscale model of vascular tumour growth, and integrate it with an experimentally verified network of central metabolism in HEPG2 cells. This resultant combined model links spatially heterogeneous vascular tumour growth with known metabolic networks within tumour cells and accounts for blood flow, angiogenesis, vascular remodelling and nutrient/growth factor transport within a growing tumour, as well as the movement of, and interactions between normal and cancer cells. Model simulations report for the first time, predictions of spatially resolved time courses of core metabolites in HEPG2 cells. These simulations can be performed at a sufficient scale to incorporate clinically relevant features of different tumour systems using reasonable computational resources. Our results predict larger than expected temporal and spatial heterogeneity in the intracellular concentrations of glucose, oxygen, lactate pyruvate, f16bp and Acetyl-CoA. The integrated multiscale model developed here provides an ideal quantitative framework in which to study the relationship between dosage, timing, and scheduling of anti-neoplastic agents and the physiological effects of tumour metabolism at the cellular level. Such models, therefore, have the potential to inform treatment decisions when drug response is dependent on the metabolic state of individual cancer cells.

Rapid process synthesis supported by a unified modular software framework

Although known to be very powerful, the widespread application of model-based techniques is still significantly hampered in the area of bio-processes. Reasons for this situation can be found along the whole chain to set up and implement such approaches. In a time-consuming step, models are typically hand-crafted. Whether alternatives of better models exist to actually fulfill the final goals is undocumented, most often even unknown. In a next step, model-based process control methods are hand-coded in an error-prone procedure. For many of these methods given in the literature, only simulation studies are shown, leaving the interested reader with the unanswered question whether the implementation of a specific method in a real process is viable. As the potentially time-consuming implementation of such a method presents a risk for a rapid process development, promising candidates may be overlooked. To remediate this unsatisfactory situation, a combination of theoretical methods and information technology is proposed here. By an exemplarily realized software tool, it is shown how such an environment helps to promote model-based optimization, supervision, and control of bio-processes and allows for an inexpensive test of new ideas as well in real-life experiments. The contribution concentrates on an overview of a possible software architecture with respect to necessary methods and a meaningful information strategy, highlighting some of the more crucial building blocks. Experimental results exploiting parts of the proposed methods are given for a yeast strain synthesizing a product of industrial interest.

Current state and challenges for dynamic metabolic modeling

While the stoichiometry of metabolism is probably the best studied cellular level, the dynamics in metabolism can still not be well described, predicted and, thus, engineered. Unknowns in the metabolic flux behavior arise from kinetic interactions, especially allosteric control mechanisms. While the stoichiometry of enzymes is preserved in vitro, their activity and kinetic behavior differs from the in vivo situation. Next to this challenge, it is infeasible to test the interaction of each enzyme with each intracellular metabolite in vitro exhaustively. As a consequence, the whole interacting metabolome has to be studied in vivo to identify the relevant enzymes properties. In this review we discuss current approaches for in vivo perturbation experiments, that is, stimulus response experiments using different setups and quantitative analytical approaches, including dynamic carbon tracing. Next to reliable and informative data, advanced modeling approaches and computational tools are required to identify kinetic mechanisms and their parameters.

How informative is your kinetic model?: using resampling methods for model invalidation

Background

Kinetic models can present mechanistic descriptions of molecular processes within a cell. They can be used to predict the dynamics of metabolite production, signal transduction or transcription of genes. Although there has been tremendous effort in constructing kinetic models for different biological systems, not much effort has been put into their validation. In this study, we introduce the concept of resampling methods for the analysis of kinetic models and present a statistical model invalidation approach.

Results

We based our invalidation approach on the evaluation of a kinetic model’s predictive power through cross validation and forecast analysis. As a reference point for this evaluation, we used the predictive power of an unsupervised data analysis method which does not make use of any biochemical knowledge, namely Smooth Principal Components Analysis (SPCA) on the same test sets. Through a simulations study, we showed that too simple mechanistic descriptions can be invalidated by using our SPCA-based comparative approach until high amount of noise exists in the experimental data. We also applied our approach on an eicosanoid production model developed for human and concluded that the model could not be invalidated using the available data despite its simplicity in the formulation of the reaction kinetics. Furthermore, we analysed the high osmolarity glycerol (HOG) pathway in yeast to question the validity of an existing model as another realistic demonstration of our method.

Conclusions

With this study, we have successfully presented the potential of two resampling methods, cross validation and forecast analysis in the analysis of kinetic models’ validity. Our approach is easy to grasp and to implement, applicable to any ordinary differential equation (ODE) type biological model and does not suffer from any computational difficulties which seems to be a common problem for approaches that have been proposed for similar purposes. Matlab files needed for invalidation using SPCA cross validation and our toy model in SBML format are provided at http://www.bdagroup.nl/content/Downloads/software/software.php.

Kinetic models in industrial biotechnology - Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.

Automatic identification of structured process models based on biological phenomena detected in (fed-)batch experiments

In this paper, we present a set of methods to automatically propose structured process models from an automated analysis of (fed-)batch experiments. Therefore, the measurements are numerically compensated for the influence of feeding and sampling, and the qualitative behavior of the measurements is revealed. As measurements from fermentations are inherently noisy, we introduce a method that divides the compensated curves into several episodes in a probabilistic framework to better handle these shortcomings. The probability of biological phenomena that reveal crucial information about the underlying reaction network is calculated. Since the phenomena detection is measurement-driven, its reliability depends on the measurement situation, e.g., the number of samples taken and experiments considered, measurement noise, etc. We show a possible approach to test the uncertainty of the phenomena detection against these influences. Finally, model structures are proposed automatically based on the detected biological phenomena. An experimental validation of the approach is shown, using real fermentation data from fed-batch cultivations of Streptomyces tendae.

Understanding regulation of metabolism through feasibility analysis

Understanding cellular regulation of metabolism is a major challenge in systems biology. Thus far, the main assumption was that enzyme levels are key regulators in metabolic networks. However, regulation analysis recently showed that metabolism is rarely controlled via enzyme levels only, but through non-obvious combinations of hierarchical (gene and enzyme levels) and metabolic regulation (mass action and allosteric interaction). Quantitative analyses relating changes in metabolic fluxes to changes in transcript or protein levels have revealed a remarkable lack of understanding of the regulation of these networks. We study metabolic regulation via feasibility analysis (FA). Inspired by the constraint-based approach of Flux Balance Analysis, FA incorporates a model describing kinetic interactions between molecules. We enlarge the portfolio of objectives for the cell by defining three main physiologically relevant objectives for the cell: function, robustness and temporal responsiveness. We postulate that the cell assumes one or a combination of these objectives and search for enzyme levels necessary to achieve this. We call the subspace of feasible enzyme levels the feasible enzyme space. Once this space is constructed, we can study how different objectives may (if possible) be combined, or evaluate the conditions at which the cells are faced with a trade-off among those. We apply FA to the experimental scenario of long-term carbon limited chemostat cultivation of yeast cells, studying how metabolism evolves optimally. Cells employ a mixed strategy composed of increasing enzyme levels for glucose uptake and hexokinase and decreasing levels of the remaining enzymes. This trade-off renders the cells specialized in this low-carbon flux state to compete for the available glucose and get rid of over-overcapacity. Overall, we show that FA is a powerful tool for systems biologists to study regulation of metabolism, interpret experimental data and evaluate hypotheses.

Sloppy models, parameter uncertainty, and the role of experimental design

Computational models are increasingly used to understand and predict complex biological phenomena. These models contain many unknown parameters, at least some of which are difficult to measure directly, and instead are estimated by fitting to time-course data. Previous work has suggested that even with precise data sets, many parameters are unknowable by trajectory measurements. We examined this question in the context of a pathway model of epidermal growth factor (EGF) and neuronal growth factor (NGF) signaling. Computationally, we examined a palette of experimental perturbations that included different doses of EGF and NGF as well as single and multiple gene knockdowns and overexpressions. While no single experiment could accurately estimate all of the parameters, experimental design methodology identified a set of five complementary experiments that could. These results suggest optimism for the prospects for calibrating even large models, that the success of parameter estimation is intimately linked to the experimental perturbations used, and that experimental design methodology is important for parameter fitting of biological models and likely for the accuracy that can be expected from them.

Translating biochemical network models between different kinetic formats

Mechanistic biochemical network models describe the dynamics of intracellular metabolite pools in terms of substance concentrations, stoichiometry and reaction kinetics. Data from stimulus response experiments are currently the most informative source for in-vivo parameter estimation in such models. However, only a part of the parameters of classical enzyme kinetic models can usually be estimated from typical stimulus response data. For this reason, several alternative kinetic formats using different "languages" (e.g. linear, power laws, linlog, generic and convenience) have been proposed to reduce the model complexity. The present contribution takes a rigorous "multi-lingual" approach to data evaluation by translating biochemical network models from one kinetic format into another. For this purpose, a new high-performance algorithm has been developed and tested. Starting with a given model, it replaces as many kinetic terms as possible by alternative expressions while still reproducing the experimental data. Application of the algorithm to a published model for Escherichia coli's sugar metabolism demonstrates the power of the new method. It is shown that model translation is a powerful tool to investigate the information content of stimulus response data and the predictive power of models. Moreover, the local and global approximation capabilities of the models are elucidated and some pitfalls of traditional single model approaches to data evaluation are revealed.

Stimulus design for model selection and validation in cell signaling

Mechanism-based chemical kinetic models are increasingly being used to describe biological signaling. Such models serve to encapsulate current understanding of pathways and to enable insight into complex biological processes. One challenge in model development is that, with limited experimental data, multiple models can be consistent with known mechanisms and existing data. Here, we address the problem of model ambiguity by providing a method for designing dynamic stimuli that, in stimulus–response experiments, distinguish among parameterized models with different topologies, i.e., reaction mechanisms, in which only some of the species can be measured. We develop the approach by presenting two formulations of a model-based controller that is used to design the dynamic stimulus. In both formulations, an input signal is designed for each candidate model and parameterization so as to drive the model outputs through a target trajectory. The quality of a model is then assessed by the ability of the corresponding controller, informed by that model, to drive the experimental system. We evaluated our method on models of antibody–ligand binding, mitogen-activated protein kinase (MAPK) phosphorylation and de-phosphorylation, and larger models of the epidermal growth factor receptor (EGFR) pathway. For each of these systems, the controller informed by the correct model is the most successful at designing a stimulus to produce the desired behavior. Using these stimuli we were able to distinguish between models with subtle mechanistic differences or where input and outputs were multiple reactions removed from the model differences. An advantage of this method of model discrimination is that it does not require novel reagents, or altered measurement techniques; the only change to the experiment is the time course of stimulation. Taken together, these results provide a strong basis for using designed input stimuli as a tool for the development of cell signaling models.

A major focus of systems biology is the development of mechanism-based models of cell signaling pathways. These models hold the promise of encapsulating our understanding of complex biological processes while also predicting new behavior. However, as these models become more complex, it can be difficult to distinguish between model alternatives. One means of improved model discrimination involves making measurements of additional components in the biological system to provide more detailed data. Here we present an alternative, which is to apply a time-varying input while monitoring the same network components. This new method was able to discriminate among models with subtle mechanistic differences. A particular advantage is that for many cases, time-varying input stimulation is fairly easy to apply experimentally, whereas measuring additional network components can involve the creation of new reagents or measurement assays. Thus, we believe that the application of time-varying input stimulation will become a powerful tool in the field of systems biology as the community places increased emphasis on the development of quantitative, mechanistic, and predictive models of biological network behavior.

Dynamic Bayesian sensitivity analysis of a myocardial metabolic model

Dynamic compartmentalized metabolic models are identified by a large number of parameters, several of which are either non-physical or extremely difficult to measure. Typically, the available data and prior information is insufficient to fully identify the system. Since the models are used to predict the behavior of unobserved quantities, it is important to understand how sensitive the output of the system is to perturbations in the poorly identifiable parameters. Classically, it is the goal of sensitivity analysis to asses how much the output changes as a function of the parameters. In the case of dynamic models, the output is a function of time and therefore its sensitivity is a time dependent function. If the output is a differentiable function of the parameters, the sensitivity at one time instance can be computed from its partial derivatives with respect to the parameters. The time course of these partial derivatives describes how the sensitivity varies in time. When the model is not uniquely identifiable, or if the solution of the parameter identification problem is known only approximately, we may have not one, but a distribution of possible parameter values. This is always the case when the parameter identification problem is solved in a statistical framework. In that setting, the proper way to perform sensitivity analysis is to not rely on the values of the sensitivity functions corresponding to a single model, but to consider the distributed nature of the sensitivity functions, inherited from the distribution of the vector of the model parameters. In this paper we propose a methodology for analyzing the sensitivity of dynamic metabolic models which takes into account the variability of the sensitivity over time and across a sample. More specifically, we draw a representative sample from the posterior density of the vector of model parameters, viewed as a random variable. To interpret the output of this doubly varying sensitivity analysis, we propose visualization modalities particularly effective at displaying simultaneously variations over time and across a sample. We perform an analysis of the sensitivity of the concentrations of lactate and glycogen in cytosol, and of ATP, ADP, NAD(+) and NADH in cytosol and mitochondria, to the parameters identifying a three compartment model for myocardial metabolism during ischemia.

Visualizing regulatory interactions in metabolic networks

Background

Direct visualization of data sets in the context of biochemical network drawings is one of the most appealing approaches in the field of data evaluation within systems biology. One important type of information that is very helpful in interpreting and understanding metabolic networks has been overlooked so far. Here we focus on the representation of this type of information given by the strength of regulatory interactions between metabolite pools and reaction steps.

Results

The visualization of such interactions in a given metabolic network is based on a novel concept defining the regulatory strength (RS) of effectors regulating certain reaction steps. It is applicable to any mechanistic reaction kinetic formula. The RS values are measures for the strength of an up- or down-regulation of a reaction step compared with the completely non-inhibited or non-activated state, respectively. One numerical RS value is associated to any effector edge contained in the network. The RS is approximately interpretable on a percentage scale where 100% means the maximal possible inhibition or activation, respectively, and 0% means the absence of a regulatory interaction. If many effectors influence a certain reaction step, the respective percentages indicate the proportion in which the different effectors contribute to the total regulation of the reaction step. The benefits of the proposed method are demonstrated with a complex example system of a dynamic E. coli network.

Conclusion

The presented visualization approach is suitable for an intuitive interpretation of simulation data of metabolic networks under dynamic as well as steady-state conditions. Huge amounts of simulation data can be analyzed in a quick and comprehensive way. An extended time-resolved graphical network presentation provides a series of information about regulatory interaction within the biological system under investigation.

Metabolomics: current state and evolving methodologies and tools

In recent years, metabolomics developed to an accepted and valuable tool in life sciences. Substantial improvements of analytical hardware allow metabolomics to run routinely now. Data are successfully used to investigate genotype-phenotype relations of strains and mutants. Metabolomics facilitates metabolic engineering to optimise mircoorganisms for white biotechnology and spreads to the investigation of biotransformations and cell culture. Metabolomics serves not only as a source of qualitative but also quantitative data of intra-cellular metabolites essential for the model-based description of the metabolic network operating under in vivo conditions. To collect reliable metabolome data sets, culture and sampling conditions, as well as the cells' metabolic state, are crucial. Hence, application of biochemical engineering principles and method standardisation efforts become important. Together with the other more established omics technologies, metabolomics will strengthen its claim to contribute to the detailed understanding of the in vivo function of gene products, biochemical and regulatory networks and, even more ambitious, the mathematical description and simulation of the whole cell in the systems biology approach. This knowledge will allow the construction of designer organisms for process application using biotransformation and fermentative approaches making effective use of single enzymes, whole microbial and even higher cells.

Bioengineering novel in vitro metabolic pathways using synthetic biology

Huge numbers of enzymes have evolved in nature to function in aqueous environments at moderate temperatures and neutral pH. This gives us, in principle, the unique opportunity to construct multistep reaction systems of considerable catalytic complexity in vitro. However, this opportunity is rarely exploited beyond research scale, because such systems are difficult to assemble and to operate productively. Recent advances in DNA synthesis, genome engineering, high-throughput analytics, model-based analysis of biochemical systems and (semi-)rational protein engineering suggest that we have all the tools available to rationally design and efficiently operate such systems of enzymes, and finally harvest their potential for preparative syntheses.

Efficient classification of complete parameter regions based on semidefinite programming

Background

Current approaches to parameter estimation are often inappropriate or inconvenient for the modelling of complex biological systems. For systems described by nonlinear equations, the conventional approach is to first numerically integrate the model, and then, in a second a posteriori step, check for consistency with experimental constraints. Hence, only single parameter sets can be considered at a time. Consequently, it is impossible to conclude that the "best" solution was identified or that no good solution exists, because parameter spaces typically cannot be explored in a reasonable amount of time.

Results

We introduce a novel approach based on semidefinite programming to directly identify consistent steady state concentrations for systems consisting of mass action kinetics, i.e., polynomial equations and inequality constraints. The duality properties of semidefinite programming allow to rigorously certify infeasibility for whole regions of parameter space, thus enabling the simultaneous multi-dimensional analysis of entire parameter sets.

Conclusion

Our algorithm reduces the computational effort of parameter estimation by several orders of magnitude, as illustrated through conceptual sample problems. Of particular relevance for systems biology, the approach can discriminate between structurally different candidate models by proving inconsistency with the available data.

Emerging Corynebacterium glutamicum systems biology

Corynebacterium glutamicum is widely used for the biotechnological production of amino acids. Amino acid producing strains have been improved classically by mutagenesis and screening as well as in a rational manner using recombinant DNA technology. Metabolic flux analysis may be viewed as the first systems approach to C. glutamicum physiology since it combines isotope labeling data with metabolic network models of the biosynthetic and central metabolic pathways. However, only the complete genome sequence of C. glutamicum and post-genomics methods such as transcriptomics and proteomics have allowed characterizing metabolic and regulatory properties of this bacterium on a truly global level. Besides transcriptomics and proteomics, metabolomics and modeling approaches have now been established. Systems biology, which uses systematic genomic, proteomic and metabolomic technologies with the final aim of constructing comprehensive and predictive models of complex biological systems, is emerging for C. glutamicum. We will present current developments that advanced our insight into fundamental biology of C. glutamicum and that in the future will enable novel biotechnological applications for the improvement of amino acid production.

Application of metabolome data in functional genomics: A conceptual strategy

A gene with yet unknown physiological function can be studied by changing its expression level followed by analysis of the resulting phenotype. This type of functional genomics study can be complicated by the occurrence of 'silent mutations', the phenotypes of which are not easily observable in terms of metabolic fluxes (e.g., the growth rate). Nevertheless, genetic alteration may give rise to significant yet complicated changes in the metabolome. We propose here a conceptual functional genomics strategy based on microbial metabolome data, which identifies changes in in vivo enzyme activities in the mutants. These predicted changes are used to formulate hypotheses to infer unknown gene functions. The required metabolome data can be obtained solely from high-throughput mass spectrometry analysis, which provides the following in vivo information: (1) the metabolite concentrations in the reference and the mutant strain; (2) the metabolic fluxes in both strains and (3) the enzyme kinetic parameters of the reference strain. We demonstrate in silico that changes in enzyme activities can be accurately predicted by this approach, even in 'silent mutants'.