Kinetic models in industrial biotechnology - Improving cell factory performance

RapidRIP quantifies the intracellular metabolome of 7 industrial strains of E. coli

Fast metabolite quantification methods are required for high throughput screening of microbial strains obtained by combinatorial or evolutionary engineering approaches. In this study, a rapid RIP-LC-MS/MS (RapidRIP) method for high-throughput quantitative metabolomics was developed and validated that was capable of quantifying 102 metabolites from central, amino acid, energy, nucleotide, and cofactor metabolism in less than 5 minutes. The method was shown to have comparable sensitivity and resolving capability as compared to a full length RIP-LC-MS/MS method (FullRIP). The RapidRIP method was used to quantify the metabolome of seven industrial strains of E. coli revealing significant differences in glycolytic, pentose phosphate, TCA cycle, amino acid, and energy and cofactor metabolites were found. These differences translated to statistically and biologically significant differences in thermodynamics of biochemical reactions between strains that could have implications when choosing a host for bioprocessing.

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.

Controlled gas exchange in whole lung bioreactors

In cellular, tissue-level or whole organ bioreactors, the level of dissolved oxygen is one of the most important factors requiring control. Hypoxic environments may lead to cellular apoptosis, while hyperoxic environments may lead to cellular damage or dedifferentiation, both resulting in loss of overall tissue function. This manuscript describes the creation, characterization and validation of a bioreactor system that can control oxygen delivery based on real-time metabolic demand of cultured whole lung tissue. A mathematical model describing and predicting gas exchange within the tunable bioreactor system is developed. In addition, the inherent gas exchange properties of the bioreactor and the inherent oxygen consumption rates of native rat lungs are determined, thereby providing a quantitative relationship between system parameters and levels of dissolved oxygen. Finally, the mathematical model is validated during whole lung culture under a range of system parameters. The system presented here provides a quantitative relationship between the concentration of dissolved oxygen, tissue oxygen consumption rates, and controllable system parameters that introduce gasses into the bioreactor. This relationship not only enables the maintenance of constant levels of dissolved oxygen throughout a culture period during which cells are replicating, but also provides noninvasive and real-time estimation of the metabolic and proliferative states of native or engineered lung tissue simply through dissolved oxygen measurements. Copyright © 2017 John Wiley & Sons, Ltd.

Topological and kinetic determinants of the modal matrices of dynamic models of metabolism

Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions.

The emerging role of systems biology for engineering protein production in CHO cells

To meet the ever-growing demand for effective, safe, and affordable protein therapeutics, decades of intense efforts have aimed to maximize the quantity and quality of recombinant proteins produced in CHO cells. Bioprocessing innovations and cell engineering efforts have improved product titer; however, uncharacterized cellular processes and gene regulatory mechanisms still hinder cell growth, specific productivity, and protein quality. Herein, we summarize recent advances in systems biology and data-driven approaches aiming to unravel how molecular pathways, cellular processes, and extrinsic factors (e.g. media supplementation) influence recombinant protein production. In particular, as the available omics data for CHO cells continue to grow, predictive models and screens will be increasingly used to unravel the biological drivers of protein production, which can be used with emerging genome editing technologies to rationally engineer cells to further control the quantity, quality and affordability of many biologic drugs.

Model-Based Methods in the Biopharmaceutical Process Lifecycle

Model-based methods are increasingly used in all areas of biopharmaceutical process technology. They can be applied in the field of experimental design, process characterization, process design, monitoring and control. Benefits of these methods are lower experimental effort, process transparency, clear rationality behind decisions and increased process robustness. The possibility of applying methods adopted from different scientific domains accelerates this trend further. In addition, model-based methods can help to implement regulatory requirements as suggested by recent Quality by Design and validation initiatives. The aim of this review is to give an overview of the state of the art of model-based methods, their applications, further challenges and possible solutions in the biopharmaceutical process life cycle. Today, despite these advantages, the potential of model-based methods is still not fully exhausted in bioprocess technology. This is due to a lack of (i) acceptance of the users, (ii) user-friendly tools provided by existing methods, (iii) implementation in existing process control systems and (iv) clear workflows to set up specific process models. We propose that model-based methods be applied throughout the lifecycle of a biopharmaceutical process, starting with the set-up of a process model, which is used for monitoring and control of process parameters, and ending with continuous and iterative process improvement via data mining techniques.

Balancing gene expression without library construction via a reusable sRNA pool

Balancing protein expression is critical when optimizing genetic systems. Typically, this requires library construction to vary the genetic parts controlling each gene, which can be expensive and time-consuming. Here, we develop sRNAs corresponding to 15nt ‘target’ sequences that can be inserted upstream of a gene. The targeted gene can be repressed from 1.6- to 87-fold by controlling sRNA expression using promoters of different strength. A pool is built where six sRNAs are placed under the control of 16 promoters that span a ∼10³-fold range of strengths, yielding ∼10⁷ combinations. This pool can simultaneously optimize up to six genes in a system. This requires building only a single system-specific construct by placing a target sequence upstream of each gene and transforming it with the pre-built sRNA pool. The resulting library is screened and the top clone is sequenced to determine the promoter controlling each sRNA, from which the fold-repression of the genes can be inferred. The system is then rebuilt by rationally selecting parts that implement the optimal expression of each gene. We demonstrate the versatility of this approach by using the same pool to optimize a metabolic pathway (β-carotene) and genetic circuit (XNOR logic gate).

Total enzyme activity constraint and homeostatic constraint impact on the optimization potential of a kinetic model

The application of biologically and biochemically relevant constraints during the optimization of kinetic models reduces the impact of suggested changes in processes not included in the scope of the model. This increases the probability that the design suggested by model optimization can be carried out by an organism after implementation of design in vivo. A case study was carried out to determine the impact of total enzyme activity and homeostatic constraints on the objective function values and the following ranking of adjustable parameter combinations. The application of constraints on the model of sugar cane metabolism revealed that a homeostatic constraint caused heavier limitations of the objective function than a total enzyme activity constraint. Both constraints changed the ranking of adjustable parameter combinations: no "universal" constraint-independent top-ranked combinations were found. Therefore, when searching for the best subset of adjustable parameters, a full scan of their combinations is suggested for a small number of adjustable parameters, and evolutionary search strategies are suggested for a large number. Simultaneous application of both constraints is suggested.

Formulation, construction and analysis of kinetic models of metabolism: A review of modelling frameworks

Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction and analysis of kinetic models. Finally, we discuss opportunities and limitations hindering the development of larger kinetic reconstructions.

Genome-scale modeling of yeast: chronology, applications and critical perspectives

Over the last 15 years, several genome-scale metabolic models (GSMMs) were developed for different yeast species, aiding both the elucidation of new biological processes and the shift toward a bio-based economy, through the design of in silico inspired cell factories. Here, an historical perspective of the GSMMs built over time for several yeast species is presented and the main inheritance patterns among the metabolic reconstructions are highlighted. We additionally provide a critical perspective on the overall genome-scale modeling procedure, underlining incomplete model validation and evaluation approaches and the quest for the integration of regulatory and kinetic information into yeast GSMMs. A summary of experimentally validated model-based metabolic engineering applications of yeast species is further emphasized, while the main challenges and future perspectives for the field are finally addressed.

Kinetics of Bioethanol Production from Waste Sorghum Leaves Using Saccharomyces cerevisiae BY4743

Kinetic models for bioethanol production from waste sorghum leaves by Saccharomyces cerevisiae BY4743 are presented. Fermentation processes were carried out at varied initial glucose concentrations (12.5–30.0 g/L). Experimental data on cell growth and substrate utilisation fit the Monod kinetic model with a coefficient of determination (R2) of 0.95. A maximum specific growth rate (μmax) and Monod constant (KS) of 0.176 h−1 and 10.11 g/L, respectively, were obtained. The bioethanol production data fit the modified Gompertz model with an R2 value of 0.98. A maximum bioethanol production rate (rp,m) of 0.52 g/L/h, maximum potential bioethanol concentration (Pm) of 17.15 g/L, and a bioethanol production lag time (tL) of 6.31 h were observed. The obtained Monod and modified Gompertz coefficients indicated that waste sorghum leaves can serve as an efficient substrate for bioethanol production. These models with high accuracy are suitable for the scale-up development of bioethanol production from lignocellulosic feedstocks such as sorghum leaves.

Parameter identifiability analysis and visualization in large-scale kinetic models of biosystems

Background

Kinetic models of biochemical systems usually consist of ordinary differential equations that have many unknown parameters. Some of these parameters are often practically unidentifiable, that is, their values cannot be uniquely determined from the available data. Possible causes are lack of influence on the measured outputs, interdependence among parameters, and poor data quality. Uncorrelated parameters can be seen as the key tuning knobs of a predictive model. Therefore, before attempting to perform parameter estimation (model calibration) it is important to characterize the subset(s) of identifiable parameters and their interplay. Once this is achieved, it is still necessary to perform parameter estimation, which poses additional challenges.

Methods

We present a methodology that (i) detects high-order relationships among parameters, and (ii) visualizes the results to facilitate further analysis. We use a collinearity index to quantify the correlation between parameters in a group in a computationally efficient way. Then we apply integer optimization to find the largest groups of uncorrelated parameters. We also use the collinearity index to identify small groups of highly correlated parameters. The results files can be visualized using Cytoscape, showing the identifiable and non-identifiable groups of parameters together with the model structure in the same graph.

Results

Our contributions alleviate the difficulties that appear at different stages of the identifiability analysis and parameter estimation process. We show how to combine global optimization and regularization techniques for calibrating medium and large scale biological models with moderate computation times. Then we evaluate the practical identifiability of the estimated parameters using the proposed methodology. The identifiability analysis techniques are implemented as a MATLAB toolbox called VisId, which is freely available as open source from GitHub (https://github.com/gabora/visid).

Conclusions

Our approach is geared towards scalability. It enables the practical identifiability analysis of dynamic models of large size, and accelerates their calibration. The visualization tool allows modellers to detect parts that are problematic and need refinement or reformulation, and provides experimentalists with information that can be helpful in the design of new experiments.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0428-y) contains supplementary material, which is available to authorized users.

Engineering central metabolism - a grand challenge for plant biologists

The goal of increasing crop productivity and nutrient-use efficiency is being addressed by a number of ambitious research projects seeking to re-engineer photosynthetic biochemistry. Many of these projects will require the engineering of substantial changes in fluxes of central metabolism. However, as has been amply demonstrated in simpler systems such as microbes, central metabolism is extremely difficult to rationally engineer. This is because of multiple layers of regulation that operate to maintain metabolic steady state and because of the highly connected nature of central metabolism. In this review we discuss new approaches for metabolic engineering that have the potential to address these problems and dramatically improve the success with which we can rationally engineer central metabolism in plants. In particular, we advocate the adoption of an iterative 'design-build-test-learn' cycle using fast-to-transform model plants as test beds. This approach can be realised by coupling new molecular tools to incorporate multiple transgenes in nuclear and plastid genomes with computational modelling to design the engineering strategy and to understand the metabolic phenotype of the engineered organism. We also envisage that mutagenesis could be used to fine-tune the balance between the endogenous metabolic network and the introduced enzymes. Finally, we emphasise the importance of considering the plant as a whole system and not isolated organs: the greatest increase in crop productivity will be achieved if both source and sink metabolism are engineered.

Effects of glycerol supply and specific growth rate on methanol-free production of CALB by P. pastoris: functional characterisation of a novel promoter

As Pichia pastoris (syn. Komagataella sp.) yeast can secrete pure recombinant proteins at high rates, it is a desirable production system. The function of a novel synthetic variant of the AOX1 promoter was characterised comprehensively using a strain secreting Candida antarctica lipase B (CALB) as a model. A new time-saving approach was introduced to determine, in only one experiment, the hitherto unknown relationship between specific product formation rate (q_p) and specific growth rate (μ). Tight control of recombinant protein formation was possible in the absence of methanol, while using glycerol as a sole carbon/energy source. CALB was not synthesised during batch cultivation in excess glycerol (>10 g l⁻¹) and at a growth rate close to μ_max (0.15 h⁻¹). Between 0.017 and 0.115 h⁻¹ in glycerol-limited fedbatch cultures, basal levels of q_p > 0.4 mg g⁻¹ h⁻¹ CALB were reached, independent of the μ at which the culture grew. At μ > 0.04 h⁻¹, an elevated q_p occurred temporarily during the first 20 h after changing to fedbatch mode and decreased thereafter to basal. In order to accelerate the determination of the q_p(μ) relationship (kinetics of product formation), the entire μ range was covered in a single fedbatch experiment. By linearly increasing and decreasing glycerol addition rates, μ values were repeatedly shifted from 0.004 to 0.074 h⁻¹ and vice versa. Changes in q_p were related to changes in μ. A rough estimation of μ range suitable for production was possible in a single fedbatch, thus significantly reducing the experimental input over previous approaches comprising several experiments.

Parameter estimation in large-scale systems biology models: a parallel and self-adaptive cooperative strategy

Background

The development of large-scale kinetic models is one of the current key issues in computational systems biology and bioinformatics. Here we consider the problem of parameter estimation in nonlinear dynamic models. Global optimization methods can be used to solve this type of problems but the associated computational cost is very large. Moreover, many of these methods need the tuning of a number of adjustable search parameters, requiring a number of initial exploratory runs and therefore further increasing the computation times.

Here we present a novel parallel method, self-adaptive cooperative enhanced scatter search (saCeSS), to accelerate the solution of this class of problems. The method is based on the scatter search optimization metaheuristic and incorporates several key new mechanisms: (i) asynchronous cooperation between parallel processes, (ii) coarse and fine-grained parallelism, and (iii) self-tuning strategies.

Results

The performance and robustness of saCeSS is illustrated by solving a set of challenging parameter estimation problems, including medium and large-scale kinetic models of the bacterium E. coli, bakerés yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network.

The results consistently show that saCeSS is a robust and efficient method, allowing very significant reduction of computation times with respect to several previous state of the art methods (from days to minutes, in several cases) even when only a small number of processors is used.

Conclusions

The new parallel cooperative method presented here allows the solution of medium and large scale parameter estimation problems in reasonable computation times and with small hardware requirements. Further, the method includes self-tuning mechanisms which facilitate its use by non-experts. We believe that this new method can play a key role in the development of large-scale and even whole-cell dynamic models.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1452-4) contains supplementary material, which is available to authorized users.

Respectful Modeling: Addressing Uncertainty in Dynamic System Models for Molecular Biology

Although there is still some skepticism in the biological community regarding the value and significance of quantitative computational modeling, important steps are continually being taken to enhance its accessibility and predictive power. We view these developments as essential components of an emerging 'respectful modeling' framework which has two key aims: (i) respecting the models themselves and facilitating the reproduction and update of modeling results by other scientists, and (ii) respecting the predictions of the models and rigorously quantifying the confidence associated with the modeling results. This respectful attitude will guide the design of higher-quality models and facilitate the use of models in modern applications such as engineering and manipulating microbial metabolism by synthetic biology.

Structured model and parameter estimation in plant cell cultures of Thevetia peruviana

In this work, a mechanistic model for predicting the dynamic behavior of extracellular and intracellular nutrients, biomass production, and the main metabolites involved in the central carbon metabolism in plant cell cultures of Thevetia peruviana is presented. The proposed model is the first mechanistic model implemented for plant cell cultures of this species, and includes 28 metabolites, 33 metabolic reactions, and 61 parameters. Given the over-parametrization of the model, its nonlinear nature and the strong correlation among the effects of the parameters, a parameter estimation routine based on identifiability analysis was implemented. This routine reduces the parameter's search space by selecting the most sensitive and linearly independent parameters. Results have shown that only 19 parameters are identifiable. Finally, the model was used for analyzing the fluxes distribution in plant cell cultures of T. peruviana. This analysis shows high uptake of phosphates and parallel uptake of glucose and fructose. Furthermore, it has pointed out the main central carbon metabolism routes for promoting biomass production in this cell culture.

Comparison Tools for Parametric Identification of Kinetic Model for Ethanol Production using Evolutionary Optimization Approach

Living cells, type of substrate, enzymatic hydrolysis play an important role in the efficiency of ethanol production; however, the kinetic parameters of biochemical reactions necessary for modelling these processes are often not accessible directly through experiments. In this context, for the implementation of suitable operational strategies, it is necessary to have kinetic models able to describe the process as realistically as possible. This paper proposes a comparative study of two nonlinear techniques for parametric identification of a kinetic model for ethanol production from recycled paper sludge in order to improve process performance. The parameters of the model are optimized by two methods: using the Levenberg–Marquardt optimization approach and Genetic Algorithms. The performances of both techniques are evaluated using a numerical simulation. The optimal value of these parameters have been obtained based on Genetic Algorithm. Finally, the effect of parametric adjustment and dilution rate on productivity was demonstrated by changing the batch operation to the continuous operating model. The maximum ethanol concentration was about 13.25 g/l in batch process and about 13.9 g/l at Dilution rate: 0.005 1/h corresponding to a productivity of 0.327 in continuous process.

Biosynthesis of therapeutic natural products using synthetic biology

Natural products are a group of bioactive structurally diverse chemicals produced by microorganisms and plants. These molecules and their derivatives have contributed to over a third of the therapeutic drugs produced in the last century. However, over the last few decades traditional drug discovery pipelines from natural products have become far less productive and far more expensive. One recent development with promise to combat this trend is the application of synthetic biology to therapeutic natural product biosynthesis. Synthetic biology is a young discipline with roots in systems biology, genetic engineering, and metabolic engineering. In this review, we discuss the use of synthetic biology to engineer improved yields of existing therapeutic natural products. We further describe the use of synthetic biology to combine and express natural product biosynthetic genes in unprecedented ways, and how this holds promise for opening up completely new avenues for drug discovery and production.

Digitalization of a non-irradiated acute myeloid leukemia model

Background

Computer-aided, interdisciplinary researches for biomedicine have valuable prospects, as digitalization of experimental subjects provide opportunities for saving the economic costs of researches, as well as promoting the acquisition of knowledge. Acute myeloid leukemia (AML) is intensively studied over long periods of time. Till nowaday, most of the studies primarily focus on the leukemic cells rather than how normal hematopoietic cells are affected by the leukemic environment. Accordingly, the conventional animal models for AML are mostly myeloablated as leukemia can be induced with short latency and complete penetrance. Meanwhile, most previous computational models focus on modeling the leukemic cells but not the multi-tissue leukemic body resided by both leukemic and normal blood cells. Recently, a non-irradiated AML mouse model has been established; therefore, normal hematopoietic cells can be investigated during leukemia development. Experiments based on the non-irradiated animal model have monitored the kinetics of leukemic and (intact) hematopoietic cells in multiple tissues simultaneously; and thus a systematic computational model for the multi-tissue hematopoiesis under leukemia has become possible.

Results

In the present work, we adopted the modeling methods in previous works, but aimed to model the tri-tissue (peripheral blood, spleen and bone marrow) dynamics of hematopoiesis under leukemia. The cell kinetics generated from the non-irradiated experimental model were used as the reference data for modeling. All mathematical formulas were systematically enumerated, and model parameters were estimated via numerical optimization. Multiple validations by additional experimental data were then conducted for the established computational model. In the results, we illustrated that the important fact of functional depression of hematopoietic stem/progenitor cells (HSC/HPC) in leukemic bone marrow (BM), which must require additional experiments to be established, could also be inferred from our computation model that utilized only the cell kinetics data as the input.

Conclusion

The digitalized AML model established in the present work is effective for reconstructing the hematopoiesis under leukemia as well as simulating the hematopoietic response to leukemic cell expansion. Given the validity and efficiency, the model can be of potential utilities in future biomedical studies; additionally, the modeling method itself can be also applied elsewhere.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0308-x) contains supplementary material, which is available to authorized users.

Using simple models to describe the kinetics of growth, glucose consumption, and monoclonal antibody formation in naive and infliximab producer CHO cells

Despite their practical and commercial relevance, there are few reports on the kinetics of growth and production of Chinese hamster ovary (CHO) cells-the most frequently used host for the industrial production of therapeutic proteins. We characterize the kinetics of cell growth, substrate consumption, and product formation in naive and monoclonal antibody (mAb) producing recombinant CHO cells. Culture experiments were performed in 125 mL shake flasks on commercial culture medium (CD Opti CHO™ Invitrogen, Carlsbad, CA, USA) diluted to different glucose concentrations (1.2-4.8 g/L). The time evolution of cell, glucose, lactic acid concentration and monoclonal antibody concentrations was monitored on a daily basis for mAb-producing cultures and their naive counterparts. The time series were differentiated to calculate the corresponding kinetic rates (rx = d[X]/dt; rs = d[S]/dt; rp = d[mAb]/dt). Results showed that these cell lines could be modeled by Monod-like kinetics if a threshold substrate concentration value of [S]t = 0.58 g/L (for recombinant cells) and [S]t = 0.96 g/L (for naïve cells), below which growth is not observed, was considered. A set of values for μmax, and Ks was determined for naive and recombinant cell cultures cultured at 33 and 37 °C. The yield coefficient (Yx/s) was observed to be a function of substrate concentration, with values in the range of 0.27-1.08 × 10(7) cell/mL and 0.72-2.79 × 10(6) cells/mL for naive and recombinant cultures, respectively. The kinetics of mAb production can be described by a Luedeking-Piret model (d[mAb]/dt = αd[X]/dt + β[X]) with values of α = 7.65 × 10(-7) µg/cell and β = 7.68 × 10(-8) µg/cell/h for cultures conducted in batch-agitated flasks and batch and instrumented bioreactors operated in batch and fed-batch mode.

The steady-state assumption in oscillating and growing systems

The steady-state assumption, which states that the production and consumption of metabolites inside the cell are balanced, is one of the key aspects that makes an efficient analysis of genome-scale metabolic networks possible. It can be motivated from two different perspectives. In the time-scales perspective, we use the fact that metabolism is much faster than other cellular processes such as gene expression. Hence, the steady-state assumption is derived as a quasi-steady-state approximation of the metabolism that adapts to the changing cellular conditions. In this article we focus on the second perspective, stating that on the long run no metabolite can accumulate or deplete. In contrast to the first perspective it is not immediately clear how this perspective can be captured mathematically and what assumptions are required to obtain the steady-state condition. By presenting a mathematical framework based on the second perspective we demonstrate that the assumption of steady-state also applies to oscillating and growing systems without requiring quasi-steady-state at any time point. However, we also show that the average concentrations may not be compatible with the average fluxes. In summary, we establish a mathematical foundation for the steady-state assumption for long time periods that justifies its successful use in many applications. Furthermore, this mathematical foundation also pinpoints unintuitive effects in the integration of metabolite concentrations using nonlinear constraints into steady-state models for long time periods.

Unraveling the pharmacokinetic interaction of ticagrelor and MEDI2452 (Ticagrelor antidote) by mathematical modeling

The investigational ticagrelor‐neutralizing antibody fragment, MEDI2452, is developed to rapidly and specifically reverse the antiplatelet effects of ticagrelor. However, the dynamic interaction of ticagrelor, the ticagrelor active metabolite (TAM), and MEDI2452, makes pharmacokinetic (PK) analysis nontrivial and mathematical modeling becomes essential to unravel the complex behavior of this system. We propose a mechanistic PK model, including a special observation model for post‐sampling equilibration, which is validated and refined using mouse in vivo data from four studies of combined ticagrelor‐MEDI2452 treatment. Model predictions of free ticagrelor and TAM plasma concentrations are subsequently used to drive a pharmacodynamic (PD) model that successfully describes platelet aggregation data. Furthermore, the model indicates that MEDI2452‐bound ticagrelor is primarily eliminated together with MEDI2452 in the kidneys, and not recycled to the plasma, thereby providing a possible scenario for the extrapolation to humans. We anticipate the modeling work to improve PK and PD understanding, experimental design, and translational confidence.

Evaluation of rate law approximations in bottom-up kinetic models of metabolism

BACKGROUND

The mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.

RESULTS

In this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.

CONCLUSIONS

Overall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches.

Constructing kinetic models of metabolism at genome-scales: A review

Constraint-based modeling of biological networks (metabolism, transcription and signal transduction), although used successfully in many applications, suffer from specific limitations such as the lack of representation of metabolite concentrations and enzymatic regulation, which are necessary for a complete physiologically relevant model. Kinetic models conversely overcome these shortcomings and enable dynamic analysis of biological systems for enhanced in silico hypothesis generation. Nonetheless, kinetic models also have limitations for modeling at genome-scales chiefly due to: (i) model non-linearity; (ii) computational tractability; (iii) parameter identifiability; (iv) estimability; and (v) uncertainty. In order to support further development of kinetic models as viable alternatives to constraint-based models, this review presents a brief description of the existing obstacles towards building genome-scale kinetic models. Specific kinetic modeling frameworks capable of overcoming these obstacles are covered in this review. The tractability and physiological feasibility of these models are discussed with the objective of using available in vivo experimental observations to define the model parameter space. Among the different methods discussed, Monte Carlo kinetic models of metabolism stand out as potentially tractable methods to model genome scale networks while also addressing in vivo parameter uncertainty.

A method for analysis and design of metabolism using metabolomics data and kinetic models: Application on lipidomics using a novel kinetic model of sphingolipid metabolism

We present a model-based method, designated Inverse Metabolic Control Analysis (IMCA), which can be used in conjunction with classical Metabolic Control Analysis for the analysis and design of cellular metabolism. We demonstrate the capabilities of the method by first developing a comprehensively curated kinetic model of sphingolipid biosynthesis in the yeast Saccharomyces cerevisiae. Next we apply IMCA using the model and integrating lipidomics data. The combinatorial complexity of the synthesis of sphingolipid molecules, along with the operational complexity of the participating enzymes of the pathway, presents an excellent case study for testing the capabilities of the IMCA. The exceptional agreement of the predictions of the method with genome-wide data highlights the importance and value of a comprehensive and consistent engineering approach for the development of such methods and models. Based on the analysis, we identified the class of enzymes regulating the distribution of sphingolipids among species and hydroxylation states, with the D-phospholipase SPO14 being one of the most prominent. The method and the applications presented here can be used for a broader, model-based inverse metabolic engineering approach.

System-level modeling of acetone-butanol-ethanol fermentation

Acetone-butanol-ethanol (ABE) fermentation is a metabolic process of clostridia that produces bio-based solvents including butanol. It is enabled by an underlying metabolic reaction network and modulated by cellular gene regulation and environmental cues. Mathematical modeling has served as a valuable strategy to facilitate the understanding, characterization and optimization of this process. In this review, we highlight recent advances in system-level, quantitative modeling of ABE fermentation. We begin with an overview of integrative processes underlying the fermentation. Next we survey modeling efforts including early simple models, models with a systematic metabolic description, and those incorporating metabolism through simple gene regulation. Particular focus is given to a recent system-level model that integrates the metabolic reactions, gene regulation and environmental cues. We conclude by discussing the remaining challenges and future directions towards predictive understanding of ABE fermentation.

Metabolic engineering with multi-objective optimization of kinetic models

Kinetic models have a great potential for metabolic engineering applications. They can be used for testing which genetic and regulatory modifications can increase the production of metabolites of interest, while simultaneously monitoring other key functions of the host organism. This work presents a methodology for increasing productivity in biotechnological processes exploiting dynamic models. It uses multi-objective dynamic optimization to identify the combination of targets (enzymatic modifications) and the degree of up- or down-regulation that must be performed in order to optimize a set of pre-defined performance metrics subject to process constraints. The capabilities of the approach are demonstrated on a realistic and computationally challenging application: a large-scale metabolic model of Chinese Hamster Ovary cells (CHO), which are used for antibody production in a fed-batch process. The proposed methodology manages to provide a sustained and robust growth in CHO cells, increasing productivity while simultaneously increasing biomass production, product titer, and keeping the concentrations of lactate and ammonia at low values. The approach presented here can be used for optimizing metabolic models by finding the best combination of targets and their optimal level of up/down-regulation. Furthermore, it can accommodate additional trade-offs and constraints with great flexibility.

Toward Sustainable Amino Acid Production

Because the global amino acid production industry has been growing steadily and is expected to grow even more in the future, efficient production by fermentation is of great importance from economic and sustainability viewpoints. Many systems biology technologies, such as genome breeding, omics analysis, metabolic flux analysis, and metabolic simulation, have been employed for the improvement of amino acid-producing strains of bacteria. Synthetic biological approaches have recently been applied to strain development. It is also important to use sustainable carbon sources, such as glycerol or pyrolytic sugars from cellulosic biomass, instead of conventional carbon sources, such as glucose or sucrose, which can be used as food. Furthermore, reduction of sub-raw substrates has been shown to lead to reduction of environmental burdens and cost. Recently, a new fermentation system for glutamate production under acidic pH was developed to decrease the amount of one sub-raw material, ammonium, for maintenance of culture pH. At the same time, the utilization of fermentation coproducts, such as cells, ammonium sulfate, and fermentation broth, is a useful approach to decrease waste. In this chapter, further perspectives for future amino acid fermentation from one-carbon compounds are described.

Robust and efficient parameter estimation in dynamic models of biological systems

Background

Dynamic modelling provides a systematic framework to understand function in biological systems. Parameter estimation in nonlinear dynamic models remains a very challenging inverse problem due to its nonconvexity and ill-conditioning. Associated issues like overfitting and local solutions are usually not properly addressed in the systems biology literature despite their importance.

Here we present a method for robust and efficient parameter estimation which uses two main strategies to surmount the aforementioned difficulties: (i) efficient global optimization to deal with nonconvexity, and (ii) proper regularization methods to handle ill-conditioning. In the case of regularization, we present a detailed critical comparison of methods and guidelines for properly tuning them. Further, we show how regularized estimations ensure the best trade-offs between bias and variance, reducing overfitting, and allowing the incorporation of prior knowledge in a systematic way.

Results

We illustrate the performance of the presented method with seven case studies of different nature and increasing complexity, considering several scenarios of data availability, measurement noise and prior knowledge. We show how our method ensures improved estimations with faster and more stable convergence. We also show how the calibrated models are more generalizable. Finally, we give a set of simple guidelines to apply this strategy to a wide variety of calibration problems.

Conclusions

Here we provide a parameter estimation strategy which combines efficient global optimization with a regularization scheme. This method is able to calibrate dynamic models in an efficient and robust way, effectively fighting overfitting and allowing the incorporation of prior information.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0219-2) contains supplementary material, which is available to authorized users.

Combining modelling and experimental approaches to explain how calcium signatures are decoded by calmodulin-binding transcription activators (CAMTAs) to produce specific gene expression responses

Experimental data show that Arabidopsis thaliana is able to decode different calcium signatures to produce specific gene expression responses. It is also known that calmodulin-binding transcription activators (CAMTAs) have calmodulin (CaM)-binding domains. Therefore, the gene expression responses regulated by CAMTAs respond to calcium signals. However, little is known about how different calcium signatures are decoded by CAMTAs to produce specific gene expression responses. A dynamic model of Ca(2+) -CaM-CAMTA binding and gene expression responses is developed following thermodynamic and kinetic principles. The model is parameterized using experimental data. Then it is used to analyse how different calcium signatures are decoded by CAMTAs to produce specific gene expression responses. Modelling analysis reveals that: calcium signals in the form of cytosolic calcium concentration elevations are nonlinearly amplified by binding of Ca(2+) , CaM and CAMTAs; amplification of Ca(2+) signals enables calcium signatures to be decoded to give specific CAMTA-regulated gene expression responses; gene expression responses to a calcium signature depend upon its history and accumulate all the information during the lifetime of the calcium signature. Information flow from calcium signatures to CAMTA-regulated gene expression responses has been established by combining experimental data with mathematical modelling.

Impact of kinetic isotope effects in isotopic studies of metabolic systems

Background

Isotope labeling experiments (ILEs) are increasingly used to investigate the functioning of metabolic systems. Some enzymes are subject to kinetic isotope effects (KIEs) which modulate reaction rates depending on the isotopic composition of their substrate(s). KIEs may therefore affect both the propagation of isotopes through metabolic networks and their operation, and ultimately jeopardize the biological value of ILEs. However, the actual impact of KIEs on metabolism has never been investigated at the system level.

Results

First, we developed a framework which integrates KIEs into kinetic and isotopic models of metabolism, thereby accounting for their system-wide effects on metabolite concentrations, metabolic fluxes, and isotopic patterns. Then, we applied this framework to assess the impact of KIEs on the central carbon metabolism of Escherichia coli in the context of ¹³C-ILEs, under different situations commonly encountered in laboratories. Results showed that the impact of KIEs strongly depends on the label input and on the variable considered but is significantly lower than expected intuitively from measurements on isolated enzymes. The global robustness of both the metabolic operation and isotopic patterns largely emerge from intrinsic properties of metabolic networks, such as the distribution of control across the network and bidirectional isotope exchange.

Conclusions

These results demonstrate the necessity of investigating the impact of KIEs at the level of the entire system, contradict previous hypotheses that KIEs would have a strong effect on isotopic distributions and on flux determination, and strengthen the biological value of ¹³C-ILEs. The proposed modeling framework is generic and can be used to investigate the impact of all the isotopic tracers (²H, ¹³C, ¹⁵N, ¹⁸O, etc.) on different isotopic datasets and metabolic systems. By allowing the integration of isotopic and metabolomics data collected under stationary and/or non-stationary conditions, it may also assist interpretations of ILEs and facilitate the development of more accurate kinetic models with improved explicative and predictive capabilities.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0213-8) contains supplementary material, which is available to authorized users.

Rites of passage: requirements and standards for building kinetic models of metabolic phenotypes

The overarching ambition of kinetic metabolic modeling is to capture the dynamic behavior of metabolism to such an extent that systems and synthetic biology strategies can reliably be tested in silico. The lack of kinetic data hampers the development of kinetic models, and most of the current models use ad hoc reduced stoichiometry or oversimplified kinetic rate expressions, which may limit their predictive strength. There is a need to introduce the community-level standards that will organize and accelerate the future developments in this area. We introduce here a set of requirements that will ensure the model quality, we examine the current kinetic models with respect to these requirements, and we propose a general workflow for constructing models that satisfy these requirements.

Improving prediction fidelity of cellular metabolism with kinetic descriptions

Several modeling frameworks for describing and redirecting cellular metabolism have been developed keeping pace with the rapid development in high-throughput data generation and advances in metabolic engineering techniques. The incorporation of kinetic information within stoichiometry-only modeling techniques offers potential advantages for improved phenotype prediction and consequently more precise computational strain design. In addition to substrate-level kinetic regulatory information, the integration of a number of additional layers of regulation at the transcription, translation, and post-translation levels is sought after by many research groups. However, the practical integration of these complex biological processes into a unified framework amenable to design remains an ongoing challenge.

Some fundamental aspects of modeling auxin patterning in the context of auxin-ethylene-cytokinin crosstalk

The activities of hormones in the Arabidopsis root depend on cellular context and exhibit either synergistic or antagonistic interactions. Patterning in Arabidopsis root development is coordinated via a localized auxin concentration maximum in the root tip, mediating transcription of key regulatory genes. Auxin concentration and response are each regulated by diverse interacting hormones and gene expression and therefore cannot change independently of those hormones and genes. For example, experimental data accumulated over many years have shown that both ethylene and cytokinin regulate auxin concentration and response. Using the crosstalk of auxin-ethylene-cytokinin as a paradigm, we discuss the links between experimental data, reaction kinetics and spatiotemporal modeling to dissect hormonal crosstalk. In particular, we discuss how kinetic equations for modeling auxin concentration are formulated based on experimental data and also the underlying assumptions for deriving those kinetic equations. Furthermore, we show that, by integrating kinetic equations with spatial root structure, modeling of spatiotemporal hormonal crosstalk is a powerful tool for analyzing and predicting the roles of multiple hormone interactions in auxin patterning. Finally, we summarize important considerations in developing a spatiotemporal hormonal crosstalk model for plant root development.

Microbial bioinformatics for food safety and production

In the production of fermented foods, microbes play an important role. Optimization of fermentation processes or starter culture production traditionally was a trial-and-error approach inspired by expert knowledge of the fermentation process. Current developments in high-throughput 'omics' technologies allow developing more rational approaches to improve fermentation processes both from the food functionality as well as from the food safety perspective. Here, the authors thematically review typical bioinformatics techniques and approaches to improve various aspects of the microbial production of fermented food products and food safety.

A Nonlinear Mixed Effects Approach for Modeling the Cell-To-Cell Variability of Mig1 Dynamics in Yeast

The last decade has seen a rapid development of experimental techniques that allow data collection from individual cells. These techniques have enabled the discovery and characterization of variability within a population of genetically identical cells. Nonlinear mixed effects (NLME) modeling is an established framework for studying variability between individuals in a population, frequently used in pharmacokinetics and pharmacodynamics, but its potential for studies of cell-to-cell variability in molecular cell biology is yet to be exploited. Here we take advantage of this novel application of NLME modeling to study cell-to-cell variability in the dynamic behavior of the yeast transcription repressor Mig1. In particular, we investigate a recently discovered phenomenon where Mig1 during a short and transient period exits the nucleus when cells experience a shift from high to intermediate levels of extracellular glucose. A phenomenological model based on ordinary differential equations describing the transient dynamics of nuclear Mig1 is introduced, and according to the NLME methodology the parameters of this model are in turn modeled by a multivariate probability distribution. Using time-lapse microscopy data from nearly 200 cells, we estimate this parameter distribution according to the approach of maximizing the population likelihood. Based on the estimated distribution, parameter values for individual cells are furthermore characterized and the resulting Mig1 dynamics are compared to the single cell times-series data. The proposed NLME framework is also compared to the intuitive but limited standard two-stage (STS) approach. We demonstrate that the latter may overestimate variabilities by up to almost five fold. Finally, Monte Carlo simulations of the inferred population model are used to predict the distribution of key characteristics of the Mig1 transient response. We find that with decreasing levels of post-shift glucose, the transient response of Mig1 tend to be faster, more extended, and displays an increased cell-to-cell variability.