Toward community standards and software for whole-cell modeling

Whole-cell (WC) modeling is a promising tool for biological research, bioengineering, and medicine. However, substantial work remains to create accurate, comprehensive models of complex cells. Methods: We organized the 2015 Whole-Cell Modeling Summer School to teach WC modeling and evaluate the need for new WC modeling standards and software by recoding a recently published WC model in SBML. Results: Our analysis revealed several challenges to representing WC models using the current standards. Conclusion: We, therefore, propose several new WC modeling standards, software, and databases. Significance:We anticipate that these new standards and software will enable more comprehensive models

The effects of model complexity and size on metabolic flux distribution and control: case study in Escherichia coli

Background Significant efforts have been made in building large-scale kinetic models of cellular metabolism in the past two decades. However, most kinetic models published to date, remain focused around central carbon pathways or are built around ad hoc reduced models without clear justification on their derivation and usage. Systematic algorithms exist for reducing genome-scale metabolic reconstructions to build thermodynamically feasible and consistently reduced stoichiometric models. However, it is important to study how network complexity affects conclusions derived from large-scale kinetic models built around consistently reduced models before we can apply them to study biological systems. Results We reduced the iJO1366 Escherichia Coli genome-scale metabolic reconstruction systematically to build three stoichiometric models of different size. Since the reduced models are expansions around the core subsystems for which the reduction was performed, the models are nested. We present a method for scaling up the flux profile and the concentration vector reference steady-states from the smallest model to the larger ones, whilst preserving maximum equivalency. Populations of kinetic models, preserving similarity in kinetic parameters, were built around the reference steady-states and their metabolic sensitivity coefficients (MSCs) were computed. The MSCs were sensitive to the model complexity. We proposed a metric for measuring the sensitivity of MSCs to these structural changes. Conclusions We proposed for the first time a workflow for scaling up the size of kinetic models while preserving equivalency between the kinetic models. Using this workflow, we demonstrate that model complexity in terms of networks size has significant impact on sensitivity characteristics of kinetic models. Therefore, it is essential to account for the effects of network complexity when constructing kinetic models. The presented metric for measuring MSC sensitivity to structural changes can guide modelers and experimentalists in improving model quality and guide synthetic biology and metabolic engineering. Our proposed workflow enables the testing of the suitability of a kinetic model for answering certain study-specific questions. We argue that the model-based metabolic design targets that are common across models of different size are of higher confidence, while those that are different could be the objective of investigations for model improvement

Statistical inference in ensemble modeling of cellular metabolism

Kinetic models of metabolism can be constructed to predict cellular regulation and devise metabolic engineering strategies, and various promising computational workflows have been developed in recent years for this. Due to the uncertainty in the kinetic parameter values required to build kinetic models, these workflows rely on ensemble modeling (EM) principles for sampling and building populations of models describing observed physiologies. Sensitivity coefficients from metabolic control analysis (MCA) of kinetic models can provide important insight about cellular control around a given physiological steady state. However, despite considering populations of kinetic models and their model outputs, current approaches do not provide adequate tools for statistical inference. To derive conclusions from model outputs, such as MCA sensitivity coefficients, it is necessary to rank/compare populations of variables with each other. Currently existing workflows consider confidence intervals (CIs) that are derived independently for each comparable variable. Hence, it is important to derive simultaneous CIs for the variables that we wish to rank/compare. Herein, we used an existing large-scale kinetic model of Escherichia Coli metabolism to present how univariate CIs can lead to incorrect conclusions, and we present a new workflow that applies three different multivariate statistical approaches. We use the Bonferroni and the exact normal methods to build symmetric CIs using the normality assumptions. We then suggest how bootstrapping can compute asymmetric CIs whilst relaxing this normality assumption. We conclude that the Bonferroni and the exact normal methods can provide simple and efficient ways for constructing reliable CIs, with the exact normal method favored over the Bonferroni when the compared variables present dependencies. Bootstrapping, despite its significantly higher computational cost, is recommended when comparing non-normal distributions of variables. Additionally, we show how the Bonferroni method can readily be used to estimate required sample numbers to attain a certain CI size

Study on how underlying uncertainty in the flux values affects metabolic control analysis of optimally grown E. coli

Large-scale kinetic models of metabolism are essential for understanding and predicting the behavior of cellular systems when subject to perturbations. Despite the advances in experimental measurement technologies, the numerous parameters that are required to build kinetic models remain scarce and involve uncertainty. Even after incorporating the partially available experimental data, models still have many degrees of freedom. Due to this parametric uncertainty, some reactions are able to operate in forward and reverse directions. An operational configuration consists of reactions that operate in a unique direction. This flexibility results in the existence of alternative operational configurations representing the same physiology, with very distinct regulatory properties. In this study, we focus on one operational configuration and we investigate how the underlying uncertainty in the flux values affects the robustness of the model predictions and regulatory capabilities. To study this question, we used a large-scale kinetic model and integrated fluxomics and metabolomics data describing the physiology for aerobically grown E. coli. Because of the under-determined nature of the system, there are infinite existing flux solutions within the selected operational configuration. To account for the flux variability within the designated operational configuration, we selected a reference vector of concentrations close to their nominal value. We used the ORACLE (optimization and risk analysis of complex living entities) framework to build populations of kinetic models that are consistent with the given physiology, while satisfying the stoichiometric and thermodynamic constraints. We next performed a systematic analysis of the effect that the flux profiles have on the robustness of the regulatory properties of the system. We used the mean PCA (principle component analysis) value of the flux samples as reference when selecting flux profiles. Flux profiles across the main components of the PCA were studied. We used ORACLE to generate populations of kinetic models for these flux profiles. Then, we computed the distributions of their flux control coefficients (FCCs) along the dimensions with the highest variance. Finally, by comparing the changes among the distributions of the FCCs versus those corresponding to the reference flux profile, we were able to quantify the robustness of the regulatory predictions within a specific operational configuration

Kinetic models of metabolism that consider alternative steady-state solutions of intracellular fluxes and concentrations

Large-scale kinetic models are used for designing, predicting, and understanding the metabolic responses of living cells. Kinetic models are particularly attractive for the biosynthesis of target molecules in cells as they are typically better than other types of models at capturing the complex cellular biochemistry. Using simpler stoichiometric models as scaffolds, kinetic models are built around a steady-state flux profile and a metabolite concentration vector that are typically determined via optimization. However, as the underlying optimization problem is underdetermined, even after incorporating available experimental omics data, one cannot uniquely determine the operational configuration in terms of metabolic fluxes and metabolite concentrations. As a result, some reactions can operate in either the forward or reverse direction while still agreeing with the observed physiology. Here, we analyze how the underlying uncertainty in intracellular fluxes and concentrations affects predictions of constructed kinetic models and their design in metabolic engineering and systems biology studies. To this end, we integrated the omics data of optimally grown Escherichia coli into a stoichiometric model and constructed populations of non-linear large-scale kinetic models of alternative steady-state solutions consistent with the physiology of the E. coli aerobic metabolism. We performed metabolic control analysis (MCA) on these models, highlighting that MCA-based metabolic engineering decisions are strongly affected by the selected steady state and appear to be more sensitive to concentration values rather than flux values. To incorporate this into future studies, we propose a workflow for moving towards more reliable and robust predictions that are consistent with all alternative steady-state solutions. This workflow can be applied to all kinetic models to improve the consistency and accuracy of their predictions. Additionally, we show that, irrespective of the alternative steady-state solution, increased activity of phosphofructokinase and decreased ATP maintenance requirements would improve cellular growth of optimally grown E. coli

How uncertainty in kinetic parameters affects metabolic control analysis of optimally grown E.coli

Large-­scale kinetic models of metabolism are essential for understanding and predicting the behavior of cellular systems when subject to perturbations. Despite the advances in experimental measurement technologies, the numerous parameters that are required to build kinetic models remain scarce and involve uncertainty. Even after incorporating the partially available experimental data, models still have many degrees of freedom. Due to this parametric uncertainty, some reactions are able to operate in forward and reverse directions. An operational configuration consists of reactions that operate in a unique direction. This flexibility results in the existence of alternative operational configurations representing the same physiology, with very distinct regulatory properties. In this study, we focus on one operational configuration and we investigate how the underlying uncertainty in the kinetic parameters affects the robustness of the model predictions and regulatory capabilities. To study this question, we used a large-­scale non-­linear kinetic model built using integrated fluxomics and metabolomics data describing the physiology for aerobically grown E. coli. Because of the under-determined nature of the system, there are multiple kinetic parameters that can render the model feasible within the selected operational configuration. To account for the variability of the kinetic parameters within the designated operational configuration, we selected a reference vector of fluxes and concentrations close to their nominal values. Then, we used the ORACLE (optimization and risk analysis of complex living entities) framework to build populations of kinetic models that are consistent with the given physiology, while satisfying the stoichiometric and thermodynamic constraints. From these, we built non-­linear models to test how the system’s response to perturbations changed with respect to the chosen kinetic parameters. This allowed us to quantify the effect of the uncertainty in the kinetic parameters on the robustness of the regulatory properties of the system

Constraint-based metabolic control analysis for rational strain engineering

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