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.

Active and machine learning-based approaches to rapidly enhance microbial chemical production

ABSTRACTIn order to make renewable fuels and chemicals from microbes, new methods are required to engineer microbes more intelligently. Computational approaches, to engineer strains for enhanced chemical production typically rely on detailed mechanistic models (e.g., kinetic/stoichiometric models of metabolism) — requiring many experimental datasets for their parameterization—while experimental methods may require screening large mutant libraries to explore the design space for the few mutants with desired behaviors. To address these limitations, we developed an active and machine learning approach (ActiveOpt) to intelligently guide experiments to arrive at an optimal phenotype with minimal measured datasets. ActiveOpt was applied to two separate case studies to evaluate its potential to increase valine yields and neurosporene productivity in Escherichia coli. In both the cases, ActiveOpt identified the best performing strain in fewer experiments than the case studies used. This work demonstrates that machine and active learning approaches have the potential to greatly facilitate metabolic engineering efforts to rapidly achieve its objectives.

Biomass to Syngas: Modified Non-Stoichiometric Thermodynamic Models for the Downdraft Biomass Gasification

Biomass gasification is the most reliable thermochemical conversion technology for the conversion of biomass into gaseous fuels such as H2, CO, and CH4. The performance of a gasification process can be estimated using thermodynamic equilibrium models. This type of model generally assumes the system reaches equilibrium, while in reality the system may only approach equilibrium leading to some errors between experimental and model results. In this study non-stoichiometric equilibrium models are modified and improved with correction factors inserted into the design equations so that when the Gibbs free energy is minimized model predictions will more closely match experimental values. The equilibrium models are implemented in MatLab and optimized based on experimental values from the literature using the optimization toolbox. The modified non-stoichiometric models are shown to be more accurate than unmodified models based on the calculated root mean square error values. These models can be applied for various types of solid biomass for the production of syngas through biomass gasification processes such as wood, agricultural, and crop residues.

The effects of model complexity and size on metabolic flux distribution and control. Case study inE. coli

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 aroundad hocreduced 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. It has not been studied previously how network complexity affects the Metabolic Sensitivity Coefficients (MSCs) of large-scale kinetic models build around consistently reduced models. We reduced the iJO1366Escherichia Coligenome-scale metabolic reconstruction (GEM) systematically to build three stoichiometric models of variable size. Since the reduced models are expansions around the core subsystems for which the reduction was performed, the models are modular. We propose 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 non-linear kinetic models, preserving similarity in kinetic parameters, were built around the reference steady-states and their MSCs were computed. The analysis of the populations of MSCs for the reduced models evidences that metabolic engineering strategies - independent of network complexity - can be designed using our proposed workflow. These findings suggest that we can successfully construct reduced kinetic models from a GEM, without losing information relevant to the scope of the study. Our proposed workflow can serve as an approach for testing the suitability of a model for answering certain study-specific questions.Author SummaryKinetic models of metabolism are very useful tools for metabolic engineering. However, they are generatedad hocbecause, to our knowledge, there exists no standardized procedure for constructing kinetic models of metabolism. We sought to investigate systematically the effect of model complexity and size on sensitivity characteristics. Hence, we used the redGEM and the lumpGEM algorithms to build the backbone of three consistently and modularly reduced stoichiometric models from the iJO1366 genome-scale model for aerobically grownE.coli. These three models were of increasing complexity in terms of network topology and served as basis for building populations of kinetic models. We proposed for the first time a way for scaling up steady-states of the metabolic fluxes and the metabolite concentrations from one kinetic model to another and developed a workflow for fixing kinetic parameters between the models in order to preserve equivalency. We performed metabolic control analysis (MCA) around the populations of kinetic models and used their MCA control coefficients as measurable outputs to compare the three models. We demonstrated that we can systematically reduce genome-scale models to construct kinetic models of different complexity levels for a phenotype that, independent of network complexity, lead to mostly consistent MCA-based metabolic engineering conclusions.

Review and perspective on mathematical modeling of microbial ecosystems

Understanding microbial ecosystems means unlocking the path toward a deeper knowledge of the fundamental mechanisms of life. Engineered microbial communities are also extremely relevant to tackling some of today's grand societal challenges. Advanced meta-omics experimental techniques provide crucial insights into microbial communities, but have been so far mostly used for descriptive, exploratory approaches to answer the initial ‘who is there?’ question. An ecosystem is a complex network of dynamic spatio-temporal interactions among organisms as well as between organisms and the environment. Mathematical models with their abstraction capability are essential to capture the underlying phenomena and connect the different scales at which these systems act. Differential equation models and constraint-based stoichiometric models are deterministic approaches that can successfully provide a macroscopic description of the outcome from microscopic behaviors. In this mini-review, we present classical and recent applications of these modeling methods and illustrate the potential of their integration. Indeed, approaches that can capture multiple scales are needed in order to understand emergent patterns in ecosystems and their dynamics regulated by different spatio-temporal phenomena. We finally discuss promising examples of methods proposing the integration of differential equations with constraint-based stoichiometric models and argue that more work is needed in this direction.

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.

Genotype-specific relationships among phosphorus use, growth and abundance in Daphnia pulicaria

The framework ecological stoichiometry uses elemental composition of species to make predictions about growth and competitive ability in defined elemental supply conditions. Although intraspecific differences in stoichiometry have been observed, we have yet to understand the mechanisms generating and maintaining such variation. We used variation in phosphorus (P) content within a Daphnia species to test the extent to which %P can explain variation in growth and competition. Further, we measured 33 P kinetics (acquisition, assimilation, incorporation and retention) to understand the extent to which such variables improved predictions. Genotypes showed significant variation in P content, 33 P kinetics and growth rate. P content alone was a poor predictor of growth rate and competitive ability. While most genotypes exhibited the typical growth penalty under P limitation, a few varied little in growth between P diets. These observations indicate that some genotypes can maintain growth under P-limited conditions by altering P use, suggesting that decomposing P content of an individual into physiological components of P kinetics will improve stoichiometric models. More generally, attention to the interplay between nutrient content and nutrient-use is required to make inferences regarding the success of genotypes in defined conditions of nutrient supply.

Hydrogen-Rich Syngas Production from Gasification and Pyrolysis of Solar Dried Sewage Sludge: Experimental and Modeling Investigations

Solar dried sewage sludge (SS) conversion by pyrolysis and gasification processes has been performed, separately, using two laboratory-scale reactors, a fixed-bed pyrolyzer and a downdraft gasifier, to produce mainly hydrogen-rich syngas. Prior to SS conversion, solar drying has been conducted in order to reduce moisture content (up to 10%). SS characterization reveals that these biosolids could be appropriate materials for gaseous products production. The released gases from SS pyrolysis and gasification present relatively high heating values (up to 9.96 MJ/kg for pyrolysis and 8.02 9.96 MJ/kg for gasification) due to their high contents of H2 (up to 11 and 7 wt%, resp.) and CH4 (up to 17 and 5 wt%, resp.). The yields of combustible gases (H2 and CH4) show further increase with pyrolysis. Stoichiometric models of both pyrolysis and gasification reactions were determined based on the global biomass formula, CαHβOγNδSε, in order to assist in the products yields optimization.