Prediction of metabolic function from limited data: Lumped hybrid cybernetic modeling (L-HCM)

The Molecular Basis of Differentiation Wave Activity in Embryogenesis

As development varies greatly across the tree of life, it may seem difficult to suggest a model that proposes a single mechanism for understanding collective cell behaviors and the coordination of tissue formation. Here we propose a mechanism called differentiation waves, which unify many disparate results involving developmental systems from across the tree of life. We demonstrate how a relatively simple model of differentiation proceeds not from function-related molecular mechanisms, but from so-called differentiation waves. A phenotypic model of differentiation waves is introduced, and its relation to molecular mechanisms is proposed. These waves contribute to a differentiation tree, which is an alternate way of viewing cell lineage and local action of the molecular factors. We construct a model of differentiation wave-related molecular mechanisms (genome, epigenome, and proteome) based on bioinformatic data from the nematode Caenorhabditis elegans. To validate this approach across different modes of development, we evaluate protein expression across different types of development by comparing Caenorhabditis elegans with several model organisms: fruit flies (Drosophila melanogaster), yeast (Saccharomyces cerevisiae), and mouse (Mus musculus). Inspired by gene regulatory networks, two Models of Interactive Contributions (fully-connected MICs and ordered MICs) are used to suggest potential genomic contributions to differentiation wave-related proteins. This, in turn, provides a framework for understanding differentiation and development.

Combining Kinetic and Constraint-Based Modelling to Better Understand Metabolism Dynamics

To understand the phenotypic capabilities of organisms, it is useful to characterise cellular metabolism through the analysis of its pathways. Dynamic mathematical modelling of metabolic networks is of high interest as it provides the time evolution of the metabolic components. However, it also has limitations, such as the necessary mechanistic details and kinetic parameters are not always available. On the other hand, large metabolic networks exhibit a complex topological structure which can be studied rather efficiently in their stationary regime by constraint-based methods. These methods produce useful predictions on pathway operations. In this review, we present both modelling techniques and we show how they bring complementary views of metabolism. In particular, we show on a simple example how both approaches can be used in conjunction to shed some light on the dynamics of metabolic networks.

CODY enables quantitatively spatiotemporal predictions on in vivo gut microbial variability induced by diet intervention

Quantitatively understanding and predicting spatiotemporal dynamics of microbiota is imperative for development of tailored microbiome-directed therapeutics treatments. However, the complexity of microbial variations, due to interactions with the host, other microbes, and environmental factors, makes it challenging to identify how microbiota colonize in the human gut. Here, we describe a novel multiscale framework for COmputing the DYnamics of the gut microbiota (CODY), which enables the quantification of spatiotemporal-specific variations of gut microbiome abundance profiles, without a prior knowledge of microbiome interactions. Importantly, the predictive power of CODY is demonstrated using cross-sectional data from two longitudinal metagenomics studies—the microbiota development during early infancy and during short-term diet intervention of obese adults.

Microbial variations in the human gut are harbored in temporal and spatial heterogeneity, and quantitative prediction of spatiotemporal dynamic changes in the gut microbiota is imperative for development of tailored microbiome-directed therapeutics treatments, e.g. precision nutrition. Given the high-degree complexity of microbial variations, subject to the dynamic interactions among host, microbial, and environmental factors, identifying how microbiota colonize in the gut represents an important challenge. Here we present COmputing the DYnamics of microbiota (CODY), a multiscale framework that integrates species-level modeling of microbial dynamics and ecosystem-level interactions into a mathematical model that characterizes spatial-specific in vivo microbial residence in the colon as impacted by host physiology. The framework quantifies spatiotemporal resolution of microbial variations on species-level abundance profiles across site-specific colon regions and in feces, independent of a priori knowledge. We demonstrated the effectiveness of CODY using cross-sectional data from two longitudinal metagenomics studies—the microbiota development during early infancy and during short-term diet intervention of obese adults. For each cohort, CODY correctly predicts the microbial variations in response to diet intervention, as validated by available metagenomics and metabolomics data. Model simulations provide insight into the biogeographical heterogeneity among lumen, mucus, and feces, which provides insight into how host physical forces and spatial structure are shaping microbial structure and functionality.

Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose

Consolidated bioprocessing (CBP) of cellulose is a cost-effective route to produce valuable biochemicals by integrating saccharification, fermentation and cellulase synthesis in a single step. However, the lack of understanding of governing factors of interdependent saccharification and fermentation in CBP eludes reliable process optimization. Here, we propose a new framework that synergistically couples population balances (to simulate cellulose depolymerization) and cybernetic models (to model enzymatic regulation of fermentation) to enable improved understanding of CBP. The resulting framework, named the unified cybernetic-population balance model (UC-PBM), enables simulation of CBP driven by coordinated control of enzyme synthesis through closed-loop interactions. UC-PBM considers two key aspects in controlling CBP: (1) heterogeneity in cellulose properties and (2) cellular regulation of competing cell growth and cellulase secretion. In a case study on Clostridium thermocellum, UC-PBM not only provides a decent fit with various exometabolomic data, but also reveals that: (i) growth-decoupled cellulase-secreting pathways are only activated during famine conditions to promote the production of growth substrates, and (ii) starting cellulose concentration has a strong influence on the overall flux distribution. Equipped with mechanisms of cellulose degradation and fermentative regulations, UC-PBM is practical to explore phenotypic functions for primary evaluation of microorganisms' potential for metabolic engineering and optimal design of bioprocess.

Representing Organic Matter Thermodynamics in Biogeochemical Reactions via Substrate-Explicit Modeling

Predictive biogeochemical modeling requires data-model integration that enables explicit representation of the sophisticated roles of microbial processes that transform substrates. Data from high-resolution organic matter (OM) characterization are increasingly available and can serve as a critical resource for this purpose, but their incorporation into biogeochemical models is often prohibited due to an over-simplified description of reaction networks. To fill this gap, we proposed a new concept of biogeochemical modeling-termed substrate-explicit modeling-that enables parameterizing OM-specific oxidative degradation pathways and reaction rates based on the thermodynamic properties of OM pools. Based on previous developments in the literature, we characterized the resulting kinetic models by only two parameters regardless of the complexity of OM profiles, which can greatly facilitate the integration with reactive transport models for ecosystem simulations by alleviating the difficulty in parameter identification. The two parameters include maximal growth rate (μmax) and harvest volume (Vh) (i.e., the volume that a microbe can access for harvesting energy). For every detected organic molecule in a given sample, our approach provides a systematic way to formulate reaction kinetics from chemical formula, which enables the evaluation of the impact of OM character on biogeochemical processes across conditions. In a case study of two sites with distinct OM thermodynamics using ultra high-resolution metabolomics datasets derived from Fourier transform ion cyclotron resonance mass spectrometry analyses, our method predicted how oxidative degradation is primarily driven by thermodynamic efficiency of OM consistent with experimental rate measurements (as shown by correlation coefficients of up to 0.61), and how biogeochemical reactions can vary in response to carbon and/or oxygen limitations. Lastly, we showed that incorporation of enzymatic regulations into substrate-explicit models is critical for more reasonable predictions. This result led us to present integrative biogeochemical modeling as a unifying framework that can ideally describe the dynamic interplay among microbes, enzymes, and substrates to address advanced questions and hypotheses in future studies. Altogether, the new modeling concept we propose in this work provides a foundational platform for unprecedented predictions of biogeochemical and ecosystem dynamics through enhanced integration with diverse experimental data and extant modeling approaches.

Dynamic Modeling of CHO Cell Metabolism Using the Hybrid Cybernetic Approach With a Novel Elementary Mode Analysis Strategy

Chinese hamster ovary (CHO) cell culture has a major importance on the production of biopharmaceuticals, including recombinant therapeutic proteins such as monoclonal antibodies (MAb). Mathematical modeling of biological systems can successfully assess metabolism complexity while providing logical and systematic methods for relevant genetic target and culture parameter identification toward cell growth and productivity improvements. Most modeling approaches on CHO cells have been performed under stationary constraints, and only a few dynamic models have been presented on simplified reaction sets, due to substantial overparameterization problems. The hybrid cybernetic modeling (HCM) approach has been recently used to describe the dynamic behavior by incorporating regulation between different metabolic states by elementary mode participation control, with sets of equations evaluated by objective functions. However, as metabolic networks evaluated are constructed toward a genomic scale, and cell compartmentalization is considered, identification of the active set becomes more difficult as EM number exponentially grows. Thus, the development of robust approaches for EM active set selection and analysis with smaller computational requirements is required to impulse the use of cybernetic modeling on larger up to genome-scale networks. In this report, a novel elementary mode selection strategy, based on a polar representation of the convex solution space is presented and coupled to a cybernetic approach to model the dynamic physiologic and metabolic behavior of CHO-S cell cultures. The proposed Polar Space Yield Analysis (PSYA) was compared to other reported elementary mode selection approaches derived from Common Metabolic Objective Analysis (CMOA) used in Flux Balance Analysis (FBA), Yield Space Analysis (YSA), and Lumped Yield Space Analysis (LYSA). For this purpose, exponential growth phase dynamic metabolic models were calculated using kinetic rate equations based on previously modeled growth parameters. Finally, complete culture dynamic metabolic flux models were constructed using the HCM approach with selected elementary mode sets. The yield space elementary mode- and the polar space elementary mode- hybrid cybernetic models presented the best fits and performances. Also, a flux reaction perturbation prediction approach based on the polar yield solution space resulted useful for metabolic network flux distribution capability analysis and identification of potential genetic modifications targets.

Regulation-Structured Dynamic Metabolic Model Provides a Potential Mechanism for Delayed Enzyme Response in Denitrification Process

In a recent study of denitrification dynamics in hyporheic zone sediments, we observed a significant time lag (up to several days) in enzymatic response to the changes in substrate concentration. To explore an underlying mechanism and understand the interactive dynamics between enzymes and nutrients, we developed a trait-based model that associates a community's traits with functional enzymes, instead of typically used species guilds (or functional guilds). This enzyme-based formulation allows to collectively describe biogeochemical functions of microbial communities without directly parameterizing the dynamics of species guilds, therefore being scalable to complex communities. As a key component of modeling, we accounted for microbial regulation occurring through transcriptional and translational processes, the dynamics of which was parameterized based on the temporal profiles of enzyme concentrations measured using a new signature peptide-based method. The simulation results using the resulting model showed several days of a time lag in enzymatic responses as observed in experiments. Further, the model showed that the delayed enzymatic reactions could be primarily controlled by transcriptional responses and that the dynamics of transcripts and enzymes are closely correlated. The developed model can serve as a useful tool for predicting biogeochemical processes in natural environments, either independently or through integration with hydrologic flow simulators.

DRUM: a new framework for metabolic modeling under non-balanced growth. Application to the carbon metabolism of unicellular microalgae

Metabolic modeling is a powerful tool to understand, predict and optimize bioprocesses, particularly when they imply intracellular molecules of interest. Unfortunately, the use of metabolic models for time varying metabolic fluxes is hampered by the lack of experimental data required to define and calibrate the kinetic reaction rates of the metabolic pathways. For this reason, metabolic models are often used under the balanced growth hypothesis. However, for some processes such as the photoautotrophic metabolism of microalgae, the balanced-growth assumption appears to be unreasonable because of the synchronization of their circadian cycle on the daily light. Yet, understanding microalgae metabolism is necessary to optimize the production yield of bioprocesses based on this microorganism, as for example production of third-generation biofuels. In this paper, we propose DRUM, a new dynamic metabolic modeling framework that handles the non-balanced growth condition and hence accumulation of intracellular metabolites. The first stage of the approach consists in splitting the metabolic network into sub-networks describing reactions which are spatially close, and which are assumed to satisfy balanced growth condition. The left metabolites interconnecting the sub-networks behave dynamically. Then, thanks to Elementary Flux Mode analysis, each sub-network is reduced to macroscopic reactions, for which simple kinetics are assumed. Finally, an Ordinary Differential Equation system is obtained to describe substrate consumption, biomass production, products excretion and accumulation of some internal metabolites. DRUM was applied to the accumulation of lipids and carbohydrates of the microalgae Tisochrysis lutea under day/night cycles. The resulting model describes accurately experimental data obtained in day/night conditions. It efficiently predicts the accumulation and consumption of lipids and carbohydrates.

Genome-based Modeling and Design of Metabolic Interactions in Microbial Communities

Biotechnology research is traditionally focused on individual microbial strains that are perceived to have the necessary metabolic functions, or the capability to have these functions introduced, to achieve a particular task. For many important applications, the development of such omnipotent microbes is an extremely challenging if not impossible task. By contrast, nature employs a radically different strategy based on synergistic combinations of different microbial species that collectively achieve the desired task. These natural communities have evolved to exploit the native metabolic capabilities of each species and are highly adaptive to changes in their environments. However, microbial communities have proven difficult to study due to a lack of suitable experimental and computational tools. With the advent of genome sequencing, omics technologies, bioinformatics and genome-scale modeling, researchers now have unprecedented capabilities to analyze and engineer the metabolism of microbial communities. The goal of this review is to summarize recent applications of genome-scale metabolic modeling to microbial communities. A brief introduction to lumped community models is used to motivate the need for genome-level descriptions of individual species and their metabolic interactions. The review of genome-scale models begins with static modeling approaches, which are appropriate for communities where the extracellular environment can be assumed to be time invariant or slowly varying. Dynamic extensions of the static modeling approach are described, and then applications of genome-scale models for design of synthetic microbial communities are reviewed. The review concludes with a summary of metagenomic tools for analyzing community metabolism and an outlook for future research.