Is metabolism goal-directed? Investigating the validity of modeling biological systems with cybernetic control via omic data

Cybernetic models are uniquely juxtaposed to other metabolic modeling frameworks in that they describe the time-dependent regulation of cellular reactions in terms of dynamic metabolic goals. This approach contrasts starkly with purely mechanistic descriptions of metabolic regulation which seek to explain metabolic processes in high resolution — a clearly daunting undertaking. Over a span of three decades, cybernetic models have been used to predict metabolic phenomena ranging from resource consumption in mixed-substrate environments to intracellular reaction fluxes of intricate metabolic networks. While the cybernetic approach has been validated in its utility for the prediction of metabolic phenomena, its central feature, the goal-directed control strategy, has yet to be scrutinized through comparison with omic data. Ultimately, the aim of this work is to address the question Is metabolism-goal directed? through the analysis of biological data. To do so, this work investigates the idea that metabolism is goal-directed from three distinct angles. The first is to make a comparison of cybernetic models to other metabolic modeling frameworks. These mathematical formulations for intracellular chemical reaction networks range from purely mechanistic, kinetic models to linear programming approximations. Instead of comparing these frameworks directly on the basis of accuracy alone, a novel approach to systems biological model selection is developed. This approach compares models using information theoretic arguments. From this point of view, the model that compresses biological data best captures the most regularity in the data generated by a process. This framework is used to compare the flux predictions of cybernetic, constraint-based and kinetic models in several case studies. Cybernetic models, in the test cases examined, provide the most compact description of metabolic fluxes. This method of analysis can be extended to any systems biological model selection problem for the purposes of optimization and control. To further examine cybernetic control mechanisms, the second portion of this dissertation focuses on confronting cybernetic variable predictions with data that is representative of enzyme regulation. More specifically, the dynamic behavior of cybernetic variables, ui, which are representative of enzyme synthesis control are matched with gene expression data that represents the control of enzyme synthesis in cells. This comparison is made for the model system of cybernetic modeling, diauxic growth, and for prostaglandin (PG) metabolism in mammalian cells. Via analysis of these systems, a correlation between the dynamic behavior of cybernetic control variables and the true mechanisms that guide cellular regulation is discovered. Additionally, this result demonstrates potential use of cybernetic variables for the prediction of relative changes in gene expression levels. The last approach taken to test the veracity of cybernetic control is to develop a technique to mine objective functions from biological data. In this approach, returns on investment (ROIs) for various pathways are first established through simultaneous analysis of metabolite and gene expression data for a given metabolic system. Following this, the ROIs are used to determine a metabolic systems observed goal signal. Gene expression data is then mined to select genes that show expression changes that are similar to the goal signal\u27s behavior. This gene list is then analyzed to determine enriched biological pathways. In the final step, these pathways are then surveyed in the literature to establish feasible metabolic goals for the system of interest. This method is applied to analyze diauxic growth and prostaglandin systems and generates objective functions that are relevant to known properties of these metabolic networks from the literature. An enhanced understanding of metabolic goals in mammalian systems generated by this work reveals the potential utility of cybernetic modeling in new directions related to translational research. Overall, this investigation yields support of the notion of dynamic metabolic goals in cells through comparison of metabolic modeling approaches and through the analysis of omic data. From these results, a lucid argument is made for the use of goal-directed modeling approaches and a deeper understanding of the optimal nature of metabolic regulation is gained

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

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

Modeling human gut microbiota: from steady states to dynamic systems

Human gut microbes are an essential part of human sub-microscopic systems and involved in many critical biological processes such as Type 2 diabetes (T2D) and osteoporosis. However, the underlying mechanisms are unclear. Several mathematical modeling approaches, such as genome-scale metabolic models (GEMs) and ordinary differential equation (ODE) based models, have been used to simulate the dynamics of human gut microbiota. This thesis aims to explore, simulate, and predict the behavior of gut microbial ecosystems and the relationships between gut microbes and humans by modeling.The importance of the gut microbiome for bone metabolism and T2D has been demonstrated in mice and human cohorts. We first reconstructed a GEM for Limosilactobacillus reuteri ATCC PTA 6475, which is a probiotic that significantly reduces bone loss in older women with lower bone mineral density. To investigate the associations between T2D and the gut microbiota, GEMs for 827 gut microbial species and 1,779 community-level GEMs for T2D cohorts have also been constructed. With these GEMs, we investigated metabolic potentials such as short-chain fatty acids, amino acids, and vitamins that play vital roles in the host metabolism regulation. Furthermore, the integration of the models with machine learning method provides potential insights into the possible roles of gut microbiota in T2D.Cybernetic models, which simulate metabolic rates by integrating the control of enzyme synthesis and enzyme activities, have been applied to explore the dynamic behaviors of small-size metabolic networks. However, only a few studies have applied cybernetic theory to the microbial community so far. The remaining part of this thesis focuses on the use of cybernetic models to explore human gut microbiota\u27s interactions and population dynamics. Considering the high computing burden of the current cybernetic modeling approach for processing the full-size GEMs, we have developed a computing-efficient strategy for model reconstruction and simulation to reveal the metabolic dynamics of human gut microbiota.In this thesis, we explore the human gut microbiota from single L. reuteri species to microbial gut communities, from simple steady state systems by GEMs to complex dynamic systems by cybernetic model

Modeling the metabolic dynamics at the genome-scale by optimized yield analysis

The hybrid cybernetic model (HCM) approach is a dynamic modeling framework that integrates enzyme synthesis and activity regulation. It has been widely applied in bioreaction engineering, particularly in the simulation of microbial growth in different mixtures of carbon sources. In a HCM, the metabolic network is decomposed into elementary flux modes (EFMs), whereby the network can be reduced into a few pathways by yield analysis. However, applying the HCM approach on conventional genome-scale metabolic models (GEMs) is still a challenge due to the high computational demands. Here, we present a HCM strategy that introduced an optimized yield analysis algorithm (opt-yield-FBA) to simulate metabolic dynamics at the genome-scale without the need for EFMs calculation. The opt-yield-FBA is a flux-balance analysis (FBA) based method that can calculate optimal yield solutions and yield space for GEM. With the opt-yield-FBA algorithm, the HCM strategy can be applied to get the yield spaces and avoid the computational burden of EFMs, and it can therefore be applied for developing dynamic models for genome-scale metabolic networks. Here, we illustrate the strategy by applying the concept to simulate the dynamics of microbial communities

Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle

Collective behaviours: from biochemical kinetics to electronic circuits

In this work we aim to highlight a close analogy between cooperative behaviors in chemical kinetics and cybernetics; this is realized by using a common language for their description, that is mean-field statistical mechanics. First, we perform a one-to-one mapping between paradigmatic behaviors in chemical kinetics (i.e., non-cooperative, cooperative, ultra-sensitive, anti-cooperative) and in mean-field statistical mechanics (i.e., paramagnetic, high and low temperature ferromagnetic, anti-ferromagnetic). Interestingly, the statistical mechanics approach allows a unified, broad theory for all scenarios and, in particular, Michaelis-Menten, Hill and Adair equations are consistently recovered. This framework is then tested against experimental biological data with an overall excellent agreement. One step forward, we consistently read the whole mapping from a cybernetic perspective, highlighting deep structural analogies between the above-mentioned kinetics and fundamental bricks in electronics (i.e. operational amplifiers, flashes, flip-flops), so to build a clear bridge linking biochemical kinetics and cybernetics.Comment: 15 pages, 6 figures; to appear on Scientific Reports: Nature Publishing Grou