Time-dependent hierarchical regulation analysis: deciphering cellular adaptation

Quantifying Dynamic Regulation in Metabolic Pathways with Nonparametric Flux Inference

One of the central tasks in systems biology is to understand how cells regulate their metabolism. Hierarchical regulation analysis is a powerful tool to study this regulation at the metabolic, gene-expression, and signaling levels. It has been widely applied to study steady-state regulation, but analysis of the metabolic dynamics remains challenging because it is difficult to measure time-dependent metabolic flux. Here, we develop a nonparametric method that uses Gaussian processes to accurately infer the dynamics of a metabolic pathway based only on metabolite measurements; from this, we then go on to obtain a dynamical view of the hierarchical regulation processes invoked over time to control the activity in a pathway. Our approach allows us to use hierarchical regulation analysis in a dynamic setting but without the need for explicitly time-dependent flux measurements.

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

Metabolic pathways can be engineered to maximize the synthesis of various products of interest. With the advent of computational systems biology, this endeavour is usually carried out through in silico theoretical studies with the aim to guide and complement further in vitro and in vivo experimental efforts. Clearly, what counts is the result in vivo, not only in terms of maximal productivity but also robustness against environmental perturbations. Engineering an organism towards an increased production flux, however, often compromises that robustness. In this contribution, we review and investigate how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed by systems and control engineering. While trade-offs between production optimality and cellular robustness have already been studied diagnostically and statically, the dynamics also matter. Integration of the dynamic design aspects of control engineering with the more diagnostic aspects of metabolic, hierarchical control and regulation analysis is leading to the new, conceptual and operational framework required for the design of robust and productive dynamic pathways.

The relative importance of kinetic mechanisms and variable enzyme abundances for the regulation of hepatic glucose metabolism--insights from mathematical modeling

Background

Adaptation of the cellular metabolism to varying external conditions is brought about by regulated changes in the activity of enzymes and transporters. Hormone-dependent reversible enzyme phosphorylation and concentration changes of reactants and allosteric effectors are the major types of rapid kinetic enzyme regulation, whereas on longer time scales changes in protein abundance may also become operative. Here, we used a comprehensive mathematical model of the hepatic glucose metabolism of rat hepatocytes to decipher the relative importance of different regulatory modes and their mutual interdependencies in the hepatic control of plasma glucose homeostasis.

Results

Model simulations reveal significant differences in the capability of liver metabolism to counteract variations of plasma glucose in different physiological settings (starvation, ad libitum nutrient supply, diabetes). Changes in enzyme abundances adjust the metabolic output to the anticipated physiological demand but may turn into a regulatory disadvantage if sudden unexpected changes of the external conditions occur. Allosteric and hormonal control of enzyme activities allow the liver to assume a broad range of metabolic states and may even fully reverse flux changes resulting from changes of enzyme abundances alone. Metabolic control analysis reveals that control of the hepatic glucose metabolism is mainly exerted by enzymes alone, which are differently controlled by alterations in enzyme abundance, reversible phosphorylation, and allosteric effects.

Conclusion

In hepatic glucose metabolism, regulation of enzyme activities by changes of reactants, allosteric effects, and reversible phosphorylation is equally important as changes in protein abundance of key regulatory enzymes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-016-0237-6) contains supplementary material, which is available to authorized users.

Variability of metabolite levels is linked to differential metabolic pathways in Arabidopsis's responses to abiotic stresses

Constraint-based approaches have been used for integrating data in large-scale metabolic networks to obtain insights into metabolism of various organisms. Due to the underlying steady-state assumption, these approaches are usually not suited for making predictions about metabolite levels. Here, we ask whether we can make inferences about the variability of metabolite levels from a constraint-based analysis based on the integration of transcriptomics data. To this end, we analyze time-resolved transcriptomics and metabolomics data from Arabidopsis thaliana under a set of eight different light and temperature conditions. In a previous study, the gene expression data have already been integrated in a genome-scale metabolic network to predict pathways, termed modulators and sustainers, which are differentially regulated with respect to a biochemically meaningful data-driven null model. Here, we present a follow-up analysis which bridges the gap between flux- and metabolite-centric methods. One of our main findings demonstrates that under certain environmental conditions, the levels of metabolites acting as substrates in modulators or sustainers show significantly lower temporal variations with respect to the remaining measured metabolites. This observation is discussed within the context of a systems-view of plasticity and robustness of metabolite contents and pathway fluxes. Our study paves the way for investigating the existence of similar principles in other species for which both genome-scale networks and high-throughput metabolomics data of high quality are becoming increasingly available.

(Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis

Background

Metabolic control analysis (MCA) and supply–demand theory have led to appreciable understanding of the systems properties of metabolic networks that are subject exclusively to metabolic regulation. Supply–demand theory has not yet considered gene-expression regulation explicitly whilst a variant of MCA, i.e. Hierarchical Control Analysis (HCA), has done so. Existing analyses based on control engineering approaches have not been very explicit about whether metabolic or gene-expression regulation would be involved, but designed different ways in which regulation could be organized, with the potential of causing adaptation to be perfect.

Results

This study integrates control engineering and classical MCA augmented with supply–demand theory and HCA. Because gene-expression regulation involves time integration, it is identified as a natural instantiation of the ‘integral control’ (or near integral control) known in control engineering. This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise. It is shown however that this type of ‘integral control’ should rarely be expected to lead to the ‘perfect adaptation’: although the gene-expression regulation increases the robustness of important metabolite concentrations, it rarely makes them infinitely robust. For perfect adaptation to occur, the protein degradation reactions should be zero order in the concentration of the protein, which may be rare biologically for cells growing steadily.

Conclusions

A proposed new framework integrating the methodologies of control engineering and metabolic and hierarchical control analysis, improves the understanding of biological systems that are regulated both metabolically and by gene expression. In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the ‘perfect’ regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness. To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering.

Energy and metabolism

Although firmly grounded in metabolic biochemistry, the study of energy metabolism has gone well beyond this discipline and become integrative and comparative as well as ecological and evolutionary in scope. At the cellular level, ATP is hydrolyzed by energy-expending processes and resynthesized by pathways in bioenergetics. A significant development in the study of bioenergetics is the realization that fluxes through pathways as well as metabolic rates in cells, tissues, organs, and whole organisms are "system properties." Therefore, studies of energy metabolism have become, increasingly, experiments in systems biology. A significant challenge continues to be the integration of phenomena over multiple levels of organization. Body mass and temperature are said to account for most of the variation in metabolic rates found in nature. A mechanistic foundation for the understanding of these patterns is outlined. It is emphasized that evolution, leading to adaptation to diverse lifestyles and environments, has resulted in a tremendous amount of deviation from popularly accepted scaling "rules." This is especially so in the deep sea which constitutes most of the biosphere.

Quantitative analysis of glycerol accumulation, glycolysis and growth under hyper osmotic stress

We provide an integrated dynamic view on a eukaryotic osmolyte system, linking signaling with regulation of gene expression, metabolic control and growth. Adaptation to osmotic changes enables cells to adjust cellular activity and turgor pressure to an altered environment. The yeast Saccharomyces cerevisiae adapts to hyperosmotic stress by activating the HOG signaling cascade, which controls glycerol accumulation. The Hog1 kinase stimulates transcription of genes encoding enzymes required for glycerol production (Gpd1, Gpp2) and glycerol import (Stl1) and activates a regulatory enzyme in glycolysis (Pfk26/27). In addition, glycerol outflow is prevented by closure of the Fps1 glycerol facilitator. In order to better understand the contributions to glycerol accumulation of these different mechanisms and how redox and energy metabolism as well as biomass production are maintained under such conditions we collected an extensive dataset. Over a period of 180 min after hyperosmotic shock we monitored in wild type and different mutant cells the concentrations of key metabolites and proteins relevant for osmoadaptation. The dataset was used to parameterize an ODE model that reproduces the generated data very well. A detailed computational analysis using time-dependent response coefficients showed that Pfk26/27 contributes to rerouting glycolytic flux towards lower glycolysis. The transient growth arrest following hyperosmotic shock further adds to redirecting almost all glycolytic flux from biomass towards glycerol production. Osmoadaptation is robust to loss of individual adaptation pathways because of the existence and upregulation of alternative routes of glycerol accumulation. For instance, the Stl1 glycerol importer contributes to glycerol accumulation in a mutant with diminished glycerol production capacity. In addition, our observations suggest a role for trehalose accumulation in osmoadaptation and that Hog1 probably directly contributes to the regulation of the Fps1 glycerol facilitator. Taken together, we elucidated how different metabolic adaptation mechanisms cooperate and provide hypotheses for further experimental studies.

Osmotic changes are common environmental challenges for cells, even in multi-cellular organisms, having led to sophisticated adaptation mechanisms. In order to adapt to hyperosmotic stress, yeast cells accumulate glycerol. This is achieved by short-term responses involving metabolic and transmembrane transport changes as well as long-term transcriptional responses. By integrating experimentation and simulation of a mathematical model we resolve the quantitative and temporal characteristics of different processes contributing to glycerol accumulation. We show that osmoadaptation prioritizes the redox and energy balance in glycolysis while rerouting flux from biomass to glycerol production. We further show that the glycerol accumulation network provides osmoadaptation with robustness by compensating for the loss of certain nodes and with the flexibility necessary for responding to different stress situations. Finally we provide novel insight into the roles of transport processes in glycerol accumulation and evidence that trehalose may play a role in yeast osmoadaptation. The present work provides for the first time an integrated dynamic view on a eukaryotic osmolyte system and links signaling with regulation of gene expression and metabolic control.

Metabolism in the age of ‘omes’

Much research in comparative physiology is now performed using ‘omics’ tools and many results are interpreted in terms of the effects of changes in gene expression on energy metabolism. However, ‘metabolism’ is a complex phenomenon that spans multiple levels of biological organization. In addition rates and directions of flux change dynamically under various physiological circumstances. Within cells, message level cannot be equated with protein level because multiple mechanisms are at play in the ‘regulatory hierarchy’ from gene to mRNA to enzyme protein. This results in many documented instances wherein change in mRNA levels and change in enzyme levels are unrelated. It is also known from metabolic control analysis that the influence of single steps in pathways on flux is often small. Flux is a system property and its control tends to be distributed among multiple steps. Consequently, change in enzyme levels cannot be equated with change in flux. Approaches developed by Hans Westerhoff and colleagues, called ‘hierarchical regulation analysis’, allow quantitative determination of the extent to which ‘hierarchical regulation’, involving change in enzyme level, and ‘metabolic regulation’, involving the modulation of the activity of preexisting enzyme, regulate flux. We outline these approaches and provide examples to show their applicability to problems of interest to comparative physiologists.

Quantitative analysis of flux regulation through hierarchical regulation analysis

Regulation analysis is a methodology that quantifies to what extent a change in the flux through a metabolic pathway is regulated by either gene expression or metabolism. Two extensions to regulation analysis were developed over the past years: (i) the regulation of V(max) can be dissected into the various levels of the gene-expression cascade, such as transcription, translation, protein degradation, etc. and (ii) a time-dependent version allows following flux regulation when cells adapt to changes in their environment. The methodology of the original form of regulation analysis as well as of the two extensions will be described in detail. In addition, we will show what is needed to apply regulation analysis in practice. Studies in which the different versions of regulation analysis were applied revealed that flux regulation was distributed over various processes and depended on time, enzyme, and condition of interest. In the case of the regulation of glycolysis in baker's yeast, it appeared, however, that cells that remain under respirofermentative conditions during a physiological challenge tend to invoke more gene-expression regulation, while a shift between respirofermentative and respiratory conditions invokes an important contribution of metabolic regulation. The complexity of the regulation observed in these studies raises the question what is the advantage of this highly distributed and condition-dependent flux regulation.

Systems biochemistry in practice: experimenting with modelling and understanding, with regulation and control

Biology and medicine have become ‘big science’, even though we may not always like this: genomics and the subsequent analysis of what the genomes encode has shown that interesting living organisms require many more than 300 gene products to interact. We once thought that somewhere in this jungle of interacting macromolecules was hidden the molecule that constitutes the secret of Life, and therewith of health and disease. Now we know that, somehow, the secret of Life is the jungle of interactions. Consequently, we need to find the Rosetta Stones, i.e. interpretations of this jungle of systems biology. We need to find, perhaps convoluted, paths of understanding and intervention. Systems biochemistry is a good place to start, as it has the foothold that what goes in must come out. In the present paper, we review two strategies, which look at control and regulation. We discuss the difference between control and regulation and prove a relationship between them.

Formulating genome-scale kinetic models in the post-genome era

The biological community is now awash in high-throughput data sets and is grappling with the challenge of integrating disparate data sets. Such integration has taken the form of statistical analysis of large data sets, or through the bottom-up reconstruction of reaction networks. While progress has been made with statistical and structural methods, large-scale systems have remained refractory to dynamic model building by traditional approaches. The availability of annotated genomes enabled the reconstruction of genome-scale networks, and now the availability of high-throughput metabolomic and fluxomic data along with thermodynamic information opens the possibility to build genome-scale kinetic models. We describe here a framework for building and analyzing such models. The mathematical analysis challenges are reflected in four foundational properties, (i) the decomposition of the Jacobian matrix into chemical, kinetic and thermodynamic information, (ii) the structural similarity between the stoichiometric matrix and the transpose of the gradient matrix, (iii) the duality transformations enabling either fluxes or concentrations to serve as the independent variables and (iv) the timescale hierarchy in biological networks. Recognition and appreciation of these properties highlight notable and challenging new in silico analysis issues.

The nature of systems biology

The advent of functional genomics has enabled the molecular biosciences to come a long way towards characterizing the molecular constituents of life. Yet, the challenge for biology overall is to understand how organisms function. By discovering how function arises in dynamic interactions, systems biology addresses the missing links between molecules and physiology. Top-down systems biology identifies molecular interaction networks on the basis of correlated molecular behavior observed in genome-wide "omics" studies. Bottom-up systems biology examines the mechanisms through which functional properties arise in the interactions of known components. Here, we outline the challenges faced by systems biology and discuss limitations of the top-down and bottom-up approaches, which, despite these limitations, have already led to the discovery of mechanisms and principles that underlie cell function.