Identification of biochemical network modules based on shortest retroactive distances

Modularity analysis offers a route to better understand the organization of cellular biochemical networks as well as to derive practically useful, simplified models of these complex systems. While there is general agreement regarding the qualitative properties of a biochemical module, there is no clear consensus on the quantitative criteria that may be used to systematically derive these modules. In this work, we investigate cyclical interactions as the defining characteristic of a biochemical module. We utilize a round trip distance metric, termed Shortest Retroactive Distance (ShReD), to characterize the retroactive connectivity between any two reactions in a biochemical network and to group together network components that mutually influence each other. We evaluate the metric on two types of networks that feature feedback interactions: (i) epidermal growth factor receptor (EGFR) signaling and (ii) liver metabolism supporting drug transformation. For both networks, the ShReD partitions found hierarchically arranged modules that confirm biological intuition. In addition, the partitions also revealed modules that are less intuitive. In particular, ShReD-based partition of the metabolic network identified a 'redox' module that couples reactions of glucose, pyruvate, lipid and drug metabolism through shared production and consumption of NADPH. Our results suggest that retroactive interactions arising from feedback loops and metabolic cycles significantly contribute to the modularity of biochemical networks. For metabolic networks, cofactors play an important role as allosteric effectors that mediate the retroactive interactions.     

Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective

Cellular metabolism is most often described and interpreted in terms of the biochemical reactions that make up the metabolic network. Genomics is providing near complete information regarding the genes/gene products participating in cellular metabolism for a growing number of organisms. As the true functional units of metabolic systems are its pathways, the time has arrived to define metabolic pathways in the context of whole-cell metabolism for the analysis of the structural design and capabilities of the metabolic network. In this study, we present the theoretical foundations for the identification of the unique set of systemically independent biochemical pathways, termed extreme pathways, based on system stochiometry and limited thermodynamics. These pathways represent the edges of the steady-state flux cone derived from convex analysis, and they can be used to represent any flux distribution achievable by the metabolic network. An algorithm is presented to determine the set of extreme pathways for a system of any complexity and a classification scheme is introduced for the characterization of these pathways. The property of systemic independence is discussed along with its implications for issues related to metabolic regulation and the evolution of cellular metabolic networks. The underlying pathway structure that is determined from the set of extreme pathways now provides us with the ability to analyse, interpret, and perhaps predict metabolic function from a pathway-based perspective in addition to the traditional reaction-based perspective. The algorithm and classification scheme developed can be used to describe the pathway structure in annotated genomes to explore the capabilities of an organism.     

Integrating genetic and network analysis to characterize genes related to mouse weight

Systems biology approaches that are based on the genetics of gene expression have been fruitful in identifying genetic regulatory loci related to complex traits. We use microarray and genetic marker data from an F2 mouse intercross to examine the large-scale organization of the gene co-expression network in liver, and annotate several gene modules in terms of 22 physiological traits. We identify chromosomal loci (referred to as module quantitative trait loci, mQTL) that perturb the modules and describe a novel approach that integrates network properties with genetic marker information to model gene/trait relationships. Specifically, using the mQTL and the intramodular connectivity of a body weight–related module, we describe which factors determine the relationship between gene expression profiles and weight. Our approach results in the identification of genetic targets that influence gene modules (pathways) that are related to the clinical phenotypes of interest.     

The Modular Organization of Protein Interactions in Escherichia coli

Escherichia coli serves as an excellent model for the study of fundamental cellular processes such as metabolism, signalling and gene expression. Understanding the function and organization of proteins within these processes is an important step towards a ‘systems’ view of E. coli. Integrating experimental and computational interaction data, we present a reliable network of 3,989 functional interactions between 1,941 E. coli proteins (∼45% of its proteome). These were combined with a recently generated set of 3,888 high-quality physical interactions between 918 proteins and clustered to reveal 316 discrete modules. In addition to known protein complexes (e.g., RNA and DNA polymerases), we identified modules that represent biochemical pathways (e.g., nitrate regulation and cell wall biosynthesis) as well as batteries of functionally and evolutionarily related processes. To aid the interpretation of modular relationships, several case examples are presented, including both well characterized and novel biochemical systems. Together these data provide a global view of the modular organization of the E. coli proteome and yield unique insights into structural and evolutionary relationships in bacterial networks.     

Flux profile and modularity analysis of time-dependent metabolic changes of de novo adipocyte formation

White adipose tissue (WAT) mass is the main determinant of obesity and associated health risks. WAT expansion results from increases in white adipocyte cell number and size, which in turn reflect a series of shifts in the cellular metabolic state. To quantitatively profile the metabolic alterations occurring during de novo adipocyte formation, metabolic flux analysis (MFA) was used in conjunction with a novel modularity analysis algorithm on differentiating 3T3-L1 preadipocytes. Use of a type I collagen gel as an effective long-term culture substrate was also assessed. The calculated flux distributions predicted the sequential activation of several intracellular cross-compartmental pathways, including lipogenesis, the pentose phosphate pathway, and the malate cycle, in good agreement with earlier isotopic tracer experiments and gene profiling studies. Partition of the adipocyte metabolic network into highly interacting reaction subgroups suggested a functional reorganization of the major pathways consistent with the lipid-loading phenotype of the adipocyte. Flux and modularity analysis results together point to the flux distribution around pyruvate as a key indicator of adipocyte lipid accumulation.     

Endogenous adipocyte apolipoprotein E is colocalized with caveolin at the adipocyte plasma membrane

Apolipoprotein (apo)E is well established as a secreted protein that plays an important role in systemic lipoprotein metabolism and vascular wall homeostasis. Recently, endogenous expression of apoE in adipocytes has been shown to play an important role in adipocyte lipoprotein metabolism and gene expression consistent with a nonsecreted cellular itinerary for apoE. We designed studies to evaluate if adipocyte apoE was retained as a constituent protein in adipocytes and to identify a cellular retention compartment. Using confocal microscopy, coimmunoprecipitation, and sucrose density cellular fractionation, we establish that endogenous apoE shares a cellular itinerary with the constituent protein caveolin-1. Altering adipocyte caveolar number by modulating cellular cholesterol flux or altering caveolin expression regulates the distribution of cellular apoE between cytoplasmic and plasma membrane compartments. A mechanism for colocalization of apoE with caveolin was established by demonstrating a noncovalent interaction between an aromatic amino acid-enriched apoE N-terminal domain with the caveolin scaffolding domain. Absent apoE expression in adipocytes alters caveolar lipid composition. These observations provide evidence for an interaction between two proteins involved in cellular lipid metabolism in a cell specialized for lipid storage and flux, and rationalize a biological basis for the impact of adipocyte apoE expression on adipocyte lipoprotein metabolism.     

Comparison of metabolic states using genome-scale metabolic models

Genome-scale metabolic models (GEMs) are comprehensive knowledge bases of cellular metabolism and serve as mathematical tools for studying biological phenotypes and metabolic states or conditions in various organisms and cell types. Given the sheer size and complexity of human metabolism, selecting parameters for existing analysis methods such as metabolic objective functions and model constraints is not straightforward in human GEMs. In particular, comparing several conditions in large GEMs to identify condition- or disease-specific metabolic features is challenging. In this study, we showcase a scalable, model-driven approach for an in-depth investigation and comparison of metabolic states in large GEMs which enables identifying the underlying functional differences. Using a combination of flux space sampling and network analysis, our approach enables extraction and visualisation of metabolically distinct network modules. Importantly, it does not rely on known or assumed objective functions. We apply this novel approach to extract the biochemical differences in adipocytes arising due to unlimited vs blocked uptake of branched-chain amino acids (BCAAs, considered as biomarkers in obesity) using a human adipocyte GEM (iAdipocytes1809). The biological significance of our approach is corroborated by literature reports confirming our identified metabolic processes (TCA cycle and Fatty acid metabolism) to be functionally related to BCAA metabolism. Additionally, our analysis predicts a specific altered uptake and secretion profile indicating a compensation for the unavailability of BCAAs. Taken together, our approach facilitates determining functional differences between any metabolic conditions of interest by offering a versatile platform for analysing and comparing flux spaces of large metabolic networks.     

Identification of distributed metabolic objectives in the hypermetabolic liver by flux and energy balance analysis

A methodology for inferring distributed metabolic objectives from time series flux data is developed by combining metabolic flux analysis, pathway identification, free energy balances, and nested optimization. This methodology is used to investigate the metabolic response of the rat liver to burn injury-induced whole body inflammation. Gibbs free energy changes were computed for stoichiometrically balanced sequences of reactions, or pathways, rather than individual reactions, to account for energetic coupling between reactions. Systematic enumeration of pathways proceeded by elementary flux mode (EFM) analysis. Together with stoichiometric balances and external metabolite flux measurements, the DeltaG(PATH)(o) criterion provided sufficient constraints to solve a series of nested optimization problems on the metabolic goal functions and associated flux distributions of fasted livers during the first-week time course of burn injury. The optimization results suggest that there is a consistent metabolic goal function for the liver that is insensitive to the changing metabolic burdens experienced by the liver during the first-week time course. As defined by the goal function coefficients, the global metabolic objective was to distribute the metabolic resources between amino acid metabolism and ketone body synthesis. These findings point to a role for the time-invariant structure of the metabolic reaction network, expressed as stoichiometric and thermodynamic constraints, in shaping the cellular metabolic objective.     

Pathway analysis of liver metabolism under stressed condition

Pathway analysis is a useful tool which reveals important metabolic network properties. However, the big challenge is to propose an objective function for estimating active pathways, which represent the actual state of network. In order to provide weight values for all possible pathways within the metabolic network, this study presents different approaches, considering the structural and physiological properties of the metabolic network, aiming at a unique decomposition of the flux vector into pathways. These methods were used to analyze the hepatic metabolism considering available data sets obtained from the perfused livers of fasted rats receiving burn injury. Utilizing unique decomposition techniques and different fluxes revealed that higher weights were always attributed to short pathways. Specific pathways, including pyruvate, glutamate and oxaloacetate pools, and urea production from arginine, were found to be important or essential in all methods and experimental conditions. Moreover the pathways, including serine production from glycine and conversion between acetoacetate and B—OH-butyrate, were assigned higher weights. Pathway analysis was also used to identify the main sources for the production of certain products in the hepatic metabolic network to gain a better understanding of the effects of burn injury on liver metabolism.     

Signatures of Arithmetic Simplicity in Metabolic Network Architecture

Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their evolutionary history and complex wiring constitutes one of the most fascinating open questions in biology, intimately related to the enigma of life''s origin itself. Is the evolution of metabolism subject to general principles, beyond the unpredictable accumulation of multiple historical accidents? Here we search for such principles by applying to an artificial chemical universe some of the methodologies developed for the study of genome scale models of cellular metabolism. In particular, we use metabolic flux constraint-based models to exhaustively search for artificial chemistry pathways that can optimally perform an array of elementary metabolic functions. Despite the simplicity of the model employed, we find that the ensuing pathways display a surprisingly rich set of properties, including the existence of autocatalytic cycles and hierarchical modules, the appearance of universally preferable metabolites and reactions, and a logarithmic trend of pathway length as a function of input/output molecule size. Some of these properties can be derived analytically, borrowing methods previously used in cryptography. In addition, by mapping biochemical networks onto a simplified carbon atom reaction backbone, we find that properties similar to those predicted for the artificial chemistry hold also for real metabolic networks. These findings suggest that optimality principles and arithmetic simplicity might lie beneath some aspects of biochemical complexity.     

Flux analysis uncovers key role of functional redundancy in formaldehyde metabolism

Genome-scale analysis of predicted metabolic pathways has revealed the common occurrence of apparent redundancy for specific functional units, or metabolic modules. In many cases, mutation analysis does not resolve function, and instead, direct experimental analysis of metabolic flux under changing conditions is necessary. In order to use genome sequences to build models of cellular function, it is important to define function for such apparently redundant systems. Here we describe direct flux measurements to determine the role of redundancy in three modules involved in formaldehyde assimilation and dissimilation in a bacterium growing on methanol. A combination of deuterium and ¹⁴C labeling was used to measure the flux through each of the branches of metabolism for growth on methanol during transitions into and out of methylotrophy. The cells were found to differentially partition formaldehyde among the three modules depending on the flux of methanol into the cell. A dynamic mathematical model demonstrated that the kinetic constants of the enzymes involved are sufficient to account for this phenomenon. We demonstrate the role of redundancy in formaldehyde metabolism and have uncovered a new paradigm for coping with toxic, high-flux metabolic intermediates: a dynamic, interconnected metabolic loop.     

Dynamics and Control of the Central Carbon Metabolism in Hepatoma Cells

Background  

The liver plays a major role in metabolism and performs a number of vital functions in the body. Therefore, the determination of hepatic metabolite dynamics and the analysis of the control of the respective biochemical pathways are of great pharmacological and medical importance. Extra- and intracellular time-series data from stimulus-response experiments are gaining in importance in the identification of in vivo metabolite dynamics, while dynamic network models are excellent tools for analyzing complex metabolic control patterns. This is the first study that has been undertaken on the data-driven identification of a dynamic liver central carbon metabolism model and its application in the analysis of the distribution of metabolic control in hepatoma cells.     

Metabolic network properties help assign weights to elementary modes to understand physiological flux distributions

MOTIVATION: Elementary modes (EMs) analysis has been well established. The existing methodologies for assigning weights to EMs cannot be directly applied for large-scale metabolic networks, since the tremendous number of modes would make the computation a time-consuming or even an impossible mission. Therefore, developing more efficient methods to deal with large set of EMs is urgent. RESULT: We develop a method to evaluate the performance of employing a subset of the elementary modes to reconstruct a real flux distribution by using the relative error between the real flux vector and the reconstructed one as an indicator. We have found a power function relationship between the decrease of relative error and the increase of the number of the selecting EMs, and a logarithmic relationship between the increases of the number of non-zero weighted EMs and that of the number of the selecting EMs. Our discoveries show that it is possible to reconstruct a given flux distribution by a selected subset of EMs from a large metabolic network and furthermore, they help us identify the 'governing modes' to represent the cellular metabolism for such a condition.     

The strength of chemical linkage as a criterion for pruning metabolic graphs

MOTIVATION: A metabolic graph represents the connectivity patterns of a metabolic system, and provides a powerful framework within which the organization of metabolic reactions can be analyzed and elucidated. A common practice is to prune (i.e. remove nodes and edges) the metabolic graph prior to any analysis in order to eliminate confounding signals from the representation. Currently, this pruning process is carried out in an ad hoc fashion, resulting in discrepancies and ambiguities across studies. RESULTS: We propose a biochemically informative criterion, the strength of chemical linkage (SCL), for a systematic pruning of metabolic graphs. By analyzing the metabolic graph of Escherichia coli, we show that thresholding SCL is powerful in selecting the conventional pathways' connectivity out of the raw network connectivity when the network is restricted to the reactions collected from these pathways. Further, we argue that the root of ambiguity in pruning metabolic graphs is in the continuity of the amount of chemical content that can be conserved in reaction transformation patterns. Finally, we demonstrate how biochemical pathways can be inferred efficiently if the search procedure is guided by SCL.     

Fundamental Escherichia coli biochemical pathways for biomass and energy production: identification of reactions

Cells grow by oxidizing nutrients using a complex network of biochemical reactions. During this process new biological material is produced along with energy used for maintaining cellular organization. Because the metabolic network is highly branched, these tasks can be accomplished using a wide variety of unique reaction sequences. However, evolutionary pressures under carbon-limited growth conditions likely select organisms that utilize highly efficient pathways. Using elementary-mode analysis, we demonstrate that the metabolism of the bacterium Escherichia coli contains four unique pathways that most efficiently convert glucose and oxygen into new cells and maintenance energy under any level of oxygen limitation. Observed regulatory patterns and experimental findings suggest growing cells use these highly efficient pathways. It is predicted that five knockout mutations generate a strain that supports growth using only the most efficient reaction sequence. The analysis approach should be generally useful for predicting metabolic capabilities and efficient network designs based on only genomic information.     

Novel aspects of the activities and subcellular distribution of enzymes of ketone body metabolism in the liver and kidney of the goldfish, Carassius auratus

The metabolic organization of ketone body metabolism of liver and kidney of the goldfish Carassius auratus was assessed by measuring maximal activities, subcellular distribution, and stereoisomer preference of ketone body enzymes. These determinations indicate that the organization of ketone body metabolism in liver and kidney of goldfish differs from that of mammals in some respects. All the enzymes of ketone body metabolism were present in liver and kidney of goldfish, with the exception of hydroxymethylglutaryl-CoA (HMG-CoA) synthetase, which was not detected in liver. Two forms of beta-hydroxybutyrate dehydrogenase (betaHBDH) with different stereospecificity for beta-hydroxybutyrate (D- and L-beta-hydroxybutyrate) were detectable in liver and kidney. All of the ketone body enzymes measured in liver were mainly in the mitochondrial fraction, with the exception of D- and L-betaHBDH, which were cytosolic. In kidney, HMG-CoA synthase, together with HMG-CoA lyase and acetoacetyl CoA thiolase (AcoAT), were found mainly in the mitochondrial fraction. L-betaHBDH was mainly cytosolic in kidney, but by contrast with liver, D-betaHBDH was mainly found in the mitochondria, and SKT was distributed in both the mitochondrial and cytosolic compartments. J. Exp. Zool. 286:434-439, 2000.     

Engineering the spatial organization of metabolic enzymes: mimicking nature's synergy

A growing body of evidence indicates that many cellular reactions within metabolic pathways are catalyzed not by free-floating 'soluble' enzymes, but via one or more membrane-associated multienzyme complexes. This type of macromolecular organization has important implications for the overall efficiency, specificity, and regulation of metabolic pathways. An ever-increasing number of biochemical and genetic studies on primary and secondary metabolism have laid a solid foundation for this model, providing compelling evidence in favor of the so-called channeling of intermediates between enzyme active sites and colocalization of enzymes inside a cell. In this review, we discuss several of nature's most notable multifunctional enzyme systems including the AROM complex and tryptophan synthase, each of which provides new fundamental insights into the structural organization of metabolic machinery within living cells. We then focus on the growing body of literature related to engineering strategies using protein chimeras and post-translational assembly mechanisms. Common among these techniques is the desire to mimic natural enzyme organization for optimizing the production of valuable metabolites with industrial and medical importance.