Metabolic networks: a signal-oriented approach to cellular models

Cardiomyocyte death in sepsis: Mechanisms and regulation (Review)

Sepsis‑induced cardiac dysfunction is one of the most common types of organ dysfunction in sepsis; its pathogenesis is highly complex and not yet fully understood. Cardiomyocytes serve a key role in the pathophysiology of cardiac function; due to the limited ability of cardiomyocytes to regenerate, their loss contributes to decreased cardiac function. The activation of inflammatory signalling pathways affects cardiomyocyte function and modes of cardiomyocyte death in sepsis. Prevention of cardiomyocyte death is an important therapeutic strategy for sepsis‑induced cardiac dysfunction. Thus, understanding the signalling pathways that activate cardiomyocyte death and cross‑regulation between death modes are key to finding therapeutic targets. The present review focused on advances in understanding of sepsis‑induced cardiomyocyte death pathways, including apoptosis, necroptosis, mitochondria‑mediated necrosis, pyroptosis, ferroptosis and autophagy. The present review summarizes the effect of inflammatory activation on cardiomyocyte death mechanisms, the diversity of regulatory mechanisms and cross‑regulation between death modes and the effect on cardiac function in sepsis to provide a theoretical basis for treatment of sepsis‑induced cardiac dysfunction.

Development and validation of multiple machine learning algorithms for the classification of G-protein-coupled receptors using molecular evolution model-based feature extraction strategy

Machine learning is one of the most potential ways to realize the function prediction of the incremental large-scale G-protein-coupled receptors (GPCR). Prior research reveals that the key to determining the overall classification accuracy of GPCR is extracting valuable features and filtering out redundancy. To achieve a more efficient classification model, we put the feature synonym problem into consideration and create a new method based on functional word clustering and integration. Through evaluating the evolution correlation between features using the transition scores in mature molecular substitution matrices, candidate features are clustered into synonym groups. Each group of the clustered features is then integrated and represented by a unique key functional word. These retained key functional words are used to form a feature knowledge base. The original GPCR sequences are then transferred into feature vectors based on a feature re-extraction strategy according to the features in the knowledge base before the training and testing stage. We create multiple machine learning models based on Naïve Bayesian (NB), random forest (RF), support vector machine (SVM), and multi-layer perceptron (MLP) algorithms. The established model is applied to classify two public data sets containing 8354 and 12,731 GPCRs, respectively. These models achieve significant performance in almost all evaluation criteria in comparison with state-of-the art. This work demonstrated the potential of the novel feature extraction strategy and provided an effective theoretical design for the hierarchical classification of GPCRs.

Substrate-dependent cluster density dynamics of Corynebacterium glutamicum phosphotransferase system permeases

Many bacteria take up carbohydrates by membrane‐integral sugar specific phosphoenolpyruvate‐dependent carbohydrate:phosphotransferase systems (PTS). Although the PTS is centrally involved in regulation of carbon metabolism in different bacteria, little is known about localization and putative oligomerization of the permease subunits (EII). Here, we analyzed localization of the fructose specific PtsF and the glucose specific PtsG transporters, as well as the general components EI and HPr from Corynebacterium glutamicum using widefield and single molecule localization microscopy. PtsF and PtsG form membrane embedded clusters that localize in a punctate pattern. Size, number and fluorescence of the membrane clusters change upon presence or absence of the transported substrate, and a direct influence of EI and HPr was not observed. In presence of the transport substrate, EII clusters significantly increased in size. Photo‐activated localization microscopy data revealed that, in presence of different carbon sources, the number of EII proteins per cluster remains the same, however, the density of these clusters reduces. Our work reveals a simple mechanism for efficient membrane occupancy regulation. Clusters of PTS EII transporters are densely packed in absence of a suitable substrate. In presence of a transported substrate, the EII proteins in individual clusters occupy larger membrane areas.

PTS 50: Past, Present and Future, or Diauxie Revisited

<b><i>Past:</i></b> The title ‘PTS 50 or The PTS after 50 years' relies on the first description in 1964 of the phosphoenolpyruvate-dependent carbohydrate:phosphotransferase system (PTS) by Kundig, Gosh and Roseman [Proc Natl Acad Sci USA 1964;52:1067-1074]. The system comprised proteins named Enzyme I, HPr and Enzymes II, as part of a novel PTS for carbohydrates in Gram-negative and Gram-positive bacteria, whose ‘biological significance remained unclear'. In contrast, studies which would eventually lead to the discovery of the central role of the PTS in bacterial metabolism had been published since before 1942. They are primarily linked to names like Epps and Gale, J. Monod, Cohn and Horibata, and B. Magasanik, and to phenomena like ‘glucose effects', ‘diauxie', ‘catabolite repression' and carbohydrate transport. <b><i>Present:</i></b> The pioneering work from Roseman's group initiated a flood of publications. The extraordinary progress from 1964 to this day in the qualitative and in vitro description of the genes and enzymes of the PTS, and of its multiple roles in global cellular control through ‘inducer exclusion', gene induction and ‘catabolite repression', in cellular growth, in cell differentiation and in chemotaxis, as well as the differences of its functions between Gram-positive and Gram-negative bacteria, was one theme of the meeting and will not be treated in detail here. <b><i>Future:</i></b> At the 1988 Paris meeting entitled ‘The PTS after 25 years', Saul Roseman predicted that ‘we must describe these interactions [of the PTS components] in a quantitative way [under] in vivo conditions'. I will present some results obtained by our group during recent years on the old phenomenon of diauxie by means of very fast and quantitative tests, measured in vivo, and obtained from cultures of isogenic mutant strains growing under chemostat conditions. The results begin to hint at the problems relating to future PTS research, but also to the ‘true science' of Roseman.

Macromolecular networks and intelligence in microorganisms

Living organisms persist by virtue of complex interactions among many components organized into dynamic, environment-responsive networks that span multiple scales and dimensions. Biological networks constitute a type of information and communication technology (ICT): they receive information from the outside and inside of cells, integrate and interpret this information, and then activate a response. Biological networks enable molecules within cells, and even cells themselves, to communicate with each other and their environment. We have become accustomed to associating brain activity - particularly activity of the human brain - with a phenomenon we call "intelligence." Yet, four billion years of evolution could have selected networks with topologies and dynamics that confer traits analogous to this intelligence, even though they were outside the intercellular networks of the brain. Here, we explore how macromolecular networks in microbes confer intelligent characteristics, such as memory, anticipation, adaptation and reflection and we review current understanding of how network organization reflects the type of intelligence required for the environments in which they were selected. We propose that, if we were to leave terms such as "human" and "brain" out of the defining features of "intelligence," all forms of life - from microbes to humans - exhibit some or all characteristics consistent with "intelligence." We then review advances in genome-wide data production and analysis, especially in microbes, that provide a lens into microbial intelligence and propose how the insights derived from quantitatively characterizing biomolecular networks may enable synthetic biologists to create intelligent molecular networks for biotechnology, possibly generating new forms of intelligence, first in silico and then in vivo.

In Silico Augmentation of the Drug Development Pipeline: Examples from the study of Acute Inflammation

The clinical translation of promising basic biomedical findings, whether derived from reductionist studies in academic laboratories or as the product of extensive high-throughput and -content screens in the biotechnology and pharmaceutical industries, has reached a period of stagnation in which ever higher research and development costs are yielding ever fewer new drugs. Systems biology and computational modeling have been touted as potential avenues by which to break through this logjam. However, few mechanistic computational approaches are utilized in a manner that is fully cognizant of the inherent clinical realities in which the drugs developed through this ostensibly rational process will be ultimately used. In this article, we present a Translational Systems Biology approach to inflammation. This approach is based on the use of mechanistic computational modeling centered on inherent clinical applicability, namely that a unified suite of models can be applied to generate in silico clinical trials, individualized computational models as tools for personalized medicine, and rational drug and device design based on disease mechanism.

Hubs and bottlenecks in plant molecular signalling networks

Conditional control of plant cell function and development relies on appropriate signal perception, signal integration and processing. The development of high throughput technologies such as proteomics and interactomics has enabled the identification of protein interaction networks that mediate signal processing from inputs to appropriate outputs. Such networks can be depicted in graphical representations using nodes and edges allowing for the immediate visualization and analysis of the network's topology. Hubs are network elements characterized by many edges (often degree grade k ≥ 5) which confer a degree of topological importance to them. The review introduces the concept of networks, hubs and bottlenecks and describes four examples from plant science in more detail, namely hubs in the redox regulatory network of the chloroplast with ferredoxin, thioredoxin and peroxiredoxin, in mitogen activated protein (MAP) kinase signal processing, in photomorphogenesis with the COP9 signalosome, COP1 and CDD, and monomeric GTPase function. Some guidance is provided to appropriate internet resources, web repositories, databases and their use. Plant networks can be generated from existing public databases and this type of analysis is valuable in support of existing hypotheses, or to allow for the generation of new concepts or ideas. However, intensive manual curating of in silico networks is still always necessary.

Translational systems approaches to the biology of inflammation and healing

Inflammation is a complex, non-linear process central to many of the diseases that affect both developed and emerging nations. A systems-based understanding of inflammation, coupled to translational applications, is therefore necessary for efficient development of drugs and devices, for streamlining analyses at the level of populations, and for the implementation of personalized medicine. We have carried out an iterative and ongoing program of literature analysis, generation of prospective data, data analysis, and computational modeling in various experimental and clinical inflammatory disease settings. These simulations have been used to gain basic insights into the inflammatory response under baseline, gene-knockout, and drug-treated experimental animals for in silico studies associated with the clinical settings of sepsis, trauma, acute liver failure, and wound healing to create patient-specific simulations in polytrauma, traumatic brain injury, and vocal fold inflammation; and to gain insight into host-pathogen interactions in malaria, necrotizing enterocolitis, and sepsis. These simulations have converged with other systems biology approaches (e.g., functional genomics) to aid in the design of new drugs or devices geared towards modulating inflammation. Since they include both circulating and tissue-level inflammatory mediators, these simulations transcend typical cytokine networks by associating inflammatory processes with tissue/organ impacts via tissue damage/dysfunction. This framework has now allowed us to suggest how to modulate acute inflammation in a rational, individually optimized fashion. This plethora of computational and intertwined experimental/engineering approaches is the cornerstone of Translational Systems Biology approaches for inflammatory diseases.

Systems biology and inflammation

Inflammation is a complex, multiscale biological response to threats - both internal and external - to the body, which is also required for proper healing of injured tissue. In turn, damaged or dysfunctional tissue stimulates further inflammation. Despite continued advances in characterizing the cellular and molecular processes involved in the interactions between inflammation and tissue damage, there exists a significant gap between the knowledge of mechanistic pathophysiology and the development of effective therapies for various inflammatory conditions. We have suggested the concept of translational systems biology, defined as a focused application of computational modeling and engineering principles to pathophysiology primarily in order to revise clinical practice. This chapter reviews the existing, translational applications of computational simulations and related approaches as applied to inflammation.

Analyzing longitudinal microbial metabolomics data

A longitudinal experimental design in combination with metabolomics and multiway data analysis is a powerful approach in the identification of metabolites whose correlation with bioproduct formation shows a shift in time. In this paper, a strategy is presented for the analysis of longitudinal microbial metabolomics data, which was performed in order to identify metabolites that are likely inducers of phenylalanine production by Escherichia coli. The variation in phenylalanine production as a function of differences in metabolism induced by the different environmental conditions in time was described by a validated multiway statistical model. Notably, most of the metabolites showing the strongest relations with phenylalanine production seemed to hardly change in time. Apparently, potential bottlenecks in phenylalanine seem to hardly change in the course of a batch fermentation. The approach described in this study is not limited to longitudinal microbial studies but can also be applied to other (biological) studies in which similar longitudinal data need to be analyzed.

Regelung – Schlüssel zum Verständnis biologischer Systeme (Control – Key to Better Understanding Biological Systems)

Zellen verfügen über sehr leistungsfähige und hierarchisch strukturierte Regulationen, um ihren Stoffwechsel zu kontrollieren und den Umgebungsbedingungen anzupassen. Erst diese Regulationen bringen Ordnung in ein potentielles Chaos von tausenden individueller Reaktionen, die in einer Zelle ablaufen. Will man die Wirkungsweise dieser Regulationen und ihre wechselseitigen Beeinflussungen verstehen, so ist eine molekularbiologisch orientierte mathematische Modellierung zellulärer Funktionseinheiten nicht nur hilfreich sondern geboten. Dabei erweist sich ein Modellierungskonzept als sehr nützlich, das auf einer Verschaltung elementarer Modellbausteine basiert, die elementaren molekularbiologischen Zellbausteinen zugeordnet sind. Die dadurch erreichte biologische Transparenz erleichtert die interdisziplinäre Kooperation zwischen Biologie und Systemwissenschaften, der im Hinblick auf eine Aufklärung der Regulationsvorgänge eine entscheidende Bedeutung zukommt. An zwei typischen zellulären Funktionseinheiten, nämlich der Kataboliten-Repression in Escherichia coli und dem Zellzyklus in Saccharomyces cerevisiae wird die überragende Bedeutung, die der Regelung in zellulären biologischen Systemen zukommt, verdeutlicht. Dabei zeigt sich, dass die Regulationen im allgemeinen hierarchisch strukturiert sind und dadurch eine hohe Effizienz aufweisen. Es liegt nahe, aus den Erkenntnissen Anregungen für die Strukturierung von Regelungen für komplexe technische Prozesse zu ziehen.

Update of KDBI: Kinetic Data of Bio-molecular Interaction database

Knowledge of the kinetics of biomolecular interactions is important for facilitating the study of cellular processes and underlying molecular events, and is essential for quantitative study and simulation of biological systems. Kinetic Data of Bio-molecular Interaction database (KDBI) has been developed to provide information about experimentally determined kinetic data of protein-protein, protein-nucleic acid, protein-ligand, nucleic acid-ligand binding or reaction events described in the literature. To accommodate increasing demand for studying and simulating biological systems, numerous improvements and updates have been made to KDBI, including new ways to access data by pathway and molecule names, data file in System Biology Markup Language format, more efficient search engine, access to published parameter sets of simulation models of 63 pathways, and 2.3-fold increase of data (19,263 entries of 10,532 distinctive biomolecular binding and 11,954 interaction events, involving 2635 proteins/protein complexes, 847 nucleic acids, 1603 small molecules and 45 multi-step processes). KDBI is publically available at http://bidd.nus.edu.sg/group/kdbi/kdbi.asp.

Translational systems biology: introduction of an engineering approach to the pathophysiology of the burn patient

The pathophysiology of the burn patient manifests the full spectrum of the complexity of the inflammatory response. In the acute phase, inflammation may have negative effects via capillary leak, the propagation of inhalation injury, and development of multiple organ failure. Attempts to mediate these processes remain a central subject of burn care research. Conversely, inflammation is a necessary prologue and component in the later stage processes of wound healing. Despite the volume of information concerning the cellular and molecular processes involved in inflammation, there exists a significant gap between the knowledge of mechanistic pathophysiology and the development of effective clinical therapeutic regimens. Translational systems biology (TSB) is the application of dynamic mathematical modeling and certain engineering principles to biological systems to integrate mechanism with phenomenon and, importantly, to revise clinical practice. This study will review the existing applications of TSB in the areas of inflammation and wound healing, relate them to specific areas of interest to the burn community, and present an integrated framework that links TSB with traditional burn research.

PEARLS: Program for Energetic Analysis of Receptor−Ligand System

Analysis of the energetics of small molecule ligand-protein, ligand-nucleic acid, and protein-nucleic acid interactions facilitates the quantitative understanding of molecular interactions that regulate the function and conformation of proteins. It has also been extensively used for ranking potential new ligands in virtual drug screening. We developed a Web-based software, PEARLS (Program for Energetic Analysis of Ligand-Receptor Systems), for computing interaction energies of ligand-protein, ligand-nucleic acid, protein-nucleic acid, and ligand-protein-nucleic acid complexes from their 3D structures. AMBER molecular force field, Morse potential, and empirical energy functions are used to compute the van der Waals, electrostatic, hydrogen bond, metal-ligand bonding, and water-mediated hydrogen bond energies between the binding molecules. The change in the solvation free energy of molecular binding is estimated by using an empirical solvation free energy model. Contribution from ligand conformational entropy change is also estimated by a simple model. The computed free energy for a number of PDB ligand-receptor complexes were studied and compared to experimental binding affinity. A substantial degree of correlation between the computed free energy and experimental binding affinity was found, which suggests that PEARLS may be useful in facilitating energetic analysis of ligand-protein, ligand-nucleic acid, and protein-nucleic acid interactions. PEARLS can be accessed at http://ang.cz3.nus.edu.sg/cgi-bin/prog/rune.pl.

Microbial metabolomics: replacing trial-and-error by the unbiased selection and ranking of targets

Microbial production strains are currently improved using a combination of random and targeted approaches. In the case of a targeted approach, potential bottlenecks, feed-back inhibition, and side-routes are removed, and other processes of interest are targeted by overexpressing or knocking-out the gene(s) of interest. To date, the selection of these targets has been based at its best on expert knowledge, but to a large extent also on 'educated guesses' and 'gut feeling'. Therefore, time and thus money is wasted on targets that later prove to be irrelevant or only result in a very minor improvement. Moreover, in current approaches, biological processes that are not known to be involved in the formation of a specific product are overlooked and it is impossible to rank the relative importance of the different targets postulated. Metabolomics, a technology that involves the non-targeted, holistic analysis of the changes in the complete set of metabolites in the cell in response to environmental or cellular changes, in combination with multivariate data analysis (MVDA) tools like principal component discriminant analysis and partial least squares, allow the replacement of current empirical approaches by a scientific approach towards the selection and ranking of targets. In this review, we describe the technological challenges in setting up the novel metabolomics technology and the principle of MVDA algorithms in analyzing biomolecular data sets. In addition to strain improvement, the combined metabolomics and MVDA approach can also be applied to growth medium optimization, predicting the effect of quality differences of different batches of complex media on productivity, the identification of bioactives in complex mixtures, the characterization of mutant strains, the exploration of the production potential of strains, the assignment of functions to orphan genes, the identification of metabolite-dependent regulatory interactions, and many more microbiological issues.

Investigating the dynamic behavior of biochemical networks using model families

MOTIVATION

Supporting the evolutionary modeling process of dynamic biochemical networks based on sampled in vivo data requires more than just simulation. In the course of the modeling process, the modeler is typically concerned not only with a single model but also with sequences, alternatives and structural variants of models. Powerful automatic methods are then required to assist the modeler in the organization and the evaluation of alternative models. Moreover, the structure and peculiarities of the data require dedicated tool support.

SUMMARY

To support all stages of an evolutionary modeling process, a new general formalism for the combinatorial specification of large model families is introduced. It allows for automatic navigation in the space of models and excludes biologically meaningless models on the basis of elementary flux mode analysis. An incremental usage of the measured data is supported by using splined data instead of state variables. With MMT2, a versatile tool has been developed as a computational engine intended to be built into a tool chain. Using automatic code generation, automatic differentiation for sensitivity analysis and grid computing technology, a high performance computing environment is achieved. MMT2 supplies XML model specification and several software interfaces. The performance of MMT2 is illustrated by several examples from ongoing research projects.

AVAILABILITY

http://www.simtec.mb.uni-siegen.de/

CONTACT

wiechert@simtec.mb.uni-siegen.de.

Prediction of RNA-binding proteins from primary sequence by a support vector machine approach

Elucidation of the interaction of proteins with different molecules is of significance in the understanding of cellular processes. Computational methods have been developed for the prediction of protein-protein interactions. But insufficient attention has been paid to the prediction of protein-RNA interactions, which play central roles in regulating gene expression and certain RNA-mediated enzymatic processes. This work explored the use of a machine learning method, support vector machines (SVM), for the prediction of RNA-binding proteins directly from their primary sequence. Based on the knowledge of known RNA-binding and non-RNA-binding proteins, an SVM system was trained to recognize RNA-binding proteins. A total of 4011 RNA-binding and 9781 non-RNA-binding proteins was used to train and test the SVM classification system, and an independent set of 447 RNA-binding and 4881 non-RNA-binding proteins was used to evaluate the classification accuracy. Testing results using this independent evaluation set show a prediction accuracy of 94.1%, 79.3%, and 94.1% for rRNA-, mRNA-, and tRNA-binding proteins, and 98.7%, 96.5%, and 99.9% for non-rRNA-, non-mRNA-, and non-tRNA-binding proteins, respectively. The SVM classification system was further tested on a small class of snRNA-binding proteins with only 60 available sequences. The prediction accuracy is 40.0% and 99.9% for snRNA-binding and non-snRNA-binding proteins, indicating a need for a sufficient number of proteins to train SVM. The SVM classification systems trained in this work were added to our Web-based protein functional classification software SVMProt, at http://jing.cz3.nus.edu.sg/cgi-bin/svmprot.cgi. Our study suggests the potential of SVM as a useful tool for facilitating the prediction of protein-RNA interactions.

Environmental conditions and transcriptional regulation inEscherichia coli: a physiological integrative approach

Bacteria develop a number of devices for sensing, responding, and adapting to different environmental conditions. Understanding within a genomic perspective how the transcriptional machinery of bacteria is modulated, as a response for changing conditions, is a major challenge for biologists. Knowledge of which genes are turned on or turned off under specific conditions is essential for our understanding of cell behavior. In this study we describe how the information pertaining to gene expression and associated growth conditions (even with very little knowledge of the associated regulatory mechanisms) is gathered from the literature and incorporated into RegulonDB, a database on transcriptional regulation and operon organization in E. coli. The link between growth conditions, signal transduction, and transcriptional regulation is modeled in the database in a simple format that highlights biological relevant information. As far as we know, there is no other database that explicitly clarifies the effect of environmental conditions on gene transcription. We discuss how this knowledge constitutes a benchmark that will impact future research aimed at integration of regulatory responses in the cell; for instance, analysis of microarrays, predicting culture behavior in biotechnological processes, and comprehension of dynamics of regulatory networks. This integrated knowledge will contribute to the future goal of modeling the behavior of E. coli as an entire cell. The RegulonDB database can be accessed on the web at the URL: http://www.cifn.unam.mx/Computational_Biology/regulondb/.

Protein function classification via support vector machine approach

Support vector machine (SVM) is introduced as a method for the classification of proteins into functionally distinguished classes. Studies are conducted on a number of protein classes including RNA-binding proteins; protein homodimers, proteins responsible for drug absorption, proteins involved in drug distribution and excretion, and drug metabolizing enzymes. Testing accuracy for the classification of these protein classes is found to be in the range of 84-96%. This suggests the usefulness of SVM in the classification of protein functional classes and its potential application in protein function prediction.

KDBI: Kinetic Data of Bio-molecular Interactions database

Understanding of cellular processes and underlying molecular events requires knowledge about different aspects of molecular interactions, networks of molecules and pathways in addition to the sequence, structure and function of individual molecules involved. Databases of interacting molecules, pathways and related chemical reaction equations have been developed. The kinetic data for these interactions, which is important for mechanistic investigation, quantitative study and simulation of cellular processes and events, is not provided in the existing databases. We introduce a new database of Kinetic Data of Bio-molecular Interactions (KDBI) aimed at providing experimentally determined kinetic data of protein-protein, protein-RNA, protein-DNA, protein-ligand, RNA-ligand, DNA-ligand binding or reaction events described in the literature. KDBI contains information about binding or reaction event, participating molecules (name, synonyms, molecular formula, classification, SWISS-PROT AC or CAS number), binding or reaction equation, kinetic data and related references. The kinetic data is in terms of one or a combination of the following quantities as given in the literature of a particular event: association/dissociation or on/off rate constant, first/second/third/. order rate constant, equilibrium rate constant, catalytic rate constant, equilibrium association/dissociation constant, inhibition constant and binding affinity constant. Each entry can be retrieved through protein or nucleic acid or ligand name, SWISS-PROT AC number, ligand CAS number and full-text search of a binding or reaction event. KDBI currently contains 8273 entries of biomolecular binding or reaction events involving 1380 proteins, 143 nucleic acids and 1395 small molecules. Hyperlinks are provided for accessing references in Medline and available 3D structures in PDB and NDB. This database can be accessed at http://xin.cz3.nus.edu.sg/group/kdbi/kdbi.asp.

Analysis of protein homeostatic regulatory mechanisms in perturbed environments at steady state

Nine different protein homeostatic regulatory mechanisms were analysed for their ability to maintain a generic protein P within a specified range of a set-point steady-state concentration while perturbed by external processes that altered the rates at which P was produced and/or consumed. Steady state regulatory effectiveness was defined by the area within a rectangular region of "perturbation space", where axes correspond to rates of positive and negative perturbations. The size of this region differed in accordance with the regulatory elements composing the homeostatic mechanism. Such elements included basic negative feedback control of transcription (in which P, at some high concentration relative to its set-point value, binds to the gene G that encodes it, thereby inhibiting transcription), multiple sequential binding of a feedback effector (two P's bind sequentially to G), and dimerization of a feedback effector (a P(2) dimer binds to G). Two homeostatic mechanisms included a cascade structure, one with and one without translational feedback control. Another mechanism included feedback control of P degradation. Finally, two mechanisms illustrated the limits of regulatory systems. One lacked all regulatory elements (and included only an invariant rate of P synthesis and degradation) while the other assumed perfect (Boolean) regulation, in which transcription is completely inhibited at [P]>[P](sp) and is fully active at [P]<[P](sp). All of the systems evaluated are known, but the analytical expressions developed here allow quantitative comparisons between them. These expressions were evaluated at values typical of the average protein in Escherichia coli. A method for building regulatory networks by linking semi-independent regulatory modules is discussed.