A biochemically-realisable relational model of the self-manufacturing cell.

As shown by Hofmeyr, the processes in the living cell can be divided into three classes of efficient causes that produce each other, so making the cell closed to efficient causation, the hallmark of an organism. They are the enzyme catalysts of covalent metabolic chemistry, the intracellular milieu that drives the supramolecular processes of chaperone-assisted folding and self-assembly of polypeptides and nucleic acids into functional catalysts and transporters, and the membrane transporters that maintain the intracellular milieu, in particular its electrolyte composition. Each class of efficient cause can be modelled as a relational diagram in the form of a mapping in graph-theoretic form, and a minimal model of a self-manufacturing system that is closed to efficient causation can be constructed from these three mappings using the formalism of relational biology. This fabrication-assembly or (F,A)-system serves as an alternative to Robert Rosen's replicative metabolism-repair or (M,R)-system, which has been notoriously problematic to realise in terms of real biochemical processes. A key feature of the model is the explicit incorporation of formal cause, which arrests the infinite regress that plagues all relational models of the cell. The (F,A)-system is extended into a detailed relational model of the self-manufacturing cell that has a clear biochemical realisation. This (F,A) cell model allows the interpretation and visualisation of concepts such as the metabolism and repair components of Rosen's (M,R)-system, John von Neumann's universal constructor, Howard Pattee's symbol-function split via the symbol-folding transformation, Marcello Barbieri's genotype-ribotype-phenotype ontology, and Tibor Gánti's chemoton.

Kinetic modelling of compartmentalised reaction networks.

This paper presents a comprehensive treatment of kinetic modelling of compartmentalised reaction networks in the context of systems biology. There is still a lot of confusion about how to go about constructing compartment models, and many published models are flawed with respect to how they handle compartmentation. The modelling framework described here answers two key questions: Which rate laws should be used to describe the rates of reactions in compartmentalised systems? How should these rate laws be incorporated in the ordinary differential equations (ODEs) that describe the dynamics of the compartmentalised system? The framework rests on the fundamental definition of reaction rate as the number of reaction events per time, which is related to the time derivative of mole amount of reactant or product, an extensive property that is directly proportional to the size of the compartment in which the reaction events occur. This means that the rates of reactions that occur in a 3-dimensional compartment are proportional to the volume of the compartment, while the rates of transfers over a 2-dimensional compartment boundary or interface between compartments are proportional to the area of the boundary. Transfer rates are often incorrectly scaled with a volume instead of an area, and the reasons why this is wrong are extensively discussed. I also show how 'textbook' rate equations, which I term canonical rate equations, should be modified for compartmental modelling and how they should be incorporated into either amount-change or concentration-change ODEs.

Supply and Demand Analysis of Autophagy.

Autophagy is an intracellular protein degradation pathway that plays a vital role in cellular homeostasis. It maintains cellular function through proteostasis and the removal of unused and harmful proteins and organelles. Moreover, it also serves as an adaptive response to metabolic perturbations. Deviation in autophagy activity has been linked to the progression of several pathologies, including neurodegenerative diseases. Preclinical trials have shown that modulating autophagy holds great promise in treating neurodegenerative diseases by clearing toxic protein aggregates. The success of autophagy modulating therapies requires extensive knowledge of the molecular machinery and, importantly, an in-depth understanding of the underlying systems properties of the autophagy system. A computational approach provides a powerful platform to interrogate and analyze the regulation, control, and behavior of reaction networks. However, the complexity of interactions involved in the autophagy pathway makes it challenging to isolate and characterize individual components. By reducing the autophagy process to a supply-demand system in which autophagosome synthesis (supply) and autophagosome degradation (demand) are linked by the autophagosomes, it is possible to determine the control of the supply and demand over the steady-state autophagosome flux and autophagosome concentration. In this chapter, we describe a methodology to perform supply and demand analysis of the autophagy system, the experimental procedure to measure the autophagy variables, and the use of the supply-demand framework to determine the distribution of flux and concentration control.

On the relevance of precision autophagy flux control in vivo - Points of departure for clinical translation.

Macroautophagy (which we will call autophagy hereafter) is a critical intracellular bulk degradation system that is active at basal rates in eukaryotic cells. This process is embedded in the homeostasis of nutrient availability and cellular metabolic demands, degrading primarily long-lived proteins and specific organelles.. Autophagy is perturbed in many pathologies, and its manipulation to enhance or inhibit this pathway therapeutically has received considerable attention. Although better probes are being developed for a more precise readout of autophagic activity in vitro and increasingly in vivo, many questions remain. These center in particular around the accurate measurement of autophagic flux and its translation from the in vitro to the in vivo environment as well as its clinical application. In this review, we highlight key aspects that appear to contribute to stumbling blocks on the road toward clinical translation and discuss points of departure for reaching some of the desired goals. We discuss techniques that are well aligned with achieving desirable spatiotemporal resolution to gather data on autophagic flux in a multi-scale fashion, to better apply the existing tools that are based on single-cell analysis and to use them in the living organism. We assess how current techniques may be used for the establishment of autophagic flux standards or reference points and consider strategies for a conceptual approach on titrating autophagy inducers based on their effect on autophagic flux . Finally, we discuss potential solutions for inherent controls for autophagy analysis, so as to better discern systemic and tissue-specific autophagic flux in future clinical applications.Abbreviations: GFP: Green fluorescent protein; J: Flux; MAP1LC3/LC3: Microtubule-associated protein 1 light chain 3; nA: Number of autophagosomes; TEM: Transmission electron microscopy; τ: Transition time.

Delving deeper: Relating the behaviour of a metabolic system to the properties of its components using symbolic metabolic control analysis.

High-level behaviour of metabolic systems results from the properties of, and interactions between, numerous molecular components. Reaching a complete understanding of metabolic behaviour based on the system's components is therefore a difficult task. This problem can be tackled by constructing and subsequently analysing kinetic models of metabolic pathways since such models aim to capture all the relevant properties of the system components and their interactions. Symbolic control analysis is a framework for analysing pathway models in order to reach a mechanistic understanding of their behaviour. By providing algebraic expressions for the sensitivities of system properties, such as metabolic flux or steady-state concentrations, in terms of the properties of individual reactions it allows one to trace the high level behaviour back to these low level components. Here we apply this method to a model of pyruvate branch metabolism in Lactococcus lactis in order to explain a previously observed negative flux response towards an increase in substrate concentration. With this method we are able to show, first, that the sensitivity of flux towards changes in reaction rates (represented by flux control coefficients) is determined by the individual metabolic branches of the pathway, and second, how the sensitivities of individual reaction rates towards their substrates (represented by elasticity coefficients) contribute to this flux control. We also quantify the contributions of enzyme binding and mass-action to enzyme elasticity separately, which allows for an even finer-grained understanding of flux control. These analytical tools allow us to analyse the control properties of a metabolic model and to arrive at a mechanistic understanding of the quantitative contributions of each of the enzymes to this control. Our analysis provides an example of the descriptive power of the general principles of symbolic control analysis.

The Precision Control of Autophagic Flux and Vesicle Dynamics-A Micropattern Approach.

Autophagy failure is implicated in age-related human disease. A decrease in the rate of protein degradation through the entire autophagy pathway, i.e., autophagic flux, has been associated with the onset of cellular proteotoxity and cell death. Although the precision control of autophagy as a pharmacological intervention has received major attention, mammalian model systems that enable a dissection of the relationship between autophagic flux and pathway intermediate pool sizes remain largely underexplored. Here, we make use of a micropattern-based fluorescence life cell imaging approach, allowing a high degree of experimental control and cellular geometry constraints. By assessing two autophagy modulators in a system that achieves a similarly raised autophagic flux, we measure their impact on the pathway intermediate pool size, autophagosome velocity, and motion. Our results reveal a differential effect of autophagic flux enhancement on pathway intermediate pool sizes, velocities, and directionality of autophagosome motion, suggesting distinct control over autophagy function. These findings may be of importance for better understanding the fine-tuning autophagic activity and protein degradation proficiency in different cell and tissue types of age-associated pathologies.

Measuring autophagosome flux.

Macroautophagy/autophagy is a proteolytic pathway that is involved in both bulk degradation of cytoplasmic proteins as well as in selective degradation of cytoplasmic organelles. Autophagic flux is often defined as a measure of autophagic degradation activity, and many techniques exist to assess autophagic flux. Although these techniques have generated invaluable information about the autophagic system, the quest continues for developing methods that not only enhance sensitivity and provide a means of quantification, but also accurately reflect the dynamic character of the pathway. Based on the theoretical framework of metabolic control analysis, where the autophagosome flux is the quantitative description of the rate a flow along a pathway, here we treat the autophagy system as a multi-step pathway. We describe a single-cell fluorescence live-cell imaging-based approach that allows the autophagosome flux to be accurately measured. This method characterizes autophagy in terms of its complete autophagosome and autolysosome pool size, the autophagosome flux, J, and the transition time, τ, for autophagosomes and autolysosomes at steady state. This approach provides a sensitive quantitative method to measure autophagosome flux, pool sizes and transition time in cells and tissues of clinical relevance. ABBREVIATIONS: ATG5/APG5, autophagy-related 5; GFP, green fluorescent protein; LAMP1, lysosomal-associated membrane protein 1; MAP1LC3/LC3, microtubule-associated protein 1 light chain 3; J, flux; MEF, mouse embryonic fibroblast; MTOR, mechanistic target of rapamycin kinase; nA, number of autophagosomes; nAL, number of autolysosomes; nL, number of lysosomes; p-MTOR, phosphorylated mechanistic target of rapamycin kinase; RFP, red fluorescent protein; siRNA, small interfering RNA; τ, transition time; TEM, transmission electron microscopy.

PySCeSToolbox: a collection of metabolic pathway analysis tools.

Summary: PySCeSToolbox is an extension to the Python Simulator for Cellular Systems (PySCeS) that includes tools for performing generalized supply-demand analysis, symbolic metabolic control analysis, and a framework for investigating the kinetic and thermodynamic aspects of enzyme-catalyzed reactions. Each tool addresses a different aspect of metabolic behaviour, control, and regulation; the tools complement each other and can be used in conjunction to better understand higher level system behaviour. Availability and implementation: PySCeSToolbox is available on Linux, Mac OS X and Windows. It is licensed under the BSD 3-clause licence. Code, setup instructions and a link to documentation can be found at https://github.com/PySCeS/PyscesToolbox. Contact: jr@sun.ac.za. Supplementary information: Supplementary data are available at Bioinformatics online.

Causation, constructors and codes.

Relational biology relies heavily on the enriched understanding of causal entailment that Robert Rosen's formalisation of Aristotle's four causes has made possible, although to date efficient causes and the rehabilitation of final cause have been its main focus. Formal cause has been paid rather scant attention, but, as this paper demonstrates, is crucial to our understanding of many types of processes, not necessarily biological. The graph-theoretic relational diagram of a mapping has played a key role in relational biology, and the first part of the paper is devoted to developing an explicit representation of formal cause in the diagram and how it acts in combination with efficient cause to form a mapping. I then use these representations to show how Von Neumann's universal constructor can be cast into a relational diagram in a way that avoids the logical paradox that Rosen detected in his own representation of the constructor in terms of sets and mappings. One aspect that was absent from both Von Neumann's and Rosen's treatments was the necessity of a code to translate the description (the formal cause) of the automaton to be constructed into the construction process itself. A formal definition of codes in general, and organic codes in particular, allows the relational diagram to be extended so as to capture this translation of formal cause into process. The extended relational diagram is used to exemplify causal entailment in a diverse range of processes, such as enzyme action, construction of automata, communication through the Morse code, and ribosomal polypeptide synthesis through the genetic code.

Tracing regulatory routes in metabolism using generalised supply-demand analysis.

BACKGROUND: Generalised supply-demand analysis is a conceptual framework that views metabolism as a molecular economy. Metabolic pathways are partitioned into so-called supply and demand blocks that produce and consume a particular intermediate metabolite. By studying the response of these reaction blocks to perturbations in the concentration of the linking metabolite, different regulatory routes of interaction between the metabolite and its supply and demand blocks can be identified and their contribution quantified. These responses are mediated not only through direct substrate/product interactions, but also through allosteric effects. Here we subject previously published kinetic models of pyruvate metabolism in Lactococcus lactis and aspartate-derived amino acid synthesis in Arabidopsis thaliana to generalised supply-demand analysis. RESULTS: Multiple routes of regulation are brought about by different mechanisms in each model, leading to behavioural and regulatory patterns that are generally difficult to predict from simple inspection of the reaction networks depicting the models. In the pyruvate model the moiety-conserved cycles of ATP/ADP and NADH/NAD(+) allow otherwise independent metabolic branches to communicate. This causes the flux of one ATP-producing reaction block to increase in response to an increasing ATP/ADP ratio, while an NADH-consuming block flux decreases in response to an increasing NADH/NAD(+) ratio for certain ratio value ranges. In the aspartate model, aspartate semialdehyde can inhibit its supply block directly or by increasing the concentration of two amino acids (Lys and Thr) that occur as intermediates in demand blocks and act as allosteric inhibitors of isoenzymes in the supply block. These different routes of interaction from aspartate semialdehyde are each seen to contribute differently to the regulation of the aspartate semialdehyde supply block. CONCLUSIONS: Indirect routes of regulation between a metabolic intermediate and a reaction block that either produces or consumes this intermediate can play a much larger regulatory role than routes mediated through direct interactions. These indirect routes of regulation can also result in counter-intuitive metabolic behaviour. Performing generalised supply-demand analysis on two previously published models demonstrated the utility of this method as an entry point in the analysis of metabolic behaviour and the potential for obtaining novel results from previously analysed models by using new approaches.

Defining and measuring autophagosome flux­concept and reality.

The autophagic system is involved in both bulk degradation of primarily long-lived cytoplasmic proteins as well as in selective degradation of cytoplasmic organelles. Autophagic flux is often defined as a measure of autophagic degradation activity, and a number of methods are currently utilized to assess autophagic flux. However, despite major advances in measuring various molecular aspects of the autophagic machinery, we remain less able to express autophagic flux in a highly sensitive, robust, and well-quantifiable manner. Here, we describe a conceptual framework for defining and measuring autophagosome flux at the single-cell level. The concept discussed here is based on the theoretical framework of metabolic control analysis, which distinguishes between the pathway along which there is a flow of material and the quantitative measure of this flow. By treating the autophagic system as a multistep pathway with each step characterized by a particular rate, we are able to provide a single-cell fluorescence live-cell imaging-based approach that describes the accurate assessment of the complete autophagosome pool size, the autophagosome flux, and the transition time required to turn over the intracellular autophagosome pool. In doing so, this perspective provides clarity on whether the system is at steady state or in a transient state moving towards a new steady state. It is hoped that this theoretical account of quantitatively measuring autophagosome flux may contribute towards a new direction in the field of autophagy, a standardized approach that allows the establishment of systematic flux databases of clinically relevant cell and tissue types that serve as important model systems for human pathologies.

Incorporating covalent and allosteric effects into rate equations: the case of muscle glycogen synthase.

Several enzymes have been described that undergo both allosteric and covalent regulation, but, to date, there exists no succinct kinetic description that is able to account for both of these mechanisms of regulation. Muscle glycogen synthase, an enzyme implicated in the pathogenesis of several metabolic diseases, is activated by glucose 6-phosphate and inhibited by ATP and phosphorylation at multiple sites. A kinetic description of glycogen synthase could provide insight into the relative importance of these modifiers. In the present study we show, using non-linear parameter optimization with robust weight estimation, that a Monod-Wyman-Changeux model in which phosphorylation favours the inactive T conformation provides a satisfactory description of muscle glycogen synthase kinetics. The best-fit model suggests that glucose 6-phosphate and ATP compete for the same allosteric site, but that ATP also competes with the substrate UDP-glucose for the active site. The novelty of our approach lies in treating covalent modification as equivalent to allosteric modification. Using the obtained rate equation, the relationship between enzyme activity and phosphorylation state is explored and shown to agree with experimental results. The methodology we propose could also be applied to other enzymes that undergo both allosteric and covalent modification.

A generic rate equation for catalysed, template-directed polymerisation.

Biosynthetic networks link to growth and reproduction processes through template-directed synthesis of macromolecules such as polynucleotides and polypeptides. No rate equation exists that captures this link in a way that it can effectively be incorporated into a single computational model of the overall process. This paper describes the derivation of such a generic steady-state rate equation for catalysed, template-directed polymerisation reactions with varying monomer stoichiometry and varying chain length. The derivation is based on a classical Michaelis-Menten mechanism with template binding and an arbitrary number of chain elongation steps that produce a polymer composed of an arbitrary number of monomer types. The rate equation only requires the identity of the first dimer in the polymer sequence; for the remainder only the monomer composition needs be known. Further simplification of a term in the denominator yielded an equation requiring no positional information at all, only the monomer composition of the polymer; this equation still gave an excellent estimate of the reaction rate provided that either the monomer concentrations are at least half-saturating, or the polymer is very long.

Regulation of glycogen synthase from mammalian skeletal muscle--a unifying view of allosteric and covalent regulation.

It is widely accepted that insufficient insulin-stimulated activation of muscle glycogen synthesis is one of the major components of non-insulin-dependent (type 2) diabetes mellitus. Glycogen synthase, a key enzyme in muscle glycogen synthesis, is extensively regulated, both allosterically (by glucose-6-phosphate, ATP, and others) and covalently (by phosphorylation). Although glycogen synthase has been a topic of intense study for more than 50 years, its kinetic characterization has been confounded by its large number of phosphorylation states. Questions remain regarding the function of glycogen synthase regulation and the relative importance of allosteric and covalent modification in fulfilling this function. In this review, we consider both earlier kinetic studies and more recent site-directed mutagenesis and crystal structure studies in a detailed qualitative discussion of the effects of regulation on the kinetics of glycogen synthase. We propose that both allosteric and covalent modification of glycogen synthase may be described by a Monod-Wyman-Changeux model in terms of apparent changes to L, the equilibrium constant for transition between the T and R conformers. As, with the exception of L, all parameters of this model are independent of the glycogen synthase phosphorylation state, the need to determine kinetic parameters for all possible states is eliminated; only the relationship between a particular state and L must be established. We conclude by suggesting that renewed efforts to characterize the relationship between phosphorylation and the kinetics of glycogen synthase are essential in order to obtain a better quantitative understanding of the function of glycogen synthesis regulation. The model we propose may prove useful in this regard.

Supply-demand analysis a framework for exploring the regulatory design of metabolism.

The living cell can be thought of as a collection of linked chemical factories, a molecular economy in which the principles of supply and demand obtain. Supply-demand analysis is a framework for exploring and gaining an understanding of metabolic regulation, both theoretically and experimentally, where regulatory performance is measured in terms of flux control and homeostatic maintenance of metabolite concentrations. It is based on a metabolic control analysis of a supply-demand system in steady state in which the degree of flux and concentration control by the supply and demand blocks is related to their local properties, which are quantified as the elasticities of supply and demand. These elasticities can be visualized as the slopes of the log-log rate characteristics of supply and demand. Rate characteristics not only provide insight about system behavior around the steady state but can also be expanded to provide a view of the behavior of the system over a wide range of concentrations of the metabolic intermediate that links the supply and the demand. The theoretical and experimental results of supply-demand analysis paint a picture of the regulatory design of metabolic systems that differs radically from what can be called the classical view of metabolic regulation, which generally explains the role of regulatory mechanisms only in terms of the supply, completely ignoring the demand. Supply-demand analysis has recently been generalized into a computational tool that can be used to study the regulatory behavior of kinetic models of metabolic systems up to genome-scale.

The logic of kinetic regulation in the thioredoxin system.

BACKGROUND: The thioredoxin system consisting of NADP(H), thioredoxin reductase and thioredoxin provides reducing equivalents to a large and diverse array of cellular processes. Despite a great deal of information on the kinetics of individual thioredoxin-dependent reactions, the kinetic regulation of this system as an integrated whole is not known. We address this by using kinetic modeling to identify and describe kinetic behavioral motifs found within the system. RESULTS: Analysis of a realistic computational model of the Escherichia coli thioredoxin system revealed several modes of kinetic regulation in the system. In keeping with published findings, the model showed that thioredoxin-dependent reactions were adaptable (i.e. changes to the thioredoxin system affected the kinetic profiles of these reactions). Further and in contrast to other systems-level descriptions, analysis of the model showed that apparently unrelated thioredoxin oxidation reactions can affect each other via their combined effects on the thioredoxin redox cycle. However, the scale of these effects depended on the kinetics of the individual thioredoxin oxidation reactions with some reactions more sensitive to changes in the thioredoxin cycle and others, such as the Tpx-dependent reduction of hydrogen peroxide, less sensitive to these changes. The coupling of the thioredoxin and Tpx redox cycles also allowed for ultrasensitive changes in the thioredoxin concentration in response to changes in the thioredoxin reductase concentration. We were able to describe the kinetic mechanisms underlying these behaviors precisely with analytical solutions and core models. CONCLUSIONS: Using kinetic modeling we have revealed the logic that underlies the functional organization and kinetic behavior of the thioredoxin system. The thioredoxin redox cycle and associated reactions allows for a system that is adaptable, interconnected and able to display differential sensitivities to changes in this redox cycle. This work provides a theoretical, systems-biological basis for an experimental analysis of the thioredoxin system and its associated reactions.