Jan-Hendrik S. Hofmeyr

Regulating the cellular economy of supply and demand

Cellular metabolism is a molecular economy that is functionally organised into supply and demand blocks linked by metabolic products and cofactor cycles. Supply–demand analysis allows the behaviour, control and regulation of metabolism as a whole to be understood quantitatively in terms of the elasticities of supply and demand, which are experimentally measurable properties of the individual blocks. The kinetic and thermodynamic aspects of regulation are clearly distinguished. One important result is the demonstration that when flux is controlled by one block, the other block determines to which degree the concentration of the linking metabolite is homeostatically maintained.

The reversible Hill equation: how to incorporate cooperative enzymes into metabolic models.

MOTIVATION Realistic simulation of the kinetic properties of metabolic pathways requires rate equations to be expressed in reversible form, because substrate and product elasticities are drastically different in reversible and irreversible reactions. This presents no special problem for reactions that follow reversible Michaelis-Menten kinetics, but for enzymes showing cooperative kinetics the full reversible rate equations are extremely complicated, and anyway in virtually all cases the full equations are unknown because sufficiently complete kinetic studies have not been carried out. There is a need, therefore, for approximate reversible equations that allow convenient simulation without violating thermodynamic constraints. RESULTS We show how the irreversible Hill equation can be generalized to a reversible form, including effects of modifiers. The proposed equation leads to behaviour virtually indistinguishable from that predicted by a kinetic form of the Adair equation, despite the fact that the latter is a far more complicated equation. By contrast, a reversible form of the Monod-Wyman-Changeux equation that has sometimes been used leads to predictions for the effects of modifiers at high substrate concentration that differ qualitatively from those given by the Adair equation.

The xylose reductase/xylitol dehydrogenase/xylulokinase ratio affects product formation in recombinant xylose-utilising Saccharomyces cerevisiae

Abstract Data simulations based on a kinetic model implied that under simplified simulation conditions a 1:≥10:≥4 relation of the xylose reductase (XR)/xylitol dehydrogenase (XDH)/xylulokinase (XK) ratio was optimal in minimising xylitol formation during xylose utilisation in yeast. The steady-state level of the intermediary xylitol depended also, to a great extent, on the NADH and NAD+ concentrations. Anaerobic xylose utilisation was investigated for three different recombinant, XR-, XDH- and XK-expressing Saccharomyces cerevisiae strains, TMB 3002, TMB 3003 and TMB 3004, to verify the model predictions. Overexpression of XK was found to be necessary for ethanol formation from xylose. Furthermore, the xylitol formation decreased with decreasing XR/XDH ratio, while the ethanol formation increased. Of the three strains, TMB 3004, which was the strain with a XR/XDH/XK ratio corresponding to the theoretical optimal ratio, fermented xylose to ethanol most efficiently.

Defining and measuring autophagosome flux—concept 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.

Metabolic regulation: A control analytic perspective

A possible basis for a quantitative theory of metabolic regulation is outlined. Regulation is defined here as the alteration of reaction properties to augment or counteract the mass-action trend in a network reactions. In living systems the enzymes that catalyze these reactions are the “handles” through which such alteration is effected. It is shown how the elasticity coefficients of an enzyme-catalyzed reaction with respect to substrates and products are the sum of a massaction term and a regulatory kinetic term; these coefficients therefore distinguish between massaction effects and regulatory effects and are recognized as the key to quantifying regulation. As elasticity coefficients are also basic ingredients of metabolic control analysis, it is possible to relate regulation to such concepts as control, signalling, stability, and homeostasis. The need for care in the choice of relative or absolute changes when considering questions of metabolic regulation is stressed. Although the concepts are illustrated in terms of a simple coupled reaction system, they apply equally to more complex systems. When such systems are divided into reaction blocks, co-response coefficients can be used to measure the elasticities of these blocks.

Effects of ethanol, octanoic and decanoic acids on fermentation and the passive influx of protons through the plasma membrane of Saccharomyces cerevisiae

Ethanol, octanoic and decanoic acids are known toxic products of alcoholic fermentation and inhibit yeast functions such as growth and fermentation. pH-stat measurements showed that, in a concentration range up to 20 mg/l, octanoic and decanoic acids increase the rate of passive H+ influx across the plasma membrane of Saccharomyces cerevisiae IGC 3507. Decanoic acid was more active than octanoic acid, which agrees with its higher liposolubility. The fatty acids probably act as H+ carriers, since the magnitude of the effect depended on pH and correlated with the concentration of protonated fatty acids. Esterification of the fatty acids partially abolished the enhancing effect on passive H+ influx. Passive H+ influx showed saturation kinetics with half-maximal activity at 6.6 μM H+ (pH 5.2). Contrary to previous findings, ethanol inhibited H+ influx exponentially up to a concentration of 8% (v/v). At higher concentrations, ethanol reactivated H+ influx; the original rate of H+ uptake was reached at 14% (v/v) ethanol. In the same concentration ranges that affected passive H+ influx, ethanol, octanoic and decanoic acids inhibited the fermentation rate. This inhibitory effect of the fatty acids on fermentation rate depended on liposolubility, pH, and esterification in the same way as that found for their effect on passive H+ influx. Inhibition of fermentation by octanoic and decanoic acids could therefore result from their effect on the rate of passive H+ influx.

Complexity, Modeling, and Natural Resource Management

This paper contends that natural resource management (NRM) issues are, by their very nature, complex and that both scientists and managers in this broad field will benefit from a theoretical understanding of complex systems. It starts off by presenting the core features of a view of complexity that not only deals with the limits to our understanding, but also points toward a responsible and motivating position. Everything we do involves explicit or implicit modeling, and as we can never have comprehensive access to any complex system, we need to be aware both of what we leave out as we model and of the implications of the choice of our modeling framework. One vantage point is never sufficient, as complexity necessarily implies that multiple (independent) conceptualizations are needed to engage the system adequately. We use two South African cases as examples of complex systems—restricting the case narratives mainly to the biophysical domain associated with NRM issues— that make the point that even the behavior of the biophysical subsystems themselves are already complex. From the insights into complex systems discussed in the first part of the paper and the lessons emerging from the way these cases have been dealt with in reality, we extract five interrelated generic principles for practicing science and management in complex NRM environments. These principles are then further elucidated using four further South African case studies—organized as two contrasting pairs—and now focusing on the more difficult organizational and social side, comparing the human organizational endeavors in managing such systems.

The logic of kinetic regulation in the thioredoxin system

BackgroundThe 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.ResultsAnalysis 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.ConclusionsUsing 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.

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.

Kinetic and thermodynamic aspects of enzyme control and regulation.

This paper develops concepts for assessing and quantifying the regulation of the rate of an enzyme-catalyzed reaction. We show how generic reversible rate equations can be recast in two ways, one making the distance from equilibrium explicit, thereby allowing the distinction between kinetic and thermodynamic control of reaction rate, as well as near-equilibrium and far-from-equilibrium reactions. Recasting in the second form separates mass action from rate capacity and quantifies the degree to which intrinsic mass action contributes to reaction rate and how regulation of an enzyme-catalyzed reaction either enhances or counteracts this mass-action behavior. The contribution of enzyme binding to regulation is analyzed in detail for a number of enzyme-kinetic rate laws, including cooperative reactions.