Potency of progestogens used in hormonal therapy: toward understanding differential actions.

Progestogens are widely used in contraception and in hormone therapy. Biochemical and molecular biological evidence suggests that progestogens differ widely in their affinities and transcriptional effects via different steroid receptors, and hence cannot be considered as a single class of compounds. Consistent with these observations, recent clinical evidence suggests that, despite their similar progestogenic actions, these differences underlie different side-effect profiles for cardiovascular disease and susceptibility to infectious diseases. However, choice of progestogen for maximal benefit and minimal side-effects is hampered by insufficient comparative clinical and molecular studies to understand their relative mechanisms of action, as well as their relative potencies for different assays and clinical effects. This review evaluates the usage, meaning and significance of the terms affinity, potency and efficacy in different models systems, with a view to improved understanding of their physiological and pharmacological significance. This article is part of a Special Issue entitled 'Menopause'.

Control of specific growth rate in Saccharomyces cerevisiae.

In this contribution we resolve the long-standing dispute whether or not the Monod constant (K(S)), describing the overall affinity of an organism for its growth-limiting substrate, can be related to the affinity of the transporter for that substrate (K(M)). We show how this can be done via the control of the transporter on the specific growth rate; they are identical if the transport step has full control. The analysis leads to the counter-intuitive result that the affinity of an organism for its substrate is expected to be higher than the affinity of the enzyme that facilitates its transport. Experimentally, we show this indeed to be the case for the yeast Saccharomyces cerevisiae, for which we determined a K(M) value for glucose more than two times higher than the K(S) value in glucose-limited chemostat cultures. Moreover, we calculated that at glucose concentrations of 0.03 and 0.29 mM, the transport step controls the specific growth rate at 78 and 49 %, respectively.

Summation theorems for flux and concentration control coefficients of dynamic systems.

Metabolic control analysis (MCA) was developed to quantify how system variables are affected by parameter variations in a system. In addition, MCA can express the global properties of a system in terms of the individual catalytic steps, using connectivity and summation theorems to link the control coefficients to the elasticity coefficients. MCA was originally developed for steady-state analysis and not all summation theorems have been derived for dynamic systems. A method to determine time-dependent flux and concentration control coefficients for dynamic systems by expressing the time domain as a function of percentage progression through any arbitrary fixed interval of time is reported. Time-dependent flux and concentration control coefficients of dynamic systems, provided that they are evaluated in this novel way, obey the same summation theorems as steady-state flux and concentration control coefficients, respectively.

Conditions for effective allosteric feedforward and feedback in metabolic pathways.

Whether an allosteric feedback or feedforward modifier actually has an effect on the steady-state properties of a metabolic pathway depends not only on the allosteric modifier effect itself, but also on the control properties of the affected allosteric enzyme in the pathway of which it is part. Different modification mechanisms are analysed: mixed inhibition, allosteric inhibition and activation of the reversible Monod-Wyman-Changeux and reversible Hill models. In conclusion, it is shown that, whereas a modifier effect on substrate and product binding (specific effects) can be an effective negative feedback mechanism, it is much less effective as a positive feedforward mechanism. The prediction is that catalytic effects that change the apparent limiting velocity would be more effective in feedforward activation.

Comparing the regulatory behaviour of two cooperative, reversible enzyme mechanisms.

It is shown that both the reversible Hill equation and a generalised, reversible Monod-Wyman-Changeux equation can give analogous regulatory behaviour when embedded in a model metabolic pathway.

Experimental evidence for allosteric modifier saturation as predicted by the bi-substrate Hill equation.

The cooperative enzyme reaction rates predicted by the bi-substrate Hill equation and the bi-substrate Monod-Wyman-Changeux (MWC) equation when allosterically inhibited are compared in silico. Theoretically, the Hill equation predicts that when the maximum inhibitory effect at a certain substrate condition has been reached, an increase in allosteric inhibitor concentration will have no effect on reaction rate, that is the Hill equation shows allosteric inhibitor saturation. This saturating inhibitory effect is not present in the MWC equation. Experimental in vitro data for pyruvate kinase, a bi-substrate cooperative enzyme that is allosterically inhibited, are presented. This enzyme also shows inhibitor saturation, and therefore serves as experimental evidence that the bi-substrate Hill equation predicts more realistic allosteric inhibitor behaviour than the bi-substrate MWC equation.

Evaluation of a simplified generic bi-substrate rate equation for computational systems biology.

The evaluation of a generic simplified bi-substrate enzyme kinetic equation, whose derivation is based on the assumption of equilibrium binding of substrates and products in random order, is described. This equation is much simpler than the mechanistic (ordered and ping-pong) models, in that it contains fewer parameters (that is, no K(i) values for the substrates and products). The generic equation fits data from both the ordered and the ping-pong models well over a wide range of substrate and product concentrations. In the cases where the fit is not perfect, an improved fit can be obtained by considering the rate equation for only a single set of product concentrations. Due to its relative simplicity in comparison to the mechanistic models, this equation will be useful for modelling bi-substrate reactions in computational systems biology.

Software tools that facilitate kinetic modelling with large data sets: an example using growth modelling in sugarcane.

A solution to manage cumbersome data sets associated with large modelling projects is described. A kinetic model of sucrose accumulation in sugarcane is used to predict changes in sucrose metabolism with sugarcane internode maturity. This results in large amounts of output data to be analysed. Growth is simulated by reassigning maximal activity values, specific to each internode of the sugarcane plant, to parameter attributes of a model object. From a programming perspective, only one model definition file is required for the simulation software used; however, the amount of input data increases with each extra interrnode that is modelled, and likewise the amount of output data that is generated also increases. To store, manipulate and analyse these data, the modelling was performed from within a spreadsheet. This was made possible by the scripting language Python and the modelling software PySCeS through an embedded Python interpreter available in the Gnumeric spreadsheet program.

Is there an optimal ribosome concentration for maximal protein production?

A core model is presented for protein production in Escherichia coli to address the question whether there is an optimal ribosomal concentration for non-ribosome protein production. Analysing the steady-state solution of the model over a range of mRNA concentrations, indicates that such an optimum ribosomal content exists, and that the optimum shifts to higher ribosomal contents at higher specific growth rates.

Experimental supply-demand analysis of anaerobic yeast energy metabolism.

Experimental supply-demand analysis of yeast fermentative energy metabolism shows that control of the glycolytic flux is shared between supply and demand. In glucose limited chemostat cultures the supply block was modulated in a dilution rate change and demand block via a benzoic acid titration. Under these conditions the supply block had a flux control of 0.90 and the demand block a flux control of 0.10.

ThermoKinetic modelling. Membrane potential as a dependent variable in ion transport processes.

We show how to incorporate the membrane potential and its effects on the kinetics of ion transport processes into kinetic models.

Modelling cellular processes with Python and Scipy.

This paper shows how Python and Scipy can be used to simulate the time-dependent and steady-state behaviour of reaction networks, and introduces Pysces, a Python modelling toolkit.

How to distinguish between the vacuum cleaner and flippase mechanisms of the lmrA multi-drug transporter in Lactococcus lactis.

A numerical model of the LmrA multi-drug transport system of Lactococcus lactis is used to explore the possibility of distinguishing experimentally between two putative transport mechanisms, i.e., the vacuum-cleaner and the flippase mechanisms. This comparative model also serves as an example of numerical simulation with the scripting language Python and its scientific add-on Scipy.

Analysis of sucrose accumulation in the sugar cane culm on the basis of in vitro kinetic data.

Sucrose accumulation in developing sugar cane (Saccharum officinarum) is accompanied by a continuous synthesis and cleavage of sucrose in the storage tissues. Despite numerous studies, the factors affecting sucrose accumulation are still poorly understood, and no consistent pattern has emerged which pinpoints certain enzyme activities as important controlling steps. Here, we develop an approach based on pathway analysis and kinetic modelling to assess the biochemical control of sucrose accumulation and futile cycling in sugar cane. By using the concept of elementary flux modes, all possible routes of futile cycling of sucrose were enumerated in the metabolic system. The available kinetic data for the pathway enzymes were then collected and assembled in a kinetic model of sucrose accumulation in sugar cane culm tissue. Although no data were fitted, the model agreed well with independent experimental results: in no case was the difference between calculated and measured fluxes and concentrations greater than 2-fold. The model thus validated was then used to assess different enhancement strategies for increasing sucrose accumulation. First, the control coefficient of each enzyme in the system on futile cycling of sucrose was calculated. Secondly, the activities of those enzymes with the numerically largest control coefficients were varied over a 5-fold range to determine the effect on the degree of futile cycling, the conversion efficiency from hexoses into sucrose, and the net sucrose accumulation rate. In view of the modelling results, overexpression of the fructose or glucose transporter or the vacuolar sucrose import protein, as well as reduction of cytosolic neutral invertase levels, appear to be the most promising targets for genetic manipulation. This offers a more directed improvement strategy than cumbersome gene-by-gene manipulation. The kinetic model can be viewed and interrogated on the World Wide Web at http://jjj.biochem.sun.ac.za.

Understanding glucose transport by the bacterial phosphoenolpyruvate:glycose phosphotransferase system on the basis of kinetic measurements in vitro.

The kinetic parameters in vitro of the components of the phosphoenolpyruvate:glycose phosphotransferase system (PTS) in enteric bacteria were collected. To address the issue of whether the behavior in vivo of the PTS can be understood in terms of these enzyme kinetics, a detailed kinetic model was constructed. Each overall phosphotransfer reaction was separated into two elementary reactions, the first entailing association of the phosphoryl donor and acceptor into a complex and the second entailing dissociation of the complex into dephosphorylated donor and phosphorylated acceptor. Literature data on the K(m) values and association constants of PTS proteins for their substrates, as well as equilibrium and rate constants for the overall phosphotransfer reactions, were related to the rate constants of the elementary steps in a set of equations; the rate constants could be calculated by solving these equations simultaneously. No kinetic parameters were fitted. As calculated by the model, the kinetic parameter values in vitro could describe experimental results in vivo when varying each of the PTS protein concentrations individually while keeping the other protein concentrations constant. Using the same kinetic constants, but adjusting the protein concentrations in the model to those present in cell-free extracts, the model could reproduce experiments in vitro analyzing the dependence of the flux on the total PTS protein concentration. For modeling conditions in vivo it was crucial that the PTS protein concentrations be implemented at their high in vivo values. The model suggests a new interpretation of results hitherto not understood; in vivo, the major fraction of the PTS proteins may exist as complexes with other PTS proteins or boundary metabolites, whereas in vitro, the fraction of complexed proteins is much smaller.

Subtleties in control by metabolic channelling and enzyme organization.

Because of its importance to cell function, the free-energy metabolism of the living cell is subtly and homeostatically controlled. Metabolic control analysis enables a quantitative determination of what controls the relevant fluxes. However, the original metabolic control analysis was developed for idealized metabolic systems, which were assumed to lack enzyme-enzyme association and direct metabolite transfer between enzymes (channelling). We here review the recently developed molecular control analysis, which makes it possible to study non-ideal (channelled, organized) systems quantitatively in terms of what controls the fluxes, concentrations, and transit times. We show that in real, non-ideal pathways, the central control laws, such as the summation theorem for flux control, are richer than in ideal systems: the sum of the control of the enzymes participating in a non-ideal pathway may well exceed one (the number expected in the ideal pathways), but may also drop to values below one. Precise expressions indicate how total control is determined by non-ideal phenomena such as ternary complex formation (two enzymes, one metabolite), and enzyme sequestration. The bacterial phosphotransferase system (PTS), which catalyses the uptake and concomitant phosphorylation of glucose (and also regulates catabolite repression) is analyzed as an experimental example of a non-ideal pathway. Here, the phosphoryl group is channelled between enzymes, which could increase the sum of the enzyme control coefficients to two, whereas the formation of ternary complexes could decrease the sum of the enzyme control coefficients to below one. Experimental studies have recently confirmed this identification, as well as theoretically predicted values for the total control. Macromolecular crowding was shown to be a major candidate for the factor that modulates the non-ideal behaviour of the PTS pathway and the sum of the enzyme control coefficients.

Implications of macromolecular crowding for signal transduction and metabolite channeling.

The effect of different total enzyme concentrations on the flux through the bacterial phosphoenolpyruvate:carbohydrate phosphotransferase system (PTS) in vitro was determined by measuring PTS-mediated carbohydrate phosphorylation at different dilutions of cell-free extract of Escherichia coli. The dependence of the flux on the protein concentration was more than linear but less than quadratic. The combined flux-response coefficient of the four enzymes constituting the glucose PTS decreased slightly from values of approximately 1.8 with increasing protein concentrations in the assay. Addition of the macromolecular crowding agents polyethylene glycol (PEG) 6000 and PEG 35000 led to a sharper decrease in the combined flux-response coefficient, in one case to values of approximately 1. PEG 6000 stimulated the PTS flux at lower protein concentrations and inhibited the flux at higher protein concentrations, with the transition depending on the PEG 6000 concentration. This suggests that macromolecular crowding decreases the dissociation rate constants of enzyme complexes. High concentrations of the microsolute glycerol did not affect the combined flux-response coefficient. The data could be explained with a kinetic model of macromolecular crowding in a two-enzyme group-transfer pathway. Our results suggest that, because of the crowded environment in the cell, the different PTS enzymes form complexes that live long on the time-scale of their turnover. The implications for the metabolic behavior and control properties of the PTS, and for the effect of macromolecular crowding on nonequilibrium processes, are discussed.

Limits to inducer exclusion: inhibition of the bacterial phosphotransferase system by glycerol kinase.

The uptake of methyl alpha-D-glucopyranoside by the phosphoenolpyruvate-dependent phosphotransferase system of Salmonella typhimurium could be inhibited by prior incubation of the cells with glycerol. Inhibition was only observed for glycerol preincubation times longer than 45 s and required the preinduction of both the glucose and the glycerol-catabolizing systems. Larger extents of inhibition by glycerol correlated with higher intracellular levels of glycerol kinase when the glp regulon had been induced to different extents. Preincubation with lactate did not inhibit methyl alpha-D-glucopyranoside uptake significantly, although both lactate and glycerol were oxidized by the cells. The cellular free-energy state of the cells (intracellular [ATP]/[ADP] ratio) was virtually identical for lactate and glycerol preincubation, suggesting that the inhibition of phosphotransferase-mediated uptake was not a metabolic effect. In vitro, phosphotransferase activity was inhibited to a maximal extent of 32% upon titrating cell-free extracts with high concentrations of commercial glycerol kinase. The results show that uptake systems that have hitherto been regarded merely as targets of the phosphotransferase system component IIA(Glc) also have the capacity themselves to retroinhibit the phosphotransferase system flux, presumably by sequestration of the available IIA(Glc), provided that these systems are induced to appropriate levels.

How to recognize monofunctional units in a metabolic system.

In intracellular metabolic networks, it is often useful to discern subsystems (modules) of which the metabolites are only produced or consumed by reactions within that subsystem or by a limited number of fluxes crossing the borders of the subsystem. In many cases such subsystems function as units with respect to their effect on the remainder of the system. In this paper we show that the co-response of two metabolic variables outside that subsystem to a perturbation of a subsystem reaction does not depend on which subsystem reaction is perturbed if three conditions are fulfilled: (1) the reactions outside the subsystem are not affected directly by metabolites belonging to the subsystem; (2) there are no conservation relations linking the subsystem to the rest; and (3) the subsystem is linked to the remainder of the system only via one degree of freedom in fluxes. We propose the name "monofunctional units" for subsystems fulfilling these three criteria. Identification of such units greatly simplifies metabolic control analysis. Only one reaction per unit needs to be perturbed to analyse control in the system. Difficulties, such as the inaccessibility of some reactions to experimental perturbation, may be circumvented by perturbing another reaction within the unit that leads to the same co-response coefficients. The analysis can also serve to identify unsuspected regulatory interactions in the metabolic network. The differences in the behaviour between metabolic units and other types of subsystems are illustrated by numerical examples.

Changes in the cellular energy state affect the activity of the bacterial phosphotransferase system.

The effect of different cellular free-energy states on the uptake of methyl alpha-D-glucopyranoside, an analogue of glucose, by the Escherichia coli phosphoenolpyruvate:carbohydrate phosphotransferase system was investigated. The intracellular [ATP]/[ADP] ratio was varied by changing the expression of the atp operon, which codes for the H+-ATPase, or by adding an uncoupler of oxidative phosphorylation or an inhibitor of respiration. Corresponding initial phosphotransferase uptake rates were determined using an improved uptake assay that works with growing cells in steady state. The results show that the initial uptake rate was decreased under conditions of lowered intracellular [ATP]/[ADP] ratios, irrespective of which method was used to change the cellular energy state. When either the expression of the atp operon was changed or 2,4-dinitrophenol was added to wild-type cells, the relationship between initial phosphotransferase uptake rate and the logarithm of the [ATP]/[ADP] ratio was approximately linear. These results suggest that the cellular free-energy state, as reflected in the intracellular [ATPI]/[ADP] ratio, plays an important role in regulating the activity of the phosphotransferase system.