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Balanced complexes in biochemical networks are at core of several theoretical and computational approaches that make statements about the properties of the steady states supported by the network. Recent computational approaches have employed balanced complexes to reduce metabolic networks, while ensuring preservation of particular steady-state properties; however, the underlying factors leading to the formation of balanced complexes have not been studied, yet. Here, we present a number of factorizations providing insights in mechanisms that lead to the origins of the corresponding balanced complexes. The proposed factorizations enable us to categorize balanced complexes into four distinct classes, each with specific origins and characteristics. They also provide the means to efficiently determine if a balanced complex in large-scale networks belongs to a particular class from the categorization. The results are obtained under very general conditions and irrespective of the network kinetics, rendering them broadly applicable across variety of network models. Application of the categorization shows that all classes of balanced complexes are present in large-scale metabolic models across all kingdoms of life, therefore paving the way to study their relevance with respect to different properties of steady states supported by these networks.HighlightsBalanced complexes are ubiquitous in real-world networks, and facilitate insights in steady state flux phenotypes in large-scale metabolic networks.Novel factorizations are proposed that explain the formation of balanced complexes and enable their categorization.The results also provide a computationally-efficient tool for the identification of balanced complexes in large-scale networks.Examination of metabolic network models across all kingdoms of life shows that all categories naturally arise in this type of networks.

Bradyrhizobium diazoefficiens is a rhizobium able to convert atmospheric nitrogen into ammonium by establishing mutualistic symbiosis with soybean. It has been recognized as an important parent strain for microbial agents and is widely applied in agricultural and environmental fields. In order to study the metabolic properties of symbiotic nitrogen fixation and the differences between a free-living cell and a symbiotic bacteroid, a genome-scale metabolic network of B. diazoefficiens USDA110 was constructed and analyzed. The metabolic network, iYY1101, contains 1031 reactions, 661 metabolites, and 1101 genes in total. Metabolic models reflecting free-living and symbiotic states were determined by defining the corresponding objective functions and substrate input sets, and were further constrained by high-throughput transcriptomic and proteomic data. Constraint-based flux analysis was used to compare the metabolic capacities and the effects on the metabolic targets of genes and reactions between the two physiological states. The results showed that a free-living rhizobium possesses a steady state flux distribution for sustaining a complex supply of biomass precursors while a symbiotic bacteroid maintains a relatively condensed one adapted to nitrogen-fixation. Our metabolic models may serve as a promising platform for better understanding the symbiotic nitrogen fixation of this species.

We study steady-state flux of particles diffusing on a flat surface and trapped by absorbing spikes of arbitrary length periodically protruding from a reflecting base. It is assumed that the particle concentration, far from this comblike boundary, is kept constant. To find the flux, we use a boundary regularization approach that replaces the initial highly rough and heterogeneous boundary by an effective boundary which is smooth and uniform. After such a replacement, the two-dimensional diffusion problem becomes essentially one-dimensional, and the steady-state flux can be readily found. Our main results are simple analytical expressions determining the position of the smooth effective boundary and its uniform trapping rate as functions of the spike length and interspike distance. It is shown that the steady-state flux to the effective boundary is identical to its counterpart to the initial boundary at large distances from this boundary. Our analytical results are corroborated by Brownian dynamics simulations.

Microbial cells need to adapt to changing environmental conditions to survive. There is an evolutionary advantage to grow fast; this requires high metabolic rates, and an efficient allocation of enzymatic resources. Here we study a general control theory called qORAC, developed previously, which allows cells to adaptively control their enzyme allocations to achieve maximal steady state flux. The control is robust to perturbations in the environment, but those perturbations themselves do not feature in the control. In this paper we focus on the archetypical pathway, the linear chain with reversible Michaelis-Menten kinetics, together with qORAC control. First we assume that the metabolic pathway is in quasi-steady state with respect to enzyme synthesis. Then we show that the map between steady state metabolite and enzyme concentrations is a smooth bijection. Using this information, we finally show that the unique (and hence flux-maximising) steady state of this system is locally stable. We provide further evidence that it may in fact be globally stable.

Flux analysis is performed to infer intracellular metabolic activity using measured rates. By applying the highly curated human metabolic reconstruction Recon 2 as the reference model, the investigation of cancer cell metabolic fluxes can encompass the full metabolic potential of a human cell. But in its full form, Recon 2 is unsuitable for conventional metabolic flux analysis due to a large number of redundant elements. Here, we describe a procedure to reduce Recon 2 to an appropriate scale for cancer cell flux analysis such that calculated flux intervals are still informative, without compromising the opportunity to explore alternative pathways encoded in Recon 2 that may reveal novel metabolic features.

Temperature affects all enzymes simultaneously in a metabolic system. The enzyme concentration in a biochemical system can be considered as invariant under fast and small temperature change. Therefore, the total sensitivity of a steady state flux through a pathway with respect to the temperature can be expressed as: the apparent activation energy of a steady state pathway flux equals the sum of weighted activation energies of the individual reactions contributing to the flux, where the weighting factors are the flux control coefficients of these reactions in the context of the network. Correspondingly, since the elasticity of any enzyme with respect to temperature is always nonzero, only the reactions with a nonzero flux control coefficient contribute accordingly to the temperature sensitivity of the pathway.

An effective time constant for first-order processes is defined to capture the dynamics of systems represented by partial differential equations. In this chapter, the methodology is applied to passive and electrically assisted drug controlled transdermal delivery devices in two case studies. The analysis, which is carried out using Laplace-transformed variables, results in a first-order approximation and does not require time-domain solutions. Numerical experiments are included to illustrate the effectiveness of the index under different conditions and to estimate the time it takes to establish a steady-state flux across the membrane.

Transdermal delivery of high molecular weight compound is a great challenge due to the barrier function of the skin's outer stratum corneum (SC) layer. The aim of the present work was to characterize in vitro transdermal delivery of cyclosporine A through rat skin and the drug transdermal enhancing effect of PP electret applied individually and in combination with chemical enhancer. The permeated cumulative amount and steady state flux of the cyclosporine A were determined in following situations: (a) under application of PP electret, (b) after application of ethyl oleate, (c) combination PP electret and ethyl oleate. All the techniques could enhance cyclosporine A transdermal delivery. The combination of PP electret and ethyl oleate proved to be the most effective technique.

This study utilizes mortar specimens, to design 3 different a/c ratios of 2.25, 2.75, and 3.25. The aggregate volume ratios (Vf) are 46 %, 52 %, and 57 %, respectively, while the w/c ratio is 0.5, and undergoing a 9, 12, and 15 A/m2 constant current density Accelerated Lithium Migration Technique after curing for 3 months. Results show that, on specimens applied with the same current density, the time of Li+ to pass through the specimen, and steady state flux and migration coefficient all exhibit a positive linear correlation with Vf. At the same time, the non-steady state migration coefficient for Li+ have a negative linear correlation with Vf.

A generalized theory has been proposed for a crossflow membrane filtration process, comprising of intermediate pore blocking followed by cake formation, in sequence. A phase space plot has been generated to identify the three filtration domains namely, pore blocking dominant, comparable resistances and cake dominating process. It is found that the crossflow velocity (in terms of steady state flux) has significant effect on the onset of the cake formation. It is observed that the intermediate pore blocking has very narrow region of dominance, so most experimental data are likely to lie in the cake controlling region. The operator can effectively control the characteristics of filtration by changing the crossflow velocity and transmembrane pressure.

This paper presents an extension of stoichiometric analysis in systems where the catalytic compounds (enzymes) are also intermediates of the metabolic network (dual property), so they are produced and degraded by the reaction network itself. To take this property into account, we introduce the definition of enzyme-maintaining mode, a set of reactions that produces its own catalyst and can operate at stationary state. Moreover, an enzyme-maintaining mode is defined as elementary with respect to a given reaction if the removal of any of the remaining reactions causes the cessation of any steady state flux through this reference reaction. These concepts are applied to determine the network structure of a simple self-maintaining system.

Mathematical modeling of skin transport is considered a valuable alternative of in-vitro and in-vivo investigations especially considering ethical and economical questions. Mechanistic diffusion models describe skin transport by solving Fick's 2nd law of diffusion in time and space; however models relying entirely on a consistent experimental data set are missing. For a two-dimensional model membrane consisting of a biphasic stratum corneum (SC) and a homogeneous epidermal/dermal compartment (DSL) methods are presented to determine all relevant input parameters. The data were generated for flufenamic acid (M(W) 281.24g/mol; logK(Oct/H2O) 4.8; pK(a) 3.9) and caffeine (M(W) 194.2g/mol; logK(Oct/H2O) -0.083; pK(a) 1.39) using female abdominal skin. K(lip/don) (lipid-donor partition coefficient) was determined in equilibration experiments with human SC lipids. K(cor/lip) (corneocyte-lipid) and K(DSL/lip) (DSL-lipid) were derived from easily available experimental data, i.e. K(SC/don) (SC-donor), K(lip/don) and K(SC/DSL) (SC-DSL) considering realistic volume fractions of the lipid and corneocyte phases. Lipid and DSL diffusion coefficients D(lip) and D(DSL) were calculated based on steady state flux. The corneocyte diffusion coefficient D(cor) is not accessible experimentally and needs to be estimated by simulation. Based on these results time-dependent stratum corneum concentration-depth profiles were simulated and compared to experimental profiles in an accompanying study.

The purpose of this work was to study the effect of various permeation enhancers on the permeation of salbutamol sulphate (SS) buccal patches through buccal mucosa in order to improve the bioavailability by avoiding the first pass metabolism in the liver and possibly in the gut wall and also achieve a better therapeutic effect. The influence of various permeation enhancers, such as dimethyl sulfoxide (DMSO), linoleic acid (LA), isopropyl myristate (IPM) and oleic acid (OA) on the buccal absorption of SS from buccal patches containing different polymeric combinations such as hydroxypropyl methyl cellulose (HPMC), carbopol, polyvinyl alcohol (PVA), polyvinyl pyrollidone (PVP), sodium carboxymethyl cellulose (NaCMC), acid and water soluble chitosan (CHAS and CHWS) and Eudragit-L100 (EU-L100) was investigated. OA was the most efficient permeation enhancer increasing the flux greater than 8-fold compared with patches without permeation enhancer in HPMC based buccal patches when PEG-400 was used as the plasticizer. LA also exhibited a better permeation enhancing effect of over 4-fold in PVA and HPMC based buccal patches. In PVA based patches, both OA and LA were almost equally effective in improving the SS permeation irrespective of the plasticizer used. DMSO was more effective as a permeation enhancer in HPMC based patches when PG was the plasticizer. IPM showed maximum permeation enhancement of greater than 2-fold when PG was the plasticizer in HPMC based buccal patches.

The objective of this study was to develop a family of compartmental models to describe in a strictly quantitative manner the transdermal iontophoretic transport of drugs in vitro.Two structurally different compartmental models describing the in vitro transport during iontophoresis and one compartmental model describing the in vitro transport in post-iontophoretic period are proposed. These models are based on the mass transfer from the donor compartment to the acceptor compartment via the skin as an intermediate compartment. In these models, transdermal iontophoretic transport is characterized by 5 parameters: 1) kinetic lag time (tL), 2) steady-state flux during iontophoresis (Jss), 3) skin release rate constant (K(R)), 4) the first-order rate constant of the iontophoretic driving force from the skin to the acceptor compartment (I1), and 5) passive flux in the post-iontophoretic period (Jpas). The developed models were applied to data on the iontophoretic transport in human stratum corneum in vitro of R-apomorphine after pretreatment with phosphate buffered saline pH 7.4 (PBS) and after pretreatment with surfactant (SFC), as well as the iontophoretic transport of 0.5 mg ml(-1) rotigotine at pH 5 (RTG).All of the proposed models could be fitted to the transport data of PBS, SFC, and RTG groups both during the iontophoresis and in the post-iontophoretic period. The incorporation of parameter I1 failed to improve the fitting performance of the model. This might indicate a negligible contribution of iontophoretic driving force to the mass transfer in the direction from the skin to the acceptor compartment, although it plays an important role in loading the skin with the drug. The estimated values of Jss of PBS, SFC, and RTG were identical (p0.05) to the values obtained with the diffusion lag time method. Moreover, time required to achieve steady-state flux can be estimated based on the parameter tL and the reciprocal value of parameter K(R). In addition, accumulation of drug molecules in the skin is reflected in a reduction of the value of the K(R) parameter.The developed in vitro models demonstrated their strength and consistency to describe the drug transport during and post-iontophoresis.

Carvedilol is a nonselective beta-adrenergic blocking agent and is employed for the treatment of hypertension. Carvedilol is subjected to considerable first-pass metabolism when it is administered orally. Transdermal preparation of carvedilol was prepared to achieve a sustained effect and to reduce the dose size & dosing frequency as compared to multiple oral dosing and also developed to minimize first pass metabolism. Various polymers such as Ethyl cellulose, PVP K-30, HPMC K15M and Carbopol 934 were selected on the basis of their adhering property and nature of non toxicity, to develop transdermal film of carvedilol. The patches fabricated by EC and Carbopol (F-5 and F-6) were showed very good folding endurance compared to patches containing PVP K-30 and HPMC K15M. Based on physicochemical and in-vitro permeation studies, F-3 and F-5 were chosen as the best formulations. Among these two patches, F-5 film was found to have maximum in vitro permeation, maximum steady state flux and maximum permeability coefficient of drug. Key words: Transdermal patch, Carvedilol, ethylcellulose, PVP K-30, HPMC K15M and Carbopol 934

A representative stoichiometric model is essential to perform metabolic flux analysis (MFA) using experimentally measured consumption (or production) rates as constraints. For Human Embryonic Kidney (HEK) cell culture, there is the opportunity to use an extremely well-curated and annotated human genome-scale model Recon 2 for MFA. Performing MFA using Recon 2 without any modification would have implied that cells have access to all functionality encoded by the genome, which is not realistic. The majority of intracellular fluxes are poorly determined as only extracellular exchange rates are measured. This is compounded by the fact that there is no suitable metabolic objective function to suppress non-specific fluxes. We devised a heuristic to systematically reduce Recon 2 to emphasize flux through core metabolic reactions. This implies that cells would engage these dominant metabolic pathways to grow, and any significant changes in gross metabolic phenotypes would have invoked changes in these pathways. The reduced metabolic model becomes a functionalized version of Recon 2 used for identifying significant metabolic changes in cells by flux analysis.

A quantitative structure-permeability relationship was developed using Artificial Neural Network (ANN) modeling to study penetration across a polydimethylsiloxane membrane. A set of 254 compounds and their experimentally derived maximum steady state flux values used in this study was gathered from the literature. A total of 42 molecular descriptors were calculated for each compound. A genetic algorithm was used to select important molecular descriptors and supervised ANN was used to correlate selected descriptors with the experimentally derived maximum steady-state flux through the polydimethylsiloxane membrane (log J). Calculated molecular descriptors were used as the ANN's inputs and log J as the output. Developed model indicates that molecular shape and size, inter-molecular interactions, hydrogen-bonding capacity of drugs, and conformational stability could be used to predict drug absorption through skin. A 12-descriptor nonlinear computational neural network model has been developed for the estimation of log J values for a data set of 254 drugs. Described model does not require experimental parameters and could potentially provide useful prediction of membrane penetration of new drugs and reduce the need for actual compound synthesis and flux measurements.

The aims of the study were three-fold: to assess the skin uptake of the industrial catalyst dimethylethylamine (DMEA) (a) in vitro from water solutions by fresh guinea-pig and human skin specimens, (b) in gaseous form in vivo in human volunteers, and (c) to estimate the relevance of the uptake as an occupational hazard.Specimens from the in vitro and in vivo experiments were analysed by gas chromatography using a nitrogen-sensitive detector.DMEA, diluted with water or isotonic saline solution was applied to fresh human or guinea-pig skin, mounted in Teflon flow-through cells with a perfusion fluid flow rate of 1.5 ml/h, samples being collected at 2-h intervals for 48 h. Three healthy male volunteers each had their right forearm exposed (in a Plexiglass chamber) for 4 h to DMEA at each of three different levels (250, 500 and 1000 mg/m3 air). Urine was collected up to 24 h after the start of each experiment.DMEA penetrated both guinea-pig and human skin. The median steady-state flux and permeability coefficient (Kp) values, were 0.009 mg/cm2 x h and 0.001 cm/h, respectively, for guinea-pig skin, and 0.017 mg/cm2 x h and 0.003 cm/h, respectively, for human skin. The median uptake in the three volunteers at the different DMEA exposure levels (250, 500 or 1000 mg/m3) was 44, 64 and 88 micrograms, respectively. The median Kp for all experiments was 0.037 cm/h.Uptake of DMEA through the skin is of far less importance than simultaneous uptake via the airways. Thus, the amount of DMEA excreted in urine is a variable of limited use for the purposes of biological monitoring. Although a wide range of Kp values was obtained in the in vitro experiments, both for guinea-pig and human skin, there was no marked difference in median Kp values between the two types of skin. The Kp values were lower than those obtained for human forearm skin in vivo. However, future studies of other tertiary aliphatic amines may show the in vitro method to yield values predictive of those obtained in in vivo studies.

A method to determine elasticities of individual enzymes within a metabolic pathway is developed. The method is based on measurements of steady-state metabolite pools and flux rates rather than the usual kinetic in vitro measurements on isolated enzymes. In this respect, it is an extension of the "double modulation method" by Kacser & Burns (1979, Biochem. Soc. Trans. 7, 1149-1160). The approach requires the use of effectors to modulate specifically the activities of individual enzymes. The number of specific effectors necessary to determine all elasticities depends upon the number of metabolites influencing the enzyme reaction rates. Two sets of implicit equations for the enzyme elasticities are derived. These equations hold for any pathway of any complexity but are, because of their complexity, studied in detail only for the simple case of a metabolic chain. For this case, enzyme elasticities can be calculated from measured metabolite concentrations and flux rates provided that certain conditions are met for the relative positions within the pathway of the modulated enzymes. For a metabolic chain in which the rate law of each enzyme is affected only by the reaction substrate(s) and product(s), the existence of two effectors specific for different enzymes allows determination of the kinetic laws of all enzymes positioned between the two target enzymes.

Purpose: To assess iontophoretic transdermal delivery of glibenclamide across pigskin for its transdermal development. Methods: In vitro iontophoretic transdermal delivery of glibenclamide across the pigskin was investigated at three different drug concentrations in the donor cell of the diffusion apparatus, using cathodal iontophoresis (current density 0.5 mA cm-2) along with the passive controls. Results: For passive permeation, the steady state flux significantly increased with the donor drug concentration. At all concentration levels, iontophoresis considerably increased the permeation rate compared to passive controls. Flux enhancement was highest at the lowest drug load and lowest at the highest drug load. The highest flux value obtained was 0.0603 μmol cm-2 h-1 and the target flux for glibenclamide was 0.3933 μmol h-1. Required permeation rate was achieved by iontophoresis using a much smaller application area. Conclusion: Permeation rate of drugs across the pigskin can be considerably enhanced by the use of Iontophoresis. Keywords: Glibenclamide; Iontophoresis; Pigskin; Transdermal drug delivery.

The present paper provides a model based on dimensional analysis that gives the basis for design of the cross-flow microfiltration processes. This gives the permeate flux f in terms of the pressure drop across the filtration membrane ΔP and the velocity V of cross-flow of the feed fluid in the membrane tubes. The model is compared with an extensive series of experimental results with magnesium hydroxide slurries. The model has certain similarities with previous ones and can be used for unit optimization.

The present invention relates to A medical device for the pulsatile administration of a drug through intact skin at a first steady state flux during a first delivery period and a second steady state flux during a second delivery period, said first flux being substantially higher than said second flux; said first and second delivery periods comprising a substantial portion of a predetermined administration period, characterised in that said device comprises:… a) a reservoir of said drug containing an amount of drug sufficient to adminster drug at said first and second steady state fluxes throughout said administration period;… b) a reservoir of a skin permeation enhancer for said drug; said reservoir containing an amount of said permeation enhancer sufficient to permit administration of said drug at said first flux only through said first delivery period; and… c) means for maintaining said device on the skin in drug and permeation enhancer transferring relationship thereto.

Flux coupling analysis is a method to identify blocked and coupled reactions in a metabolic network at steady state. We present a new approach to flux coupling analysis, which uses a minimum set of generators of the steady state flux cone. Our method does not require to reconfigure the network by splitting reversible reactions into forward and backward reactions. By distinguishing different types of reactions (irreversible, pseudo-irreversible, fully reversible), we show that reaction coupling relationships can only hold between certain reaction types. Based on this mathematical analysis, we propose a new algorithm for flux coupling analysis.

The availability of human tissue for experimental purposes is often problematical and use is thus made of animal tissue as models of the human tissue. In this study, porcine vaginal mucosa was used as an in vitro permeability model for human vaginal mucosa using tritium-labelled permeants (17beta-estradiol, r-arecoline, vasopressin, oxytocin and water). Fresh porcine and human vaginal tissues were frozen in liquid nitrogen and stored at -85 degrees C. In vitro permeability studies were performed using a flow-through diffusion apparatus (24 h, 20 degrees C, 1.5 ml/h). The mean steady state flux values for water, r-arecoline and vasopressin were approximately 4, 12 and 5% lower, while those for 17beta-estradiol and oxytocin were approximately 17 and 53% higher, through porcine vaginal mucosa as compared to human vaginal mucosa, respectively. Using a F-test (comparing whole curves), statistically significant differences in the diffusion of 17beta-estradiol, r-arecoline and oxytocin were indicated when comparing human and porcine vaginal mucosa. Generally, porcine vaginal mucosa seems a good in vitro permeability model for human vaginal mucosa. However, permeability of these two mucosa towards all permeants tested does not always correspond closely. These differences must always be considered when using porcine tissue as an in vitro permeability model for human vaginal mucosa.

The objective of this study was to assess the in vitro the iontophoretic delivery of Timolol across human dermatomed skin in order to determine whether therapeutic doses of this drug can be delivered. Anodal iontophoresis of Timolol was performed by manipulating the donor vehicle and the current density. It was observed that by reducing simultaneously the competitive ions (NaCl) from 8 to 4 g/l and the pH from 7.4 to 4.7, the iontophoretic flux was significantly increased by a factor of 1.5 (669+/-81 microg/cm h). In order to simulate the situation in a transdermal patch, the iontophoretic delivery of Timolol was also studied after adding an artificial porous membrane placed between the Timolol formulation and the human dermatomed skin. No significant difference was observed in the steady state flux across the skin when an artificial membrane was added. Furthermore, a linear relationship was found between current density and steady state flux. These results indicate that the iontophoretic delivery of Timolol can be accurately controlled by the applied current. Assuming a one to one in vitro/in vivo correlation the Timolol transport in vitro results in therapeutic plasma concentrations in humans with very low current densities limiting possible skin irritation.

The lag times and steady-state flux predicted by a specific case of the compartment model, which was recently proposed to generate finite-dose percutaneous permeation pharmacokinetics, are compared with those predicted by the diffusion model. When the intercompartmental transfer rate constants are defined so that the three statistical moments of the compartmental model (the mean residence times of a drug in the vehicle and that in the skin and the variance of residence time in the vehicle) are identical to those in the diffusion model, the lag times and steady-state flux values predicted by the two models are the same.

Potential health hazards of new Army weapon systems are of concern to health and safety professionals, the general public, and weapon system developers. One concern is the potential for dermal absorption from materials and chemicals. High explosives, such as CBR-12, which is intended for sue in the 60mm M720El and M768 mortar shells, may be modified so that they will be less likely to explode from the unplanned stimuli. The purpose of this effort was to estimate the impact of such a modification on dermal absorption. We investigated the penetration of powdered explosives through dermatomed rat skin in static diffusion cells for up to six hours. We compared "Composition B" with a replacement explosive, CBR.12. We detected penetration of very small amounts of one of the components of each explosive. Steady state flux of trinitrotoluene from "Composition B" was 1.14 ug/cm2/hr and steady state flux of dinitroanisole from CBR-12 was 0.74 ug/cm2/hr. These rates of penetration are not expected to be hazardous.

Control analysis has been applied experimentally to many pathways (Fell, 1992). However, the effort required to measure the elasticity, control and response coefficients makes a full empirical analysis unrealistic in all but rather simple systems. Consequently, most investigations have considered single enzymes or pathways, ignoring interactions with other cellular pathways. The most experimentally accessible way to measure regulation in complex systems like whole cells is to group reactions together into much larger blocks. The control and regulation of a simplified network of blocks that includes all the reactions in the cell can then be analysed. This is known as the top-down (Brand, 1996) or modular (Schuster et al., 1993) approach to control analysis. Top-down approaches have been used either to analyse the reactions in whole cells or organs around a single intermediate (Brand, 1996; Soboll et al., 1998) or to analyse a limited number of reactions around several intermediates (Groen et al., 1982; Kashiwaya et al., 1994). There has been no analysis of the grouped reactions of a whole cell with multiple intermediates. Such an analysis is necessary if we are to quantify and understand the importance of interactions between different major pathways in the cell, because it is only when we include all of the reactions that the full complexity appears. A great strength of control analysis is that it provides the methodology and language to describe this complexity meaningfully.