Elusive control

The concept of a single rate-limiting step was proven to be too simplistic for understanding control and regulation of metabolism. Consequently, searches have identified relatively few steps with high control. Here we review a number of such searches and indicate what mechanisms may be responsible for this elusiveness of control. It turns out that this elusiveness of control has itself led to increased understanding of the roles played in metabolic control and regulation of such diverse factors as distributiveness of control, condition dependence, enzyme elasticity, homeostasis, control hierarchies, the input into a pathway, coenzyme sequestration, and redundancy and diversity of control function.     

Metabolic control analysis of plant metabolism

Metabolic control analysis and its major coefficients are introduced. The importance of measuring both elasticity and concentration-control coefficients as well as flux-control coefficients is stressed. The conditions that need to be met before control analysis can be applied experimentally are emphasized. It is argued that successful application of this approach requires methods for the measurement of flux, maximum catalytic activities of enzymes and substrate contents. The measurement of flux by consumption of substrate, production of product, and the distribution of isotope after metabolism of labelled substrates is discussed. The need to ensure that measurements of enzymes and substrates are reliable and authenticated is stressed. Particular emphasis is placed on the ease with which such measurements can be invalidated in plant tissues, and ways for countering these difficulties are discussed.     

Application of fuzzy-logic models for metabolic control analysis

A priori information or valuable qualitative knowledge can be incorporated explicitly to describe enzyme kinetics making use of fuzzy-logic models. Although restricted to linear relationships, it is shown that fuzzy-logic augmented models are not only able to capture non-linear features of enzyme kinetics but also allow the proper mathematical treatment of metabolic control analysis. The explicit incorporation of valuable qualitative knowledge is crucial, particularly when handling data estimated from in vivo kinetics studies, since this experimental information is scarce and usually contains measurement errors. Therefore, data-driven techniques, such as the one presented in this work, form a serious alternative to established kinetics approaches.     

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.I dedicate this paper to Henrik Kacser, co-founder of and guiding light in the field of metabolic control analysis. His recent death leaves us bereft of a fount of wisdom and kindness, but his work remains as a monument along the path of our search for an understanding of metabolic behavior.     

Analysis of protein synthesis dynamic model in eukaryotic cells: Input control

This paper presents the analysis of initiation control model of protein synthesis via eukaryotic initiation factor (eIF)-2 unit, introduced by [N.S. Bar, D.R. Morris, Dynamic model of the process of protein synthesis in eukaryoric cells, Bulletin of Mathematical Biology 69 (2007) 361-393, doi:10.1007/s11538-006-9128-2.] and propose methods to control it.Linearization of the model is presented as a measure to simplify the analysis and control application. The properties of the linear model were investigated and compared to the non-linear model using simulations. It was shown that the linear model is (marginally) stable and the states converge to a finite value. Linear optimal control theory can then be applied to the model under the value range where the linearized model is accurate. The effect of the input signals GCN2·tRNA and eIF-2 on the non-linear system was investigated. A few characteristics known from in vitro experiments of the initiation process were proven from a mathematical aspect and some conclusions about the function of the initiation complexes such as eIF2B and the ternary complex were derived. Consistent with published experiments, it was shown that overexpression of eIF-2 increases the concentration of 48S initiation complex and promote initiation rate. A state feedback control was applied in order to manipulate the initiation rate and it was proven that the 48S initiation complex can be driven to a desired value by calculating an input control law using measurement techniques available today. If this strategy can be implemented de facto, then a genuine control on protein synthesis process can be obtained.     

Metabolic flux control analysis of branch points: an improved approach to obtain flux control coefficients from large perturbation data

An overview of published approaches for the metabolic flux control analysis of branch points revealed that often not all fundamental constraints on the flux control coefficients have been taken into account. This has led to contradictory statements in literature on the minimum number of large perturbation experiments required to estimate the complete set of flux control coefficients C(J) for a metabolic branch point. An improved calculation procedure, based on approximate Lin-log reaction kinetics, is proposed, providing explicit analytical solutions of steady state fluxes and metabolite concentrations as a function of large changes in enzyme levels. The obtained solutions allow direct calculation of elasticity ratios from experimental data and subsequently all C(J)-values from the unique relation between elasticity ratio's and flux control coefficients. This procedure ensures that the obtained C(J)-values satisfy all fundamental constraints. From these it follows that for a three enzyme branch point only one characterised or two uncharacterised large flux perturbations are sufficient to obtain all C(J)- values. The improved calculation procedure is illustrated with four experimental cases.     

Metabolic control analysis of an enzymatic biofuel cell

Metabolic control analysis (MCA) is an analytical technique that aims to quantify the distribution of control that enzymes exhibit over the steady‐state fluxes through a metabolic network. In an enzymatic biofuel cell, the flux of interest is the electrical current generated by the system. Regardless of transport limitations and other constraints, kinetic limitations can become potential bottlenecks in the operation of a biofuel cell. We have used an indirect approach to MCA to investigate a common osmium‐mediated glucose oxidase/laccase enzymatic biofuel cell. The results of the analysis show that the control of the electron flux strongly depends on the total mediator concentrations and the extent of polarization of the individual electrodes. The effect of varying oxygen concentrations is also examined, as oxygen is required for the cathode, but it participates in a non‐productive reaction at the anode. Under normal operating conditions the electrodes will be highly polarized and will both contain high mediator concentrations. This configuration will result in a dominant FCC at the anode, and the conditions that are needed for balanced flux control between the anode and cathode are explored. As increasingly complex bioelectrocatalytic systems and architectures are envisioned, MCA will be a valuable framework to facilitate their design and subsequent operation. Biotechnol. Bioeng. 2009;102: 1624–1635. © 2008 Wiley Periodicals, Inc.     

Analysis of tumour-immune evasion with chemo-immuno therapeutic treatment with quadratic optimal control

A simple mathematical model for the growth of tumour with discrete time delay in the immune system is considered. The dynamical behaviour of our system by analysing the existence and stability of our system at various equilibria is discussed elaborately. We set up an optimal control problem relative to the model so as to minimize the number of tumour cells and the chemo-immunotherapeutic drug administration. Sensitivity analysis of tumour model reveals that parameter value has a major impact on the model dynamics. We numerically illustrate how does these delay can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumour. Finally, epidemiological implications of our analytical findings are addressed critically.     

Kinetic properties required for sustained or paradoxical control of metabolic fluxes under large changes in enzyme activities

The effect that an increase in the activity of an enzyme has on its flux normally decreases with activity increase. To achieve a large increase in flux by manipulating a single step would therefore require a high initial effect that maintains or increases when the activity is increased, what has been called sustained or paradoxical control. Using metabolic control analysis for large responses, we derive conditions for sustained or paradoxical control in terms of elasticity coefficients. These are used to characterise types of rate laws contributing to this behaviour. The result that simple pathways, with normal kinetics, subject to large activity changes can lead to paradoxical control behaviour suggests that this type of pattern may be much more ubiquitous than could have, in principle, been suspected.     

Transition time control analysis of a glycolytic system under different glucose concentrations. Control of transition time versus control of flux

Control and Response Coefficients of transition time have been determined in a rat liver glycolytic system under different glucose concentrations. Results have been compared with the Flux Control and Flux Response Coefficients measured in the same conditions, showing that transition time and flux are different responses of the system, subject to different regulation and control. Control Coefficients of flux and transition time show a very different profile in each condition of glucose concentration assayed. Ratio of Flux Control coefficients of glucokinase over phosphofructokinase at 5 and 20 mM glucose concentration changes from 3.2 to 0.5, while the same ratio in the case of Transition Time Control Coefficients moves from 0.6 to 0.93. Moreover, the absolute values of Transition Time Control Coefficients in glycolytic conditions are one order of magnitude bigger than in gluconeogenic conditions. Values of Response Coefficients also show that the transition time has a bigger sensitivity to changes in glucose concentration than the flux in all conditions assayed, but particularly in glycolytic ones.     

Experimental determination of flux control distribution in biochemical systems: in vitro model to analyze transient metabolite concentrations

Determination of the control coefficients allows the identification of rate-controlling steps in a reaction system. However, the measurement of the flux control coefficients in a biochemical system is not a trivial task, except for some special cases. We have developed a theoretical basis for the direct determination of these coefficients from dynamic responses. In order to show the validity of this methodology experimentally, the dynamic approach is applied to an in vitro reconstituted partial glycolytic pathway to determine the flux control coefficients of hexokinase and phosphofructokinase. It is shown that the dynamic approach gives consistent results, which agree well with values obtained by the direct enzyme titration method. The detailed procedure and potential applications to other systems, such as immobilized enzyme or cell reactors, are discussed. (c) 1993 Wiley & Sons, Inc.     

A mathematical modelling framework for elucidating the role of feedback control in translation termination

Translation is the final stage of gene expression where messenger RNA is used as a template for protein polymerization from appropriate amino acids. Release of the completed protein requires a release factor protein acting at the termination/stop codon to liberate it. In this paper we focus on a complex feedback control mechanism involved in the translation and synthesis of release factor proteins, which has been observed in different systems. These release factor proteins are involved in the termination stage of their own translation. Further, mutations in the release factor gene can result in a premature stop codon. In this case translation can result either in early termination and the production of a truncated protein or readthrough of the premature stop codon and production of the complete release factor protein. Thus during translation of the release factor mRNA containing a premature stop codon, the full length protein negatively regulates its production by its action on a premature stop codon, while positively regulating its production by its action on the regular stop codon. This paper develops a mathematical modelling framework to investigate this complex feedback control system involved in translation. A series of models is established to carefully investigate the role of individual mechanisms and how they work together. The steady state and dynamic behaviour of the resulting models are examined both analytically and numerically.     

Quality control of inkjet technology for DNA microarray fabrication

A robust manufacturing process is essential to make high-quality DNA microarrays, especially for use in diagnostic tests. We investigated different failure modes of the inkjet printing process used to manufacture low-density microarrays. A single nozzle inkjet spotter was provided with two optical imaging systems, monitoring in real time the flight path of every droplet. If a droplet emission failure is detected, the printing process is automatically stopped. We analyzed over 1.3 million droplets. This information was used to investigate the performance of the inkjet system and to obtain detailed insight into the frequency and causes of jetting failures. Of all the substrates investigated, 96.2% were produced without any system or jetting failures. In 1.6% of the substrates, droplet emission failed and was correctly identified. Appropriate measures could then be taken to get the process back on track. In 2.2%, the imaging systems failed while droplet emission occurred correctly. In 0.1% of the substrates, droplet emission failure that was not timely detected occurred. Thus, the overall yield of the microarray manufacturing process was 99.9%, which is highly acceptable for prototyping.     

Sensitivity analysis of stoichiometric networks: an extension of metabolic control analysis to non-steady state trajectories

A sensitivity analysis of general stoichiometric networks is considered. The results are presented as a generalization of Metabolic Control Analysis, which has been concerned primarily with system sensitivities at steady state. An expression for time-varying sensitivity coefficients is given and the Summation and Connectivity Theorems are generalized. The results are compared to previous treatments. The analysis is accompanied by a discussion of the computation of the sensitivity coefficients and an application to a model of phototransduction.     

An optimal control problem for ovine brucellosis with culling

A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnseba et al. [A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2–11. Available at http://www.math.u-bordeaux1.fr/～pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost.     

Arthropod prey of shelterbelt-associated birds: linking faecal samples with biological control of agricultural pests

Abstract  The value of insectivorous birds as agents for biological control of arthropod pests has been little studied, especially in Australia. This paper reports on the extent to which arthropods from various pest and non-pest taxa feature in the diets of birds captured in farm shelterbelts in central western New South Wales. The parameters examined were the types of arthropod fragments in bird faeces and percentage volume and frequency of occurrence of each component. The faecal data were compared with samples of the arthropod fauna trapped in shelterbelts during the period the birds were captured. In 26 of 29 faecal samples, arthropod fragments were the predominant components, the most common being from Coleoptera, Hymenoptera (especially Formicidae), Orthoptera and Araneae. The recognisable pest taxa in faecal samples were Scarabaeidae and wingless grasshopper Phaulacridium vittatum (Sjöstedt) (Orthoptera: Acrididae). The results indicate that the native bird species common in farm shelterbelts preyed on a range of arthropod taxa including several that are pests of crops and pastures. Accordingly, conservation of birds in farmlands could contribute to suppression of arthropod pests.     

Robust identification of metabolic control for microbial l-methionine production following an easy-to-use puristic approach

The identification of promising metabolic engineering targets is a key issue in metabolic control analysis (MCA). Conventional approaches make intensive use of model-based studies, such as exploiting post-pulse metabolic dynamics after proper perturbation of the microbial system. Here, we present an easy-to-use, purely data-driven approach, defining pool efflux capacities (PEC) for identifying reactions that exert the highest flux control in linear pathways. Comparisons with linlog-based MCA and data-driven substrate elasticities (DDSE) showed that similar key control steps were identified using PEC. Using the example of l-methionine production with recombinant Escherichia coli, PEC consistently and robustly identified main flux controls using perturbation data after a non-labeled ¹²C-l-serine stimulus. Furthermore, the application of full-labeled ¹³C-l-serine stimuli yielded additional insights into stimulus propagation to l-methionine. PEC analysis performed on the ¹³C data set revealed the same targets as the ¹²C data set. Notably, the typical drawback of metabolome analysis, namely, the omnipresent leakage of metabolites, was excluded using the ¹³C PEC approach.