Control analysis applied to the whole body: control by body organs over plasma concentrations and organ fluxes of substances in the blood

Metabolism in the age of ‘omes’

Much research in comparative physiology is now performed using ‘omics’ tools and many results are interpreted in terms of the effects of changes in gene expression on energy metabolism. However, ‘metabolism’ is a complex phenomenon that spans multiple levels of biological organization. In addition rates and directions of flux change dynamically under various physiological circumstances. Within cells, message level cannot be equated with protein level because multiple mechanisms are at play in the ‘regulatory hierarchy’ from gene to mRNA to enzyme protein. This results in many documented instances wherein change in mRNA levels and change in enzyme levels are unrelated. It is also known from metabolic control analysis that the influence of single steps in pathways on flux is often small. Flux is a system property and its control tends to be distributed among multiple steps. Consequently, change in enzyme levels cannot be equated with change in flux. Approaches developed by Hans Westerhoff and colleagues, called ‘hierarchical regulation analysis’, allow quantitative determination of the extent to which ‘hierarchical regulation’, involving change in enzyme level, and ‘metabolic regulation’, involving the modulation of the activity of preexisting enzyme, regulate flux. We outline these approaches and provide examples to show their applicability to problems of interest to comparative physiologists.

The principle of sufficiency and the evolution of control: using control analysis to understand the design principles of biological systems

Control analysis can be used to try to understand why (quantitatively) systems are the way that they are, from rate constants within proteins to the relative amount of different tissues in organisms. Many biological parameters appear to be optimized to maximize rates under the constraint of minimizing space utilization. For any biological process with multiple steps that compete for control in series, evolution by natural selection will tend to even out the control exerted by each step. This is for two reasons: (i) shared control maximizes the flux for minimum protein concentration, and (ii) the selection pressure on any step is proportional to its control, and selection will, by increasing the rate of a step (relative to other steps), decrease its control over a pathway. The control coefficient of a parameter P over fitness can be defined as (∂N/N)/(∂P/P), where N is the number of individuals in the population, and ∂N is the change in that number as a result of the change in P. This control coefficient is equal to the selection pressure on P. I argue that biological systems optimized by natural selection will conform to a principle of sufficiency, such that the control coefficient of all parameters over fitness is 0. Thus in an optimized system small changes in parameters will have a negligible effect on fitness. This principle naturally leads to (and is supported by) the dominance of wild-type alleles over null mutants.

Control over the contribution of the mitochondrial membrane potential (DeltaPsi) and proton gradient (DeltapH) to the protonmotive force (Deltap). In silico studies

The protonmotive force across the inner mitochondrial membrane (Deltap) has two components: membrane potential (DeltaPsi) and the gradient of proton concentration (DeltapH). The computer model of oxidative phosphorylation developed previously by Korzeniewski et al. (Korzeniewski, B., Noma, A., and Matsuoka, S. (2005) Biophys. Chem. 116, 145-157) was modified by including the K+ uniport, K+/H+ exchange across the inner mitochondrial membrane, and membrane capacitance to replace the fixed DeltaPsi/DeltapH ratio used previously with a variable one determined mechanistically. The extended model gave good agreement with experimental results. Computer simulations showed that the contribution of DeltaPsi and DeltapH to Deltap is determined by the ratio of the rate constants of the K+ uniport and K+/H+ exchange and not by the absolute values of these constants. The value of Deltap is mostly controlled by ATP usage. The metabolic control over the DeltaPsi/DeltapH ratio is exerted mostly by K+ uniport and K+/H+ exchange in the presence of these processes, and by the ATP usage, ATP/ADP carrier, and phosphate carrier in the absence of them. The K+ circulation across the inner mitochondrial membrane is controlled mainly by K+ uniport and K+/H+ exchange, whereas H+ circulation by ATP usage. It is demonstrated that the secondary K+ ion transport is not necessary for maintaining the physiological DeltaPsi/DeltapH ratio.

The biochemistry of drugs and doping methods used to enhance aerobic sport performance

Optimum performance in aerobic sports performance requires an efficient delivery to, and consumption of, oxygen by the exercising muscle. It is probable that maximal oxygen uptake in the athlete is multifactorial, being shared between cardiac output, blood oxygen content, muscle blood flow, oxygen diffusion from the blood to the cell and mitochondrial content. Of these, raising the blood oxygen content by raising the haematocrit is the simplest acute method to increase oxygen delivery and improve sport performance. Legal means of raising haematocrit include altitude training and hypoxic tents. Illegal means include blood doping and the administration of EPO (erythropoietin). The ability to make EPO by genetic means has resulted in an increase in its availability and use, although it is probable that recent testing methods may have had some impact. Less widely used illegal methods include the use of artificial blood oxygen carriers (the so-called ‘blood substitutes’). In principle these molecules could enhance aerobic sports performance; however, they would be readily detectable in urine and blood tests. An alternative to increasing the blood oxygen content is to increase the amount of oxygen that haemoglobin can deliver. It is possible to do this by using compounds that right-shift the haemoglobin dissociation curve (e.g. RSR13). There is a compromise between improving oxygen delivery at the muscle and losing oxygen uptake at the lung and it is unclear whether these reagents would enhance the performance of elite athletes. However, given the proven success of blood doping and EPO, attempts to manipulate these pathways are likely to lead to an ongoing battle between the athlete and the drug testers.

Control over action potential, calcium peak and average fluxes in the cyclic quasi-steady-state ion transport system in cardiac myocytes: in silico studies

MCA (metabolic control analysis) was originally developed to deal with steady-state systems. In the present theoretical study, the control analysis is applied to the cyclic quasi-steady-state system of ion transport in cardiac myocytes. It is demonstrated that the metabolic control of particular components (channels, exchangers, pumps) of the system over such quasi-steady-state variables as action potential amplitude, action potential duration, area under the Ca2+ peak and average fluxes through particular channels during one oscillation period can be defined and calculated. It is shown that the control over particular variables in the analysed, periodical system is distributed among many (potentially all) components of the system. Nevertheless, some components seem to exert much more control than other components, and different variables are controlled to the greatest extent by different channels. Finally, it is hypothesized that the Na+ and K+ transport system exerts a significant control over the Ca2+ transport system, but not vice versa.

Multi-level regulation and metabolic scaling

Metabolic control analysis has revealed that flux through pathways is the consequence of system properties, i.e. shared control by multiple steps, as well as the kinetic effects of various pathways and processes over each other. This implies that the allometric scaling of flux rates must be understood in terms of properties that pertain to the regulation of flux rates. In contrast,proponents of models considering the scaling of branching or fractal-like systems suggest that supply rates determine metabolic rates. Therefore, the allometric scaling of supply alone provides a sufficient explanation for the allometric scaling of metabolism. Examination of empirical data from the literature of comparative physiology reveals that basal metabolic rates (BMR)are driven by rates of energy expenditure within internal organs and that the allometric scaling of BMR can be understood in terms of the scaling of the masses and metabolic rates of internal organs. Organ metabolic rates represent the sum of tissue metabolic rates while, within tissues, cellular metabolic rates are the outcome of shared regulation by multiple processes. Maximal metabolic rates (MMR, measured as maximum rates of O2 consumption, V̇O2max) during exercise also scale allometrically, are also subject to control by multiple processes, but are due mainly to O2 consumption by locomotory muscles. Thus, analyses of the scaling of MMR must consider the scaling of both muscle mass and muscle energy expenditure. Consistent with the principle of symmorphosis, allometry in capacities for supply (the outcome of physical design constraints) is observed to be roughly matched by allometry in capacities for demand (i.e. for energy expenditure). However, physiological rates most often fall far below maximum capacities and are subject to multi-step regulation. Thus, mechanistic explanations for the scaling of BMR and MMR must consider the manner in which capacities are matched and how rates are regulated at multiple levels of biological organization.

Metabolic engineering: advances in modeling and intervention in health and disease

The field of metabolic engineering encompasses a powerful set of tools that can be divided into (a) methods to model complex metabolic pathways and (b) techniques to manipulate these pathways for a desired metabolic outcome. These tools have recently seen increased utility in the medical arena, and this paper aims to review significant accomplishments made using these approaches. The modeling of metabolic pathways has been applied to better understand disease-state physiology in a variety of cellar, subcellular, and organ systems, including the liver, heart, mitochondria, and cancerous cells. Metabolic pathway engineering has been used to generate cells with novel biochemical functions for therapeutic use, and specific examples are provided in the areas of glycosylation engineering and dopamine-replacement therapy. In order to document the potential of applying both metabolic modeling and pathway manipulation, we describe pertinent advances in the field of diabetes research. Undoubtedly, as the field of metabolic engineering matures and is applied to a wider array of problems, new advances and therapeutic strategies will follow.

Use and limitations of modular metabolic control analysis in medicine and biotechnology

By Metabolic Control Analysis (MCA), it has been shown that control on flux is in most cases shared by several enzymes rather than concentrated on one "rate-limiting step." This analysis also allows the quantification of the control exerted by groups (modules) of enzymes. The modules may correspond to spatial compartments or to functional units. A brief outline of the modular approach to MCA is given. The criteria by which the system can be modularized and the concept of monofunctional unit are explained. Various studies in which control analysis was applied to biotechnological and medical issues are reviewed. In particular, MCA has turned out to be helpful in the assessment of the severity of enzyme deficiencies. Another application is the search for target enzymes or enzyme groups where pharmaceuticals can suppress the metabolism of pathogenic microorganisms most. In biotechnology, modular and "traditional" control analyses are valuable tools for choosing the most promising targets for genetic manipulation so as to increase a biosynthetic flux. As control coefficients are linear approximations, the effect of enhancing the activities of enzymes to a larger extent is often overestimated. Further limitations such as the restriction to stationary states, uncertainties due to spatial heterogeneities and the impact of experimental error are discussed.

How aneuploidy affects metabolic control and causes cancer

The complexity and diversity of cancer-specific phenotypes, including de-differentiation, invasiveness, metastasis, abnormal morphology and metabolism, genetic instability and progression to malignancy, have so far eluded explanation by a simple, coherent hypothesis. However, an adaptation of Metabolic Control Analysis supports the 100-year-old hypothesis that aneuploidy, an abnormal number of chromosomes, is the cause of cancer. The results demonstrate the currently counter-intuitive principle that it is the fraction of the genome undergoing differential expression, not the magnitude of the differential expression, that controls phenotypic transformation. Transforming the robust normal phenotype into cancer requires a twofold increase in the expression of thousands of normal gene products. The massive change in gene dose produces highly non-linear (i.e. qualitative) changes in the physiology and metabolism of cells and tissues. Since aneuploidy disrupts the natural balance of mitosis proteins, it also explains the notorious genetic instability of cancer cells as a consequence of the perpetual regrouping of chromosomes. In view of this and the existence of non-cancerous aneuploidy, we propose that cancer is the phenotype of cells above a certain threshold of aneuploidy. This threshold is reached either by the gradual, stepwise increase in the level of aneuploidy as a consequence of the autocatalysed genetic instability of aneuploid cells or by tetraploidization followed by a gradual loss of chromosomes. Thus the initiation step of carcinogenesis produces aneuploidy below the threshold for cancer, and the promotion step increases the level of aneuploidy above this threshold. We conclude that aneuploidy offers a simple and coherent explanation for all the cancer-specific phenotypes. Accordingly, the gross biochemical abnormalities, abnormal cellular size and morphology, the appearance of tumour-associated antigens, the high levels of secreted proteins responsible for invasiveness and loss of contact inhibition, and even the daunting genetic instability that enables cancer cells to evade chemotherapy, are all the natural consequence of the massive over- and under-expression of proteins.

Flux control exerted by overt carnitine palmitoyltransferase over palmitoyl-CoA oxidation and ketogenesis is lower in suckling than in adult rats

We examined the potential of overt carnitine palmitoyltransferase (CPT I) to control the hepatic catabolism of palmitoyl-CoA in suckling and adult rats, using a conceptually simplified model of fatty acid oxidation and ketogenesis. By applying top-down control analysis, we quantified the control exerted by CPT I over total carbon flux from palmitoyl-CoA to ketone bodies and carbon dioxide. Our results show that in both suckling and adult rat, CPT I exerts very significant control over the pathways under investigation. However, under the sets of conditions we studied, less control is exerted by CPT I over total carbon flux in mitochondria isolated from suckling rats than in those isolated from adult rats. Furthermore the flux control coefficient of CPT I changes with malonyl-CoA concentration and ATP turnover rate.

Top-down control analysis of systems with more than one common intermediate

The analysis of the control of complex metabolic systems can be greatly simplified by application of the top-down approach of metabolic control analysis, in which the reactions of the system are grouped together into a small number of blocks connected by a common intermediate. The experimental application of the top-down approach has so far been limited to systems that have only a single intermediate. In this study, we demonstrate that the connectivity and summation theorems of metabolic control analysis hold with any number of intermediates between the metabolic blocks, and in doing so show that top-down analysis is valid for systems with multiple intermediates and so can be applied to most metabolic systems regardless of their complexity; an example of such an application is provided. Top-down control analysis has successfully described the control of mitochondrial respiration by dividing the system into three blocks, the respiratory chain, phosphorylation system and proton leak, all linked by a single intermediate, proton motive force. Here, we subdivide the respiratory chain into succinate consumers and cytochrome oxidase so that a second intermediate, cytochrome c redox state, is generated. Despite the fact that the redox state of cytochrome c is not measured, we solve the control over the system fluxes. In common with previous studies, we find that under conditions where there is no ATP turnover (state 4), respiration is largely controlled by proton leak, while at maximal ATP turnover (state 3) respiration is controlled by the respiratory chain and the phosphorylating system. In state 4,85% of the control by the respiratory chain resides with cytochrome oxidase. As ATP turnover increases, the respiration rate increases, and the control by the respiratory chain shifts from cytochrome oxidase to the succinate consumers, so that in state 3 83% of the control by the respiratory chain lies in the reactions between succinate and cytochrome c and only 17% resides with cytochrome oxidase.