Composite control of cell function: metabolic pathways behaving as single control units

Patient-specific Boolean models of signalling networks guide personalised treatments

Prostate cancer is the second most occurring cancer in men worldwide. To better understand the mechanisms of tumorigenesis and possible treatment responses, we developed a mathematical model of prostate cancer which considers the major signalling pathways known to be deregulated. We personalised this Boolean model to molecular data to reflect the heterogeneity and specific response to perturbations of cancer patients. A total of 488 prostate samples were used to build patient-specific models and compared to available clinical data. Additionally, eight prostate cell line-specific models were built to validate our approach with dose-response data of several drugs. The effects of single and combined drugs were tested in these models under different growth conditions. We identified 15 actionable points of interventions in one cell line-specific model whose inactivation hinders tumorigenesis. To validate these results, we tested nine small molecule inhibitors of five of those putative targets and found a dose-dependent effect on four of them, notably those targeting HSP90 and PI3K. These results highlight the predictive power of our personalised Boolean models and illustrate how they can be used for precision oncology.

On functional module detection in metabolic networks

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models.

Flux coupling analysis of metabolic networks is sensitive to missing reactions

Genome-scale metabolic reconstructions are comprehensive, yet incomplete, models of real-world metabolic networks. While flux coupling analysis (FCA) has proved an appropriate method for analyzing metabolic relationships and for detecting functionally related reactions in such models, little is known about the impact of missing reactions on the accuracy of FCA. Based on an alternative characterization of flux coupling relations using elementary flux modes, this paper studies the changes that flux coupling relations may undergo due to missing reactions. In particular, we show that two uncoupled reactions in a metabolic network may be detected as directionally, partially or fully coupled in an incomplete version of the same network. Even a single missing reaction can cause significant changes in flux coupling relations. In case of two consecutive Escherichia coli genome-scale networks many fully coupled reaction pairs in the incomplete network become directionally coupled or even uncoupled in the more complete reconstruction. In this context, we found gene expression correlation values being significantly higher for the pairs that remained fully coupled than for the uncoupled or directionally coupled pairs. Our study clearly suggests that FCA results are indeed sensitive to missing reactions. Since the currently available genome-scale metabolic models are incomplete, we advise to use FCA results with care.

Super life--how and why 'cell selection' leads to the fastest-growing eukaryote

What is the highest possible replication rate for living organisms? The cellular growth rate is controlled by a variety of processes. Therefore, it is unclear which metabolic process or group of processes should be activated to increase growth rate. An organism that is already growing fast may already have optimized through evolution all processes that could be optimized readily, but may be confronted with a more generic limitation. Here we introduce a method called 'cell selection' to select for highest growth rate, and show how such a cellular site of 'growth control' was identified. By applying pH-auxostat cultivation to the already fast-growing yeast Kluyveromyces marxianus for a sufficiently long time, we selected a strain with a 30% increased growth rate; its cell-cycle time decreased to 52 min, much below that reported to date for any eukaryote. The increase in growth rate was accompanied by a 40% increase in cell surface at a fairly constant cell volume. We show how the increase in growth rate can be explained by a dominant (80%) limitation of growth by the group of membrane processes (a 0.7% increase of specific growth rate to a 1% increase in membrane surface area). Simultaneous activation of membrane processes may be what is required to accelerate growth of the fastest-growing form of eukaryotic life to growth rates that are even faster, and may be of potential interest for single-cell protein production in industrial 'White' biotechnology processes.

Computing algebraic functions with biochemical reaction networks

In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analytical approach to study signaling networks, we construct functional motifs from the bottom up. We formulate conceptual networks of biochemical reactions that implement elementary algebraic operations over the domain and range of positive real numbers. We discuss how the steady state behavior relates to algebraic functions, and study the stability of the networks' fixed points. The primitive networks are then combined in feed-forward networks, allowing us to compute a diverse range of algebraic functions, such as polynomials. With this systematic approach, we explore the range of mathematical functions that can be constructed with these networks.

Flux coupling analysis of genome-scale metabolic network reconstructions

In this paper, we introduce the Flux Coupling Finder (FCF) framework for elucidating the topological and flux connectivity features of genome-scale metabolic networks. The framework is demonstrated on genome-scale metabolic reconstructions of Helicobacter pylori, Escherichia coli, and Saccharomyces cerevisiae. The analysis allows one to determine whether any two metabolic fluxes, v(1) and v(2), are (1) directionally coupled, if a non-zero flux for v(1) implies a non-zero flux for v(2) but not necessarily the reverse; (2) partially coupled, if a non-zero flux for v(1) implies a non-zero, though variable, flux for v(2) and vice versa; or (3) fully coupled, if a non-zero flux for v(1) implies not only a non-zero but also a fixed flux for v(2) and vice versa. Flux coupling analysis also enables the global identification of blocked reactions, which are all reactions incapable of carrying flux under a certain condition; equivalent knockouts, defined as the set of all possible reactions whose deletion forces the flux through a particular reaction to zero; and sets of affected reactions denoting all reactions whose fluxes are forced to zero if a particular reaction is deleted. The FCF approach thus provides a novel and versatile tool for aiding metabolic reconstructions and guiding genetic manipulations.

Metabolic control analysis in drug discovery and disease

Metabolic control analysis (MCA) provides a quantitative description of substrate flux in response to changes in system parameters of complex enzyme systems. Medical applications of the approach include the following: understanding the threshold effect in the manifestation of metabolic diseases; investigating the gene dose effect of aneuploidy in inducing phenotypic transformation in cancer; correlating the contributions of individual genes and phenotypic characteristics in metabolic disease (e.g., diabetes); identifying candidate enzymes in pathways suitable as targets for cancer therapy; and elucidating the function of "silent" genes by identifying metabolic features shared with genes of known pathways. MCA complements current studies of genomics and proteomics, providing a link between biochemistry and functional genomics that relates the expression of genes and gene products to cellular biochemical and physiological events. Thus, it is an important tool for the study of genotype-phenotype correlations. It allows genes to be ranked according to their importance in controlling and regulating cellular metabolic networks. We can expect that MCA will have an increasing impact on the choice of targets for intervention in drug discovery.

Metabolomics--the link between genotypes and phenotypes

Metabolites are the end products of cellular regulatory processes, and their levels can be regarded as the ultimate response of biological systems to genetic or environmental changes. In parallel to the terms 'transcriptome' and proteome', the set of metabolites synthesized by a biological system constitute its 'metabolome'. Yet, unlike other functional genomics approaches, the unbiased simultaneous identification and quantification of plant metabolomes has been largely neglected. Until recently, most analyses were restricted to profiling selected classes of compounds, or to fingerprinting metabolic changes without sufficient analytical resolution to determine metabolite levels and identities individually. As a prerequisite for metabolomic analysis, careful consideration of the methods employed for tissue extraction, sample preparation, data acquisition, and data mining must be taken. In this review, the differences among metabolite target analysis, metabolite profiling, and metabolic fingerprinting are clarified, and terms are defined. Current approaches are examined, and potential applications are summarized with a special emphasis on data mining and mathematical modelling of metabolism.

A functional genomics strategy that uses metabolome data to reveal the phenotype of silent mutations

A large proportion of the 6,000 genes present in the genome of Saccharomyces cerevisiae, and of those sequenced in other organisms, encode proteins of unknown function. Many of these genes are "silent, " that is, they show no overt phenotype, in terms of growth rate or other fluxes, when they are deleted from the genome. We demonstrate how the intracellular concentrations of metabolites can reveal phenotypes for proteins active in metabolic regulation. Quantification of the change of several metabolite concentrations relative to the concentration change of one selected metabolite can reveal the site of action, in the metabolic network, of a silent gene. In the same way, comprehensive analyses of metabolite concentrations in mutants, providing "metabolic snapshots," can reveal functions when snapshots from strains deleted for unstudied genes are compared to those deleted for known genes. This approach to functional analysis, using comparative metabolomics, we call FANCY-an abbreviation for functional analysis by co-responses in yeast.

Metabolic networks: a signal-oriented approach to cellular models

Complete genomes, far advanced proteomes, and even 'metabolomes' are available for at least a few organisms, e.g., Escherichia coli. Systematic functional analyses of such complete data sets will produce a wealth of information and promise an understanding of the dynamics of complex biological networks and perhaps even of entire living organisms. Such complete and holistic descriptions of biological systems, however, will increasingly require a quantitative analysis and the help of mathematical models for simulating whole systems. In particular, new procedures are required that allow a meaningful reduction of the information derived from complex systems that will consequently be used in the modeling process. In this review the biological elements of such a modeling procedure will be described. In a first step, complex living systems must be structured into well-defined and clearly delimited functional units, the elements of which have a common physiological goal, belong to a single genetic unit, and respond to the signals of a signal transduction system that senses changes in physiological states of the organism. These functional units occur at each level of complexity and more complex units originate by grouping several lower level elements into a single, more complex unit. To each complexity level corresponds a global regulator that is epistatic over lower level regulators. After its structuring into modules (functional units), a biological system is converted in a second step into mathematical submodels that by progressive combination can also be assembled into more aggregated model structures. Such a simplification of a cell (an organism) reduces its complexity to a level amenable to present modeling capacities. The universal biochemistry, however, promises a set of rules valid for modeling biological systems, from unicellular microorganisms and cells, to multicellular organisms and to populations.

'Slave' metabolites and enzymes. A rapid way of delineating metabolic control

Although control of fluxes and concentrations tends to be distributed rather than confined to a single rate-limiting enzyme, the extent of control can differ widely between enzymes in a metabolic network. In some cases, there are enzymes that lack control completely. This paper identifies one surprising origin of such lack of control: If, in a metabolic system, there is a metabolite that affects the catalytic rate of only one enzyme, the corresponding enzyme cannot control any metabolic variable other than the concentration of that metabolite. We call such enzymes 'slave enzymes', and the corresponding metabolites 'slave metabolites'. Implications of the existence of slave enzymes for the control properties of enzymes further down the metabolic pathway are discussed and examined for the glycolytic pathway of yeast. Inadvertent assumptions in metabolic models may cause the latter incorrectly to calculate absence of metabolic control. The phenomenon of slave enzymes may well be important in enhancing metabolic signal transduction.

Engineering a living cell to desired metabolite concentrations and fluxes: pathways with multifunctional enzymes

With molecular genetics enabling modulation of the concentrations of cellular enzymes, metabolic engineering becomes limited by the question of which modulations of the enzyme concentrations are required to bring about a desired pattern of cellular metabolism. In an earlier paper (Kholodenko et al. (1998). Biotechnol. Bioeng. 59, 239-247) we derived a method to determine the required modulations. This method, however, cannot be immediately applied to cellular pathways with enzymes catalyzing more than one step in metabolism (multifunctional enzymes). In the present paper we show to which extent the presence of multifunctional enzymes limits biotechological ambitions, which one might otherwise pursue in vain. In particular, it is impossible to change the concentration of a single intermediate and leave the rest of metabolism unperturbed if that intermediate interacts directly with a multifunctional enzyme. The analytical machinery of Metabolic Control Analysis is used to relate the desired and ensuing changes in the metabolic pattern. An explicit solution to this problem of engineering metabolism is then given in the form of a single matrix equation.

Internal regulation of ATP turnover, glycolysis and oxidative phosphorylation in rat hepatocytes

Previously [Ainscow, E.K. & Brand, M.D. (1999) Eur. J. Biochem. 263, 671-685], top-down control analysis was used to describe the control pattern of energy metabolism in rat hepatocytes. The system was divided into nine reaction blocks (glycogen breakdown, glucose release, glycolysis, lactate production, NADH oxidation, pyruvate oxidation, mitochondrial proton leak, mitochondrial phosphorylation and ATP consumption) linked by five intermediates (intracellular glucose 6-phosphate, pyruvate and ATP levels, cytoplasmic NADH/NAD ratio and mitochondrial membrane potential). The kinetic responses (elasticities) of reaction blocks to intermediates were determined and used to calculate control coefficients. In the present paper, these elasticities and control coefficients are used to quantify the internal regulatory pathways within the cell. Flux control coefficients were partitioned to give partial flux control coefficients. These describe how strongly one block of reactions controls the flux through another via its effects on the concentration of a particular intermediate. Most flux control coefficients were the sum of positive and negative partial effects acting through different intermediates; these partial effects could be large compared to the final control strength. An important result was the breakdown of the way ATP consumption controlled respiration: changes in ATP level were more important than changes in mitochondrial membrane potential in stimulating oxygen consumption when ATP consumption increased. The partial internal response coefficients to changes in each intermediate were also calculated; they describe how steady state concentrations of intermediates are maintained. Increases in mitochondrial membrane potential were opposed mostly by decreased supply, whereas increases in glucose-6-phosphate, NADH/NAD and pyruvate were opposed mostly by increased consumption. Increases in ATP were opposed significantly by both decreased supply and increased consumption.

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.

Modular control analysis of slipping enzymes

A theory is developed that deals with the metabolic control exerted by enzymes that catalyze two or more, incompletely coupled reactions. The starting point is modular (top-down) metabolic control theory. Slipping enzymes are considered as modules with more than one independent flux. Control by the coupled reaction is distinguished quantitatively from control by the extent of slippage. This is achieved by appropriate linear transformation of fluxes or logarithms thereof. Different transformations are proposed and discussed. Our examples include free-energy transducing proton pumps and the Na+, K+-ATPase. It is shown that control coefficients can be calculated on the basis of a description of slipping enzymes in terms of linear non-equilibrium thermodynamics.

Metabolic design: how to engineer a living cell to desired metabolite concentrations and fluxes

A biotechnological aim of genetic engineering is to increase the intracellular concentration or secretion of valuable compounds, while making the other concentrations and fluxes optimal for viability and productivity. Efforts to accomplish this based on over-expression of the enzyme, catalyzing the so-called "rate-limiting step," have not been successful. Here we develop a method to determine the enzyme concentrations that are required to achieve such an aim. This method is called Metabolic Design Analysis and is based on the perturbation method and the modular ("top-down") approach-formalisms that were first developed for the analysis of biochemical regulation such as, Metabolic Control Analysis. Contrary to earlier methods, the desired alterations of cellular metabolism need not be small or confined to a single metabolite or flux. The limits to the alterations of fluxes and metabolite concentrations are identified. To employ Metabolic Design Analysis, only limited kinetic information concerning the pathway enzymes is needed.

Internal regulation of a modular system: the different faces of internal control

The living cell houses a multitude of molecular processes that operate simultaneously in a mutually consistent fashion. A certain degree of organization stands out, e.g. in terms of the various metabolic pathways, transcription versus translation, signal transduction versus metabolism. This paper shows that by taking one of the aforementioned organizational principles into account, the complexity of understanding cell function quantitatively may be reduced significantly. To this aim the definition of the corresponding type of organization is refined and the conceptual tools used in the analysis of the control of cell function are adjusted. The approach is elaborated for a theoretical model of cell function, in which the latter depends on a constellation of interdependent but unconnected modules. The organization of a system is reduced to global control within a limited set of partaking modules and the links between them. Information about the systems total internal control and regulability is then drastically reduced to the information specifying global control and the regulability of the pathways that constitute the system. It is shown quantitatively how control at a lower level of organization bears on the control of the cell as a whole. The approach centers on writing the product of control (matrix) and elasticity (matrix) at a number of different levels of aggregation; these products equalling the identity (matrix) under different conditions. We demonstrate that there are at least three ways in which control and regulability of a system can be matched. In one, the true control within and between the modules of the systems is the inverse of the primary regulability (i.e. elasticity plus stoichiometry). In a second, the control internal to a module (but partly determined through the other modules) is matched by the inverse of newly defined 'global' regulabilities for each module separately, which comprise the regulatory impact of the remainder of the system. In the third, the regulabilities are the ones intrinsic to the module and the control is taken equal to the control that would reign in the absence of the regulatory interactions between the units. In making these distinctions, it becomes transparent how much control stems from control within the organizational modules, and how much derives from the regulatory interactions between them. Control through other modules turns out to be equivalent, at steady state, to control within a module. The implications of this type of cellular organization for the location of the steady-state operating point is discussed.