Why do protein kinase cascades have more than one level?
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Animals↗
Biomedical subjects
B N Kholodenko
Publications and source records attributed to B N Kholodenko.
Control analysis of glycolytic oscillations.
The principles involved in the control of the frequency of sustained metabolic oscillations are developed in the context of glycolytic oscillations in Saccharomyces cerevisiae. To this purpose, an existing mathematical model that describes the experimentally obtained oscillations was simplified to a core model. Frequency, relative phase, average concentrations and amplitudes of the oscillations were well approximated by writing the two remaining metabolic variables of the core model (representing [ATP] and [hexose]) as harmonic functions of time and by requiring them to fulfill the differential equations. The extent to which an enzyme (-conglomerate) controls the frequency in a sustained oscillation is defined as the log-log derivative of that frequency with respect to enzyme activity. In both the full model and the core model this control of frequency and the control over the average concentrations proved to be distributed over the enzymes. We identified a summation theorem, stating that the sum of such control coefficients over all processes equals unity for frequency and zero for the average concentrations.
Catalysis↗
Molecular control analysis: control within proteins and molecular processes.
Molecular control analysis is a method for analysing the extent to which the different elementary steps or rate constants within a molecular process limit the steady-state rate (or other variables) of that process. Any process which may be described by a kinetic diagram of transitions between states of the system may be analysed by molecular control analysis, and this approach has previously been used to analyse control within enzymes, transporters, enzyme complexes, channelled pathways, and group-transfer pathways. We outline the theory of molecular control analysis here, and illustrate its use by analysing control within enzymes (three beta-lactamases). Further potential applications include signal-transduction processes, protein folding, and chemical reactions.
Animals↗
Strong control on the transit time in metabolic channelling.
A suite of different characteristic times is used to describe the temporal behavior of a metabolic pathway. Here we focus on the 'transit' time, that is the average time it takes for a molecule, entering the steady-state pathway as a substrate, to exit the pathway as a product. We show that metabolic channelling results in dramatic changes in control exerted by pathway enzymes on the transit time. In an 'ideal' pathway a doubling of the enzyme concentrations halves the transit time. In a dynamic channel such an increase can reduce the transit time by a factor of four or more.
Enzymes↗
Paradoxical control properties of enzymes within pathways: can activation cause an enzyme to have increased control?
It is widely assumed that within a metabolic pathway inhibition of an enzyme causes the control exerted by that enzyme over the flux through its own reaction to increase, whereas activation causes its control to decrease. This assumption forms the basis of a number of experimental methods. For a pathway conceptually divided into two enzyme groups connected via a single metabolite we have derived a general condition under which this assumption is false, and thus the pathway shows paradoxical control behaviour, i.e. increased control with activation and decreased control with inhibition of an enzyme or group of enzymes. Paradoxical control behaviour occurs widely when enzyme activity is altered by changing Km (if an enzyme is already close to saturation by its substrate), but may also occur with changes in Vmax. when the elasticity to the linking metabolite increases with its concentration (as in some cases of sigmoidal and exponential kinetics or for reactions catalysed by isoenzymes). These findings suggest that enzymes with sigmoidal kinetics may have low control in the absence of activation, but may gain control with activation, and thus have beneficial regulatory properties.
Allosteric Regulation↗
Effect of channelling on the concentration of bulk-phase intermediates as cytosolic proteins become more concentrated.
This paper shows that metabolic channelling can provide a mechanism for decreasing the concentration of metabolites in the cytoplasm when cytosolic proteins become more concentrated. A dynamic complex catalysing the direct transfer of an intermediate is compared with the analogous pathway lacking a channel (an "ideal" pathway). In an ideal pathway a proportional increase in protein content does not result in a change in the steady-state concentration of the bulk-phase intermediate, whereas in a channelling pathway the bulk-phase intermediate either decreases or increases depending on the elemental rate constants within the enzyme mechanisms. When the concentration of the enzymes are equal, the pool size decreases with increasing protein concentration if the elemental step depleting the bulk-phase intermediate exerts more control on its concentration than the step supplying the intermediate. Results are illustrated numerically, and a simplified dynamic channel is analysed in which the concentration of the enzyme-enzyme forms. For such a "hit-and-run" channel it is shown that, when the product-releasing step of the enzyme located upstream is close to equilibrium, the pool size decreases as the concentrations of the enzymes increase in proportion, regardless of the rate, equilibrium constants and concentration ratios of the two sequential enzymes.
Cytosol↗
[Control of the rate of the glucokinase reaction by its elementary stages].
Limitation of an enzymatic reaction by its elemental steps is characterized by so-called control coefficients for (quasi)stationary reaction rate. Established paradigm of "limiting step" cannot describe the control of glucokinase reaction. Flux control is distributed between several elemental steps (ATP binding, ADP release, etc.); this distribution significantly changes when reaction conditions are modified, i.e., changes in glucose or ATP concentrations occur. At about 1 mM ATP and 2-5 mM glucose, impact of ATP binding stage on total flux control is positive and it exceeds 50% if ATP binds after glucose. However, if ATP binds before glucose then control coefficient for ATP binding is negative. At high substrate concentrations, impact of product dissociation on flux control becomes significant. Distribution of control between elemental steps cannot be predicted by changes of Gibbs energy or by the rate constants of elemental steps.
Adenosine Triphosphate↗
Calcium indirectly increases the control exerted by the adenine nucleotide translocator over 2-oxoglutarate oxidation in rat heart mitochondria.
The effect of calcium on the control exerted by the adenine nucleotide translocator over respiration in isolated heart mitochondria was investigated in order to determine whether calcium directly stimulates the translocator. At respiration rates intermediate between states 3 and 4, Ca2+ is shown to increase the control over 2-oxoglutarate oxidation exerted by the adenine nucleotide translocator in rat heart mitochondria. This did not occur when succinate was the respiratory substrate, even though the control exerted by the translocator was substantial, indicating that Ca2+ does not have a direct effect on the adenine nucleotide translocator. Ca2+ increased the uncoupled oxidation rate of 2-oxoglutarate, but not succinate. Using the summation theorem for flux control, the effect of Ca2+ is explained by a shift of the control over respiration rate toward the adenine nucleotide translocator, from the respiratory chain, presumably as the result of the activation of the 2-oxoglutarate dehydrogenase complex.
Adenosine Triphosphate↗
Composite control of cell function: metabolic pathways behaving as single control units.
This paper shows that under some conditions the control exerted by a part of a metabolic network (a pathway) on a flux or concentration in any other part can be described through a single (overall) control coefficient. This has the following implications: (i) the relative contributions of a pathway enzyme to the regulation of the pathway (output) flux and of any flux or concentration outside are identical; therefore, the control analysis of the pathway 'in isolation' allows one to determine the control exerted by any pathway enzyme on the rest of the cell by estimation of the control efficient of just one, arbitrarily chosen enzyme; (ii) the relative control of any two metabolic variables outside the pathway (measured as the ratio of the control coefficients over these two variables outside) is the same for all pathway enzymes. These properties allow one to substitute effectively a pathway by a single (super)reaction and make it possible to consider such a pathway as a metabolic unit within the cellular enzyme network.
Cells↗
Control theory of metabolic channelling.
Various factors appear to control muscle energetics, often in conjunction. This calls for a quantitative approach of the type provided by Metabolic Control Analysis for intermediary metabolism and mitochondrial oxidative phosphorylation. To the extent that direct transfer of high energy phosphates and spatial organization plays a role in muscle energetics however, the standard Metabolic Control Theory does not apply, neither do its theorems regarding control. This paper develops the Control Theory that does apply to the muscle system. It shows that direct transfer of high energy phosphates bestows a system with enhanced control: the sum of the control exerted by the participating enzymes on the flux of free energy from the mitochondrial matrix to the actinomyosin may well exceed the 100% mandatory for ideal metabolic pathways. It is also shown how sequestration of high energy phosphates may allow for negative control on pathway flux. The new control theory gives method functionally to diagnose the extent to which channelling and metabolite sequestration occur.
Animals↗
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.
Animals↗
Control in channelled pathways. A matrix method calculating the enzyme control coefficients.
The usual equations expressing the enzyme control coefficients (quantitative indicators of 'global' control properties of a pathway) via the elasticity coefficients (reflecting local kinetic properties of an enzyme reaction), cannot be applied to a variety of 'non-ideal' pathways, in particular to pathways with metabolic channelling. Here we show that the relationship between the control and elasticity coefficients can be obtained by considering such a metabolic pathway as a network of elemental chemical conversions (steps). To calculate the control coefficients of enzymes one should first determine the elasticity coefficients of such elemental steps and then take their appropriate combinations. Although the method is illustrated for a channelled pathway it can be used for any non-ideal pathway including those with high enzyme concentrations where the sequestration of metabolites by enzymes cannot be neglected.
Journal Article↗
Defining control coefficients in non-ideal metabolic pathways.
The extent to which an enzyme controls a flux has been defined as the effect on that flux of a small modulation of the activity of that enzyme divided by the magnitude of the modulation. We here show that in pathways with metabolic channelling or high enzyme concentrations and conserved moieties involving both enzymic and non-enzymic species, this definition is ambiguous; the magnitude of the corresponding flux control coefficient depends on how the enzyme activity is modulated. This is illustrated with two models of biochemically relevant pathways, one in which dynamic metabolite channelling plays a role, and one with a moiety-conserved cycle. To avoid such ambiguity, we view biochemical pathways in a more detailed manner, i.e., as a network of elemental steps. We define 'elemental control coefficients' in terms of the effect on a flux of an equal modulation of the forward and reverse rate constant of any such elemental step (which may correspond to transitions between enzyme states). This elemental control coefficient is independent of the method of modulation. We show how metabolic control analysis can proceed when formulated in terms of the elemental control coefficients and how the traditional control coefficients are related to these elemental control coefficients. An 'impact' control coefficient is defined which quantifies the effect of an activation of all elemental processes in which an enzyme is involved. It equals the sum of the corresponding elemental control coefficients. In ideal metabolic pathways this impact control coefficient reduces to the traditional flux control coefficient. Differences between the traditional control coefficients are indicative of non-ideality of a metabolic pathway, i.e. of channelling or high enzyme concentrations.
Journal Article↗
The macroworld versus the microworld of biochemical regulation and control.
Our understanding of cell physiology has been helped greatly by viewing metabolism as a set of reactions catalysed by independent catalysts (enzymes) in ideal solutions. Yet the differences between this idealized cell and reality have strong implications for biochemical regulation and control. We show here that in the real cell an enzyme controls cell physiology in more than a single way. These different controlling modes in the real 'macroworld' can be related to one another by implementing a new type of control analysis, which is formulated in terms of the 'microworld' of the elemental processes.
Cells↗
Molecular biology for flux control.
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Enzymes↗
Coenzyme cycles and metabolic control analysis: the determination of the elasticity coefficients from the generalised connectivity theorem.
Metabolic control analysis allows one to express the elasticity coefficients (which describe the "local" kinetic features of enzymes) in terms of the control coefficients (quantitative indicators of the "global" control properties). However, when coenzymes (or metabolites linked by conservation constraints) are present in the pathway this procedure yields the "apparent" values of elasticity coefficients that correspond to the kinetic responses of the enzymes to such a simultaneous change of the coenzyme forms which leaves the total concentration of these forms unchanged (e.g., NAD+ + NADH in the glycolysis). We show that a generalised connectivity theorem (Kholodenko et al, Eur. J. Biochem. (1994) 225, 179-186) makes it possible to express the elasticity coefficients with respect to every coenzyme form separately. Such expressions include (i) the control coefficients and (ii) the responses to changes in the total concentrations of the coenzymes.
Coenzymes↗
Control theory of one enzyme.
The analogue of metabolic control theory is developed for the control of reactions catalyzed by single enzymes. The control exerted by any of the elemental transitions of enzyme catalytic cycles on reaction rate and on concentrations (probabilities) of enzyme states is quantified in line with the principle of detailed balance. For enzyme reactions with arbitrary kinetic schemes, e.g., with several enzyme cycles, reflecting coupling and slipping of reactions, it is derived what the various sums of the control coefficients are equal to (cycle summation theorems). Total control on flux, state probability and ratios of branch fluxes are 1, 0 and 0, respectively. The general connectivity theorems are derived which indicate how control is determined by the kinetics of the elemental steps. In addition, for enzymes catalyzing single (or completely coupled) processes the control coefficients are expressed in terms of actual and standard free energy differences across the steps. The prevalent qualitative contention that the step with the smallest forward rate constant, or with the largest free energy drop is the step limiting the performance of the enzyme is shown to fail. The new theory should allow subtle analysis of the control of an enzyme catalyzed reaction.
Enzymes↗
Control by enzymes, coenzymes and conserved moieties. A generalisation of the connectivity theorem of metabolic control analysis.
The control and regulation of metabolic systems are determined by their responses to changes in the internal metabolites (the internal state) and parameters of the system. In many cases, the concentrations of the intermediates are constrained by moiety conservations, for example those requiring that all intermediate forms of any enzyme sum to the conserved total concentration of that enzyme. In this study, we show how responses to changes in the internal state are related to responses to changes in the total amounts of conserved moieties. The relationship between these two different measures of control leads to a generalisation of the connectivity theorems. The results have important implications for the study of a variety of phenomena such as metabolite (coenzyme) sequestration, group-transfer and channelling. The relationships we derive make it possible to determine the control features of these pathways. As an illustration, two examples are chosen. The first shows the effect of sequestration of substrate moiety while the second deals with the sequestration of the enzyme moieties and enzyme/enzyme interactions.
Coenzymes↗