Hysteretic properties of soluble F1 ATPase from Escherichia coli. II. Nucleotide effects on the slow changes of the enzyme kinetic behaviour

Kinetic and hysteretic behavior of ATP hydrolysis of the highly stable dimeric ATP synthase of Polytomella sp

The F1FO-ATP synthase of the colorless alga Polytomella sp. exhibits a robust peripheral arm constituted by nine atypical subunits only present in chlorophycean algae. The isolated dimeric enzyme exhibits a latent ATP hydrolytic activity which can be activated by some detergents. To date, the kinetic behavior of the algal ATPase has not been studied. Here we show that while the soluble F1 sector exhibits Michaelis-Menten kinetics, the dimer exhibits a more complex behavior. The kinetic parameters (Vmax and Km) were obtained for both the F1 sector and the dimeric enzyme as isolated or activated by detergent, and this activation was also seen on the enzyme reconstituted in liposomes. Unlike other ATP synthases, the algal dimer hydrolyzes ATP on a wide range of pH and temperature. The enzyme was inhibited by oligomycin, DCCD and Mg-ADP, although oligomycin induced a peculiar inhibition pattern that can be attributed to structural differences in the algal subunit-c. The hydrolytic activity was temperature-dependent and exhibited activation energy of 4 kcal/mol. The enzyme also exhibited a hysteretic behavior with a lag phase strongly dependent on temperature but not on pH, that may be related to a possible regulatory role in vivo.

Invariance and optimality in the regulation of an enzyme

BACKGROUND

The Michaelis-Menten equation, proposed a century ago, describes the kinetics of enzyme-catalyzed biochemical reactions. Since then, this equation has been used in countless, increasingly complex models of cellular metabolism, often including time-dependent enzyme levels. However, even for a single reaction, there remains a fundamental disconnect between our understanding of the reaction kinetics, and the regulation of that reaction through changes in the abundance of active enzyme.

RESULTS

We revisit the Michaelis-Menten equation under the assumption of a time-dependent enzyme concentration. We show that all temporal enzyme profiles with the same average enzyme level yield identical substrate degradation- a simple analytical conclusion that can be thought of as an invariance principle, and which we validate experimentally using a β-galactosidase assay. The ensemble of all time-dependent enzyme trajectories with the same average concentration constitutes a space of functions. We develop a simple model of biological fitness which assigns a cost to each of these trajectories (in the form of a function of functions, i.e. a functional). We then show how one can use variational calculus to analytically infer temporal enzyme profiles that minimize the overall enzyme cost. In particular, by separately treating the static costs of amino acid sequestration and the dynamic costs of protein production, we identify a fundamental cellular tradeoff.

CONCLUSIONS

The overall metabolic outcome of a reaction described by Michaelis-Menten kinetics is ultimately determined by the average concentration of the enzyme during a given time interval. This invariance in analogy to path-independent phenomena in physics, suggests a new way in which variational calculus can be employed to address biological questions. Together, our results point to possible avenues for a unified approach to studying metabolism and its regulation.

REVIEWERS

This article was reviewed by Sergei Maslov, William Hlavacek and Daniel Kahn.

A functionally inactive, cold-stabilized form of the Escherichia coli F1Fo ATP synthase

An unusual effect of temperature on the ATPase activity of E. coli F1Fo ATP synthase has been investigated. The rate of ATP hydrolysis by the isolated enzyme, previously kept on ice, showed a lag phase when measured at 15 degrees C, but not at 37 degrees C. A pre-incubation of the enzyme at room temperature for 5 min completely eliminated the lag phase, and resulted in a higher steady-state rate. Similar results were obtained using the isolated enzyme after incorporation into liposomes. The initial rates of ATP-dependent proton translocation, as measured by 9-amino-6-chloro-2-methoxyacridine (ACMA) fluorescence quenching, at 15 degrees C also varied according to the pre-incubation temperature. The relationship between this temperature-dependent pattern of enzyme activity, termed thermohysteresis, and pre-incubation with other agents was examined. Pre-incubation of membrane vesicles with azide and Mg2+, without exogenous ADP, resulted in almost complete inhibition of the initial rate of ATPase when assayed at 10 degrees C, but had little effect at 37 degrees C. Rates of ATP synthesis following this pre-incubation were not affected at any temperature. Azide inhibition of ATP hydrolysis by the isolated enzyme was reduced when an ATP-regenerating system was used. A gradual reactivation of azide-blocked enzyme was slowed down by the presence of phosphate in the reaction medium. The well-known Mg2+ inhibition of ATP hydrolysis was shown to be greatly enhanced at 15 degrees C relative to at 37 degrees C. The results suggest that thermohysteresis is a consequence of an inactive form of the enzyme that is stabilized by the binding of inhibitory Mg-ADP.

Structure and function of the ATPase-ATP synthase complex of mitochondria as compared to chloroplasts and bacteria

An overview of the structure and function of the mitochondrial ATPase-ATP synthase complex is presented. Attempts are made to identify the analogies and differences between mitochondrial, chloroplastic and bacterial complexes. The relatively more precise information available on the structure of the E. coli enzyme is used to try and understand the apparently more complex structure of the mitochondrial enzyme. Recent ideas on the mechanism of ATP hydrolysis and ATP synthesis will be summarized.

Isolation and properties of an isocitrate dehydrogenase from Anacystis nidulans

A NADP+-specific isocitrate dehydrogenase (EC 1.1.1.42) was isolated and purified over 400-fold from Anacystis nidulans. The enzyme activity responded slowly to rapid changes in ligand (NADP+, isocitrate, Mg2+-ions) or enzyme concentration as well as to rapid changes in temperature. These are properties characteristic of the hysteretic enzymes. In addition, the enzyme activity was subject to product (alpha-ketoglutarate) inhibition. ATP, ADP and CDP also inhibited the enzyme. Unlike several other cyanobacterial enzymes, the isocitrate dehydrogenase of Anacystis is not under redox control.