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A convenient method for enzyme kinetic studies is introduced. The method includes identification of reaction mechanism and estimation of the associated kinetic constants with a minimum number of experiments. The application of the method is illustrated by using literature data. Factors limiting the application of this method are also discussed.
The enzyme kinetic parameters of the degradation of luteinizing hormone-releasing hormone (LH-RH) and L-cystine-bis-(4-nitroanilide) (Cys-NA) by rat hypothalamic (HYP) and pituitary (PIT) extracts and the effect of various oligopeptides on the rate of LH-RH inactivation were investigated in vitro. The 105,000 x g supernatant of 1 rat HYP inactivated 57 microgram LH-RH during a 30 min incubation (Km = 12.4 microM, V max = 2.33 microgram LH-RH/mg protein/min), and of one rat anterior PIT, 48 microgram LH-RH during 30 min of incubation (Km = 12.2 microM, V max = 8.0 microgram LH-RH/mg protein/min). The synthetic substrate Cys-NA competitively inhibited LH-RH degradation with a Ki of 8.5 microM in the HYP and 6 microM in the PIT enzyme preparation. Vice versa, LH-RH also competitively inhibited the cleavage of Cys-NA with inhibition constants of 14 microM (HYP) and 15 microM (PIT) indicating that the 2 substrates are probably cleaved by the same enzyme. The most effective inhibitors of LH-RH degradation were found to be angiotensin-related peptides, neurotensin, bradykinin, and bacitracin. A relatively weak effect was obtained with oxytocin, enkephalin and puromycin. It is concluded that endogenous oligopeptides such as angiotensins, neurotensin, bradykinin, etc., may possibly influence H-RH degradation in the PIT and the HYP. The synthetic substrate Cys-NA may be an appropriate substrate for measuring the activity of an LH-RH-degrading peptidase, which therefore could be classified as arylamidase.
The use of a commercial oscillating-tube densitometer with an accuracy of 4 . 10(-7) g/cm3 for the determination of enzyme-kinetics constants is tested. This method is applied to the investigation of the influence of vitamin C (sodium ascorbate) on the glycolytic enzymes invertase, dextransucrase and dextranase. Invertase is inhibited uncompetitively, dextransucrase non-competitively. There is no significant effect of the vitamin on dextranase. The comparison of the mechanisms of the three enzymes suggests that only those reaction steps are inhibited by vitamin C in which fructose is released from the enzyme.
Microbes adjust their metabolism to environmental challenges by changing protein expression levels, metabolite concentrations, and reaction rates. Average expression levels in large proteome sectors change coherently, while individual proteins show divergent shifts even within the same pathway. Here, we establish a metabolic model that integrates local enzyme kinetics and global network architecture to predict the joint growth response of proteins and metabolites. Under nutrient limitation, we predict a remarkably simple pattern of proteome reallocation with growth rate: protein expression levels change linearly but heterogeneously. For a given enzyme, the direction of change is determined by its local kinetic constants - catalytic rate and substrate affinity - and by the degree of nutrient restriction affecting its embedding pathway. This double-graded growth response of the proteome is mediated by restriction-dependent metabolite levels, which are predicted to decrease with growth rate in a nonlinear way. The model establishes three specific growth laws: protein expression changes of individual enzymes are negatively correlated with their expression and with their substrate saturation at high growth; average changes of pathways and larger functional sectors are correlated with their internal variance. These predictions are in quantitative agreement with measured system-wide proteomics and metabolomics data of E. coli. Enzyme-specific response patterns are a starting point for model-guided interventions into bacterial metabolism.
Catalysis and specifically autocatalysis are the quintessential building blocks of life. Yet, although autocatalytic networks are necessary, they are not sufficient for the emergence of life-like properties, such as replication and adaptation. The ultimate and potentially fatal threat faced by molecular replicators is parasitism; if the polymerase error rate exceeds a critical threshold, even the fittest molecular species will disappear. Here we have developed an autocatalytic RNA early life mathematical network model based on enzyme kinetics, specifically the steady-state approximation. We confirm previous models showing that these second-order autocatalytic cycles are sustainable, provided there is a sufficient nucleotide pool. However, molecular parasites become untenable unless they sequentially degenerate to hyperparasites (i.e. parasites of parasites). Parasite resistance-a parasite-specific host response decreasing parasite fitness-is acquired gradually, and eventually involves an increased binding affinity of hyperparasites for parasites. Our model is supported at three levels; firstly, ribozyme polymerases display Michaelis-Menten saturation kinetics and comply with the steady-state approximation. Secondly, ribozyme polymerases are capable of sustainable auto-amplification and of surmounting the fatal error threshold. Thirdly, with growing sequence divergence of host and parasite catalysts, the probability of self-binding is expected to increase and the trend towards cross-reactivity to diminish. Our model predicts that primordial host-RNA populations evolved via an arms race towards a host-parasite-hyperparasite catalyst trio that conferred parasite resistance within an RNA replicator niche. While molecular parasites have traditionally been viewed as a nuisance, our model argues for their integration into the host habitat rather than their separation. It adds another mechanism-with biochemical precision-by which parasitism can be tamed and offers an attractive explanation for the universal coexistence of catalyst trios within prokaryotes and the virosphere, heralding the birth of a primitive molecular immunity.
Equilibrium statistical mechanics is much concerned with problems involving intermolecularinteractions, either in lattices or in pure fluids or solutions. The possibility of enzyme-enzyme interactions suggests that the same problems might be studied profitably at steady state as well as at equilibrium. In the systems we consider, each of the identical enzyme molecules of the system undergoes steady-state stochastic cycling among states i equal 1,....,n. But the molecules do not cycle independently. Two neghboring molecules, in states i and j, interact with a free energy wij (a function of the distance r in the solution case). The instantaneous transition probabilities between states for a given molecule will depend on the instantaneous interactions between the molecule in question and its neighbors. The primary question of interest is how the enzyme flux is influenced by the interactions. The general problem is outlined here and some simple special cases are treated. The discussion will be continued in a following paper [Hill, T. L. (1977) Proc. Natl. Acad. Sci. USA 74, in press]
In previous papers of this series, emphasis has been placed on the steady-state phase transition and critical properties of large lattices of interacting, symmetrical, and identical enzyme molecules. The present paper is concerned with a number of examples of enzyme--enzyme interactions that do not belong to the class of models of the earlier papers. These are more biochemically oriented and include heterologous dimers, a linear chain with unsymmetrical interactions, and concerted isologous dimers (half-the-sites reactivity).
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Malic enzyme from pigeon liver is alkylated by the substrate analogue bromopyruvate, resulting in the concomitant loss of its oxidative decarboxylase and oxalacetate decarboxylase activities, but not its ability to reduce alpha-keto acids. The inactivation of oxidative decarboxylase activity follows saturation kinetics, indicating the formation of an enzyme-bromopyruvate complex (K congruent to 8 mM) prior to alkylation. The inactivation is inhibited by metal ions and pyridine nucleotide cofactors. Protection of malic enzyme by the substrates L-malate and pyruvate and the inhibitors tartronate and oxalate requires the presence of the above cofactors, which tighten the binding of these carboxylic acids in accord with the ordered kinetic scheme (Hsu, R. Y., Lardy, H. A., and Cleland, W. W. (1967), J. Biol. Chem. 242, 5315-5322). Bromopyruvate is reduced to L-bromolactate by malic enzyme and is an effective inhibitor of L-malate and pyruvate in the overall reaction. The apparent kinetic constants (90 muM-0.8 mM) are one to two orders of magnitude lower than the half-saturation constant (K) of inactivation, indicating a similar tightening of bromopyruvate binding in the E-NADP+ (NADPH)-Mn2+ (Mg2+)-BP complexes. During alkylation, bromopyruvate interacts initially at the carboxylic acid substrate pocket of the active site, as indicated by the protective effect of substrates and the ability of this compound to form kinetically viable complexes with malic enzyme, particularly as a competitive inhibitor of pyruvate carboxylation with a Ki (90 muM) in the same order as its apparent Michaelis constant of 98 muM. Subsequent alkylation of a cysteinyl residue blocks the C-C bond cleavage step. The incorporation of radioactivity from [14C]bromopyruvate gives a half-site stoichiometry of two carboxyketomethyl residues per tetramer, indicating strong negative cooperativity between the four subunits of equal size, or alternatively the presence of structurally dissimilar active sites.
This paper continues an earlier one [Hill, T.L. (1977) Proc. Natl . Acad. Sci. USA 74, 3632-3632] and presents further introductory examples. Most attention is devoted to a closed linear chain of two-state enzyme molecules with nearest-neighbor interactions. The one-dimensional Ising theory can be used here. The Bragg-Williams (mean field) approximation is introduced to deal with a one-, two-, or three-dimensional lattice of enzyme molecules, at steady state, with an arbitrary kinetic diagram. The behavior of the flux in a phase transition is noted. Finally, a treatment is given for the first effect (second "viral" coefficient) of interactions on the flux in a dilute solution of two-state enzyme molecules.
We describe a technique whereby it is possible to measure enzyme activity in a singel cell. The model chosen involved the measurement of myeloperoxidase activity in a polymorphonuclear neutrophil leukocyte. Details of the apparatus are described. The experiments necessary to optimize the reaction conditions are summarized. The nature of the phases of the reaction are described. The technique appears to have further application in measurement of the activities of other enzymes in leukocytes or other cells.
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The conversion of D,L-alpha-13C-histidine to similarly labeled alpha-13C histamine by bacterial and mammalian histidine decarboxylase was studied by 13C-NMR spectroscopy and GLC-mass spectrometry. The results obtained with the partially purified bacterial enzyme were in essentially perfect agreement with results obtained simultaneously with a standard radioisotopic method using carboxyl-labeled-14C-L-histidine. For a crude tissue preparation of the mammalian enzyme, the radioisotopic method indicated an activity three times that based on 13C-NMR measurement of alpha-13C-histamine. The difference in results was accountable in terms of additional 13C-NMR signals attributable to products other than histamine due in part to enzymatic degradation of the latter.
A new method for discovering the minimum degree of rate equations using only the experimental graphs and a straight-edge (transparent ruler) is presented. This method is then illustrated by an analysis of the wavy v vs [S] curves and non-linear double-reciprocal plots reproducibly given by NAD-dependent 15-hydroxyprostaglandin dehydrogenase for which a new improved purification is described. It is shown by this analysis that the enzyme has a complex mechanism involving cooperatively linked dependent sites and requiring a rate equation of at least fourth degree in prostaglandin and NAD+ with no kinetically significant dead-end complexes.
The kinetic parameters Km, k+2 and k+2/Km of the pancreatic ribonucleases (EC 3.1.4.22) from cow, giraffe, horse, rat and lesser rorqual have been determined, using 2',3'-cyclic cytidine monophosphate and 2',3'-cuclic uridine monophosphate as substrates. No large differences were found between the activities of the five enzymes. The relative differences between the activities of the five enzymes are mainly due to differences in the rates of hydrolysis and not to differences in the affinities for the substrates.
Optimum incubation conditions for determination of ethylmorphine-N-demethylation with newborn and adult rat liver homogenate have been determined: 1 ml 1:20 liver homogenate in 1.15% KCl, 1 ml 0.1 M phosphate buffer with ethylmorphine, NADP, and glucose-6-P, final concentrations 10, 0.33 and 5 mM, respectively, no nicotinamide, no MgCl2, 1 ml 0.5 M phosphate buffer; 3 ml final volume, 20 min incubation time. With both age groups NADH increases the activity to the same extent. With NADPH, saturation could be achieved only with newborn liver, but not with adult liver homogenate. Postnatally, the activity increases about fivefold, with a break at the 10th day of life. The Lineweaver-Burk plot was linear with newborn liver homogenate, whereas for all other age groups the graphs showed an angle. Statistical analysis pointed out that a two-enzyme model fits the experimental data only insignificantly better than a one-enzyme model. From other experimental evidence and manifold reproduction without any exception of these results, however, it may be concluded that there are different monooxygenases which show different affinities towards one substrate (ethylmorphine) and which show different developmental patterns.
The interaction of mitogenic factors on a single cell type and the comparative activity of a given factor in diverse cell types have been studied by applying the principles of Michaelis-Menten kinetics to clonal growth data. Such comparisons are facilitated by derivation of two parameters; Km mitogen, the mitogen concentration that gives half-maximal clonal growth and a theoretical maximal growth rate, RMAX T. Both parameters are analogous to the Km and VMAX as applied to enzymatic reactions. Use of these parameters permits meaningful comparisons between cells with different growth rates. Using kinetic analysis of dose-response data, we found that normal human epithelial cells require 200 times more fetal bovine serum protein (FBSP) than a malignant line to multiply at their respective half-maximal rates. Further, the Km FBSP of normal cells was reduced to that of the malignant line by the inclusion of growth factors (EGF or FGF, and hydrocortisone) in the medium. On the other hand, even though greater levels of serum were required when growth factors and hydrocortisone were not present, their inclusion did not alter RMAX T. Interactions between mitogenic factors were shown to be unidirectional. Although EGF reduced the Km FBSP, FBSP did not change the Km EGF. The same type of analysis revealed that hydrocortisone, which potentiated the mitogenic activity of EGF did not change the Km EGF. Kinetic analysis of cell growth should prove useful in studies on the relation between growth and tumor promotion as well as in the evaluation of growth-inhibiting chemotherapeutic agents.