Kinetic studies of dogfish liver glutamate dehydrogenase.

Initial-rate studies were made of the oxidation of L-glutamate by NAD+ and NADP+ catalysed by highly purified preparations of dogfish liver glutamate dehydrogenase. With NAD+ as coenzyme the kinetics show the same features of coenzyme activation as seen with the bovine liver enzyme [Engel & Dalziel (1969) Biochem. J. 115, 621--631]. With NADP+ as coenzyme, initial rates are much slower than with NAD+, and Lineweaver--Burk plots are linear over extended ranges of substrate and coenzyme concentration. Stopped-flow studies with NADP+ as coenzyme give no evidence for the accumulation of significant concentrations of NADPH-containing complexes with the enzyme in the steady state. Protection studies against inactivation by pyridoxal 5'-phosphate indicate that NAD+ and NADP+ give the same degree of protection in the presence of sodium glutarate. The results are used to deduce information about the mechanism of glutamate oxidation by the enzyme. Initial-rate studies of the reductive amination of 2-oxoglutarate by NADH and NADPH catalysed by dogfish liver glutamate dehydrogenase showed that the kinetic features of the reaction are very similar with both coenzymes, but reactions with NADH are much faster. The data show that a number of possible mechanisms for the reaction may be discarded, including the compulsory mechanism (previously proposed for the enzyme) in which the sequence of binding is NAD(P)H, NH4+ and 2-oxoglutarate. The kinetic data suggest either a rapid-equilibrium random mechanism or the compulsory mechanism with the binding sequence NH4+, NAD(P)H, 2-oxoglutarate. However, binding studies and protection studies indicate that coenzyme and 2-oxoglutarate do bind to the free enzyme.     

The binding of oxidized coenzymes by glutamate dehydrogenase and the effects of glutarate and purine nucleotides

1. The binding of NAD(+) and NADP(+) to glutamate dehydrogenase has been studied in sodium phosphate buffer, pH7.0, by equilibrium dialysis. Approximate values for the dissociation constants are 0.47 and 2.5mm respectively. For NAD(+) the value agrees with that estimated from initial-rate results. 2. In the presence of the substrate analogue glutarate both coenzymes are bound more firmly, and there is one active centre per enzyme subunit. The binding results cannot be described in terms of independent and identical active centres, and binding is stronger at low coenzyme concentrations than at high concentrations. Either the six subunits of the oligomer are not identical or there are negative interactions between them in the binding of coenzymes in ternary complexes with glutarate. The latter explanation is favoured. 3. The binding studies support the conclusions drawn from earlier kinetic studies of the glutamate reaction. 4. ADP and GTP respectively decrease and increase the affinity of the enzyme for NAD(+) and NADP(+), in both the presence and absence of glutarate. The negative binding interactions in the presence of glutarate are abolished by ADP, which decreases the affinity for the coenzymes at low concentrations of the latter. 5. In the presence of glutarate, GTP and NAD(+) or NADP(+), the association of enzyme oligomers is prevented, and the solubility of the enzyme is decreased; the complex of enzyme and ligands readily crystallizes. 6. The results are discussed in relation to earlier kinetic studies.     

Rearrangement of L-2-hydroxyglutarate to L-threo-3-methylmalate catalyzed by adenosylcobalamin-dependent glutamate mutase

Adenosylcobalamin-dependent enzymes catalyze a variety of chemically difficult isomerizations in which a nonacidic hydrogen on one carbon is interchanged with an electron-withdrawing group on an adjacent carbon. We describe a new isomerization, that of L-2-hydroxyglutarate to L-threo-3-methylmalate, involving the migration of the carbinol carbon. This reaction is catalyzed by glutamate mutase, but k(cat) = 0.05 s(-)(1) is much lower than that for the natural substrate, L-glutamate (k(cat) = 5.6 s(-)(1)). EPR spectroscopy confirms that the major organic radical that accumulates on the enzyme is the C-4 radical of L-2-hydroxyglutarate. Pre-steady-state kinetic measurements revealed that L-2-hydroxyglutarate-induced homolysis of AdoCbl occurs very rapidly, with a rate constant approaching those measured previously with glutamate and methylaspartate as substrates. These observations are consistent with the rearrangement of the 2-hydroxyglutaryl radical being the rate-determining step in the reaction. The slow rearrangement of the 2-hydroxyglutaryl radical can be attributed to the poor stabilization by the hydroxyl group of the migrating glycolyl moiety of the radical transiently formed on the migrating carbon. In contrast, with the normal substrate the migrating carbon atom bears a nitrogen substituent that better stabilizes the analogous glycyl moiety. These studies point to the importance of the functional groups attached to the migrating carbon in facilitating the carbon skeleton rearrangement.     

The role of the nicotinamide and adenine subsites in the negative co-operativity of coenzyme binding to glyceraldehyde-3-phosphate dehydrogenase.

The interaction of 3-aminopyridine-adenine dinucleotide, an NAD ⁺ 2 analogue which is fluorescent at the pyridine end of the molecule, with rabbit muscle glyceraldehyde-3-phosphate dehydrogenase was investigated. The fluorescence properties of the AAD⁺ molecule were used to monitor the nicotinamide subsites ou the GPDHase tetramer, the fluorescent aminopyridine moiety of the molecule serving as an intrinsic probe. Although the binding of AAD⁺ wag found to be negatively co-operative, no conformational changes induced at the nicotinamide subsite upon coenzyme binding were found to be transmitted to neighboring subunits. These findings, in conjunction with our earlier findings and with the observation that different NAD⁺ analogues which differ in the chemistry of the pyridine moiety bind with different extents of co-operativity, enable us to offer specific roles for the nicotinamide and the adenine subsites in generating the negative co-operativity.It is suggested that the structure of the pyridine moiety of the coenzyme controls the mode of binding of the pyridine moiety to the nicotinamide subsite. This, in turn, controls the orientation of the adenine moiety with respect to its subsite, thereby determining the mode of the interactions between the adenine and its binding domain. As the propagation of conformational changes caused by these interactions to neighboring subunits is believed to be the cause of the negative co-operativity exhibited by this enzyme towards coenzyme binding, the structure of the pyridine moiety controls this phenomenon.     

Dual nucleotide specificity of bovine glutamate dehydrogenase. The role of negative co-operativity.

The thionicotinamide analogues of NAD+ and NADP+ were shown to be good alternative coenzymes for bovine glutamate dehydrogenase, with similar affinity and approx. 40% of the maximum velocity obtained with the natural coenzymes. Both thionicotinamide analogues show non-linear Lineweaver-Burk plots, which with the natural coenzymes have been attributed to negative co-operativity. Since the reduced thionicotinamide analogues have an isosbestic point at 340nm and have an absorption maximum at 400nm, it is possible to monitor reduction of natural coenzyme and thionicotinamide analogue simultaneously by dual-wavelength spectroscopy. When glutamate dehydrogenase is presented with NADP+ and thio-NADP+ simultaneously, the enzyme oligomer senses saturation of its coenzyme-binding sites irrespective of the exact nature of the coenzyme and locks the oligomer into its highly saturated form even when low saturation of the monitored coenzyme is present. These experiments substantiate the suggestion that glutamate dehydrogenase shows negative co-operativity in its catalytically active form.     

Protection of glutamate dehydrogenase by nicotinamide–adenine dinucleotide against reversible inactivation by pyridoxal 5′-phosphate as a sensitive indicator of conformational change induced by substrates and substrate analogues

1. The steady residual activity of ox liver glutamate dehydrogenase at equilibrium with the reversible inactivator pyridoxal 5'-phosphate was measured in the presence and absence of various protecting agents. 2. NAD(+) (up to 15mm) and its 3-acetylpyridine analogue (up to 5mm) both failed to protect, in contrast with NADH. 3. Partial protection was given by glutarate and by succinate. Adipate and pentanoate were much less effective. 4. Correspondingly, whereas succinate and glutarate were both shown to be strong inhibitors of the catalytic reaction, competitive with glutamate, adipate was only weakly competitive, and the still weaker inhibition by pentanoate was non-competitive. 5. When the enzyme was saturated with glutarate, NAD(+) became a good, although still partial, protecting agent. In the absence of protection, 1.8mm-pyridoxal 5'-phosphate decreased enzyme activity to 9%, in the presence of 150mm-glutarate to 29%, and with glutarate and 1mm-NAD(+) only to 73%. 6. 2-Oxoglutarate also promoted protection by NAD(+), but neither pentanoate nor succinate did so. The finding with succinate is remarkable in view of findings 3 and 4 above. 7. It seems possible that substrates or analogues possessing the glutarate structure promote a conformational change that alters the mode of NAD(+) binding. This may explain why glutamate is a much better substrate than norvaline or aspartate and why negative interactions in coenzyme binding occur only in the formation of ternary complexes with glutamate or its analogues.     

Transport of C5 dicarboxylate compounds by Pseudomonas putida.

Induced glutarate and 2-oxoglutarate uptake and transport by Pseudomonas putida were investigated in whole cells and membrane vesicles, respectively. Uptake of 2-oxoglutarate, but not glutarate, was against a concentration gradient to 1.7-fold greater than the initial extracellular concentration. Membrane vesicles transported 2-oxoglutarate and glutarate against gradients to intramembrane concentrations fivefold greater than the initial extravesicle concentrations. The rates of transport of both compounds were greatest in the presence of the artificial electron donor system phenazine methosulfate-ascorbate. Malate and D-lactate were the only naturally occurring compounds that served as electron donors. Uptake and transport were inhibited by KCN, NaN3, and 2,2-dinitrophenol. Kinetic parameters of transport were: glutarate, apparent Km--1.22 mM, Vmax--400 nmol/min per mg of membrane protein; 2-oxoglutarate, apparent Km--131 microM, Vmax--255 nmol/min per mg of membrane protein. Studies of competitive inhibition indicated a common system for transport of five C5 dicarboxylate compounds. The apparent Km and Ki values with 2-oxoglutarate as a substrate placed the substrate affinity for transport in the order 2-oxoglutarate greater than glutarate greater than D-2-hydroxyglutarate and L-2-hydroxyglutarate greater than glutaconate.     

Kinetic studies of glutamate dehydrogenase with glutamate and norvaline as substrates. Coenzyme activation and negative homotropic interactions in allosteric enzymes

1. Kinetic studies of glutamate dehydrogenase were made with wide concentration ranges of the coenzymes NAD(+) and NADP(+) and the substrates glutamate and norvaline. Initial-rate parameters were evaluated. 2. Deviations from Michaelis-Menten behaviour towards higher activity were observed with increasing concentrations of either coenzyme with glutamate as substrate, but not with norvaline as substrate. 3. In phosphate buffer, pH7.0, Lineweaver-Burk plots with either coenzyme as variable and a constant, large glutamate concentration showed three or four linear regions of different slope with relatively sharp discontinuities. Maximum rates obtained by extrapolation and Michaelis constants for the coenzymes increased in steps with increase of coenzyme concentration. 4. In the absence of evidence of heterogeneity of the enzyme and coenzyme preparations, the results are interpreted in terms of negative homotropic interactions between the enzyme subunits. It is suggested that sharp discontinuities in Lineweaver-Burk plots or reciprocal binding plots may be characteristic of this new type of interaction, which can be explained in terms of an Adair-Koshland model, but not by the model of Monod, Wyman & Changeux.     

The reaction of bovine glutamate dehydrogenase with periodate-oxidised ADP

1. The reactive analogue oADP produced by periodate oxidation of ADP has been studied as a potential affinity label for the enzyme bovine glutamate dehydrogenase, using circular dichroism (CD) difference spectroscopy to monitor specific binding. 2. The analogue binds stoichiometrically, rapidly and reversibly to the adenine nucleotide binding site with Kd approximately equal to 12 microM (20 degrees C, pH 7) with characteristic intensification of the adenine nucleotide CD at 260 nm. 3. This complex is unstable and decays with a half-life of about 1.5 h; the analogue then becomes attached as a Schiff base to a number of subsidiary sites, including the enzyme active site, with partial inactivation of the enzyme. 4. Depending upon initial concentration of oADP, the enzyme activity is progressively lost during the slow reaction; following borohydride reduction, up to four molecules of analogue are bound/subunit. 5. Protection against loss of enzyme activity is afforded by the coenzyme NAD+ plus glutarate or L-hydroxyglutarate (an effective inhibitor), or by glutarate alone, but not by NAD+ alone. 6. Spectroscopic and protection studies indicate that after the decay of the specific CD signal, the enzyme retains the capacity to bind ADP, but that this is progressively lost in parallel with decay of enzymic activity. 7. The results are consistent with proximity or functional interaction between the adenine nucleotide site and the coenzyme binding portion of the active site. 8. Thus oADP does not act as a true affinity label for the adenine nucleotide binding site, but the reaction subsequent to binding at that site shows some specificity directed towards the active site.     

pH-induced co-operative effects in hysteretic enzymes. 1. A theoretical model of a new type of co-operative behaviour controlled by pH

A new model which provides an explanation for pH-induced co-operativity of hysteretic enzymes is proposed. The essence of the model is that a region, or a domain, of the enzyme undergoes a spontaneous 'slow' conformational change which does not affect the geometry of the active site. The region which undergoes this spontaneous conformational transition bears an ionizable group. Kinetic co-operativity occurs if the pK of this ionizable group changes upon this conformational transition. Thus co-operativity does not arise from a distortion of the active site. An interesting prediction of the model is that at 'extreme' pH values co-operativity must be suppressed. Although the kinetic equation pertaining to the model is of the 2:2 type, co-operativity is not maximum or minimum at half-saturation of the enzyme by the substrate, as occurs with 2:2 binding isotherms. A new index of maximum or minimum kinetic co-operativity, whether this extreme occurs at half-saturation or not, has been proposed which allows the change of kinetic co-operativity to be followed as a function of pH. It is believed that this model will be useful in explaining the behaviour of enzymes attached to biological polyelectrolytes, such as membranes or cell envelopes.     

Pre-steady-state kinetic studies on the Glu171Gln active site mutant of adenosylcobalamin-dependent glutamate mutase

Glutamate-171 is involved in recognizing the amino group of the substrate in glutamate mutase. The effect of mutating this residue to glutamine on the ability of the enzyme to catalyze the homolysis of adenosylcobalamin has been investigated using UV-visible stopped-flow spectroscopy. Although Glu171 does not contact the coenzyme, the mutation results in the apparent rate constants for substrate-induced homolysis of the coenzyme that are slower by 7-fold and 13-fold with glutamate and methylaspartate, respectively, than those measured for the wild-type enzyme; furthermore, it weakens the binding of these substrates by approximately 50-fold and approximately 400-fold, respectively. These observations lend support to the idea that the enzyme may use substrate binding energy to accelerate homolysis of the coenzyme. The mutation also results in isotope effects on coenzyme homolysis that are much smaller than the very large effects observed when the wild-type enzyme is reacted with deuterated substrates. This observation is consistent with adenosylcobalamin homolysis being slowed relative to hydrogen abstraction from the substrate.     

The allosteric mechanism of bovine liver glutamate dehydrogenase. Evidence from circular-dichroism studies for a conformational change in the ternary complex enzyme-(oxidized nicotinamide-adenine dinucleotide)-glutarate.

1. Computer averaging of multiple scans was used to refine the circular dichroism spectrum of bovine liver glutamate dehydrogenase, revealing well-defined structure in the aromatic region. 2. The circular dichroism of NAD+ bound to glutamate dehydrogenase is strongly negative at 260nm, probably owing to immobilization of the adenosine moiety. Loss of the characteristic adenine-nicotinamide interaction suggests that the coenzyme is bound in an unstacked conformation. 3. Glutarate and succinate, substrate analogues that are both inhibitors competitive with glutamate, do not significantly perturb the circular-dichroism spectrum of the enzyme in the absence of NAD+. 4. In the presence of NAD+, 150nM-succinate decreases the negative circular dichroism corresponding to bound coenzyme, but does not affect the protein circular dichroism. However, ISOmM-glutarate causes profound alternations of the circular-dichroism spectra of the bound NAD+ and of the enzyme, indicative of a protein conformational change. This direct evidence of conformational change specifically promoted by C5 dicarboxylates confirms the previous inference from protection studies. 5. The conformational change is discussed in relation to the allosteric mechanism of glutamate dehydrogenase.     

Formation of transient complexes in the glutamate dehydrogenase catalyzed reaction.

The reaction of glutamate dehydrogenase and glutamate (gl) with NAD+ and NADP+ has been studied with stopped-flow techniques. The enzyme was in all experiments present in excess of the coenzyme. The results indicate that the ternary complex (E-NAD(P)H-kg) is present as an intermediate in the formation of the stable complex (E-NAD(P)H-gl). The identification of the complexes is based on their absorption spectra. The binding of the coenzyme to (E-gl) is the rate-limiting step in the formation of (E-NAD(P)H-kg) while the dissociation of alpha-ketoglutarate (kg) from this complex is the rate-limiting step in the formation of (E-NAD(P)H-gl). The Km for glutamate was 20-25 mM in the first reaction and 3 mM in the formation of the stable complex. The Km values were independent of the coenzyme. The reaction rates with NAD+ were approximately 50% greater than those with NADP+. Furthermore, high glutamate concentration inhibited the formation of (E-NADH-kg) while no substrate inhibition was found with NADP+ as coenzyme. ADP enhanced while GTP reduced the rate of (E-NAD(P)H-gl) formation. The rate of formation of (E-NAD(P)H-kg) was inhibited by ADP, while it increased at high glutamate concentration when small amounts of GTP were added. The results show that the higher activity found with NAD+ compared to NADP+ under steady-state assay conditions do not necessarily involve binding of NAD+ to the ADP activating site of the enzyme. Moreover, the substrate inhibition found at high glutamate concentration under steady-state assay condition is not due to the formation of (E-NAD(P)H-gl) as this complex is formed with Km of 3 mM glutamate, and the substrate inhibition is only significant at 20-30 times this concentration.     

Substrate specificity via ternary complex formation with glutamate dehydrogenase.

Very littly discrimination is observed in the binary binding of dicarboxylic acid substrate analogues to glutamate dehydrogenase as monitored by proton nuclear magnetic resonance. Variation in length, charge, bulkiness and conformational rigidity resulted in only a factor of five variation in KD and apparent relaxation time, T2. Upon titration of the binary enzyme-ligand complex with coenzyme to form the ternary enzyme-ligand-coenzyme complex strong discrimination is observed. Coenzyme binds tightly only when the correct substrate is present, otherwise it binds 10 to 150 times more weakly.     

Molecular basis of negative co-operativity in rabbit muscle glyceraldehyde-3-phosphate dehydrogenase

The interactions of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase with NAD⁺ and with its fluorescent derivative 1, N⁶-etheno-adenine dinucleotide were investigated using a variety of spectroscopic methods. These techniques included: difference spectroscopy, circular dichroism, fluorescence and circular polarized luminescence. It was found that the greatest structural change in the protein tetramer occurs upon binding of the first mole of coenzyme. We have also demonstrated that progressive structural changes occur at the adenine subsite in the NAD⁺ binding site as a function of coenzyme saturation. These conformational changes are probably responsible for the progressive decrease in the affinity towards the coenzyme. It was also found that every NAD⁺ molecule induces the same conformational change of the nicotinamide subsite. These results offer a molecular explanation for the negative co-operativity in the binding of the coenzyme, without a change in the catalytic power of the NAD⁺ site as a function of coenzyme saturation. These results also offer a new explanation for the fact that enzyme exhibits half-of-the-sites reactivity towards certain ligands and full-site reactivity towards others. It is suggested that those ligands interacting at the adenine subsite of the NAD⁺ binding site induce the half-of-the-sites reactivity.Our results support the view that both the negative co-operativity in coenzyme binding and half-of-the-sites reactivity are due to ligand-induced conformational changes on an a priori symmetric glyceraldehyde-3-phosphate dehydrogenase molecule.     

Role of Arg100 in the active site of adenosylcobalamin-dependent glutamate mutase

Arginine-100 is involved in recognizing the gamma carboxylate of the substrate in glutamate mutase. To investigate its role in substrate binding and catalysis, this residue was mutated to lysine, tyrosine, and methionine. The effect of these mutations was to reduce k(cat) by 120-320-fold and to increase K(m(apparent)) for glutamate by 13-22-fold; K(m(apparent)) for adenosylcobalamin is little changed by these mutations. Even at saturating substrate concentrations, no cob(II)alamin could be detected in the UV-visible spectra of the Arg100Tyr and Arg100Met mutants. However, in the Arg100Lys mutant cob(II)alamin accumulated to concentrations similar to wild-type enzyme, which allowed the pre-steady-state kinetics of adenosylcobalamin homolysis to be investigated by stopped-flow spectroscopy. It was found that homolysis of the coenzyme is slower by an order of magnitude, compared with wild-type enzyme. Furthermore, glutamate binding is significantly weakened, so much so that the reaction exhibits second-order kinetics over the range of substrate concentrations used. The Arg100Lys mutant does not exhibit the very large deuterium isotope effects that are observed for homolysis of the coenzyme when the wild-type enzyme is reacted with deuterated substrates; this suggests that homolysis is slowed relative to hydrogen abstraction by this mutation.     

Cocrystallization of a mutant aspartate aminotransferase with a C5-dicarboxylic substrate analog: structural comparison with the enzyme-C4-dicarboxylic analog complex

A mutant Escherichia coil aspartate aminotransferase with 17 amino acid substitutions (ATB17), previously created by directed evolution, shows increased activity for beta-branched amino acids and decreased activity for the native substrates, aspartate and glutamate. A new mutant (ATBSN) was generated by changing two of the 17 mutated residues back to the original ones. ATBSN recovered the activities for aspartate and glutamate to the level of the wild-type enzyme while maintaining the enhanced activity of ATB17 for the other amino acid substrates. The absorption spectrum of the bound coenzyme, pyridoxal 5'-phosphate, also returned to the original state. ATBSN shows significantly increased affinity for substrate analogs including succinate and glutarate, analogs of aspartate and glutamate, respectively. Hence, we could cocrystallize ATBSN with succinate or glutarate, and the structures show how the enzyme can bind two kinds of dicarboxylic substrates with different chain lengths. The present results may also provide an insight into the long-standing controversies regarding the mode of binding of glutamate to the wild-type enzyme.     

Distance between the substrate and regulatory reduced coenzyme binding sites of bovine liver glutamate dehydrogenase by resonance energy transfer

Bovine liver glutamate dehydrogenase is known to bind reduced coenzyme at two sites/subunit, one catalytic and one regulatory; ADP competes for the latter site. The enzyme is here shown to be catalytically active with the thionicotinamide analogue of NADPH [( S]NADPH). For native enzyme, ultrafiltration studies revealed that [S]NADPH reversibly occupies about two sites/enzyme subunit in the absence of other ligands; by the addition of ADP, [S]NADPH binding can be limited to one molecule/subunit. The enzyme is irreversibly inactivated by reaction with 4-(iodoacetamido)salicylic acid (ISA) at lysine126 within the 2-oxoglutarate binding site [Holbrook, J.J., Roberts, P.A. & Wallis, R.B. (1973) Biochem. J. 133, 165-171]. ISA-modified enzyme binds 1 molecule [S]NADPH/subunit in the absence of ADP, suggesting that reaction at the substrate site blocks binding at the catalytic, but not at the regulatory site. The fluorescence spectrum of ISA-modified enzyme overlaps the absorption spectrum of [S]NADPH allowing a distance measurement between these sites by resonance energy transfer. [S]NADPH quenches the emission of ISA-modified enzyme, yielding 3.2 nm as the average distance between sites. ADP competes for the [S]NADPH site but does not affect the fluorescence of ISA-modified enzyme, indicating that [S]NADPH quenching is attributable to energy transfer rather than to a conformational change. The 3.2 nm thus represents the distance between the 2-oxoglutarate and reduced coenzyme regulatory sites of glutamate dehydrogenase.     

Conformational changes in bovine-liver glutamate dehydrogenase: a spin-label study.

A spin-labelled analogue of p-chloromercuribenzoate reacts specifically with glutamate dehydrogenase. The most marked change in the properties of the spin-labelled enzyme is a fivefold decrease in the rate of reduction of the coenzyme by L-glutamate and no change in the rate of oxidation by 2-oxoglutarate. The electron spin resonance spectrum is a sensitive probe for the conformational state of the enzyme. Spin-labelled glutamate dehydrogenase in the presence of saturating concentrations of NADPH and 2-oxoglutarate or L-glutamate shows a complete conformational change while in the presence of NADP+ and 2-oxoglutarate only half of the protomers have changed conformation. The conformational change upon addition of NADPH to the spin-labelled glutamate dehydrogenase in the presence of 2-oxoglutarate happens in a concerted way between 20 and 80% saturation with NADPH. One of the conformations is favoured by the activator ADP while the other is favoured by the inhibitor GTP.     

Making biochemistry count: life among the amino acid dehydrogenases

The guiding principle of the IAS Medal Lecture and of the research it covered was that searching mathematical analysis, depending on good measurements, must underpin sound biochemical conclusions. This was illustrated through various experiences with the amino acid dehydrogenases. Topics covered in the present article include: (i) the place of kinetic measurement in assessing the metabolic role of GDH (glutamate dehydrogenase); (ii) the discovery of complex regulatory behaviour in mammalian GDH, involving negative co-operativity in coenzyme binding; (iii) an X-ray structure solution for a bacterial GDH providing insight into catalysis; (iv) almost total positive co-operativity in glutamate binding to clostridial GDH; (v) unexpected outcomes with mutations at the catalytic aspartate site in GDH; (vi) reactive cysteine as a counting tool in the construction of hybrid oligomers to probe the basis of allosteric interaction; (vii) tryptophan-to-phenylalanine mutations in analysis of allosteric conformational change; (viii) site-directed mutagenesis to alter substrate specificity in GDH and PheDH (phenylalanine dehydrogenase); and (ix) varying strengths of binding of the 'wrong' enantiomer in engineered mutant enzymes and implications for resolution of racemates.