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The presence of protein aggregates in cells is a known feature of many human age-related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutaime (PolyQ) proteins in cells have been used to gain a better understanding of the biological system. However, there is considerable uncertainty about the values of some of the parameters governing the system. Currently, appropriate values are chosen by ad hoc attempts to tune the parameters so that the model output matches experimental data. The problem is further complicated by the fact that the data only offer a partial insight into the underlying biological process: the data consist only of the proportions of cell death and of cells with inclusion bodies at a few time points, corrupted by measurement error. Developing inference procedures to estimate the model parameters in this scenario is a significant task. The model probabilities corresponding to the observed proportions cannot be evaluated exactly, and so they are estimated within the inference algorithm by repeatedly simulating realizations from the model. In general such an approach is computationally very expensive, and we therefore construct Gaussian process emulators for the key quantities and reformulate our algorithm around these fast stochastic approximations. We conclude by highlighting appropriate values of the model parameters leading to new insights into the underlying biological processes.

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Reactive intermediate enzyme complexes are difficult to study directly and the use of physical methods requiring observation periods of more than a second has not been possible heretofore. Here we introduce a simple approach, the "Le Chatelier forcing method" which does for the first time produce significant concentrations of such kinetically competent central intermediates observable for extended periods of time. The method involves only the forcing of the accumulation of intermediate complexes at thermodynamic equilibrium by the use of high reactant concentrations working against a high concentration of a product, combined with a valid and applicable method of analysis. We demonstrate this approach using the glutamate dehydrogenase catalyzed reaction with the reaction product ammonia as a "dam" to oppose the forward driving force of NADP and l-glutamate. We demonstrate the accumulation of substantial amounts measurable amounts of stable enzyme-NADPH-alpha-carbinolamine and alpha-iminoglutarate complexes in three different alpha-amino acid dehydrogenases. We describe the manipulation of such Le Chatelier forced equilibria to increase the prominence of particular species and discuss the implications of these findings for previously unattainable experimental approaches.

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A pH jump approach has been developed and used to locate the opening and closing events occurring in the time course of the beef liver glutamate dehydrogenase catalyzed reaction. A comparison of the pH jump results, the resolved component time courses, and the 340 nm fluorescence signal suggests the existence and location on the reaction time course of a previously unreported prehydride transfer complex.

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A highly constrained and heavily overdetermined multiwavelength transient state kinetic approach has been used to study the oxidative deamination of L-glutamate catalyzed by beef liver glutamate dehydrogenase. Spectra generated using the known enzyme-reduced coenzyme-substrate spectrum served as models for deconvolution of kinetic scan data. Deconvolution of the multiwavelength time course array shows formation of three distinguishable intermediates in the reaction sequence, an ultrablue-shifted complex, an ultrared-shifted complex, and a blue-shifted complex. The ultrablue-shifted entity is identified as the enzyme-NADPH-alpha-iminoglutarate complex (ERI) and the ultrared as the enzyme-NADPH-alpha-carbinolamine complex (ERC). The blue-shifted complex is characterized as the E-NADPH-ketoglutarate species (ERK). The location of these species along the reaction coordinate has been determined and their kinetic competency in the reaction sequence has been established by fitting the concentration time courses of the components for both the alpha-deuterio- and the alpha-protio-L-glutamate reactions to the now highly constrained differential equations derived from a kinetic scheme involving the sequential formation of alpha-iminoglutarate, alpha-carbinolamine, and alpha-ketoglutarate-reduced coenzyme complexes, following the formation of two prehydride transfer complexes.

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A multiwavelength transient-state kinetic study of the glutamate dehydrogenase catalyzed reaction has proven that an alpha-iminoglutarate complex is an observable intermediate in the reverse direction. It also shows the existence of two enzyme-NADPH-ketoglutarate complexes, only one of which reacts with ammonia rapidly.

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We have studied the thermal denaturation of hexameric beef-liver glutamate dehydrogenase by itself and in the presence of ADP and guanidine-HCl by a variety of techniques. In differential scanning calorimetry studies, the observed melting temperature and total enthalpy of denaturation show no dependence on protein concentration, but do show significant dependence on the scan rate. This suggests that the overall denaturation process is irreversible and kinetically controlled. Isothermal unfolding kinetics from spectrophotometry confirm this result. The size of the protein, as shown by quasi-elastic light scattering measurements, does not change during the denaturation process. We interpret these results in terms of the following model: N6 reversible N'6-->6U(-->F) where N6 and N'6 are, respectively, the native hexamer and a hexameric, highly folded high-enthalpy species, U is the unfolded monomer and F is some final aggregated state. The kinetic intermediate, N'6, possesses the properties of one definition of a molten globule, having a very high enthalpy and a hexameric compact structured form. This "molten globule" is an obligatory intermediate in the unfolding pathway of the protein. The stabilization of the protein by ADP is due to the modulation of the high-enthalpy two-state predenaturational E reversible E' transition, resulting in the lowering of the energy of the native state of the protein.

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We have related the ratios of the protein fluorescence quenching and nucleotide absorbance time courses for the glutamate dehydrogenase catalyzed oxidative deamination of L-glutamate to identify the occurrence and sequential location of a previously demonstrated charge-transfer intermediate. Static studies showed the major portion of the fluorescence quenching signal to be due to radiationless singlet energy transfer from tryptophan to reduced coenzyme chromophores and that conformational changes contribute little to this signal. The ratio approach applied to the transient time courses shows correspondingly that, over most of the time range, the fluorescence quenching signal provides a quantitative measure of the sum of all posthydride transfer species. However, it also indicates the very early occurrence of a species of anomalous optical properties for the reaction catalyzed by the Clostridium symbiosum enzyme as well as that from bovine liver. Transient-state kinetic isotope effect time courses of both the fluorescence and the absorbance signals confirm that this species must be the prehydride charge-transfer complex in both enzyme reactions. Kinetic analysis of alpha-deuterio- and alpha-protio-L-glutamate reaction time courses proves the kinetic competence of the assignments. These results also demonstrate that the intramolecular transfer of a proton from the alpha-amino group of the substrate to an immediately adjacent aspartate carboxylate group on the enzyme is an obligatory initial event in the reactions catalyzed by both enzyme species, even though the occurrence of protein release from a critical lysine residue to the solvent occurs at different phases in those two reactions. The abnormally low intrinsic KIE required to simulate both the alpha-deuterio-L-glutamate reaction and its protio counterpart implies that the transition state of the hydride transfer step must be highly asymmetric.

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In contrast to steady-state kinetic isotope effects (KIE's), transient-state KIE's are dependent on both time and signal source. We developed a theory which predicts the behavior of transient-state KIE's, permits the calculation of the intrinsic KIE, and makes possible the assignment of various optical signals to either pre- or post-hydride transfer events. We proved that the behavior of KIEobs for a reversible two-step reaction for all possible values of the rate constants and all possible ratios of intermediate and product contributions obeys three simple rules (assuming that the isotope-sensitive step involves a hydride transfer): (1) If only the post-hydride species contributes to the observed signal, KIEobs = KIEint at t = 0 and then decreases with time. (2) If only the pre-hydride species contributes to the observed signal, then KIEobs = 1 at t = 0 and then decreases with time. (3) If both pre- and post-hydride species contribute to the observed signal, then KIEobs = 1 at t = 0 and then will either rise or fall with time depending on the relative molar signal coefficients of the pre- and post-hydride species. We provide experimental evidence that the phenomena predicted by this theory do in fact occur in enzyme-catalyzed reactions.

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Glutamate dehydrogenase from beef liver (bl GDH) and the corresponding enzyme from Clostridium symbiosum (cs GDH) each catalyze the same sequence of chemical events in the oxidative deamination of L-glutamate. This catalysis involves interactions between at least six conserved functional groups, each of which appears to occupy the same geometric position with respect to the substrate molecule in both enzyme--coenzyme--L-glutamate reactive ternary complexes. In both cases steady-state V/K pH profiles indicate the requirement for the transfer to the solvent of a single proton from the same abnormal lysine for L-glutamate to bind and react; the pK of that lysine is the same for both enzymes. Here we report studies of the proton traffic between enzyme and solvent using direct pH-stat back-titration and indicator dye measurements on dead-end inhibitor ternary complexes, simultaneous transient-state time courses of proton and product, and transient-state kinetic isotope studies on both enzymes. We find that in the cs GDH catalyzed reaction the single proton is released only after the hydride transfer step whereas in the bl GDH reaction this proton release occurs prior to the hydride transfer step, despite the fact that the substrate molecule undergoes the same sequence of chemical events in both reactions. Interpreting these results in the context of the X-ray crystallographic structures of cs GDH and its NAD binary complex and of thermodynamic studies of bl GDH and its complexes, we conclude that the difference in the relative times of proton release in the two enzyme-catalyzed reactions must be ascribed to a difference in the sequence of active site cleft-opening and -closing events in the two identical reaction sequences. We suggest a possible biological significance to this unusual method of modulating a common reaction to suit differing metabolic roles.

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In previous transient state kinetic work from this laboratory, we proposed a new mechanism for the glutamate dehydrogenase-catalyzed oxidative deamination reaction involving an initial replacement of a proton from lysine 126 by a single bound water molecule, followed by closure of the active site cleft and expulsion of bulk water, providing a hydrophobic environment for the ensuing hydride transfer step. Here, we report the results of further transient state fluorescence, absorbance, and kinetic isotope effect studies, which demonstrate the occurrence of an unusual intermediate in the early steps of that reaction. This phenomenon is revealed by an initial fluorescence burst that occurs in the time period where the absorbance signal is still in its lag phase. Using an extension of the proton/product ratio approach we have described earlier, we show that this intermediate is a strongly fluorescent but weakly absorbing species whose absorption maximum is red-shifted beyond that of other known complexes of this enzyme. The transient state kinetic isotope effects of the fluorescence and absorbance signals are compatible only with a reaction scheme in which the formation of the fluorescent complex precedes the hydride transfer step. The optical properties of this enzyme-oxidized coenzyme-substrate intermediate strongly suggest that it is a charge-transfer complex, similar in nature to the complex responsible for the well known "Racker band" reported in 1952 for glyceraldehyde-3-phosphatase dehydrogenase (Racker, E., and Krimsky, I. (1952) Nature 169, 1043-1044). The crystal structure studies of the enzyme-coenzyme and enzyme-L-glutamate complexes of the closely analogous Clostridium symbosium glutamate dehydrogenase, reported by the Sheffield group (Stillman, T. J., Baker, P. J., Britton, K. L., and Rice, D. W. (1993) J. Mol. Biol. 234, 1131-1139), provide a basis for a physical explanation of the phenomenon. We conclude that the charge transfer phenomenon is caused by the near apposition of the unprotonated alpha-amino group of the substrate in a form of the enzyme in which a conformational change has caused the complete closing of the active site cleft.

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We have previously characterized the thermodynamic relationships which govern the dissociation of NADPH from bovine liver glutamate dehydrogenase and the allosteric control of that mechanically and physiologically important process by a variety of effectors. We have found that the cooperative occupancy of a specific anion binding, while the occupancy of a second allosteric acetate binding site disrupts that anion binding site and opposes those effects (Singh & Fisher, 1994). We report here the results of transient-state studies on the kinetics of the various processes involved in this complex equilibrium. We find that the only intrinsically slow steps are those of NADPH binding and dissociation, that the complex kinetic behavior of the overall system is due solely to very rapid equilibrium binding processes involving phosphate, acetate, and hydrogen ions, and that these ions exert their various effects on the kinetics of the binding process by altering the equilibrium concentrations of the two kinetically significant reactive species, E and E-NADPH. The slow intrinsic rates of NADPH association and dissociation are ascribed to a ligand-induced conformational change involving a major alteration in the degree of closure of the enzyme's active-site cleft.

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It is known that the binding of the reduced coenzyme (NADPH) to bovine liver glutamate dehydrogenase is controlled by the presence of phosphate, acetate, and other anions as well as the pH of the medium. These effectors mediate this binding by lowering the pK (8.5) of an ionizable group on the enzyme, and this pK shift is linked to a high enthalpy E <--> E' transition in the protein. In this study, we have measured enthalpy changes and proton transfer for enzyme-NADPH binding under a variety of combinations of phosphate, acetate, and hydrogen in the pairs acetate-NADPH and H(+)-phosphate, and negative interactions are seen in the pairs H(+)-NADPH, phosphate-NADPH, acetate-phosphate, and H(+)-acetate. We present a general model to account for all of these effects. This model incorporates a newly defined coenzyme binding subsite. The observed phenomena are interpreted in terms of the extent of loading of the specific anion-binding site on the enzyme that regulates the ionization of an enzyme group of pK 8.5. A proton is cooperatively shared with two phosphate groups at this site. Furthermore, we conclude that this cooperative trimolecular binding to the enzyme constitutes an allosteric driving force for the high enthalpy two-state transition observed in the ligand binding reactions of this enzyme.

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We introduce a novel transient-state kinetic approach which can resolve proton and product time courses into a series of individual steps that comprise the reaction path. We have applied this approach to the oxidative deamination reaction catalyzed by bovine liver glutamate dehydrogenase, measuring both the product (NADPH) and proton time courses at various pH values. The global treatment (over all pH values) resolves the very early portion of this reaction quantitatively and provides a continuous time course for each of the six protonic species. We propose the following mechanism: L-glutamate binds to an open conformation of the enzyme-NADP complex, forming salt bridges between its alpha- and gamma-carboxyl groups and the protonated forms of enzyme lysine residues 114 and 90, respectively. In this position, the alpha-H atom of the substrate is too far from the nicotinamide ring for hydride transfer to occur. In the next step, three events occur in a concerted manner: lysine 126 loses a proton and acquires a single water molecule; the active site cleft closes; bulk water is expelled; the substrate and coenzyme are forced closer together and remain in a nonaqueous environment during the ensuing chemical events, returning to an open conformation only in time to allow the product release steps to occur. Thus, substrate binding accomplishes a number of important tasks which are themselves an integral part of the catalytic mechanism. Combining the novel transient state approach developed here with steady-state kinetic information can produce a detailed mechanistic resolution of otherwise hidden steps.

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We have used the stopped-flow indicator dye method to measure proton release and product formation simultaneously in the initial transient-state portion of the glutamate dehydrogenase-catalyzed oxidative deamination of L-glutamate. We observe a measurably slow release of a proton from the enzyme-NADP-L-glutamate complex. This proton release precedes the hydride transfer step, as indicated by the distinct lag in the product formation signal. We show that the proton release step corresponds to an obligatory intermediate in the reaction sequence. We also find that compounds which are competitive inhibitors of L-glutamate are capable of inducing this phenomenon. We prove that this unanticipated prehydride transfer event cannot be due to the release of an alpha-amino group proton from the substrate.

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We propose a testable general mechanism by which ligand binding energy can be used to drive a catalytic step in an enzyme catalyzed reaction or to do other forms of work involving protein molecules. This energy transduction theory is based on our finding of the widespread occurrence of ligand binding-induced protein macrostate interconversions each having a large invariant delta H0 accompanied by a small but highly variable delta G0. This phenomenon, which can be recognized by the large delta Cp0's it generates, can provide the necessary energy input step but is not in itself sufficient to constitute a workable transduction mechanism. A viable mechanism requires the additional presence of an 'energy transmission step' which is terminated to trigger the 'power' stroke at a precise location on the reaction coordinate, followed by an energetically inexpensive 'return' step to restore the machine to its initial conditions. In the model we propose here, these additional steps are provided by the existence of ligand inducible 2-state transitions in the free enzyme and in each of the enzyme complexes that occur along the reaction coordinate, and by the selective blocking of certain of these interconversions by high energetic barriers. We provide direct experimental evidence supporting the facts that these additional mechanistic components do exist and that the liver glutamate dehydrogenase reaction is indeed driven by just such machinery. We describe some aspects of the chemical nature of these transitions, and evidence for their occurrence in other systems.

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The usefulness of the indicator dye method for the detection of transient enzyme-product intermediates has been very limited due to the near impossibility of resolving the apparent single exponential time courses resulting from sequences of steps linked by rather similar rate constants. We propose here a novel approach, the proton-product time course method, a procedure which can extract a great deal of the mechanistic information which remains buried in conventional proton release-time course measurements. The method involves nothing more than measuring the ratio, r, of the moles of H+ released to the moles of product formed as a function of time. We derive the theory relating this r function to mechanisms of varying complexity, explore the theoretical behavior of the function in various possible mechanistic situations, and employ the new approach in an experimental system. We demonstrate the fact that the proton/product time course ratio method can provide evidence of the existence of hidden steps in transient state kinetic studies, that it can determine accurate thermodynamic pK values of the intermediate complexes involved in those steps, and that it can produce time courses of individual intermediates which are obscure to conventional kinetic methods.

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