Enzymatic reaction sequences as coupled multiple traces on a multidimensional landscape

We propose that an enzyme-catalyzed reaction is best described by a large, three-dimensional potential energy surface, defined by the number of enzyme conformers in one dimension, the number of reaction steps as the second and Gibbs free energy as the third. Aside from accommodating experimental observations that do not fit current mechanistic paradigms, such a surface enables multiple intersecting reaction pathways, pathway funneling, ligand binding energy transduction and kinetic coupling between alternative reaction pathways. The landscape also confers flexibility, enabling an enzyme to seek out an optimal pathway for any reaction conditions that might occur. Thus, coupled pathways enable relatively minor differences in experimental conditions to result in abrupt phenomenological changes in the observed behavior of the reaction.     

A hypothesis for the role of dithiol-disulfide interchange in solute transport and energy-transducing processes

We have recently shown that the physical mechanism for delta approximately mu H+-driven changes in the Km for three different transport systems is an oxidation-reduction reaction involving a dithiol-disulfide interconversion [Robillard, G.T. and Konings, W.N. (1981) Biochemistry, 20, 5025-5032; Konings, W.N. and Robillard, G.T. (1982) Proc. Natl Acad. Sci. USA, in the press]. Based on the similarities between the data from these three systems and published data from other systems, we now propose that dithiol-disulfide interchange may play a general role in membrane-related processes such as transport, energy transduction and hormone-receptor interactions. We propose that the affinities of the substrate-binding sites are regulated by a dithiol and a disulfide situated at different depths in the membrane. In addition we propose that the oxidation states of these two redox centers are coupled by dithiol-disulfide interchange such that, when one is oxidized, the other is reduced. Since a transmembrane electrical potential, delta psi, or a pH gradient, delta pH, can alter the redox state, it can change the affinity of the substrate-binding sites. The delta approximately mu H+-induced changes in affinity are sufficient to drive active transport (symport or antiport) and energy-transducing processes. A similar mechanism can be applied to transport systems driven by phosphorylated enzyme intermediates instead of delta approximately mu H+. Changes of the redox potential in a given compartment during metabolism could also control the affinity of ligand binding even in the absence of a delta approximately mu H+. The ligand-binding affinities of facilitated diffusion transport systems and receptor proteins may be regulated in this manner.     

DSL ligand endocytosis physically dissociates Notch1 heterodimers before activating proteolysis can occur

Cleavage of Notch by furin is required to generate a mature, cell surface heterodimeric receptor that can be proteolytically activated to release its intracellular domain, which functions in signal transduction. Current models propose that ligand binding to heterodimeric Notch (hNotch) induces a disintegrin and metalloprotease (ADAM) proteolytic release of the Notch extracellular domain (NECD), which is subsequently shed and/or endocytosed by DSL ligand cells. We provide evidence for NECD release and internalization by DSL ligand cells, which, surprisingly, did not require ADAM activity. However, losses in either hNotch formation or ligand endocytosis significantly decreased NECD transfer to DSL ligand cells, as well as signaling in Notch cells. Because endocytosis-defective ligands bind hNotch, but do not dissociate it, additional forces beyond those produced through ligand binding must function to disrupt the intramolecular interactions that keep hNotch intact and inactive. Based on our findings, we propose that mechanical forces generated during DSL ligand endocytosis function to physically dissociate hNotch, and that dissociation is a necessary step in Notch activation.     

Molecular recognition and processing of periodic signals in cells: study of activation of membrane ATPases by alternating electric fields.

A molecule which is immobilized, oriented or tumbling more slowly than the frequency of a periodic field, may interact with the field to produce chemical effects that are uncommon in a homogeneous solution. Among these effects are the alteration of the rate of a chemical reaction and the exchange of energy between the oscillating field and the conformation of the molecule. When certain conditions are satisfied, this exchange allows the molecule to absorb and couple the energy of the field to drive an endergonic reaction. The efficiency of energy coupling depends on field strength and frequency and on the ligand concentration. There are windows of these parameters to achieve efficient coupling. These windows can be expressed in terms of the rate constants and equilibrium constants of the catalytic reactions, and the amplitude and frequency of the periodic field. This mechanism allows cells to receive, process and transmit energy of high and medium level periodic potentials by means of membrane enzymes or receptors. A theory for the transduction of electric energy, electroconformational coupling (ECC) will be discussed. The electric field induced cation pumping activities of Na,K-ATPase and Ca-ATPase of human erythrocytes and the ATP synthetic activity of beef heart mitochondrial ATPase will then be used to test an ECC membrane transport model. For the processing of low level periodic signals, a theory of an oscillatory activation barrier (OAB), which considers resonance transduction between an oscillating field and the activation barrier of the rate limiting step in an enzymic reaction, will be discussed. The OAB mechanism successfully interprets the AC stimulated ATP hydrolysis activity of Ecto-ATPase from chicken oviduct and F0F1-ATPase from beef heart. We propose that mechanisms similar to an OAB model are adopted by cells to sense weak electric, acoustic, mechanical, concentration (i.e., chemical potential) and other types of signals, and to communicate with other cells by these signals. The experimental data and mechanistic information presented in this communication give us a glimpse of the molecular electronic designs in living cells. This information is also relevant with respect to environmental issues. Environmental electromagnetic fields and sonic pollutants may interfere with normal communications of cells and organisms. Their benefit, if any, and detrimental effects can be assessed and dealt with only if we fully understand mechanisms of cellular interactions with these fields and pollutants, at the molecular level.     

New trends in cryoenzymology: probing the functional role of protein dynamics by single-step kinetics

Cryoenzymology was initially used to slow down enzyme-catalyzed reactions so as to stabilize intermediates for further study. During the course of this early work, it became clear that cryoenzymology could be extended to other ends and some of these are described. First, the use of a cryosolvent on its own (or together with temperature) as a perturbant has allowed a resolution of the substrate binding steps of certain enzymes (myosin, D-amino acid oxidase, peroxidase and cytochrome P450). Second, by the use of cryosolvent and temperature, coupled with the classical physico-chemical perturbants, one can selectively modulate the various steps of an enzyme pathway. This approach can lead to an understanding of the mechanism of enzyme regulation. Finally, by carrying out experiments over a wide range of temperatures (-30 degrees C- +30 degrees C) and pressure (up to several kbars) in specially constructed fast reaction equipment, one can study the thermodynamic properties of the individual rate constants describing the interconversions of reaction intermediates. Experiments with creatine kinase, cytochrome P450 and peroxidase are described. The thermodynamic parameters delta H, delta G, delta S and delta V are thus measured and when this is done under different solvent conditions one can, at least within the theories available, attempt an approach to the problem of protein dynamics.     

Dehydration of ribonucleotides catalyzed by ribonucleotide reductase: the role of the enzyme

This article focuses on the second step of the catalytic mechanism for the reduction of ribonucleotides catalyzed by the enzyme Ribonucleotide Reductase (RNR). This step corresponds to the protonation/elimination of the substrate's C-2' hydroxyl group. Protonation is accomplished by the neighbor Cys-225, leading to the formation of one water molecule. This is a very relevant step since most of the known inhibitors of this enzyme, which are already used in the fight against certain forms of cancer, are 2'-substituted substrate analogs. Even though some theoretical studies have been performed in the past, they have modeled the enzyme with minimal gas-phase models, basically represented by a part of the side chain of the relevant amino acids, disconnected from the protein backbone. This procedure resulted in a limited accuracy in the position and/or orientation of the participating residues, which can result in erroneous energetics and even mistakes in the choice of the correct mechanism for this step. To overcome these limitations we have used a very large model, including a whole R1 model with 733 residues plus the substrate and 10 A thick shell of water molecules, instead of the minimal gas-phase models used in previous works. The ONIOM method was employed to deal with such a large system. This model can efficiently account for the restrained mobility of the reactive residues, as well as the long-range enzyme-substrate interactions. The results gave additional information about this step, which previous small models could not provide, allowing a much clearer evaluation of the role of the enzyme. The interaction energy between the enzyme and the substrate along the reaction coordinate and the substrate steric strain energy have been obtained. The conclusion was that the barrier obtained with the present model was very similar to the one previously determined with minimal gas-phase models. Therefore, the role of the enzyme in this step was concluded to be mainly entropic, rather than energetic, by placing the substrate and the two reactive residues in a position that allows for the highly favorable concerted trimolecular reaction, and to protect the enzyme radical from the solvent.     

Thermodynamic analyses of the catalytic pathway of F1-ATPase from Escherichia coli. Implications regarding the nature of energy coupling by F1-ATPases

Thermodynamic properties of 12 different F1-ATPase enzymes were analyzed in order to gain insights into the catalytic mechanism and the nature of energy coupling to delta mu H+. The enzymes were normal soluble Escherichia coli F1, a group of nine beta-subunit mutant soluble E. coli F1 enzymes (G142S, K155Q, K155E, E181Q, E192Q, M209I, D242N, D242V, R246C), and both soluble and membrane-bound bovine heart mitochondrial F1. Unisite activity was studied by use of Gibbs free energy diagrams, difference energy diagrams, and derivation of linear free energy relationships. This allowed construction of binding energy diagrams for both the unisite ATP hydrolysis and ATP synthesis reaction pathways, which were in agreement. The binding energy diagrams showed that the step of Pi binding is a major energy-requiring step in ATP synthesis, as is the step of ATP release. It is suggested that there are two major catalytic enzyme conformations, and ATP- and an ADP-binding conformation. The effects of the mutations on the rate-limiting steps of multisite as compared to unisite activity were correlated, suggesting a direct link between the rate-limiting steps of the two types of activity. Multisite activity was analyzed by Arrhenius plots and by study of relative promotion from unisite to multisite rate. Changes in binding energy due to mutation were seen to have direct effects on multisite catalysis. From all the data, a model is derived to describe the mechanism of ATP synthesis. ATP hydrolysis, and energy coupling to delta mu H+ in F1F0-ATPases.     

Minimum energy conformations of proline-containing helices.

Proline occurs frequently in transmembrane alpha-helices of transport and receptor proteins even though statistical surveys demonstrate the overwhelming preference of this residue for a non-alpha-helical, hydrophilic environment. As a result, membrane-buried proline has been proposed to be functionally important, with function arising from structural discontinuity or destabilization of the helix. Destabilization may occur by Pro-mediated conformational transitions between discrete states, and may be manifested in membrane protein systems through reversible processes such as channel opening and closing or signal transduction. In this study, computer modeling of a model transmembrane alpha-helix, (Ala)8-Leu-Pro-Phe-(Ala)8, in a medium of low polarity (dielectric = 2), is used to examine the occurrence and energetic accessibility of Pro-mediated conformational interconversions. Leu psi and chi 1, Pro psi, and Phe phi and chi 1 torsion angles were assigned random values so that a data base of 200 conformations for each of the cis and trans states was generated. The conformations were minimized and low-energy structures organized into families. This analysis demonstrated that the most populated lowest energy family is the Trans-I conformation, corresponding to proline in a kinked alpha-helix. Two additional trans structures, Trans-II and Trans-III, as well as a cis conformation, Cis-I, are also energetically competitive. Interconversions between the trans states could thus be mediated by changes at a single torsion angle, accompanied by minor local hydrogen-bonding rearrangements. This work substantiates that membrane-buried proline can provide the basis for conformational transitions between discrete alpha-helix-based structures in a nonpolar environment.     

Combined DFT and electrostatics study of the proton pumping mechanism in cytochrome c oxidase

Cytochrome c oxidase is a redox-driven proton pump which converts atmospheric oxygen to water and couples the oxygen reduction reaction to the creation of a membrane proton gradient. The structure of the enzyme has been solved; however, the mechanism of proton pumping is still poorly understood. Recent calculations from this group indicate that one of the histidine ligands of enzyme's CuB center, His291, may play the role of the pumping element. In this paper, we report on the results of calculations that combined first principles DFT and continuum electrostatics to evaluate the energetics of the key energy generating step of the model-the transfer of the chemical proton to the binuclear center of the enzyme, where the hydroxyl group is converted to water, and the concerted expulsion of the proton from delta-nitrogen of His291 ligand of CuB center. We show that the energy generated in this step is sufficient to push a proton against an electrochemical membrane gradient of about 200 mV. We have also re-calculated the pKa of His291 for an extended model in which the whole Fe(a3)-CuB center with their ligands is treated by DFT. Two different DFT functionals (B3LYP and PBE0), and various dielectric models of the protein have been used in an attempt to estimate potential errors of the calculations. Although current methods of calculations do not allow unambiguous predictions of energetics in proteins within few pKa units, as required in this case, the present calculation provides further support for the proposed His291 model of CcO pump and makes a specific prediction that could be targeted in the experimental test.     

Molecular basis of the activity of the phytopathogen pectin methylesterase

We provide a mechanism for the activity of pectin methylesterase (PME), the enzyme that catalyses the essential first step in bacterial invasion of plant tissues. The complexes formed in the crystal using specifically methylated pectins, together with kinetic measurements of directed mutants, provide clear insights at atomic resolution into the specificity and the processive action of the Erwinia chrysanthemi enzyme. Product complexes provide additional snapshots along the reaction coordinate. We previously revealed that PME is a novel aspartic-esterase possessing parallel beta-helix architecture and now show that the two conserved aspartates are the nucleophile and general acid-base in the mechanism, respectively. Other conserved residues at the catalytic centre are shown to be essential for substrate binding or transition state stabilisation. The preferential binding of methylated sugar residues upstream of the catalytic site, and demethylated residues downstream, drives the enzyme along the pectin molecule and accounts for the sequential pattern of demethylation produced by both bacterial and plant PMEs.     

Stopped-flow fluorescence and steady-state kinetic studies of ligand-binding reactions of glucoamylase from Aspergillus niger.

The presteady-state and steady-state kinetics of the binding and hydrolysis of substrates, maltose and isomaltose, and the transition-state analogue, gluconolactone, by glucoamylase from Aspergillus niger were investigated using initial-rate, stopped-flow and steady-state methods. The change in the intrinsic fluorescence of the enzyme was monitored. Distinct mechanistic differences were observed in the interaction of the enzyme with maltose compared to isomaltose. Hydrolysis of maltose requires a three-step mechanism, whereas that of isomaltose involves at least one additional step. The rates of an observed conformational change, which is the second discernible step of the reactions, clearly show a tighter binding of maltose compared to isomaltose, probably because the reverse rate constants differ. Compared to the non-enzymic hydrolysis the transition-state stabilization energy of glucoamylase is approximately -66 kJ/mol with maltose and only -14 kJ/mol with isomaltose. Kinetic analysis of the binding of the inhibitor, gluconolactone, implies that independent interactions of two molecules occur. One of these, apparently, is a simple, fast association reaction in which gluconolactone is weakly bound. The other resembles binding of maltose, involving a fast association followed by a conformational change. Based on the results obtained, we propose new reaction mechanisms for Aspergillus glucoamylase.     

Promotion of Enzyme Flexibility by Dephosphorylation and Coupling to the Catalytic Mechanism of a Phosphohexomutase

The enzyme phosphomannomutase/phosphoglucomutase (PMM/PGM) from Pseudomonas aeruginosa catalyzes an intramolecular phosphoryl transfer across its phosphosugar substrates, which are precursors in the synthesis of exoproducts involved in bacterial virulence. Previous structural studies of PMM/PGM have established a key role for conformational change in its multistep reaction, which requires a dramatic 180° reorientation of the intermediate within the active site. Here hydrogen-deuterium exchange by mass spectrometry and small angle x-ray scattering were used to probe the conformational flexibility of different forms of PMM/PGM in solution, including its active, phosphorylated state and the unphosphorylated state that occurs transiently during the catalytic cycle. In addition, the effects of ligand binding were assessed through use of a substrate analog. We found that both phosphorylation and binding of ligand produce significant effects on deuterium incorporation. Phosphorylation of the conserved catalytic serine has broad effects on residues in multiple domains and is supported by small angle x-ray scattering data showing that the unphosphorylated enzyme is less compact in solution. The effects of ligand binding are generally manifested near the active site cleft and at a domain interface that is a site of conformational change. These results suggest that dephosphorylation of the enzyme may play two critical functional roles: a direct role in the chemical step of phosphoryl transfer and secondly through propagation of structural flexibility. We propose a model whereby increased enzyme flexibility facilitates the reorientation of the reaction intermediate, coupling changes in structural dynamics with the unique catalytic mechanism of this enzyme.     

Reduction of intrinsic kinetic and thermodynamic barriers for enzyme-catalysed proton transfers from carbon acid substrates

Many enzymes catalyse the heterolytic abstraction of the alpha-proton from a carbon acid substrate. Gerlt and Gassman have applied Marcus formalism to such proton transfer reactions to argue that transition states for concerted general acid-general base catalysed enolization at enzyme active sites occur late on the reaction coordinate (J. Am. Chem. Soc. 115 (1993) 11552). We postulate that as an enzyme evolves, it may decrease deltaG++ for a proton transfer step associated with substrate enolization by following the path of steepest descent on the two-dimensional surface corresponding to deltaG++, as defined by Marcus formalism. We show that for an enzyme that has decreased deltaG++ following the path of steepest descent, the values of the intrinsic kinetic (deltaG++(int,E)) and thermodynamic (deltaG(E)0) barriers for proton transfer reactions on the enzyme may be predicted from the known values of deltaG++(int,N) and deltaG(N)0 for the corresponding non-enzymic reaction and the free energy of activation on the enzyme (deltaG++(E)). In addition, the enzymic transition state will occur later on the reaction coordinate than the corresponding non-enzymic transition state (i.e. x++(E)>x++(N)) if the condition (6 - square root 2)/82deltaG++(int,N).     

Crystal Structure,SAXS and Kinetic Mechanism of Hyperthermophilic ADP-Dependent Glucokinase from Thermococcus litoralis Reveal a Conserved Mechanism for Catalysis

ADP-dependent glucokinases represent a unique family of kinases that belong to the ribokinase superfamily, being present mainly in hyperthermophilic archaea. For these enzymes there is no agreement about the magnitude of the structural transitions associated with ligand binding and whether they are meaningful to the function of the enzyme. We used the ADP-dependent glucokinase from Termococcus litoralis as a model to investigate the conformational changes observed in X-ray crystallographic structures upon substrate binding and to compare them with those determined in solution in order to understand their interplay with the glucokinase function. Initial velocity studies indicate that catalysis follows a sequential ordered mechanism that correlates with the structural transitions experienced by the enzyme in solution and in the crystal state. The combined data allowed us to resolve the open-closed conformational transition that accounts for the complete reaction cycle and to identify the corresponding clusters of aminoacids residues responsible for it. These results provide molecular bases for a general mechanism conserved across the ADP-dependent kinase family.     

Temperature dependence of the rate constants of the Escherichia coli RNA polymerase-lambda PR promoter interaction. Assignment of the kinetic steps corresponding to protein conformational change and DNA opening

The kinetics of formation and of dissociation of open complexes (RPo) between Escherichia coli RNA polymerase (R) and the lambda PR promoter (P) have been studied as a function of temperature in the physiological range using the nitrocellulose filter binding assay. The kinetic data provide further evidence for the mechanism R + P in equilibrium I1 in equilibrium I2 in equilibrium RPo, where I1 and I2 are kinetically distinguishable intermediate complexes at this promoter which do not accumulate under the reaction conditions investigated. The overall second-order association rate constant (ka) increases dramatically with increasing temperature, yielding a temperature-dependent activation energy in the range 20 kcal (near 37 degrees C) to 40 kcal (near 13 degrees C) (1 kcal = 4.184 kJ). Both isomerization steps (I1----I2 and I2----RPo) appear to be highly temperature dependent. Except at low temperatures (less than 13 degrees C) the step I1----I2, which we attribute to a conformational change in the polymerase with a large negative delta Cp degrees value, is rate-limiting at the reactant concentrations investigated and hence makes the dominant contribution to the apparent activation energy of the pseudo first-order association reaction. The subsequent step I2----RPo, which we attribute to DNA melting, has a higher activation energy (in excess of 100 kcal) but only becomes rate-limiting at low temperature (less than 13 degrees C). The initial binding step R + P in equilibrium I1 appears to be in equilibrium on the time-scale of the isomerization reactions under all conditions investigated; the equilibrium constant for this step is not a strong function of temperature and is approximately 10(7) M-1 under the standard ionic conditions of the assay (40 mM-Tris . HCl (pH 8.0), 10 mM-MgCl2, 0.12 M-KC1). The activation energy of the dissociation reaction becomes increasingly negative at low temperatures, ranging from approximately -9 kcal near 37 degrees C to -30 kcal near 13 degrees C. Thermodynamic (van't Hoff) enthalpies delta H degrees of open complex formation consequently are large and temperature-dependent, increasing from approximately 29 to 70 kcal as the temperature is reduced from 37 to 13 degrees C. The corresponding delta Cp degrees value is approximately -2.4 kcal/deg. We propose that this large negative delta Cp degrees value arises primarily from the burial of hydrophobic surface in the conformational change (I1 in equilibrium I2) in RNA polymerase in the key second step of the mechanism.(ABSTRACT TRUNCATED AT 400 WORDS)     

Rethinking the P-type ATPase problem

There are very good reasons to stop thinking about the molecular mechanism of the P-type ion-translocating ATPases in terms of the traditional E1E2 model and to start thinking about it in more progressive ways. This makes it possible to see the ion-transport cycle as a rational series of discrete steps with well defined driving forces, including the crucial energy transduction step, where the chemical energy of ATP hydrolysis is exchanged for the osmotic energy of an ion gradient. Importantly, although major enzyme conformational changes accompany each of these steps, none of them drive the energy coupling reaction. Thus, neither the E1E2 model nor conformational energy coupling, the cornerstones of traditional thinking about the P-type ATPases, are reliable paradigms for future efforts to understand how these transporters work. Alternatives must be seriously considered.     

Intracellular mitochondrial membrane potential as an indicator of hepatocyte energy metabolism: further evidence for thermodynamic control of metabolism

The lipophilic triphenylmethylphosphonium cation (TPMP+) has been employed to measure delta psi m, the electrical potential across the inner membrane of the mitochondria of intact hepatocytes. The present studies have examined the validity of this technique in hepatocytes exposed to graded concentrations of inhibitors of mitochondrial energy transduction. Under these conditions, TPMP+ uptake allows a reliable measure of delta psi m in intracellular mitochondria, provided that the ratio [TPMP+]i/[TPMP+]e is greater than 50:1 and that at the end of the incubation more than 80% of the hepatocytes exclude Trypan blue. Hepatocytes, staining with Trypan blue, incubated in the presence of Ca2+, do not concentrate TPMP+. The relationships between delta psi m and two other indicators of cellular energy state, delta GPc and Eh, or between delta psi m and J0, were examined in hepatocytes from fasted rats by titration with graded concentrations of inhibitors of mitochondrial energy transduction. Linear relationships were generally observed between delta psi m and delta GPc, Eh or J0 over the delta psi m range of 120-160 mV, except in the presence of carboxyatractyloside or oligomycin, where delta psi m remained constant. Both the magnitude and the direction of the slope of the observed relationships depended upon the nature of the inhibitor. Hepatocytes from fasted rats synthesized glucose from lactate or fructose, and urea from ammonia, at rates which were generally linear functions of the magnitude of delta psi m, except in the presence of oligomycin or carboxyatractyloside. Linear relationships were also observed between delta psi m and the rate of formation of lactate in cells incubated with fructose and in hepatocytes from fed rats. The linear property of these force-flow relationships is taken as evidence for the operation of thermodynamic regulatory mechanisms within hepatocytes.