scholarly journals Rates of reactions catalysed by a dimeric enzyme. Effects of the reaction scheme and the kinetic parameters on co-operativity

1991 ◽  
Vol 280 (1) ◽  
pp. 131-137 ◽  
Author(s):  
H Ishikawa ◽  
H Ogino ◽  
H Oshida
Keyword(s):  
Substrate Inhibition ◽  
Reaction Scheme ◽  
Rate Equations ◽  
Kinetic Behaviour ◽  
Hill Coefficients ◽  
S Curve ◽  
Almost All ◽  
The Hill ◽  
Rate Behaviour ◽  
Reaction Schemes

For the reaction S in equilibrium P catalysed by a dimeric enzyme, the reaction schemes are considered on the basis of the KNF model. For each of the ten possible schemes, the rate equation is derived on the basis of the combined steady-state and rapid-equilibrium assumptions. The curves of the plots of initial velocity v versus the substrate concentration [S] and the Hill coefficients h calculated from the rate equations depend strongly on the reaction scheme and the parameter X1. This parameter is defined by log (KS2/KS1) and is a measure of the relative affinities of the first and second protomers for the substrate. When X1 less than 0, v-[S] curves for some schemes exhibit negative co-operativity (h less than 1.0) and v-[S] curves for other schemes are similar to that of the Michaelis-Menten scheme, indicating that, even if there is interaction between the distinct protomers, sigmoidal rate behaviour is not necessarily observed. When X1 greater than 0, all the reaction schemes except one, which shows substrate-inhibition kinetic behaviour, exhibit sigmoidal kinetic behaviour (h greater than 1.0), and at the limit of X1 much greater than 0 the Hill coefficients attain the maximum possible value of 2.0. Furthermore, we have found that, even if X1 = 0, the v-[S] curve for almost all the schemes considered in the present work does not necessarily agree with that for the Michaelis-Menten scheme. This means that the deviation of the v-[S] curve from a hyperbola can be observed even if there is no interaction between the distinct protomers.

Thermodynamic framework for design of reaction rate equations and schemes

2009 ◽  
Vol 74 (9) ◽  
pp. 1375-1401 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Experimental Data ◽  
Reaction Network ◽  
Phenomenological Theory ◽  
Reaction Scheme ◽  
Rate Function ◽  
Irreversible Thermodynamics ◽  
Mass Action ◽  
Rate Equations ◽  
Additional Hypothesis ◽  
Reaction Schemes

It has been shown previously that rational thermodynamics provides general foundations of mass-action kinetic law from the principles of continuum, irreversible thermodynamics. Practical outcomes of this phenomenological theory are analyzed and compared with traditional kinetic approaches on the example of N2O decomposition. It is revealed that classical rate equations are only simplified forms of a polynomial approximation to a general rate function proved by the continuum thermodynamics. It is also shown that various special considerations that have been introduced formerly as additional hypothesis to satisfactorily describe experimental data are naturally included in the thermodynamic approach. The method, in addition, makes it possible to obtain more general mass-action-type rate equations that give better description of experimental data than the traditional ones. The method even reverses the classical kinetic paradigm – reaction scheme directly follows from the rate equation. Data fitting by this method also indicates connections to distinctions between processes at the molecular level and their representation by some macroscopic reaction network. The role of dependent and independent reactions in reaction kinetics and reaction schemes is clarified. A selected example demonstrates that this thermodynamic methodology may improve our design and understanding of thermodynamically and mathematically necessary and sufficient reaction schemes. The phenomenological theory thus sheds new, “thermodynamic” light on what has been and is done by generations of kineticists and gives new hints how to do it in a way consistent with non-equilibrium thermodynamics.

scholarly journals Deviations from Michaelis-Menten kinetics. The possibility of complicated curves for simple kinetic schemes and the computer fitting of experimental data for acetylcholinesterase, acid phosphatase, adenosine deaminase, arylsulphatase, benzylamine oxidase, chymotrypsin, fumarase, galactose dehydrogenase, β-galactosidase, lactate dehydrogenase, peroxidase and xanthine oxidase

1980 ◽  
Vol 187 (3) ◽  
pp. 739-765 ◽  
Author(s):  
W G Bardsley ◽  
P Leff ◽  
J Kavanagh ◽  
R D Waight
Keyword(s):  
Experimental Data ◽  
Rate Equation ◽  
Substrate Inhibition ◽  
Rate Equations ◽  
Double Reciprocal Plot ◽  
Binding Model ◽  
Steady State Rate ◽  
Benzylamine Oxidase ◽  
S Curve ◽  
Galactose Dehydrogenase

The possible graph shapes for one-site/two-state and substrate-modifier models are discussed. The two-state model is a version of the Monod-Wyman-Changeux model and gives a rate equation with 240 denominator terms. Discussion in terms of K and V effects is not possible. A simplified version of the mechanism can be shown to give v-versus-[S] curves that are either sigmoid or non-sigmoid. They may show substrate inhibition or no final maximum, and the double-reciprocal plots can be concave up or down. The corresponding binding model is determined by only two constants and gives a linear double-reciprocal plot. The substrate-modifier mechanism is a simple example of a mechanism where inclusion of catalytic steps leads to a genuine increase in degree of the rate equation. The v-versus-[S] curve can show such complexities as two maxima and a minimum, and the double-reciprocal plot can cross its asymptote twice, proving the rate equation to be 4:4. A simplified version is 3:3, and analysis shows that at least 18 of the 27 double-reciprocal plots that can arise with 3:3 functions are possible with this particular mechanism. Representative double-reciprocal and Scatchard plots are presented for several sets of rate-constant values. It is concluded that relatively simple mechanisms give pseudo-steady-state rate equations of high degree and considerable complexity. With extended ranges of substrate concentrations there is every reason to believe that experimental data would show the sort of deviations from Michaelis-Menten kinetics seen with calculated curves for such simple mechanisms. Narrow ranges of substrate concentration, on the other hand, would lead to inflexions and curvature being overlooked. It is not possible to discuss such deviations from Michaelis-Menten kinetics in terms of kinetic constants such as Km and V, and, in general, it is also difficult to see any simple way to explain intuitively such features as sigmoidicity, substrate inhibition, double-reciprocal convexity and decrease in degree by cancellation of common factors between numerator and denominator of rate equations. These conclusions apply with even more force when catalytic steps are included, for then the rate equations, are for multi-site mechanisms, of higher degree, allowing increasingly complex curve shapes. A number of enzymes were studied and initial-rate data were fitted by computer.(ABSTRACT TRUNCATED AT 400 WORDS)

Effect of osmotic swelling and shrinkage on Na(+)-K+ pump activity in mammalian cardiac myocytes

1993 ◽  
Vol 265 (5) ◽  
pp. C1201-C1210 ◽  
Author(s):  
D. W. Whalley ◽  
L. C. Hool ◽  
R. E. Ten Eick ◽  
H. H. Rasmussen
Keyword(s):  
Ventricular Myocytes ◽  
Pump Current ◽  
Hill Equation ◽  
Cell Swelling ◽  
Intracellular Na Activity ◽  
Single Ventricular Myocytes ◽  
Hyperosmolar Solutions ◽  
Hill Coefficients ◽  
The Hill ◽  
The Relationship

The effect on the sarcolemmal Na(+)-K+ pump of exposure to anisosmolar solutions was examined using whole cell patch clamping and ion-selective microelectrodes. Na(+)-K+ pump currents were measured in single ventricular myocytes by using pipette Na+ concentrations ([Na]pip) of 0-70 mM. The relationship between [Na]pip and pump current was well described by the Hill equation. The [Na]pip for half-maximal pump current (K0.5) was 21.4 mM in isosmolar (310 mosM) solution. K0.5 was 12.8 mM during cell swelling in hyposmolar solution (240 mosM) and 39.0 mM during cell shrinkage in hyperosmolar solution (464 mosM). The maximal pump currents, derived from the best fit of the Hill equation, and the Hill coefficients were similar in isosmolar, hyposmolar, and hyperosmolar solutions. A sustained (> 20 min) decrease in the intracellular Na+ activity developed during exposure of intact papillary muscles to hyposmolar solutions, and a sustained increase developed during exposure to hyperosmolar solutions. We conclude that osmotic myocyte swelling stimulates the sarcolemmal Na(+)-K+ pump at near-physiological levels of intracellular Na+, whereas shrinkage inhibits the pump. These changes are due to increases and decreases, respectively, in the apparent affinity of the pump for Na+.

Sodium-dependent succinate transport by isolated chick intestinal cells

1991 ◽  
Vol 260 (6) ◽  
pp. C1151-C1157 ◽  
Author(s):  
G. A. Kimmich ◽  
J. Randles ◽  
E. Bennett
Keyword(s):  
Transport System ◽  
Renal Tissue ◽  
Transport Rate ◽  
Hill Coefficient ◽  
Intestinal Epithelial ◽  
Coupled Transport ◽  
Renal Epithelium ◽  
Metabolic Intermediates ◽  
Hill Coefficients ◽  
The Hill

Isolated chick intestinal epithelial cells take up succinate by a Na(+)-coupled transport system similar in some characteristics to those described for renal epithelium. The transport system exhibits a hyperbolic dependence on succinate concentration but a sigmoidal dependence on Na+ concentration. Best nonlinear fit of the Na+ dependence data to the Hill equation indicates a Michaelis constant for half-maximal transport rate (Km) for Na+ of approximately 20 mM, a maximal transport rate (Vmax) of 1.1 nmol succinate.min-1.mg protein-1, and a Hill coefficient of 2.5. Nearly equivalent fit was obtained with trial Hill coefficients down to 2.0. The data for succinate dependence indicated a Km of 25 microM and Vmax of 1.05 nmol.min-1.mg protein-1. The kinetic parameters indicate a higher affinity, lower capacity system than for succinate transport in the renal brush-border system. Thiocyanate-induced diffusion potentials cause no change in Na(+)-dependent succinate influx despite pronounced effects on the influx of tetraphenylphosphonium and on Na(+)-dependent alpha-methylglucoside (AMG) and alanine uptake. Several other dicarboxylic and tricarboxylic metabolic intermediates (but not the dicarboxylic amino acids) compete with succinate for uptake via the transport system. The data are consistent with the likelihood that these cells have a succinate transport system with a 2Na+:1succinate stoichiometry per transport cycle. The system catalyzes no net charge transfer and is therefore different from the potential-responsive succinate transporter described for renal tissue.

scholarly journals Beyond non-integer Hill coefficients: A novel approach to analyzing binding data, applied to Na+-driven transporters

2015 ◽  
Vol 145 (6) ◽  
pp. 555-563 ◽  
Author(s):  
Silvia Ravera ◽  
Matthias Quick ◽  
Juan P. Nicola ◽  
Nancy Carrasco ◽  
L. Mario Amzel
Keyword(s):  
Hill Equation ◽  
Integer Coefficient ◽  
Novel Approach ◽  
Binding Data ◽  
Na Ions ◽  
Hill Coefficients ◽  
Integer Exponent ◽  
The Individual ◽  
The Hill ◽  
Analyze Data

Prokaryotic and eukaryotic Na+-driven transporters couple the movement of one or more Na+ ions down their electrochemical gradient to the active transport of a variety of solutes. When more than one Na+ is involved, Na+-binding data are usually analyzed using the Hill equation with a non-integer exponent n. The results of this analysis are an overall Kd-like constant equal to the concentration of ligand that produces half saturation and n, a measure of cooperativity. This information is usually insufficient to provide the basis for mechanistic models. In the case of transport using two Na+ ions, an n < 2 indicates that molecules with only one of the two sites occupied are present at low saturation. Here, we propose a new way of analyzing Na+-binding data for the case of two Na+ ions that, by taking into account binding to individual sites, provides far more information than can be obtained by using the Hill equation with a non-integer coefficient: it yields pairs of possible values for the Na+ affinities of the individual sites that can only vary within narrowly bounded ranges. To illustrate the advantages of the method, we present experimental scintillation proximity assay (SPA) data on binding of Na+ to the Na+/I− symporter (NIS). SPA is a method widely used to study the binding of Na+ to Na+-driven transporters. NIS is the key plasma membrane protein that mediates active I− transport in the thyroid gland, the first step in the biosynthesis of the thyroid hormones, of which iodine is an essential constituent. NIS activity is electrogenic, with a 2:1 Na+/I− transport stoichiometry. The formalism proposed here is general and can be used to analyze data on other proteins with two binding sites for the same substrate.

The hydrolysis of maleimide in alkaline solution

1976 ◽  
Vol 54 (9) ◽  
pp. 1400-1404 ◽  
Author(s):  
Remigio Germano Barradas ◽  
Stephen Fletcher ◽  
John Douglas Porter
Keyword(s):  
Alkaline Solution ◽  
Reaction Scheme ◽  
Rate Equations ◽  
Bulk Concentration ◽  
Rate Of Reaction ◽  
Ph Range ◽  
Derived Data ◽  
Hydrolysis Of

The hydrolysis of maleimide has been investigated in the pH range 8.5–14. Polarographic limiting currents were well-defined, so that the bulk concentration of reactant during reduction could be clearly followed as a function of time. Logarithmic analysis of derived data indicated an arrest in the rate of reaction at circa pH 12, and a reaction scheme is proposed to explain this. In this scheme, the neutral maleimide molecule exists in equilibrium with its anion, and both of these species may undergo hydrolysis at the appropriate pH. From derived rate equations, the pKa of maleimide was found to be 10.0, whilst estimates of the rates of hydrolysis were also calculated.

scholarly journals Ring of Negative Charge in BK Channels Facilitates Block by Intracellular Mg2+ and Polyamines through Electrostatics

2006 ◽  
Vol 128 (2) ◽  
pp. 185-202 ◽  
Author(s):  
Yaxia Zhang ◽  
Xiaowei Niu ◽  
Tinatin I. Brelidze ◽  
Karl L. Magleby
Keyword(s):  
Negative Charge ◽  
Outward Current ◽  
Bk Channels ◽  
Inward Rectification ◽  
Dependent Manner ◽  
Conduction Pathway ◽  
Boltzmann Function ◽  
Voltage Dependent ◽  
Hill Coefficients ◽  
The Hill

Intracellular Mg2+ and natural polyamines block outward currents in BK channels in a highly voltage-dependent manner. Here we investigate the contribution of the ring of eight negatively charged residues (4 x E321/E324) at the entrance to the inner vestibule of BK channels to this block. Channels with or without (E321N/E324N) the ring of negative charge were expressed in oocytes and unitary currents were recorded from inside-out patches over a range of intracellular Mg2+ and polyamine concentrations. Removing the ring of charge greatly decreased the block, increasing KBap (0 mV) for Mg2+ block from 48.3 ± 3.0 to 143 ± 8 mM, and for spermine block from 8.0 ± 1.0 to 721 ± 9 mM (150 mM symmetrical KCl). Polyamines with fewer amine groups blocked less: putrescine < spermidine < spermine. An equation that combined an empirical Hill function for block together with a Boltzmann function for the voltage dependence of KBap described the voltage and concentration dependence of the block for channels with and without the ring of charge. The Hill coefficients for these descriptions were <1 for both Mg2+ and spermine block, and were unchanged by removing the ring of charge. When KCli was increased from 150 mM to 3 M, the ring of charge no longer facilitated block, Mg2+ block was reduced, spermine block became negligible, and the Hill coefficients became ∼1.0. BK channels in cell-attached oocyte patches displayed inward rectification, which was reduced for channels without the ring of charge. Taken together, these observations suggest that the ring of negative charge facilitates block through a preferential electrostatic attraction of Mg2+ and polyamine over K+. This preferential attraction of multivalent blockers over monovalent K+ would decrease the K+ available at the inner vestibule to carry outward current in the presence of Mg2+ or polyamines, while increasing the concentration of blocker available to enter and block the conduction pathway.

Kinetics of volume-sensitive K transport in human erythrocytes: evidence for asymmetry

1989 ◽  
Vol 256 (6) ◽  
pp. C1214-C1223 ◽  
Author(s):  
D. M. Kaji
Keyword(s):  
Statistical Significance ◽  
High Capacity ◽  
Human Erythrocytes ◽  
Kinetic Properties ◽  
Maximal Velocity ◽  
Hill Coefficients ◽  
The Difference ◽  
K Concentration ◽  
The Hill ◽  
External K

The kinetic properties of volume-sensitive K fluxes in swollen human erythrocytes were investigated. Swelling-activated Cl-dependent K influx was a saturable function of external K concentration with a low affinity (apparent Km of 115-130 mM) and high capacity [maximal velocity (Vmax) = 20-30 mmol.l original cells-1.h-1 (mmol.loc-1.h-1)]. The Vmax and apparent Km for Cl-dependent K efflux were lower (Km = 47 mM; Vmax = 2.2 mmol.loc-1.h-1). The Hill coefficients for both K efflux and influx were close to unity, suggesting a single binding site for K. The increase of external K trans-stimulated K efflux, but the increase of intracellular K had no effect on Cl-dependent K influx in swollen cells. Under zero trans conditions, the Vmax (18 vs. 3 mmol.loc-1.h-1) and Km (138 vs. 32) were markedly different for influx and efflux, respectively. These results provide evidence for intrinsic functional asymmetry, such that the transporter is more prevalent and stable in the outward-facing conformation. The mean ratio of Km to Vmax for efflux (12.1) was 1.56 times larger than the same ratio for influx (7.8), but the difference between the means did not reach statistical significance. These kinetic observations are analyzed in terms of the simple carrier and the cotransport models.

scholarly journals Roles of active-site residues in catalysis, substrate binding, cooperativity, and the reaction mechanism of the quinoprotein glycine oxidase

2020 ◽  
Vol 295 (19) ◽  
pp. 6472-6481
Author(s):  
Kyle J. Mamounis ◽  
Erik T. Yukl ◽  
Victor L. Davidson
Keyword(s):  
Active Site ◽  
Protein Function ◽  
Marine Bacterium ◽  
Substrate Binding ◽  
Active Site Residues ◽  
X Ray Crystallography ◽  
Steady State Kinetics ◽  
Hill Coefficients ◽  
The Hill ◽  
Glycine Oxidase

The quinoprotein glycine oxidase from the marine bacterium Pseudoalteromonas luteoviolacea (PlGoxA) uses a protein-derived cysteine tryptophylquinone (CTQ) cofactor to catalyze conversion of glycine to glyoxylate and ammonia. This homotetrameric enzyme exhibits strong cooperativity toward glycine binding. It is a good model for studying enzyme kinetics and cooperativity, specifically for being able to separate those aspects of protein function through directed mutagenesis. Variant proteins were generated with mutations in four active-site residues, Phe-316, His-583, Tyr-766, and His-767. Structures for glycine-soaked crystals were obtained for each. Different mutations had differential effects on kcat and K0.5 for catalysis, K0.5 for substrate binding, and the Hill coefficients describing the steady-state kinetics or substrate binding. Phe-316 and Tyr-766 variants retained catalytic activity, albeit with altered kinetics and cooperativity. Substitutions of His-583 revealed that it is essential for glycine binding, and the structure of H583C PlGoxA had no active-site glycine present in glycine-soaked crystals. The structure of H767A PlGoxA revealed a previously undetected reaction intermediate, a carbinolamine product-reduced CTQ adduct, and exhibited only negligible activity. The results of these experiments, as well as those with the native enzyme and previous variants, enabled construction of a detailed mechanism for the reductive half-reaction of glycine oxidation. This proposed mechanism includes three discrete reaction intermediates that are covalently bound to CTQ during the reaction, two of which have now been structurally characterized by X-ray crystallography.

scholarly journals Validity of the Force-Velocity Relation for Muscle Contraction in the Length Region, l ≤ l0

1967 ◽  
Vol 50 (5) ◽  
pp. 1125-1137 ◽  
Author(s):  
Yorimi Matsumoto
Keyword(s):  
Length Change ◽  
Hill Equation ◽  
Isometric Tension ◽  
Resting Tension ◽  
Reference Length ◽  
Velocity Relation ◽  
Force Velocity ◽  
Almost All ◽  
The Hill ◽  
Isotonic Shortening

Considerable attention has been directed to the characteristic force-velocity relation discovered by A. V. Hill in the study of muscle kinematics. Models of contractile process were tested on the basis of their compatibility with the Hill equation. However, almost all the isotonic data have been restricted to one length, l0, the maximum length with almost no resting tension; the velocities measured are those initial values when the load begins to move. The force-velocity curve extrapolates to zero velocity for isometric tension, but only for the tension at that one length. Very few efforts have been made to study the profiles of the curves throughout the range of lengths over which shortening takes place. In examining the length region, l ≤ l0, for an isotonically contracting muscle, not only is the force-velocity relation valid for the initial reference length, l0, but also for any other length. The analysis in this report indicates that the constants a/P0 and b/l0 remain fixed throughout the length change of afterloaded isotonic shortening in the Rana pipiens sartorius muscles.

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