Graphic method for determination of allosteric constants

The maximum slope of the plot, appearing in the paper of Watari & Isogai (1976), was derived algebraically as a function of allosteric constants c and α_mor β_m (= cα_m), and the relation between L, c, and α_mor β_m, was also obtained, where $\text{L =}\text{T}{}_{\mathrm{o}}\text{R}{}_{\mathrm{o}}\text{, c =}\text{K}{}_{\mathrm{R}}\text{K}{}_{\mathrm{T}}\text{, α}{}_{\mathrm{m}}\text{=}\text{F}{}_{\mathrm{m}}\text{K}{}_{\mathrm{R}}\text{, β}{}_{\mathrm{m}}\text{=}\text{F}{}_{\mathrm{m}}\text{K}{}_{\mathrm{T}}\text{, R}{}_{\mathrm{o}}\text{and}\text{T}{}_{\mathrm{o}}$ are concentrations of unligated R and T states respectively, K_Rand K_T are microscopic dissociation constants, and F_m is the ligand concentration at the maximum slope of the plot. When the maximum slope is increased by one, the value becomes Hill constant, n. Nomographs which enable easier estimation of allosteric constants, L and c, were constructed from the two given values, the maximum slope of the plot, n ? 1, and α_mor β_m, in the cases where the maximum number of ligands, N, was 2 and 4. In the nomograph, log c is plotted against log L²c^N keeping the value of the maximum slope of the plot and that of α_mor β_m constant. These nomographs show that the representation is symmetrical in the cases of L²c^N > 1 and L²c^N < 1.     

Effects of oligomycin and quercetin on the hydrolytic activities of the (Na+ + K+)-dependent ATPase

Quercetin inhibited a dog kidney ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ preparation without affecting $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ for ATP or $\text{K}{}_{0.5}$ for cation activators, attributable to the slowly-reversible nature of its inhibition. Dimethyl sulfoxide, a selector of E₂ enzyme conformations, blocked this inhibition, while the K⁺-phosphatase activity was at least as sensitive to quercetin as the ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ activity, all consistent with quercetin favoring E₁ conformations of the enzyme. Oligomycin, a rapidly-reversible inhibitor, decreased the $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ for ATP and the $\text{K}{}_{0.5}$ for cation activators, and its inhibition was also diminished by dimethyl sulfoxide. Although oligomycin did not inhibit the K⁺-phosphatase activity under standard assay conditions, a reaction presumably catalyzed by E₂ conformations, its effects are nevertheless accommodated by a quantitative model for that reaction depicting oligomycin as favoring E₁ conformations. The model also accounts quantitatively for effects of both dimethyl sulfoxide and oligomycin on $\text{V}{}_{\mathrm{<mtext>max</mtext>}}$, $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ for substrate, and $\text{K}{}_{0.5}$ for K⁺, as well as for stimulation of phosphatase activity by both these reagents at low K⁺ but high Na⁺ concentrations.     

Bacillus subtilis aminopeptidase: specificity toward amino acyl-beta-naphthylamides.

The kinetic parameters for the hydrolyses of different l-α-amino acid-β-naphthylamides by Bacillus subtilis aminopeptidase have been measured for the native enzyme and for the enzyme activated in 5 mm Co(NO₃)₂. In most cases Co²⁺ activation decreased K_m(app) values and increased k_cat values, in other cases k_m(app) and k_cat values were increased; for the remainder of the substrates tested k_m(app) values and k_cat values were decreased. In all cases tested the ratios of $\text{(}\text{k}\text{cat}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)</mtext>}}\text{)}\text{CO}{}^{\mathrm{2+}}\text{/(}\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)nativ</mtext>}}\text{)}$ were increased (2- to 108-fold). For the native enzyme the order of specificity toward the l-amino acid-β-naphthylamides was Arg > Met > Trp > Lys > Leu and for the Co²⁺ activated enzyme the order of specificity was Lys > Arg > Met > Trp > Leu. The native enzyme hydrolyzed Pro-β-naphthylamide, but not α-Glu-β-naphthylamide; Co²⁺ activation of the enzyme affected an appreciable rate of hydrolysis of the latter substrate.     

Protein affinities for small molecules: conceptions and misconceptions.

There is much confusion and error in published treatments of data for multiple binding of ligands (e.g., substrates) by proteins (e.g., enzymes). There is a widespread impression that if the equilibrium binding, r, of ligand, A, by a protein with n sites can be fitted to an equation with two hyperbolic terms, i.e., $\text{r=}\text{n}{}_{\mathrm{\alpha }}\text{k}{}_{\mathrm{\alpha }}\text{(A)}\text{1+k}{}_{\mathrm{\alpha }}\text{(A)}\text{+}\text{n}{}_{\mathrm{\beta }}\text{k}{}_{\mathrm{\beta }}\text{(A)}\text{1+k}{}_{\mathrm{\beta }}\text{(A)}\text{(n}{}_{\mathrm{\alpha }}\text{+n}{}_{\mathrm{\beta }}\text{=n)}$ then k_β and k_β are always the intrinsic binding constants for two sets of sites. Such a conclusion is often incorrect. For example, in many cases, the protein is constituted of identical protomers with initially identical sites for binding ligands, and yet graphical representations of the binding data appear to behave as if the sites are partitioned between two classes. Although the use of a linear combination of hyperbolic terms to represent binding of ligands by macromolecules always yields empirical parameters k_α, k_β … k_λ, they cannot correspond to site binding constants when there are interactions between sites. In some circumstances their values may even be imaginary, complex numbers. On the other hand, stoichiometric binding constants can be assigned unambiguously without making any assumption regarding the nature of the interactions among binding sites. These principles are illustrated concretely by analyses of binding measurements for several different proteins containing two to six sites.     

Lifetime of microsomal cytochrome P-450 and steroidogenic enzymes in rat testis as influenced by human chorionic gonadotrophin

The lifetime of different microsomal steroidogenic enzymes and the cytochrome components of the NADPH-cytochrome P-450 pathway have been determined in rat testis by measuring their decrease logarithmically after hypophysectomy. Although both cytochrome P-450 and 17α-hydroxylase show biphasic decay curves, the first decay curve contains 89–94% of the cytochrome P-450 and 17α-hydroxylase levels. Steroidogenic enzymes which are located mainly in the leydig cells, decay much faster than microsomal protein, $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 12}$ days, which represents mainly decay of tubular protein. The similarity between the major half-life of cytochrome P-450, $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.3}$ days, 17α-hydroxylase, $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 2.3}$ days and the C₁₇–C₂₀ lyase, $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.4}$ days and the uniformity of their response to human chorionic gonadotrophin (HCG) provides additional evidence that these two steroidogenic enzymes require cytochrome P-450. Both the 17α-hydroxylase and the C₁₇–C₂₀ lyase were shown to have a constant activity per nmole of cytochrome P-450 during a sixfold change in the level of cytochrome P-450 brought about by HCG treatment of rats with intact pituitaries. The decay of 17β-hydroxysteroid dehydrogenase, $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 4.5}$ days, was slower than P-450 dependent enzymes. Rats with intact pituitaries are not under maximal stimulation by endogenous LH because addition of HCG increases the levels of microsomal and mitochondrial cytochrome P-450 220 and 1620%, respectively. The rates of synthesis during the increase from one cytochrome P-450 level to another was calculated at $\text{0.118}\text{2}$ testes/day for microsomal cytochrome P-450 and 0.10 nmoles/2 testes/day for mitochondrial cytochrome P-450. Treatment of hypophysectomized rats with HCG results in large increases of cytochrome P-450, 17α-hydroxylase, C₁₇–C₂₀ lyase and 5α-reductase, but not cytochrome b₅, microsomal protein, 7α-hydroxylase, or the 17β-hydroxysteroid dehydrogenase. While it is clear that the two cytochrome P-450 dependent hydroxylases involved in steroidogenesis and the 5α-reductase are under the control of gonadotrophin, it is not clear how 17β-hydroxysteroid dehydrogenase levels are maintained or in what manner the 5α-reductase level is controlled in mature animals.     

Hymenolepis diminuta: The non-saturable component of methionine uptake

Lussier P. E., Podesta R. B. and Mettrick D. F. 1982. Hymenolepis diminuta: the non-saturable component of methionine uptake. International Journal for Parasitoiogy12: 265–270. The concentration dependence of in vitro unidirectional methionine influx by Hymenolepis diminuta was analysed by the relation: $\text{J =}\text{(J}{}_{\mathrm{<mtext>m</mtext>}}\text{C}{}_{\mathrm{<mtext>b</mtext>}}\text{)}\text{(K}{}_{\mathrm{t}}\text{+ C}{}_{\mathrm{<mtext>b</mtext>}}\text{)}\text{+ K}{}_{\mathrm{d}}\text{(C}{}_{\mathrm{<mtext>b</mtext>}}\text{)}$, where J_m is the maximum uptake rate, K_t is the the apparent affinity constant and C_b is the medium substrate concentration. The linear component was separated using an asymptotic least squares curve fitting procedure and the resulting constant, K_d, is thought to be an apparent permeability coefficient. K_d may be a reflection of a simple diffusive component, a second mediated component or a combination of a passive and mediated influx. The low Q₁₀ value of the K_d's for methionine uptake (Q₁₀ = 1.31) indicated that this component is probably a reflection of diffusion within the membrane. However, the decrease in the K_d component in the presence of leucine and glycine, implies that there is also a small, second, mediated component in addition to the diffusive component. K_d derived from the asymptotic portion of the concentration-flux relation was compared with the residual flux of methionine after near complete inhibition of the mediated component with leucine and glycine. The K_d component was found to be pH-sensitive, increasing as the pH decreased and was not affected by external sodium. Results indicate that the mediated component of methionine influx was accelerated by increasing external Na⁺ and H⁺ concentrations.     

Isolation and characterization of isocitrate lyase of castor endosperm

Isocitrate lyase (threo-D_S-isocitrate glyoxylate-lyase, EC 4.1.3.1) has been purified to homogeneity from castor endosperm. The enzyme is a tetrameric protein (molecular weight about 140,000; gel filtration) made up of apparently identical monomers (subunit molecular weight about 35,000; gel electrophoresis in the presence of sodium dodecyl sulfate). Thermal inactivation of purified enzyme at 40 and 45 °C shows a fast and a slow phase, each accounting for half of the intitial activity, consistent with the equation: , where A₀ and A_t are activities at time zero at t, and k₁ and k₂ are first-order rate constants for the fast and slow phases, respectively. The enzyme shows optimum activity at pH 7.2–7.3. Effect of [S]on enzyme activity at different pH values (6.0–7.5) suggests that the proton behaves formally as an “uncompetitive inhibitor.” A basic group of the enzyme (site) is protonated in this pH range in the presence of substrate only, with a pK_a equal to 6.9. Successive dialysis against EDTA and phosphate buffer, pH 7.0, at 0 °C gives an enzymatically inactive protein. This protein shows kinetics of thermal inactivation identical to the untreated (native) enzyme. Full activity is restored on adding Mg²⁺ (5.0 mm) to a solution of this protein. Addition of Ba²⁺ or Mn²⁺ brings about partial recovery. Other metal ions are not effective.     

Pyruvate flux into resealed ghosts from human erythrocytes

The kinetics of pyruvate transport across the isolated red blood cell membrane were studied by a simple and precise spectrophotometric method: following the oxidation of NADH via lactate dehydrogenase trapped within resealed ghosts. The initial rate of pyruvate entry was linear. Influx was limited by saturation at high pyruvate concentration. Pyruvate influx was greatly stimulated by increasing ionic strength in the outer but not the inner aqueous compartment. The $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ ranged from 15.0 mM at $\text{μ = 0.05}$ to 3.7 mM at $\text{μ = 0.01}$, while the $\text{V}$ went from $\text{0.611 · 10}{}^{-15}$ to $\text{0.137 · 10}{}^{-15}\text{mol}\text{·}\text{min}{}^{-1}\text{·}\text{ghost}{}^{-1}$. Ionic strength was shown to affect the translocation step and not pyruvate binding. The energy of activation of pyruvate flux into resealed ghosts was 25 kcal/mol, similar to that found in intact red blood cells. Inhibitors of pyruvate influx included such anions as thiocyanate, chloride, bicarbonate, α-cyanocinnamate, salicylate and ketomalonate (but not acetate); noncompetitive inhibitors were phloretin, 1-fluoro-2,4-dinitrobenzene, 4-acetamido-4′-isothiocyanate-stilbene-2,2′-disulfonic acid and o-phenanthroline/CuSO₄ mixtures. The last reagent, known to induce disulfide links in certain membrane proteins, blocked the ionic strength stimulation of pyruvate influx in this study.     

Optimizing enzyme assays with one or two coupling enzymes

The cost of assays using one or two coupling enzymes is optimized by using equations to calculate the minimum amount(s) of enzyme(s) which should be used to obtain a given time (t₉₉) in which 99% of the rate V₀ of the first reaction is obtained. Using two coupling enzymes and given a value of t₉₉, the induction period L = L₁ + L₂ fulfills the requirement $\text{t}{}_{99}\text{2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{4.6}\text{≥ L ≥}\text{t}{}_{99}\text{4.6}$, allowing one to choose a cost lower than that derived from the until-now generally applied assumption of t₉₉ = 4.6L. Being $\text{α =}\text{L}{}_1\text{L}{}_2$, in optimized assays the values α, t₉₉, and L are related by $\text{T}{}_{99}\text{=4.6}\text{(1+α)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{1+α}\text{L}$, thus allowing (graphical) calculation of the amounts of coupling enzymes which will minimize the cost for every chosen t₉₉ or L. Maximum practical rates, allowed in some supposed interesting cases, have been calculated.     

Modifications of redox equilibria with semiquinone stabilization upon pyruvate binding to L-lactate cytochrome c oxidoreductase (flavocytochrome b2)

Spectral redox titrations of flavin and cytochrome b₂ moieties of flavocytochrome b₂ were achieved in the absence and in the presence of pyruvate under equilibrium conditions at 18° C; direct measurements of spin flavosemiquinone proportions have been carried out by EPR determinations at the same temperature. Our results show that the equilibria involving flavin are largely affected by the presence of pyruvate; the semiquinone proportion markedly increases almost till unit near half-reduction of cytochrome b₂; at 10 mM pyruvate, the dismutation constant, $\text{K}{}_{\mathrm{dism}}\text{=}\text{(}\text{F}{}_{\mathrm{s}}\text{)}{}^2\text{(}\text{F}{}_{\mathrm{o}}\text{)}{}^1\text{(}\text{F}{}_{\mathrm{r}}\text{)}$ increases by a factor ≥ 10.     

Steady-state kinetics of ADP-arsenate and ATP-synthesis in Rhodospirillum rubrum chromatophores

(1) Rates of ATP synthesis and ADP-arsenate synthesis catalyzed by Rhodospirillum rubrum chromatophores were determined with the firefly luciferase method and by a coupled enzyme assay involving hexokinase and glucose-6-phosphate dehydrogenase. (2) V_m for ADP-arsenate synthesis was about 2-times lower than V_m for ATP-synthesis. With saturating [ADP], K(As_i) was about 20% higher than K(P_i). With saturating [anion], K(ADP) was during arsenylation about 20% lower than during phosphorylation. (3) Plots of $\text{1}\text{v}$ vs. $\text{1}\text{[}\text{substrate}\text{]}$ were non-linear at low concentrations of the fixed substrate. The non-linearity was such as to suggest a positive cooperativity between sites binding the variable substrate, resulting in an increased $\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ ratio. High concentrations of the fixed substrate cause a similar increase in $\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{K}{}_{\mathrm{<mtext>m</mtext>}}$, but abolish the cooperativity of the sites binding the variable substrate. (4) Low concentrations of inorganic arsenate (As_i) stimulate ATP synthesis supported by low concentrations of P_i and ADP about 2-fold. (5) At high ADP concentrations, the apparent K_i of As_i for inhibition of ATP-synthesis was 2–3-times higher than the apparent K_m of As_i for arsenylation; the apparent K_i of P_i for inhibition of ADP-arsenate synthesis was about 40% lower than the apparent K_m of P_i for ATP synthesis. (6) The results are discussed in terms of a model in which P_i and As_i compete for binding to a catalytic as well as an allosteric site. The interaction between these sites is modulated by the ADP concentration. At high ADP concentrations, interaction between these sites occurs only when they are occupied with different species of anion.     

The synthesis and properties in enzymic reactions of substrate analogs containing the methylphosphonyl group.

The properties of the methylphosphonyl group as a substrate analog for the phosphoryl moiety of various biological phosphoryl donors have been investigated in several enzymic phosphoryl transfer reactions. The synthesis and characterization of adenosine 5′-[β-methylphosphonyl]diphosphate, adenosine 5′-methylphosphonate, acetyl methylphosphonate, and methylphosphonoenolpyruvate are fully described. Adenosine 5′-[β-methylphosphonyl]diphosphate is not a substrate for adenylate kinase, hexokinase, 3-phosphoglycerate kinase, glycerol kinase, phosphofructokinase, creatine kinase, alkaline phosphatase, or nucleoside 5′-diphosphate kinase. Competitive inhibition of ATP was observed with hexokinase and 3-phosphoglycerate kinase with $\text{K}{}_{\mathrm{i}}\text{K}{}_{\mathrm{m}}\text{～- 10}$. Adenosine 5′-methylphosphonate was a substrate for adenylate deaminase and 5′-nucleotidase, but not for adenylate kinase, acid phosphatase, 5′-phosphodiesterase, or 3′-phosphodiesterase. Acetyl methylphosphonate inhibits the reaction of acetyl phosphate with acetate kinase, but methylphosphonoenolpyruvate has no effect upon the reaction of phosphoenolpyruvate with pyruvate kinase. The results indicate that with the exception of 5′-nucleotidase, the methyphosphonyl group is incapable of undergoing phosphoryl transfer. One interpretation among others is that a metaphosphate-type mechanism is required for these processes.     

The asymptotic normality of a simple batch epidemic process

A group of n susceptible individuals exposed to a contagious disease isconsidered. It is assumed that at each point in time one or more susceptible individuals can contract the disease. The progress of this simple batch epidemic is modeled by a stochastic process X_n(t), t∈[0, ∞), representing the number of infectiveindividuals at time t. In this paper our analysis is restricted to simple batch epidemics with transition rates given by $\text{[α}{}^2\text{X}{}_{\mathrm{n}}\text{(t){n ?X}{}_{\mathrm{n}}\text{(t) +X}{}_{\mathrm{n}}\text{(0)}]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{, t∈[0, ∞), α∈(0, ∞)}$. This class of simple batch epidemics generalizes a model used and motivated by McNeil (1972) to describe simple epidemic situations. It is shown for this class of simple batch epidemics, that X_n(t), with suitable standardization, converges in distribution as n→∞ to a normal random variable for all t∈(0, t₀), and t₀ is evaluated.     

Equilibrium constants for association of guanidinium and ammonium ions with oxyanions: The effect of changing basicity of the oxyanion

Using guanidinium and n-butylammonium cations (C⁺) as models for the positively charged side chains in arginine and lysine, we have determined the association constants with various oxyanions by potentiometric titration. For a dibasic acid, H₂A, three association complexes may exist: $\text{K}{}_{\mathrm{<mtext>1M</mtext>}}\text{=}\text{[CHA]}\text{[C}{}^{\mathrm{+}}\text{]}\text{[HA}{}^{\mathrm{?}}\text{]}$; $\text{K}{}_{\mathrm{<mtext>1D</mtext>}}\text{=}\text{[CA}{}^{\mathrm{?}}\text{]}\text{[C}{}^{\mathrm{+}}\text{]}\text{[A}{}^{\mathrm{2?}}\text{]}$; $\text{K}{}_{\mathrm{<mtext>2D</mtext>}}\text{=}\text{[C}{}_2\text{A]}\text{[C}{}^{\mathrm{+}}\text{]}\text{[CA}{}^{\mathrm{?}}\text{]}$. For guanidinium ion and phosphate, K_1M = 1.4, K_1D = 2.6, and K_2D = 5.1. The data for carboxylates indicate that the basicity of the oxyanion does not affect the association constant: acetate, pK_a = 4.8, K_1M = 0.37; formate, pK_a = 3.8, K_1M = 0.32; and chloroacetate, pK_a = 2.9, K_1M = 0.43, all with guanidinium ion. Association constants are also reported for carbonate, dimethylphosphinate, benzylphosphonate, and adenylate anions.     

Presteady-state kinetic study of the elementary processes in the chymotrypsin-catalyzed hydrolysis of specific ester substrate. Rate-limiting association process due to the secondary binding.

Presteady-state kinetic studies of α-chymotrypsin-catalyzed hydrolysis of a specific chromophoric substrate, N-(2-furyl)acryloyl-l-tryptophan methyl ester, were performed by using a stopped-flow apparatus both under [E]₀ ? [S]₀ and [S]₀ ? [E]₀ conditions in the pH range of 5–9, at 25 °C. The results were accounted for in terms of the three-step mechanism involving enzyme-substrate complex (E · S) and acylated enzyme (ES′); no other intermediate was observed. This substrate was shown to react very efficiently, i.e., the maximum of the second-order acylation rate constant ($\text{k}{}_2\text{K}{}_{\mathrm{s}}\text{′}\text{)}{}_{\mathrm{<mtext>max</mtext>}}\text{= 4.2 × 10}{}^7\text{M}{}^{\mathrm{?1}}\text{s}{}^{\mathrm{?1}}$. The limiting values of K_s′ (dissociation constant of E · S), K₂ (acylation rate) and k₃ (deacylation rate) were obtained from the pH profiles of these parameters to be 0.6 ± 0.2 × 10^?5 m, 360 ± 15 s^?1 and 29.3 ± 0.8 s^?1, respectively. Likewise small values were observed for K_i of N-(2-furyl)-acryloyl-l-tryptophan and N-(2-furyl)acryloyl-d-tryptophan methyl ester and K_m of N-(2-furyl)acryloyl-l-tryptophan amide. The strong affinities observed may be due to intense interaction of β-(2-furyl)acryloyl group with a secondary binding site of the enzyme. This interaction led to a $\text{k}{}_{\mathrm{?1}}\text{k}{}_2$ value lower than unity, i.e., the rate-limiting process of the acylation was the association, even with the relatively low k₂ value of this methyl ester substrate, compared to those proposed for labile p-nitrophenyl esters.     

Kinetics and mechanism of the F1 isozyme of horse liver aldehyde dehydrogenase.

The reaction mechanism of the F1 isozyme of horse liver aldehyde dehydrogenase (EC 1.2.1.3) was investigated using both steady-state and rapid kinetic techniques. Using the steady-state substrate velocity patterns, the NADH inhibition patterns at several aldehyde concentrations, and the substrate analog (adenosine diphosphoribose and chloral hydrate) inhibition patterns, the enzymic catalysis was shown to involve ordered addition of NAD followed by aldehyde. This mechanism was confirmed using the kinetics of the hydrolysis of p-nitrophenyl acetate as an indicator of the dehydrogenase substrate binding. Steady-state experiments with deuteroacetaldehyde showed the V to be unchanged, but the K_m increased (). Stopped flow experiments where E-NAD was rapidly mixed with aldehyde showed a burst of NADH formation followed by slower steady-state turnover. This result clearly indicates that the rate limiting step lies after NAD reduction. The NADH off rate (0.7 s^?1) as estimated by displacement of NADH from the E-NADH complex upon rapid addition of NAD was found to be very close to the steady-state site turnover number (0.3 s^?1). This fact and the relatively small effect of aldehyde R-group on maximal velocity suggest that the slow rate of NADH release contributes significantly to limitation of the enzyme catalytic velocity.     

Equilibrium constants under physiological conditions for the reactions of L-phosphoserine phosphatase and pyrophosphate: L-serine phosphotransferase

The observed equilibrium constants (K_obs) for the l-phosphoserine phosphatase reaction [EC 3.1.3.3] have been determined under physiological conditions of temperature (38 °C) and ionic strength (0.25 m) and physiological ranges of pH and free [Mg²⁺]. Using Σ and square brackets to indicate total concentrations $\text{K}{}_{\mathrm{<mtext>obs</mtext>}}\text{=}\text{Σ L-serine][Σ P}{}_{\mathrm{i}}\text{]}\text{Σ L-phosphoserine]H}{}_2\text{O]}\text{, K =}\text{L-H · serine}{}^{\mathrm{\pm }}\text{]HPO}{}_4{}^{\mathrm{2?}}\text{]}\text{[L-H · phosphoserine}{}^{\mathrm{2?}}\text{]H}{}_2\text{O]}$. The value of K_obs has been found to be relatively sensitive to pH. At 38 °C, K⁺] = 0.2 m and free [Mg²⁺] = 0; K_obs = 80.6 m at pH 6.5, 52.7 m at pH 7.0 [ΔG_obs⁰ = ?10.2 kJ/mol (?2.45 kcal/mol)], and 44.0 m at pH 8.0 ([H₂O] = 1). The effect of the free [Mg²⁺] on K_obs was relatively slight; at pH 7.0 ([K⁺] = 0.2 m) K_obs = 52.0 m at free [Mg²⁺] = 10^?3, m and 47.8 m at free [Mg²⁺] = 10^?2, m. K_obs was insignificantly affected by variations in ionic strength (0.12–1.0 m) or temperature (4–43 °C) at pH 7.0. The value of K at 38 °C and I = 0.25 m has been calculated to be 34.2 ± 0.5 m [ΔG_obs⁰ = ?9.12 kJ/mol (?2.18 kcal/ mol)]([H₂O] = 1). The K for the phosphoserine phosphatase reaction has been combined with the K for the reaction of inorganic pyrophosphatase [EC 3.6.1.1] previously estimated under the same physiological conditions to calculate a value of 2.04 × 10⁴, m [ΔG_obs⁰ = ?28.0 kJ/mol (?6.69 kcal/mol)] for the K of the pyrophosphate:l-serine phosphotransferase [EC 2.7.1.80] reaction. $\text{K}{}_{\mathrm{<mtext>obs</mtext>}}\text{=}\text{[}\text{Σ L-serine}\text{][}\text{Σ}\text{P}{}_{\mathrm{<mtext>i</mtext>}}\text{]}\text{[}\text{Σ L-phosphoserine}\text{][}\text{H}{}_2\text{O}\text{]}\text{, K =}\text{[L-H · serine}{}^{\mathrm{\pm }}\text{]HPO}{}_4{}^{\mathrm{2?}}\text{]}\text{[L-H · phosphoserine}{}^{\mathrm{2?}}\text{]H}{}_2\text{O}$. Values of K_obs for this reaction at 38 °C, pH 7.0, and I = 0.25 m are very sensitive to the free [Mg²⁺], being calculated to be 668 [ΔG_obs⁰ = ?16.8 kJ/mol (?4.02 kcal/mol)] at free [Mg²⁺] = 0; 111 [ΔG_obs⁰ = ?12.2 kJ/mol (?2.91 kcal/mol)] at free [Mg²⁺] = 10^?3, m; and 9.1 [ΔG_obs⁰ = ?5.7 kJ/mol (?1.4 kcal/mol) at free [Mg²⁺] = 10^?2, m). K_obs for this reaction is also sensitive to pH. At pH 8.0 the corresponding values of K_obs are 4000 [ΔG_obs⁰ = ?21.4 kJ/mol (?5.12 kcal/mol)] at free [Mg²⁺] = 0; and 97.4 [ΔG_obs⁰ = ?11.8 kJ/ mol (?2.83 kcal/mol)] at free [Mg²⁺] = 10^?3, m. Combining K_obs for the l-phosphoserine phosphatase reaction with K_obs for the reactions of d-3-phosphoglycerate dehydrogenase [EC 1.1.1.95] and l-phosphoserine aminotransferase [EC 2.6.1.52] previously determined under the same physiological conditions has allowed the calculation of K_obs for the overall biosynthesis of l-serine from d-3-phosphoglycerate. $\text{K}{}_{\mathrm{<mtext>obs</mtext>}}\text{=}\text{[}\text{Σ L-serine}\text{][}\text{Σ NADH}\text{][}\text{Σ}\text{P}{}_{\mathrm{<mtext>i</mtext>}}\text{][}\text{Σ}\text{α-}\text{ketoglutarate}\text{]}\text{[Σ d-3-}\text{phosphoglycerate}\text{][Σ NAD}{}^{\mathrm{+}}\text{][Σ L-glutamat0]}$ The value of K_obs for these combined reactions at 38 °C, pH 7.0, and I = 0.25 m (K⁺ as the monovalent cation) is 1.34 × 10^?2, m at free [Mg²⁺] = 0 and 1.27 × 10^?2, m at free [Mg²⁺] = 10^?3, m.