A quantum model for controlled enzymic reactions

A quantum model for the general enzymic reaction,E+S ⇌ ES → P, is presented, starting with the assumptions that any chemical substanceS, which may be a substrate for a particularE _(S)-enzyme is a microphysical system and any enzymeE-molecule, capable of interacting with anS-substrate is a “measuring system” which will “measure” one or more of theS-observables. According to the above assumptions a stochastic model of the reaction is constructed and a computer simulation of the steady state performed. The results thus obtained predicted fluctuations in the enzymic reaction rate, function of the substrate “perturbation”. On an experimental basis it is demonstrated that the irradiation of an enzymic substrate with low energies results in the inducement of a dose-dependent oscillatory behavior in the corresponding enzymic reaction rate. In the reaction type, the oscillations thus induced in theE-activity by the corresponding substrates are out-of-phase, realizing a biochemical discriminating net. Likewise, in an reaction type, the oscillations induced by the irradiatedS-substrate in the activities of the respective enzyme, realize a biochemical switching net.     

Self-organization and dynamics of an open futile cycle

The dynamic behaviour of an open futile cycle composed of two enzymes has been investigated in the vicinity of a steady-state. A necessary condition required for damped or sustained oscillations of the system is that enzyme E₂, which controls recycling of the substrate S₂, be inhibited by an excess of this substrate. In order for the system to be neutrally stable and therefore to exhibit sustained oscillations, it is not necessary for antagonist enzyme E₁ to be activated by its product S₂. If it is enzyme E₁ which is inhibited by an excess of its substrate S₁, the system has a saddle point. Other conditions for stability or instability of the system have been determined. If the enzyme E₁, which is not inhibited by the substrate, exhibits a slow conformational transition of the mnemonical type, this transition dramatically alters the stability behavior of the system. If the mnemonical enzyme E₁ were exhibiting a positive kinetic co-operativity, decreasing the rate of the conformational transition of the mnemonical enzyme will increase the stability of the whole system and will tend to damp the oscillations in the vicinity of the steady-state. If conversely the mnemonical enzyme E₁ were exhibiting a negative kinetic co-operativity, decreasing the rate of the enzyme conformational transition will decrease the stability of the system and will tend to create or amplify oscillations of the system taken as a whole. If these results may be extended to more complex metabolic cycles, involving more than two enzymes, it may be tentatively considered that positive co-operativity associated with slow transition has emerged in the course of evolution in order to limit temporal instabilities of metabolic cycles. Alternatively one may speculate that the “biological function” of negative co-operativity is to create or amplify these temporal instabilities.     

On a possible biological spectroscopy

A new type of physical transition, denotedS→S ^*, has been detected in irradiated organic molecules (λ=546 nm) through their interaction with specific biological macromolecules. In a specific enzyme-substrate interaction, a clear enhancement of the reaction rate is observed, when the substrate is irradiated with sharply well defined times. These “efficient irradiation times” are always of the 5k sec type (k=1, 2, 3, …). They have been consistently revealed in a great number of specific biological interactions. The present note demonstrates an important property, i.e. that forevery irradiation time aS→S ^* transition is induced in organic molecules. It is shown that for any irradiation times different from the 5k sec type (k=1, 2, 3, …) states of theS ^* type may occur, but the biological macromolecules may “detect” only theS ^* states induced by irradiations of the 5k sec type.     

Solubilization and characterization of the leukotriene C4 synthetase of rat basophil leukemia cells: A novel,participate glutathione S-transferase

Rat basophil leukemia cell homogenates effectively catalyze the conversion of leukotriene A₄ to a mixture of leukotrienes C₄ and D₄ in the presence of glutathione. These homogenates also catalyze the formation of adducts of halogenated nitrobenzene with glutathione, as determined spectrophotometrically. While all the classical glutathione S-transferase activity resides in the soluble fraction of the homogenates, the thiol ether leukotriene-generating activity is found in the particulate fraction. This “leukotriene C synthetase” activity has been solubilized from a crude high-speed particulate fraction by means of the nonionic detergent, Triton X-100. The solubilized enzyme is incapable of converting 2,4-dinitrochlorobenzene to a colored product in the presence of glutathione. Nor will it react with 3,4-dichloronitrobenzene. On the other hand, under optimal conditions, this enzyme preparation is capable of generating about 0.1 nmol leukotriene C mg protein^?1 min^?1 in a reaction which continues in linear fashion for at least 10 min. This dissociation in substrate specificity, as well as differences in the inhibition profile, distinguish the enzyme activity in the particulate fraction from rat basophil leukemia cell homogenates from the microsomal glutathione S-transferase which has been described in rat liver homogenates, suggesting that this “leukotriene C synthetase” is a new and unique enzyme.     

Properties of a discrete high molecular weight poly(A) containing mitochondrial RNA

Pulse-labeled mitochondrial RNA from hamster cells contains a number of discrete high molecular weight poly[A(+)] and poly[A(?)] RNAs. Characterization of the largest and most plentiful of the poly[A(+)] RNAs, the “20S_E RNA,” showed it to be a labile, unmethylated component with a molecular weight ～- 730,000. Hybridization of the 20S_E RNA to mtDNA was 60–70% inhibited in the presence of excess 17S rRNA, suggesting a significant degree of primary sequence homology between these RNA species. In vitro treatment with RNAse III converted the 20S_E RNA to a poly[A(?)] “17S” product, while similar treatment of mitochondrial 17S rRNA or a poly[A(+)] 12S_E RNA had no effect on these RNAs. These data support the proposition that the 20S_E RNA is a precursor to the 17S rRNA.     

Hormonal specificity of the melanotropin-sensitive adenylate cyclase of mouse melanoma and effect of cyclic amp on the tyrosinase activity of mouse melanoma cells,in vitro

Transplantable mouse melanomas possess a melantropin-sensitive adenylate cyclase system which is responsive to α-melanotropin, β-melanotropin, adrenocorticotropin (ACTH) and prostglandin E₁. It was found that sensitivity to ACTH was not directed towrds the ACTH activity but to the intrinsic melanotropin activity of the ACTH molecule. Therefore, the melanotropin-sensitive adenylate cyclase system is hormonally specific to the intrinsic melanotropin activity of peptide hormones and is unique in the melanoma tissue. The significance of the sensitivity to prostaglandin E₁ is obscure at present. The melanotropin-sensitive adenylate cyclase requires the presence of Mg²⁺ or Mn²⁺ for its enzymatic activity. Ca²⁺ inhibit the enzyme in the presence of a wide range of concentrations of Mg²⁺. The enzymic activity is ATP concentration-dependent and the saturation concentration appears to be 1 mM. The enzyme is very labile in the unfractionated tumor homogenates. A washed 11 000 × g particulate fraction, representing about 30–60% of the total enzymic activity, was found to be more stable and could be stored at 5°C for 2 h without appreaciable loss of the activity. This fraction retained sensitivity to melanotropin, prostaglandin E₁ and NaF. About 20% of the activity of the tumor homogenate could not be sedimented by centrifugation at 105 000 × g for 60 min. This “soluble” fraction was not responsive to melanotropin, prostglandin E₁ and NaF and might be a degradative product produced by the fractionation. Cyclic AMP and α-melanotropin were able to increase the tyrosinase activity of isolated mouse melanoma-cells in vitro under the same conditions.     

Probing the electronic structures and properties of neutral and charged arsenic sulfides (As n S(−1,0,+1), n = 1–7) using Gaussian-3 theory

The structures and energies of neutral and charged arsenic sulfides As _n S^(?1,0,+1) (n?=?1–7) were systematically investigated using the G3 method. The bonding properties and the stabilities of As _n S and their ions were discussed. The adiabatic electron affinities (AEAs) and adiabatic ionization potentials (AIPs) were presented. The ground-state structures of As _n S can be considered as the lowest-energy structure of neutral As _n+1 by replacing an As atom with a S atom, that is, “substitutional structure”, in which the feature of sulfur bonding is edge-bridging. The ground-state structures of As _n S⁺ tend to be derived from the lowest-energy structure of cation As _n ⁺ by attaching to a S atom, that is, “attaching structure”, in which the sulfur can be three-fold coordinated. There is no rule to be found for the ground-state structure of anion As _n S^?, in which the sulfur can be a terminal atom. There are odd-even alternations in both AEAs and AIPs as a function of size of As _n S. The dissociation energies of S, S^?, and/or S⁺ from neutral As _n S and their ions were calculated to examine their stabilities.     

Differences between CTP and ATP as substrates for the (Na + K)-ATPase

CTP was a poorer substrate than ATP when substituted in the (Na + K)-ATPase reaction assay, not only in terms of K_m but also of V. CDP was a poorer inhibitor than ADP, so product inhibition cannot account for CTP being a poorer substrate. In the Na-ATPase reaction, which the enzyme also catalyzes, substituting CTP for ATP resulted in greater activity, arguing against CTP being less effective than ATP in forming the enzyme-phosphate intermediate common to both reactions. Ligands that favor the E₂ conformational state of the enzyme, K⁺, Mg²⁺, and Mn₂⁺, inhibited the (Na + K)-CTPase reaction more than the (Na + K)-ATPase. Conversely, Triton X-100, which favors the E₁ conformational state of the enzyme, K⁺, Mg²⁺, and Mn²⁺, inhibited the (Na + K)-CTPase ATPase reaction but stimulated the (Na + K)-CTPase. Although the (Na + K)-ATPase reaction sequence probably involves cyclical interconversion between E₁ and E₂ conformational states (and is thus inhibitable by ligands favoring either state), the K-phosphatase reaction catalyzed by the enzyme apparently functions entirely in the E₂ state. This reaction is better stimulated by CTP plus Na⁺ than by ATP plus Na⁺; moreover, CTP lessens inhibition by Triton X-100, and ATP lessens inhibition by inorganic phosphate (which reacts with the E₂ state). These observations indicate that CTP is a poorer substrate than ATP because it is less effective in promoting conversion of E₂ to E₁, essential for the (Na + K)-dependent reaction mechanism. However, contrary to this rationale, dimethyl sulfoxide stimulated the (Na + K)-CTPase reaction although by other criteria, including inhibition of the (Na + K)-ATPase, the reagent appears to favor the E₂ over the E₁ conformational state.     

1-Aminocyclopropanecarboxylate synthase, a key enzyme in ethylene biosynthesis

1-Aminocyclopropanecarboxylate (ACC) synthase, which catalyzes the conversion of S-adenosylmethionine (SAM) to ACC and methylthioadenosine, was demonstrated in tomato extract. Methylthioadenosine was then rapidly hydrolyzed to methylthioribose by a nucleosidase present in the extract. ACC synthase had an optimum pH of 8.5, and a K_m of 20 μm with respect to SAM. S-Adenosylethionine also served as a substrate for ACC synthase, but at a lower efficiency than that of SAM. Since S-adenosylethionine had a higher affinity for the enzyme than SAM, it inhibited the reaction of SAM when both were present. S-Adenosylhomocysteine was, however, an inactive substrate. The enzyme was activated by pyridoxal phosphate at a concentration of 0.1 μm or higher, and competitively inhibited by aminoethoxyvinylglycine and aminooxyacetic acid, which are known to inhibit pyridoxal phosphate-mediated enzymic reactions. These results support the view that ACC synthase is a pyridoxal enzyme. The biochemical role of pyridoxal phosphate is catalyzing the formation of ACC by α,γ-elimination of SAM is discussed.     

Kinetic manifestations of allosteric interactions in models of regulatory enzymes with "indirect" co-operativity

The shape of the plots of initial reaction rate (ν) versus initial substrate concentration ([S]₀) and versus initial concentration of allosteric effector ([F]₀) for the model of allosteric enzyme of Monod, Wyman &; Changeux (1965) and for the model of dissociating regulatory enzyme has been analysed by means of the inconstant exponent (q) for substrate or effector concentration, respectively. It has been shown that allosteric interactions in above-mentioned models with “indirect” co-operativity may be manifested not only by the sigmoidal shape of the plot of ν versus [S]₀ or ν versus [F]₀ (with one point of inflexion) but also by the increase in the magnitude of exponent q in progress of saturation process of the enzyme by the substrate or by the effector in the absence of the sigmoidal shape of these plots. It has been shown also that the plot of ν versus [S]₀ has two inflexion points when the parameters have certain definite values. One of these inflexion points (or even both at definite values of the parameters) is hardly discernible. At certain definite values of the parameters two inflexion points may be kinetically manifested by such phenomenon as “negative” co-operativity (q < 1). This is possible if one of the interconvertable enzyme forms exceeds another not only in the affinity to the substrate but also in the value of the rate constant for catalytic breakdown of the enzyme-substrate complex.     

The action of four proposed chloride movement modifiers on acetylcholine responses of central neurones of Helix aspersa

1. Intracellular recordings were made from identified neurones in the visceral, (abdominal) ganglion of the snail, Helix aspersa. The hyperpolarising response of neurone E4 is a pure chloride event and has a reversal potential, (E_Cl), of −69.7 ± 1.7mV, (n = 4). This can be compared to depolarising responses of neurones E1 and E2 which are sodium mediated.2. Four membrane transport system antagonists, all thought to affect trans-membrane chloride movement, were investigated with respect to the two different acetylcholine responses described.3. Piretanide irreversibly blocks the hyperpolarising response in cell E4, (1–10 μM), increasing its inhibition with time but without changing E_Cl.4. Furosemide irreversibly blocks both types of acetylcholine responses at concentrations in the nanomolar range; no change in E_Cl or E_Na was associated with the inhibition but the “passive” membrane resistance appeared to decrease. Inhibition increased with time, normally causing a significant effect after 10–30 min.5. S.I.T.S. and ethacrynic acid appear very similar in effect; both reversibly block the two responses to acetylcholine and recovery after washing is virtually complete. The onset of antagonism is rapid and both compounds are slightly more effective against the hyperpolarising (“H”), response than the depolarising (“D”) response (threshold ∼10⁻⁵ M compared to ∼ 10⁻⁴ M). No change in E_Cl or E_Na was noted.6. Piretanide and furosemide probably exert their effect by interactions with the neuronal cell membrane, disrupting the integrity of this structure, whereas S.I.T.S. and ethacrynic acid may interact more specifically with the acetylcholine receptor protein.     

Disparity in productive binding mode of the slow-reacting enantiomer determines the novel catalytic behavior of Candida antarctica lipase B

In the context of specifying the origin of enzyme enantioselectivity, the present study explores the lipase enantioselectivity towards secondary alcohols of similar structure from the perspective of substrate binding. By carrying out molecular mechanics minimization as well as molecular dynamics simulation on tetrahedral reaction intermediates which are used as a model of transition state, we identify an unconventional productive binding mode (PBM)—M/H permutation type for Candida antarctica lipase B (CALB). The in silico results also indicate that different PBMs of the slow-reacting enantiomer do exist in one lipase even when there is little structural differences between substrates, e.g. compounds with Ph or CH₂CH₂Ph group display the M/H permutation type PBM while molecules with CH₂Ph show the M/L permutation type PBM. By relating the PBMs of substrates to the experimentally determined E-values obtained by Hoff et al. [16], we find that disparity in PBM of the slow-reacting enantiomer determines why E-values of substrates with CH₂Ph were lower than E-values of substrates with Ph or CH₂CH₂Ph group. The modeling results also suggest that the “pushed aside” effect of the F atom and Br atom accommodates the medium size substituent of the substrate better in the stereospecificity pocket of the enzyme.     

Premicellar complexes of sphingomyelinase mediate enzyme exchange for the stationary phase turnover

During the steady state reaction progress in the scooting mode with highly processive turnover, Bacillus cereus sphingomyelinase (SMase) remains tightly bound to sphingomyelin (SM) vesicles (Yu et al., Biochim. Biophys. Acta 1583, 121-131, 2002). In this paper, we analyze the kinetics of SMase-catalyzed hydrolysis of SM dispersed in diheptanoylphosphatidyl-choline (DC₇PC) micelles. Results show that the resulting decrease in the turnover processivity induces the stationary phase in the reaction progress. The exchange of the bound enzyme (E*) between the vesicle during such reaction progress is mediated via the premicellar complexes (E_i^#) of SMase with DC₇PC. Biophysical studies indicate that in E_i^# monodisperse DC₇PC is bound to the interface binding surface (i-face) of SMase that is also involved in its binding to micelles or vesicles. In the presence of magnesium, required for the catalytic turnover, three different complexes of SMase with monodisperse DC₇PC (E_i^# with i = 1, 2, 3) are sequentially formed with Hill coefficients of 3, 4 and 8, respectively. As a result, during the stationary phase reaction progress, the initial rate is linear for an extended period and all the substrate in the reaction mixture is hydrolyzed at the end of the reaction progress. At low mole fraction (X) of total added SM, exchange is rapid and the processive turnover is limited by the steps of the interfacial turnover cycle without becoming microscopically limited by local substrate depletion or enzyme exchange. At high X, less DC₇PC will be monodisperse, E_i^# does not form and the turnover becomes limited by slow enzyme exchange. Transferred NOESY enhancement results show that monomeric DC₇PC in solution is in a rapid exchange with that bound to E_i^# at a rate comparable to that in micelles. Significance of the exchange and equilibrium properties of the E_i^# complexes for the interpretation of the stationary phase reaction progress is discussed.     

Stabilization of glucoso-6-phosphate dehydrogenase by its substrate and cofactor in an ultrasonic field

The inactivation kinetics of glucoso-6-phosphate dehydrogenase (GPDH) and its complexes with glucoso-6-phosphate and NADP⁺ was characterized in aqueous solutions at 36–47°C under treatment with low frequency (27 kHz, 60 W/cm²) and high frequency ultrasound (880 kHz, 1 W/cm²). To this end, we measured three effective first-order inactivation rate constants: thermal k _in ^* , total (thermal and ultrasonic) k _in, and ultrasonic k _in(US). The values of the constants were found to be higher for the free enzyme than for its complexes GPDH-GP and GPDH-NADP⁺ at all temperatures, which confirms the enzyme stabilization by its substrate and cofactor under both thermal and ultrasonic inactivation. Effective values of the activation energies (E _a) were determined and the preexponential factors of the rate constants and thermodynamic activation parameters of inactivation processes (ΔH*, ΔS*, and ΔG*) were calculated from the temperature dependences of the inactivation rate constants of GPDH and its complexes. The sonication of aqueous solutions of free GPDH and its complexes was accompanied by a reduction of E _a and ΔH* values in comparison with the corresponding values for thermal inactivation. The E _a, ΔH*, and ΔS* inactivation values for GPDH are lower than the corresponding values for its complexes. A linear dependence between the growth of the ΔH* and ΔS* values was observed for all the inactivation processes for free GPDH and its complexes.     

Characterization and gene deletion analysis of four homologues of group 3 pyridine nucleotide disulfide oxidoreductases from Thermococcus kodakarensis

Enzymatic characterization of the four group 3 pyridine nucleotide disulfide oxidoreductase (PNDOR) homologues TK1299, TK0304, TK0828, and TK1481 from Thermococcus kodakarensis was performed, with a focus on their CoA-dependent NAD(P)H: elemental sulfur (S⁰) oxidoreductase (NSR) and NAD(P)H oxidase (NOX) activities. TK1299 exhibited NSR activity with a preference for NADPH and showed strict CoA-dependency similar to that of the Pyrococcus furiosus homologue PF1186. During the assays, the non-enzymatic formation of H₂S from S⁰ and free CoA–SH was observed, and the addition of enzyme and NADPH enhanced H₂S evolution. A catalytic cycle of TK1299 was proposed suggesting that CoA–SH acted to solubilize S⁰ by forming CoA persulfides, followed by reduction of an enzyme–S–S–CoA intermediate produced after both enzymatic and non-enzymatic evolution of H₂S from the CoA persulfide, with NADPH as an electron donor. TK1481 showed NSR activity independently of CoA–SH, implying a direct reaction with S⁰. TK1299, TK1481, and TK0304 exhibited high NOX activity, and the NADH-dependent activities were inhibited by the addition of free CoA–SH. Multiple disruptions of the four group 3 PNDOR homologues in T. kodakarensis demonstrated that none of these homologues were essential for S⁰-dependent growth. Many disruptants grew better than the parent strain, but a few multiple disruptants showed decreased growth properties after aerobic inoculation into a pyruvate-containing medium without S⁰, suggesting the complicated participation of these group 3 PNDORs in sensitivity/resistance to dissolved oxygen when S⁰ was absent.     

15-ketoprostaglandin delta13 reductase from human placenta: purification, kinetics, and inhibitor binding.

An NADH-dependent 15-ketoprostaglandin Δ¹³ reductase has been purified to near homogeneity from human placenta by a procedure which includes affinity chromatography on blue Sepharose. The enzyme utilizes as substrates 15-ketoprostaglandins of the E, F, A, and B series, and the reaction is experimentally irreversible. Molecular weight estimations on Sephadex G-100 and sodium dodecyl sulfate disc gel electrophoresis suggest that the enzyme is a dimer. The subunits appear to be similar in size if not identical and have a molecular weight of 35,000. The mechanism of the reaction of 15-ketoprostaglandin E₂ and NADH catalyzed by this enzyme has been investigated by steady-state kinetic methods. The 13,14-dihydro-15-ketoprostaglandin product is an inhibitor of the reaction, being competitive with respect to 15-ketoprostaglandin E₂ and noncompetitive with respect to NADH; NAD⁺ does not inhibit the reaction. NADPH and Cibacron blue 3G-A are “dead-end” inhibitors of the reaction; both act competitively with respect to NADH and noncompetitively with respect to 15-ketoprostaglandin E₂. These observations are consistent with a rapid equilibrium random mechanism with the formation of an unreactive enzyme · NADH · 13,14-dihydro-15-ketoprostaglandin E₂ complex. The interaction of NADPH and Cibacron blue 3G-A with the free enzyme was investigated further by fluorimetry. Both substances bind to the free enzyme and quench its fluorescence. This property was utilized to titrate the enzyme, and a value of 3.28 × 10^?11 mol of binding sites/mU of enzyme was obtained.     

Equilibrium ligand binding assays using labeled substrates: nature of the errors introduced by radiochemical impurities

The effects of radiochemical impurities in a labeled substrate on the characteristics of the experimental equilibrium binding plots were examined. The protein (receptor) was assumed to be a monomer or an oligomer composed of identical, noninteracting subunits. The substrate was assumed to be chemically and radiochemically impure (Case I) or just radiochemically impure (Case II). In both cases, the apparent free substrate concentration required for half-saturation of the protein, [S]_0.5,app, increases linearly with increasing total protein concentration. Reciprocal plots and Scatchard plots are nonlinear. The curvature of both plots is opposite to that observed for the heterogeneity of binding sites. Hill plots are curved with average slopes >1 in the region of half-saturation. If the radiochemical impurity goes undetected, the experimental data might lead an investigator to suggest a number of unnecessarily complicated binding models. The plots obtained in the presence of a radiochemical impurity are very similar to those seen when the receptor protein is a dissociable dimer and K_s (monomer) <K_s (dimer). However, in the dimer model the variation of [S]_0.5 with total protein concentration is nonlinear. The most direct way of assessing the radiochemical purity of a labeled substrate is to vary the binding protein concentration at a fixed concentration of S¹. If all of the radioactivity resides in S¹, the concentration of the PS¹ complex will approach [S¹]_t as [P]_t increases, while the free unbound radioactivity will be driven toward zero. If the labeled substrate is radiochemically impure, “saturating” protein will not bind all of the label. This procedure will detect some types of major impurities missed by paper chromatography (e.g., ³H₂O and nonreactive isomers of S¹).     

A theoretical investigation into the cooperativity effect between the H∙∙∙O and H∙∙∙F– interactions and electrostatic potential upon 1:2 (F–:N-(Hydroxymethyl)acetamide) ternary-system formation

The cooperativity effects between the O/N–H???F^– anionic hydrogen-bonding and O/N–H???O hydrogen-bonding interactions and electrostatic potentials in the 1:2 (F^–:N-(Hydroxymethyl)acetamide (signed as “ha”)) ternary systems are investigated at the B3LYP/6-311++G** and MP2/6-311++G** levels. A comparison of the cooperativity effect in the “F^–???ha???ha” and “FH???ha^–???ha” systems is also carried out. The result shows that the increase of the H???O interaction energy in the O–H???O–H, N–H???O–H or N–H???O?=?C link is more notable than that in the O–H???O?=?C contact upon ternary-system formation. The cooperativity effect is found in the complex formed by the O/N–H???F^– and O/N–H???O interactions, while the anti-cooperativity effect is present in the system with only the O/N–H???F^– H-bond or the “FH???ha^–???ha” complex by the N^–???H–F contact. Atoms in molecules (AIM) analysis and shift of electron density confirm the existence of cooperativity. The most negative surface electrostatic potential (V _S,min ) correlates well with the interaction energy E′ _{int.(ha???F–)} and synergetic energy E _syn., respectively. The relationship between the change of V _S,min (i.e., ΔV _S,min ) and E _syn. is also found.

Perturbation Theory in the Catalytic Rate Constant of the Henri–Michaelis–Menten Enzymatic Reaction

The Henry–Michaelis–Menten (HMM) mechanism of enzymatic reaction is studied by means of perturbation theory in the reaction rate constant k ₂ of product formation. We present analytical solutions that provide the concentrations of the enzyme (E), the substrate (S), as well as those of the enzyme-substrate complex (C), and the product (P) as functions of time. For k ₂ small compared to k _?1, we properly describe the entire enzymatic activity from the beginning of the reaction up to longer times without imposing extra conditions on the initial concentrations E _o and?S _o , which can be comparable or much different.