m-Alkyl, α,α,α-trifluoroacetophenones: A new class of potent transition state analog inhibitors of acetylcholinesterase

A series of m-alkyl α,α,α-trifluoroacetophenones (1–5) was synthesized and evaluated as inhibitors of acetylcholinesterase from Torpedo california. All ketones (1–5) were found to be potent inhibitors of the enzyme; m-t-butyl α,α,α-trifluoroacetophenone (4) was the most potent inhibitor with a K_i value of 3.7 pM.     

4,4,14α-trimethyl 9β,19-cyclo-5α-26-homocholesta-24,26-dien-3β-ol: a potent mechanism-based inactivator of Δ- to Δ-sterol methyl transferase

The title compound (4A) was synthesized and tested as a mechanism-based inactivator of the sterol methyl transferase (SMT) enzyme from Prototheca wickerhamii. Using cycloartenol as substrate, 4A was found to exhibit time-dependent inactivation kinetics, generating a K_i value of 30 μM and K_inact value of 0.30 min⁻¹.     

E-Combretastatin and E-resveratrol structural modifications: Antimicrobial and cancer cell growth inhibitory β-E-nitrostyrenes

As part of a broad-based SAR investigation of E-resveratrol (strong sirtuin activator and antineoplastic) and the anticancer vascular-targeting combretastatin-type stilbenes, a series of twenty-three β-E-nitrostyrenes was synthesized in order to evaluate potential antineoplastic, antitubulin, and antimicrobial activities. The β-E-nitrostyrenes evaluated ranged from monosubstituted phenols to trimethoxy and 3-methoxy-4,5-methylenedioxy derivatives. Two of the β-nitrostyrenes were synthesized as water-soluble sodium phosphate derivatives (4t, 4v). All except four (4r, 4s, 4t, 4u) of the series significantly inhibited a minipanel of human cancer cell lines. All but eight led to an IC₅₀ of <10 μM for inhibition of tubulin polymerization, and all except three (4l, 4t, 4v) displayed antimicrobial activity.     

Structure-activity relationships of anthraquinone derivatives derived from bromaminic acid as inhibitors of ectonucleoside triphosphate diphosphohydrolases (E-NTPDases)

Reactive blue 2 (RB-2) had been characterized as a relatively potent ectonucleoside triphosphate diphosphohydrolase (E-NTPDase) inhibitor with some selectivity for NTPDase3. In search for the pharmacophore and to analyze structure-activity relationships we synthesized a series of truncated derivatives and analogs of RB-2, including 1-amino-2-sulfo-4-ar(alk)ylaminoanthraquinones, 1-amino-2-methyl-4-arylaminoanthraquinones, 1-amino-4-bromoanthraquinone 2-sulfonic acid esters and sulfonamides, and bis-(1-amino-4-bromoanthraquinone) sulfonamides, and investigated them in preparations of rat NTPDase1, 2, and 3 using a capillary electrophoresis assay. Several 1-amino-2-sulfo-4-ar(alk)ylaminoanthraquinone derivatives inhibited E-NTPDases in a concentration-dependent manner. The 2-sulfonate group was found to be required for inhibitory activity, since 2-methyl-substituted derivatives were inactive. 1-Amino-2-sulfo-4-p-chloroanilinoanthraquinone (18) was identified as a nonselective competitive blocker of NTPDases1, 2, and 3 (K_i 16–18 μM), while 1-amino-2-sulfo-4-(2-naphthylamino)anthraquinone (21) was a potent inhibitor with preference for NTPDase1 (K_i 0.328 μM) and NTPDase3 (K_i 2.22 μM). Its isomer, 1-amino-2-sulfo-4-(1-naphthylamino)anthraquinone (20), was a potent and selective inhibitor of rat NTPDase3 (K_i 1.5 μM).     

Purification and characterization of a trypsin-like enzyme with fibrinolytic activity present in the abdomen of horn fly, Haematobia irritans irritans (Diptera: Muscidae)

This work describes the purification and characterization of a trypsin-like enzyme with fibrinolytic activity present in the abdomen of Haematobia irritans irritans (Diptera: Muscidae). The enzyme was purified using a one-step process, consisting of affinity chromatography on SBTI-Sepharose. The purified protease showed one major active proteinase band on reverse zymography with 0.15% gelatin, corresponding to a molecular mass of 25.5 kDa, with maximum activity at pH 9.0. The purified trypsin-like enzyme preferentially hydrolyzed synthetic substrates with arginine residue at the P1 position. The K _m values determined for three different substrates were 1.88 × 10^–4, 1.28 × 10^–4, and 1.40 × 10^–4 M for H--benzoyl-Ile-Glu-Gly-Arg-p-nitroanilide (S2222), dl-Ile-Pro-Arg-p-nitroanilide (S2288), and DL-Phe-Pip-Arg-p-nitroanilide (S2238), respectively. The enzyme was strongly inhibited by typical serine proteinase inhibitors such as SBTI (soybean trypsin inhibitor, K _i = 0.19 nM) and BuXI (Bauhinia ungulata factor Xa inhibitor, K _i = 0.48 nM), and less inhibited by LDTI (leech-derived tryptase inhibitor, K _i = 1.5 nM) and its variants LDTI 2T and 5T (0.8 and 1.5 nM, respectively). The most effective inhibitor for this protease was r-aprotinin (r-BPTI) with a K _i value of 39 pM. Synthetic serine protease inhibitors presented only weak inhibition, e.g., benzamidine with K _i = 3.0 × 10^–4 M and phenylmethylsulfonyl fluoride (PMSF) showed traces of inhibition. The purified trypsin-like enzyme also digested natural substrates such as fibrinogen and fibrin net. The protease showed higher activity against fibrinogen and fibrin than did bovine trypsin. These data suggest that the proteolytic enzyme of H. irritans irritans is more specific to proteins from blood than are the vertebrate digestive enzymes. This enzyme's characteristics may be an adaptation resulting from the feeding behavior of this hematophagous insect.     

Cyclobranol: a substrate for C25-methyl sterol side chains and potent mechanism-based inactivator of plant sterol methyltransferase

Cyclobranol 8A, an analog of the cycloartenol substrate 1A for the plant sterol C24-methyltransferase (SMT), was shown to be an acceptor of the soybean SMT1 as well as an inhibitor of enzyme action. The K_m and k_cat for 8A was 37 μM and 0.006 min⁻¹, respectively. The enzyme-generated product was identified by MS and ¹H NMR to be a C24, C25-doubly alkylated Δ²⁴⁽²⁸⁾-olefin 10A. Inhibitor treatment was concentration and time-dependent affording an apparent K_i of 25 μM, a maximum rate of inactivation of 0.15 min⁻¹ and a partition ratio (k_cat/k_inact) calculated to be 0.04.     

Aromatase inactivation by 2-substituted derivatives of the suicide substrate androsta-1,4-diene-3,17-dione

To gain the structure–activity relationship of Δ¹-androstenediones (Δ¹-ADs) as mechanism-based inactivator of aromatase, series of 2-alkyl- and 2-alkoxy-substitiuted Δ¹-ADs (6 and 9) as well as 2-bromo-Δ¹-AD (14) were synthesized and tested. All of the inhibitors examined blocked aromatase in human placental microsomes in a competitive manner. In a series of 2-alkyl-Δ¹-ADs (6), n-hexyl compound 6f was the most powerful inhibitor with an apparent K_i value of 31 nM. The inhibitory activities of 2-alkoxy steroids 9 decreased in relation to length of the alkyl chain up to n-hexyloxy group (K_i: 95 nM for methoxy 9a). All of the alkyl steroids 6 along with the alkoxy steroid 9, except for the ethyl and n-propyl compounds 6b and 6c, caused a time-dependent inactivation of aromatase. The inactivation rates (k_inact: 0.020–0.084 min⁻¹) were comparable to that of the parent compound Δ¹-AD. The inactivation was prevented by the substrate AD, and no significant effect of l-cysteine on the inactivation was observed in each case. The results indicate that the 2-hexyl compound 6f act as the most powerful mechanism-based inactivator of aromatase among Δ¹-AD analogs and may be submitted to the preclinical study in estrogen-dependent breast cancer.     

Cyclic AMP and intracellular ionic activities innecturus gallbladder

Summary Open-tip and liquid ion-exchanger microelectrodes were used to study the effects of cAMP (6mm, added to the serosal medium) on apical membrane potential (E _m ) and intracellular sodium, potassium, and chloride activities (a _Na ⁱ ,a _K ⁱ ,a _Cl ⁱ ) inNecturus gallbladder under open-circuit conditions. Transepithelial potential difference (E _Tr ) was also measured. In the presence of cAMP,a _Cl ⁱ fell from about 1.5 times its equilibrium value to a level that corresponded to electrochemical equilibrium across the apical and basolateral cell membranes. Under these conditionsa _Na ⁱ decreased anda _K ⁱ increased,E _m was unchanged andE _Tr increased from virtually zero to a small but significant serosal positive value. The cAMP-induced increase ina _K ⁱ was abolished when Cl^–-free incubation media were used. Addition of the Ca⁺⁺-ionophore A23187 (0.5 g/ml) to the serosal medium had no effect onE _m ,E _Tr , ora _Cl ⁱ . When A23187 was added to the mucosal medium,E _m and the basolateral membrane potential hyperpolarized by about 20 mV and an increase in the outwardly directed electrochemical driving force for Cl^– was observed. These results indicate that cAMP inhibits coupled transapical Na–Cl entry into epithelial cells ofNecturus gallbladder and suggest that this inhibition may not be mediated by an increase in intracellular Ca⁺⁺ concentration.     

3-(1′,1′-Dimethylbutyl)-1-deoxy-Δ-THC and related compounds: synthesis of selective ligands for the CB2 receptor

The synthesis and pharmacology of 15 1-deoxy-Δ⁸-THC analogues, several of which have high affinity for the CB₂ receptor, are described. The deoxy cannabinoids include 1-deoxy-11-hydroxy-Δ⁸-THC (5), 1-deoxy-Δ⁸-THC (6), 1-deoxy-3-butyl-Δ⁸-THC (7), 1-deoxy-3-hexyl-Δ⁸-THC (8) and a series of 3-(1′,1′-dimethylalkyl)-1-deoxy-Δ⁸-THC analogues (2, n=0–4, 6, 7, where n=the number of carbon atoms in the side chain−2). Three derivatives (17–19) of deoxynabilone (16) were also prepared. The affinities of each compound for the CB₁ and CB₂ receptors were determined employing previously described procedures. Five of the 3-(1′,1′-dimethylalkyl)-1-deoxy-Δ⁸-THC analogues (2, n=1–5) have high affinity (K_i=<20 nM) for the CB₂ receptor. Four of them (2, n=1–4) also have little affinity for the CB₁ receptor (K_i=>295 nM). 3-(1′,1′-Dimethylbutyl)-1-deoxy-Δ⁸-THC (2, n=2) has very high affinity for the CB₂ receptor (K_i=3.4±1.0 nM) and little affinity for the CB₁ receptor (K_i=677±132 nM).

Scheme 3. (a) (C₆H₅)₃PCH₃⁺ Br⁻, n-BuLi/THF, 65°C; (b) LiAlH₄/THF, 25°C; (c) KBH(sec-Bu)₃/THF, −78 to 25°C then H₂O₂/NaOH.     

Asymptotic theory for analyzing dose-response survival data with application to the low-dose extrapolation problem

A model of the form P(t, d)=1−;exp{-(t)σ^K_i=0q_idⁱ}, q_i 0, is proposed for analyzing dose-response survival data with right censoring. The q_i's in the dose polynomial are estimated by maximizing the Cox partial likelihood, and given these estimates. Λ(t) is estimated nonparametrically by an estimator proposed by Breslow. Large-sample properties of these estimators are established. Estimates and related large-sample properties are provided for the “virtually safe dose” and other parameters for assessing low-dose carcinogenic risk as a function of age, using data from animal carcinogenesis experiments.     

Factor Xa (FXa) inhibitor from the nymphs of the camel tick Hyalomma dromedarii

An inhibitor of factor Xa (FXa) was isolated from the nymphs of the camel tick Hyalomma dromedarii by a combination of chromatography on DEAE-cellulose and Sephacryl S-300 columns. The isolated nymphal FXa inhibitor turned out to be a homogenous preparation of a single polypeptide chain (15 kDa) as judged by both the native and denatured SDS-PAGE. Its pI value ranged from 7.7 to 7.9. The inhibitor is a potent anticoagulant since it prolonged both the activated partial thromboplastin time (APTT) and the prothrombin time (PT) of the camel plasma in a concentration-dependent manner. Its activity was threefold lower toward thrombin than FXa, but it did not inhibit any of the proteases; trypsin, α-chymotrypsin, papain, pepsin and subtilisin. The inhibitor binds at two sites on FXa uncompetitively with an inhibition constant (K_i) value of 134 nM.     

Synthesis of pentopyranosyl-containing thiodisaccharides. Inhibitory activity against β-glycosidases

β-(1→4)-Thiodisaccharides formed by a pentopyranose unit as reducing or non reducing end have been synthesized using a sugar enone derived from a hexose or pentose as Michael acceptor of a 1-thiopentopyranose or 1-thiohexopyranose derivatives. Thus, 2-propyl per-O-acetyl-3-deoxy-4-S-(β-d-Xylp)-4-thiohexopyranosid-2-ulose (3) and benzyl per-O-acetyl-3-deoxy-4-S-(β-d-Galp)-4-thiopentopyranosid-2-ulose (11) were obtained in almost quantitative yields. The carbonyl function of these uloses was reduced with NaBH₄ or K-Selectride, and the stereochemical course of the reduction was highly dependent on the reaction temperature, reducing agent and solvent. Unexpectedly, reduction of 3 with NaBH₄–THF at 0 °C gave a 3-deoxy-4-S-(β-d-Xylp)-4-thio-α-d-ribo-hexopyranoside derivative (6) as major product (74% yield), with isomerization of the sulfur-substituted C-4 stereocenter of the pyranone. Reduction of 11 gave always as major product the benzyl 3-deoxy-4-S-(Galp)-4-thio-β-d-threo-pentopyranoside derivative 14, which was the only product isolated (80% yield) in the reduction with K-Selectride in THF at −78 °C. Deprotection of 14 and its epimer at C-2 (13) afforded, respectively the free thiodisaccharides 19 and 18. They displayed strong inhibitory activity against the β-galactosidase from Escherichia coli. Thus, compound 18 proved to be a non-competitive inhibitor of the enzyme (K_i = 0.80 mM), whereas 19 was a mixed-type inhibitor (K_i = 32 μM).     

Effect of light intensity and ammonium-N on carotenogenesis ofTrentepohlia odorata andDunaliella bardawil

AxenicTrentepohlia odorata was cultured at three different NH₄Cl levels (3.5 × 10^–2, 3.5 × 10^–3, 3.5 × 10^–4 M) and three different light intensities (48, 76, 122 µmol m^–2 s^–1). Chloride had no effect on growth over this range of concentration. High light intensity and high NH₄Cl concentration enhanced the specific growth rate. The carotenoid content increased under a combination of high light intensity and low N concentration. WhenD. bardawil was exposed to the same combination of growth conditions, there was an increase in its carotenoid content. The light saturation and the light inhibition constants (K _s andK _i, respectively) for growth, and the saturation constant (K _m) for NH₄Cl were determined. TheK _s andK _i values were higher inT. odorata (66.7 and> 122 mol m^–2 s^–1, respectively) than inD. bardawil (5.1 and 14.7 µmol m^–2 s^–1, respectively). TheK _m value determined at 122 µmol m^–2 s^–1, however, was lower inT. odorata (0.048 µM) than inD. bardawil (0.062 µM).Author for correspondence     

1H-Pyrazole-1-carboxamidines: new inhibitors of nitric oxide synthase

1H-Pyrazole-1-carboxamidines were prepared as potential inhibitors of the three isozymes of nitric oxide synthase. All of the compounds were found to be competitive inhibitors of all three isoforms. The most selective compound prepared was 1H-pyrazole-N-(3-aminomethylanilino)-1-carboxamidine (14), which is 100-fold selective for nNOS over eNOS with a K_i value of 2 μM.     

Effects of potassium on the anion and cation contents of primary cultures of mouse astrocytes and neurons

Inastrocytes, as [K⁺]_o was increased from 1.2 to 10 mM, [K⁺]_i and [Cl^–]_i were increased, whereas [Na⁺]_i was decreased. As [K⁺]_o was increased from 10 to 60 mM, intracellular concentration of these three ions showed no significant change. When [K⁺]_o was increased from 60 to 122 mM, an increase in [K⁺]_i and [Cl^–]_i and a decrease in [Na⁺]_i were observed.Inneurons, as [K⁺]_o was increased from 1.2 to 2.8 mM, [Na⁺]_i and [Cl^–]_i were decreased, whereas [K⁺]_i was increased. As [K⁺]_o was increased from 2.8 to 30 mM, [K⁺]_i, [Na⁺]_i and [Cl^–]_i showed no significant change. When [K⁺]_o was increased from 30 to 122 mM, [K⁺]_i and [Cl^–]_i were increased, whereas [Na⁺]_i was decreased. Inastrocytes, pH_i increased when [K⁺]_o was increased. Inneurons, there was a biphasic change in pH_i. In lower [K⁺]_o (1.2–2.8 mM) pH_i decreased as [K⁺]_o increased, whereas in higher [K⁺]_o (2.8–122 mM) pH_i was directly related to [K⁺]_o. In bothastrocytes andneurons, changes in [K⁺]_o did not affect the extracellular water content, whereas the intracellular water content increased as the [K⁺]_o increased. Transmembrane potential (E_m) as measured with Tl-204 was inversely related to [K⁺]_o between 1.2 and 90 mM, a ten-fold increase in [K⁺]_o depolarized the astrocytes by about 56 mV and the neurons about 52 mV. The E_m values measured with Tl-204 were close to the potassium equilibrium potential (E_k) except those in neurons at lower [K⁺]_o. However, they were not equal to the chloride equilibrium potential (E_Cl) at [K⁺]_o lower than 30 mM in both astrocytes and neurons. Results of this study demonstrate that alteration of [K⁺]_o produced different changes in [K⁺]_i, [Na⁺]_i, [Cl^–]_i, and pH_i in astrocytes and neurons. The data show that astrocytes can adapt to alterations in [K⁺]_o, in such a way to maintain a more suitable environment for neurons.     

Inhibition of ribonuclease A by nucleoside–dibasic acid conjugates

We report the inhibition of the ribonucleolytic activity of ribonuclease A (RNase A) by nucleoside–dibasic acid conjugates for the first time. Agarose gel and precipitation assays show that the spacer length and the pK_a of the carboxylic group have an important role in the inhibitory capacity. Kinetic experiments indicate a competitive mode of inhibition with inhibition constant (K_i) value of 132 ± 3 μM for Oxa-aT. Docking studies revealed that the carboxylic group of the most active compounds is within hydrogen bonding distance of His-12, Lys-41 and His-119.     

1-Methoxy-, 1-deoxy-11-hydroxy- and 11-Hydroxy-1-methoxy-Δ-tetrahydrocannabinols: new selective ligands for the CB2 receptor

Three series of new cannabinoids were prepared and their affinities for the CB₁ and CB₂ cannabinoid recptors were determined. These are the 1-methoxy-3-(1′,1′-dimethylalkyl)-, 1-deoxy-11-hydroxy-3-(1′,1′-dimethylalkyl)- and 11-hydroxy-1-methoxy-3-(1′,1′-dimethylalkyl)-Δ⁸-tetrahydrocannabinols, which contain alkyl chains from dimethylethyl to dimethylheptyl appended to C-3 of the cannabinoid. All of these compounds have greater affinity for the CB₂ receptor than for the CB₁ receptor, however only 1-methoxy-3-(1′,1′-dimethylhexyl)-Δ⁸-THC (JWH-229, 6e) has effectively no affinity for the CB₁ receptor (K_i=3134±110 nM) and high affinity for CB₂ (K_i=18±2 nM).     

A simplified method for the purification of human red blood cell glyoxalase. I. Characteristics, immunoblotting, and inhibitor studies

Glyoxalase I (EC 4.4.1.5) was purified from human red blood cells by a simplified method using S-hexylglutathione affinity chromatography with a modified concentration gradient of S-hexylglutathione for elution. The pure protein had a specific activity of 1830 U/mg of protein, where the overall yield was 9%. The pure protein had a molecular mass of 46,000 D, comprised of two subunits of 23,000 D each, and an isoelectric point value of 5.1. TheK _M value for methylglyoxal-glutathione hemithioacetal was 192±8 µM and thek _cat value was 10.9±0.2 × 10⁴ min^–1 (N = 15). The glyoxalase I inhibitor S-p-bromobenzylglutathione had aK _i value of 0.16±0.04 µM and S-p-nitrobenzoxycarbonylglutathione, previously thought to inhibit only glyoxalase II, also inhibited glyoxalase I with aK _i value of 3.12±0.88 µM. Reduced glutathione was a weak competitive inhibitor of glyoxalase I with aK _i value of 18±8 mM. The polyclonal antibodies were raised to the purified enzyme and were found to react specifically with glyoxalase I antigen by immunoblotting. This procedure gave a protein of high purity with simple low pressure chromatographic techniques with a moderate but adequate yield for small-scale preparations.     

Effects of plant species on phosphorus availability in a range of grassland soils

Vegetative conversion from grass to forest may influence soil nutrient dynamics and availability. A short-term (40 weeks) glasshouse experiment was carried out to investigate the impacts of ryegrass (Lolium perenne) and radiata pine (Pinus radiata) on soil phosphorus (P) availability in 15 grassland soils collected across New Zealand using ³³P isotopic exchange kinetics (IEK) and chemical extraction methods. Results from this study showed that radiata pine took up more P (4.5–33.5 mg P pot^–1) than ryegrass (1.1–15.6 mg pot^–1) from the soil except in the Temuka soil in which the level of available P (e.g., E _1min P_i, bicarbonate extractable P_i) was very high. Radiata pine tended to be better able to access different forms of soil P, compared with ryegrass. There were no significant differences in the level of water soluble P (Cp, intensity factor) between soils under ryegrass and radiata pine, but the levels of Cp were generally lower compared with original soils due to plant uptake. The growth of both ryegrass and radiata pine resulted in the redistribution of soil P from the slowly exchangeable P_i pool (E _{> 10m} P_i, reduced by 31.8% on the average) to the rapidly exchangeable P_i (E _1min-1d P_i, E _1d-10m P_i) pools in most soils. The values of R/r ₁ (the capacity factor) were also generally greater in most soils under radiata pine compared with ryegrass. Specific P mineralisation rates were significantly greater for soils under radiata pine (8.4–21.9%) compared with ryegrass (0.5–10.8%), indicating that the growth of radiata pine enhanced mineralisation of soil organic P. This may partly be ascribed to greater root phosphatase activity for radiata pine than for ryegrass. Plant species × soil type interactions for most soil variables measured indicate that the impacts of plant species on soil P dynamics was strongly influenced by soil properties.     

Optimal temperature and concentration profiles in a cascade of CSTR's performing Michaelis-Menten reactions with first order enzyme deactivation

A necessary condition is found for the intermediate temperatures and substrate concentrations in a series of CSTR's performing an enzyme-catalyzed reaction which leads to the minimum overall volume of the cascade for given initial and final temperatures and substrate concentrations. The reaction is assumed to occur in a single phase under steady state conditions. The common case of Michaelis-Menten kinetics coupled with first order deactivation of the enzyme is considered. This analysis shows that intermediate stream temperatures play as important a role as intermediate substrate concentrations when optimizing in the presence of nonisothermal conditions. The general procedure is applied to a practical example involving a series of two reactors with reasonable values for the relevant five operating parameters. These parameters are defined as dimensionless ratios involving activation energies (or enthalpy changes of reaction), preexponential factors, and initial temperature and substrate concentration. For negligible rate of deactivation, the qptimality condition corresponds to having the ratio of any two consecutive concentrations as a single-parameter increasing function of the previous ratio of consecutive concentrations.List of Symbols C _E,0 mol.m^–3 Initial concentration of active enzyme - C _E,i mol.m^–3 Concentration of active enzyme at the outlet of the i-th reactor - C _S,0 mol.m^–3 Initial concentration of substrate - C _S,i mol.m^–3 Concentration of substrate at the outlet of the i-th reactor - Da _i Damköhler number associated with the i-th reactor ((V _i.k_v,0.C_E,0)/(Q.C_S,0)) - Da _min Minimum value of the overall Damköhler number - Da _tot Overall Damköhler number - E _d J.mol^–1 Activation energy of the step of deactivation of the enzyme - E _m J.mol^–1 Standard enthalpy change of the step of binding of substrate to the enzyme - E _v J.mol^–1 Activation energy of the step of enzymatic transformation of substrate - i Integer variable - j Dummy integer variable - k Dummy integer variable - k _d,i s^–1 Kinetic constant associated with the deactivation of enzyme in the i-th reactor (k _d,o·exp{–E _d/(R.T _i}) - k _d,0 s^–1 Preexponential factor of the kinetic constant associated with the deactivation of the enzyme - K _m,i mol.m^–3 Equilibrium constant associated with the binding of substrate to the enzyme in the i-th reactor, (k _m,o·exp{–E _m}(R.T _i}) - K _m,0 mol.m^–3 Preexponential factor of the Michaelis-Menten constant associated with the binding of substrate to the enzyme - k _v,i s^–1 Kinetic constant associated with the transformation of the substrate by the enzyme in the i-th reactor (k _v,o·exp{–E _v/(R.T _i})) - k _v,0 s^–1 Preexponential factor of the kinetic constant associated with the transformation of the substrate by the enzyme - N Number of reactors in the series - Q m³.s^–1 Volumetric flow rate of reacting liquid through the reactor network - R J.K^–1.mol^–1 Ideal gas constant - T _i K Absolute temperature at the outlet of the i-th reactor - T ₀ K Initial absolute temperature - V _i m³ Volume of the i-th reactor - v _max mol.m^–3.s^–1 Maximum rate of reaction under saturation conditions of substrate - x _i Normalized concentration of substrate (C_S,i/C_{S, 0}) - x _i,opt Optimum value of the normalized concentration of substrate - y _i Dimensionless temperature (exp{–T ₀/T _i}) - y _i,opt Optimum value of the dimensionless temperature Greek Symbols Dimensionless preexponential factor associated with the Michaelis-Menten constant (K _m,0/C_s,0) - Dimensionless activation energy of the step of enzymatic transformation of substrate (E _v/R.T₀)) - Dimensionless standard enthalpy change of the step of binding of substrate to the enzyme (E _m/(R.T₀)) - Dimensionless activation energy of the step of deactivation of the enzyme (E _d/(R.T₀)) - Dimensionless deactivation preexponential factor ((k _d,0.C_S,0)/(k_v,0.C_E,0)