Initial Enzyme Concentration Research Articles

Conductimetric Assay of a Bacterial Lipase, Using Triacetin as a Substrate

Abstract A conductimetric method has been applied to measure lipase activity. When using triacetin as a substrate, a linear relationship between initial rate and enzyme concentration is demonstrated up to 600 U in the cell (4 ml). Kinetic parameters of triacetin hydrolysis have been derived from conductimetric data, in the concentration range of solubility of the substrate. The limiting parameters (temperature, choice of buffer, substrate) are discussed in the last part.

Kinetics of suicide substrates steady-state treatments and computer-aided exact solutions

A steady-state differential equation that describes the kinetics of suicide substrate was derived for a scheme presented by Walsh et al. (Walsh, C., Cromartie, T., Marcotte, P. and Spencer, R. (1978) Methods Enzymol. 53, 437–448). Using its analytical solutions, the progress curves of substrate disappearance, product formation and enzyme inactivation were calculated for a hypothetical model system, and were compared with the exact solutions which were obtained by the numerical computation on a set of rate equations. The results obtained with the present analytical solutions were much more consistent with the exact solutions than those obtained using Waley's solutions (Waley, S.G. (1980) Biochem. J. 185, 771–773). The most important factor for a system of suicide substrates was found to be the term (1 + r) μ instead of rμ as proposed by Waley, where r is the ratio of the rate constant of product formation to that of enzyme inactivation and μ is the ratio of initial concentration of enzyme to that of suicide substrate. In cases where this term has a value greater than unity, all the molecules of suicide substrate are used up leaving some enzyme molecules still active. To the contrary, in cases where the term has a value smaller than unity, all the enzyme molecules are inactivated with some molecules of suicide substrate being left unreacted. When the term is equal to unity, then all the enzyme molecules are inactivated and all the molecules of the suicide substrate are converted. Practical methods for estimating kinetic parameters are described.

Enzymatic hydrolysis of cellulose: Evaluation of cellulase culture filtrates under use conditions

AbstractCulture filtrates from three mutant strains of Trichoderma reesei grown on lactose and on cellulose were compared under use conditions on four cellulose substrates. Cellulose culture filtrates contained five to six times as much cellulase as lactose culture filtrates. Unconcentrated cellulose culture filtrates produced up to 10% sugar solutions from 15% cellulose in 24 h. Specific activity in enzyme assays and efficiency in saccharification tests were low for enzymes from all the mutants. Over a wide range the percent saccharification of a substrate in a given times was directly proportional to the logarithm of the ratio of initial concentrations of enzyme and substrate. As a result of this, dilute enzyme is more efficient than concentrated enzyme, but if high sugar concentrations are desired, very large quantities of enzyme are required. Since the slopes of these plots varied, the relative activity of cellulase on different substrates may be affected by enzyme concentration.

Concentration-dependent inactivation of superoxide dismutase

The inactivation yield of superoxide dismutase (superoxide: superoxide oxidoreductase, EC 1.15.1.1) from bovine erythrocytes, when Co 60-γ-irradiated in air, N 2 or N 2O-saturated solutions, increases exponentially with the initial enzyme concentration. In aerated solutions at ⪯10 μM, the inactivation process continues in a concentration-dependent manner in the subsequent 72 h. This post-irradiation effect is inhibited by catalase. Above 10 μM, radiation-induced inactivation of the enzyme is partially reversed in a concentration-dependent manner and is not affected by catalase. In aerated and N 2O-saturated solutions, competitive scavenging of radiation chemical species by catalase and EDTA in combination reduces the inactivation yield by 80%; the residual yield remains dependent on enzyme concentration. Radiation-induced loss of copper and zinc initially exhibits a linear dose-response relationship and is less severe than the drop in enzyme activity.

Non-competitive inhibition of honeybee haemolymph pNP-alpha-D-glucosidase by chloramphenicol.--A study in vitro.

The haemolymph pNP-alpha-D-glucosidase activity of emerging worker bees shows a tendency towards negative cooperativity (n = 0.92). The relation between initial velocity and enzyme concentration is not exactly linear (bilogarithmic exponent = 0.91). Between 25 degrees and 31 degrees C, the activation energy, EA = 38.2 kJ/mol. Chloramphenicol administered in vitro decreases the maximum velocity and re-establishes pure Michaelian kinetics (n congruent 1.0). The Hill coefficient for the binding of chloramphenicol to the enzyme, ni = 1.13; the values of Ki = 20.7 mM, K'i = 17.3 mM, and I50 = 17.6 mM are not significantly different from one another. These data indicate that inhibition by chloramphenicol is of the pure, non-competitive type.

RELATING THE EXPONENTIAL PARAMETER IN THE CHURCHILL-USAGI CORRELATION TO UNDERLYING SYSTEM PARAMETERS

Abstract The Churchill-Usagi empirical equation for correlating data can be expressed as the sum of two asymptotes, each raised to a common power: where n is the exponential parameter and y0 ( x) y1(x ) are the asymptotes which approximate y( x ) over certain ranges of the independent variable, x. This paper attempts to present a procedure which can be used to relate n to the underlying physical system which is represented mathematically by the function, y( x ). The procedure is demonstrated on two examples: ( 1) correlating binary equilibrium data; and ( 2 role=) correlating data for the simple enzyme reaction: These two examples were chosen in part because the mathematical model for the one example ( equilibrium data) is an algebraic equation while the other one is modelled by a system of differential equations. For the equilibrium data example, it is shown that n - — lpar; I + α) / ( l - α ) where a is the “average” relative volatility of the system. In the enzyme example, it is shown that n = log ( 2 ) / [ log( s1,/ ( l - s1 ) ( γ + εs, ) ) ] where s, is a root of a certain quadratic equation and α,ε are dimensionless parameters related to k1 k2 k3 and the initial enzyme and substrate concentrations.

Effects of ultrasound on catalase and malate dehydrogenase.

Catalase and malate dehydrogenase (MDH) were subjected to the sound field produced by a transversely oscillating wire driven at 20 kHz. Catalase was not inactivated under any conditions of sonication whereas MDH inactivation increased exponentially with the duration of sonication and depended upon the initial enzyme concentration. The inactivation was not the result of collapse cavitation or thermal inactivation and was probably related to the presence of acoustic microstreaming.

The disproportionation of glyoxylate by lactate dehydrogenase

Lactate dehydrogenase (EC 1.1.1.27) catalyzes the NAD-dependent oxidation to (oxalate) and reduction (to glycollate) of glyoxylate. The kinetics of this disproportionation are in accord with the usual reaction pathway of lactate dehydrogenase:substrate inhibition with appropriate pH dependence occurs; a steady state in the ratio of NADH to NAD + is set up during the reaction, has the expected dependence on pH, and is independent of the initial glyoxylate, coenzyme, and enzyme concentration. At pH 7 the lactate dehydrogenase-NADH complex is about fivefold more likely to react with and reduce glyoxylate (at a concentration of 100 m m) than to dissociate to produce free NADH, and the ratio of the fraction of the enzyme-NADH complex which dissociates to the fraction which reacts with and reduces glyoxylate varies with glyoxylate concentration and with pH in a manner in agreement with the normal reaction pathway of the enzyme. With all concentrations of glyoxylate and over the pH range 7–9.6 both free (not enzyme bound) NAD + and free NADH are formed in the steady state of the disproportionation. From these results it is apparent that lactate dehydrogenase, like alcohol dehydrogenase (EC 1.1.1.1), catalyzes a disproportionation within the bounds of its normal kinetic reaction pathway.

Profiles of pure pancreatic secretions obtained by direct pancreatic duct cannulation in normal healthy human subjects

The development of endoscopic retrograde cannulation of the pancreatic duct allows collection of pure pancreatic juice uncontaminated by bile and duodenal secretions. We have analyzed such pure pancreatic juice to establish secretory profiles of some normal components. Fifteen healthy human volunteers were studied. Secretin (1 clinical unit per kg) was injected intravenously at time 0, and 16 min later cholecystokinin-pancreozymin (CCK-PZ) (1 Ivy dog unit per kg) was injected intravenously. Pure pancreatic juice was collected for 32 min in timed minute samples. Secretin produced an almost immediate and sustained flow of juice (3.15 ± 0.24 ml per min) with initial high concentrations of protein and enzyme. After CCK-PZ, flow increased significantly to 3.40 ± 0.29 ml per min (P < 0.02) and enzyme concentration rose some 10-fold above that found during secretin stimulation. The maximum of the CCK-PZ effect occurred 2 to 3 min after injection and its half-life was 73 to 90 sec for total protein and enzymes but only 64 sec for trypsin inhibitor. Repeat studies in 3 subjects indicate marked reproducibility for these various parameters. Trypsinogen and proelastase appeared to be secreted in a parallel fashion but nonparallel secretion for amylase, chymotrypsin, and trypsin inhibitor was observed. Amylase secretion was proportionately less and trypsin inhibitor secretion proportionately more stimulated by CCK-PZ than was chymotrypsinogen. Collections of single minute samples of pure pancreatic juice reveal a more accurate profile of secretory events than does collection of pooled samples for 10 to 20 min as hitherto performed by other workers.

Enzyme deactivation during cellulose hydrolysis

AbstractHydrolysis of cellulose by Trichoderma viride cellulase reached a plateau after some 25 hr. If the initial enzyme‐to‐substrate ratio was low, resuspension of substrate in fresh enzyme or addition of enzyme resulted in further high rate hydrolysis. This did not occur if the initial ratio was high. Over 75% hydrolysis might be achieved in the former case, while less than 60% in the latter. A model postulating inactivation of adsorbed enzyme–substrate complex which blocked further hydrolysis was proposed, and it was found to fit the data well. The proposed model had five parameters, four of which could be checked by graphical methods, and all of which had physical meanings. The parameters were estimated by a nonlinear least‐squares minimization FORTRAN computer program, using numerical integration and optimization of the parameters. The model was used to predict the resuspension data, powdered enzyme addition data, cellobiose addition data, and cellulose addition data; the deviations from the model are discussed. It was found that average values could be used for four out of the five parameters, while the fifth (initial enzyme concentration) did not correlate with independent measurements such as the filter paper activity or protein concentration.

Parameters of biological freezing damage in simple solutions: Catalase: II. Demonstration of an optimum-recovery cooling-rate curve in a membraneless system

Seeded solutions of catalase in neutral 10 m M potassium phosphate buffer exhibited characteristic rate dependencies for freeze-thaw damage: Damage increased as the cooling rate was increased, and as the warming rate was decreased. The pattern of warming-rate dependence was independent of the prior cooling rate and also of the addition of KCl or of NaCl to the buffer. In contrast, the cooling-rate curve became almost flat upon addition of 0.1 M KCl, suggesting increased damage from concentrating solute at low cooling rates. In the presence of added NaCl, frank optimum-recovery cooling-rate curves were generated. At low NaCl levels (less than 10 m M) the optimum occurred at 0.5 °C/ min; at 27 and 81 m M NaCl, the optimum shifted to 5 and 20 °C/min, respectively. By comparison with KCl, it appears that the major factor causing damage at low cooling rates in NaCl is acidification. The factor causing damage at high cooling rates remains obscure. The argument that it is due to the trapping of the enzyme molecules at interfaces at high dilution, to be subsequently damaged by shearing stress or dehydration during the recrystallization attending slow warming, is mitigated by the finding that inactivation remains a function of the initial enzyme concentration at all cooling rates. The possibility that a particular conformational state is trapped in an unfavorable temperature zone was also considered: Three simple models were formulated, and the relative order of recovery was deduced for the possible sequences of fast and slow cooling and warming. The permutation observed for catalase was inconsistent with any of these three mechanisms, although they may be pertinent for the red cell and other systems. A final possibility, not yet explored, is that rapid cooling causes damage by producing nonequilibrium freezing, with large deviations of pH and/or solute concentration from those expected at equilibrium.

Enzymic hydrolysis of 3-acetyl-estrogens or analogues by glutamate dehydrogenase with specific acylation of the estrogen binding site.

The estrogen analogues or derivatives 4‐acetyldiethylstilbestrol, 3‐acetyl‐estradiol and 3‐acetyl‐2‐nitroestrone were hydrolysed by glutamate dehydrogenase with covalent incorporation of an acetyl group into the enzyme molecule, probably through a transacylation process.When 3‐acetyl‐2‐nitroestrone was used as a ‘substrate’, spectrophotometric titration of the free product (a nitrophenol) allowed kinetic studies: there was a linear relationship between initial hydrolysis rates and enzyme concentration and Michaelis kinetics were observed suggesting an enzyme catalyzed process.The covalent incorporation of the acetyl group on the enzyme was studied using 3‐[2′‐14C]acetyl‐2‐nitroestrone: in the absence of NADH, lysine residues 419 and 422 were specifically acetylated without enzyme inactivation. In the presence of NADH, the labelling was distributed over two more lysine residues, 143 and 155, with progressive inactivation.Estradiol lowered the hydrolysis rate of 3‐acetyl‐2‐nitroestrone by glutamate dehydrogenase, protected the enzyme against acylation and against the inactivation which is observed in the presence of NADH. Moreover glutamate dehydrogenase acylated by 3‐acetyl‐2‐nitroestrone became less sensitive to its allosteric effector: estradiol. Thus, it is suggested that hydrolysis of acetyl‐estrogen or analogues by glutamate dehydrogenase and acylation of the enzyme occur in or near the estrogen binding site.

Reactivation of Alkaline Phosphatase in Ultra High-Temperature, Short-Time Processed Liquid Milk Products

Alkaline phosphatase (enzyme) reactivation was studied in liquid milk products heated to 87.8 to 121.1 C for less than 1 s in a continuous, two-phase, slug-flow heat exchanger. The effects of magnesium concentration, pH, incubation temperature, homogenization pressure, processing temperature, fat content, and initial enzyme concentration were investigated. Jersey milk from one farm showed seasonal variations in enzyme concentration and its reactivation behavior. Increased reactivation in products with high fat content was due to high initial enzyme concentration in the product. Homogenization of products before heating decreased reactivation. Maximum reactivation occurred in products heated to 104.4 C, incubated at 34 C, and adjusted to pH 6.5. Maximum velocity of reactivation and reactivation constant varied with milk samples. Activation energy for the control and samples with magnesium was 22.646 +/- .118 and 24.100 +/- .210 kJ mole-1, respectively. The enzyme from raw and reactivated cream contained two major isozymes, and the reactivated isozyme differed from the control. The official method for differentiating residual and reactivated enzymes was modified in terms of magnesium concentration and extent of reactivation of the enzyme in the reactivated product.

Kinetics and thermodynamics of isothermal seed germination

We have been successful in building a mathematical model that fits both the germination rate and the total number of seeds that germinate as a function of time. This mathematical model is the same autocatalytic reaction model that describes biochemical reactions in which enzymes play an important role. The model gives values for the initial concentration of two enzymes. From these initial enzyme concentrations an equilibrium constant is calculated and the thermodynamic model gives the change in enthalpy, entropy, free energy and the activation energy. A plot of the natural logarithm of the equilibrium constant as a function of the reciprocal of the absolute temperature gives two straight lines. The change of enthalpy for the process below 33 °C differs considerably to the change above 33 °C. The free energy as a function of the absolute temperature gives a straight line from which the change in entropy is calculated. The activation energy is determined from the slope of the natural logarithm of the rate constant as a function of the reciprocal of the absolute temperature.

An integration method of enzyme analysis

The application of an integration method of kinetic analysis to first-order and second-order reactions is discussed with particular emphasis on enzyme analyses. Transducer signals or concentrations of products or substrates are integrated for a Fixed time and the net integral of the increased or decreased signal or concentration is related to the initial substrate or enzyme concentration. Equations are developed describing the dependence of the integrals on enzyme and substrate concentrations for first- and second-order reactions, and examples are presented illustrating different cases. The application of this method to complicated enzymatic systems is discussed.

Biochemical oscillators—a search procedure

The paper shows how the describing function technique can be employed in a search for periodic solutions to large systems of nonlinear differential equations that describe chemical reaction networks of a type encountered in biological contexts. The equations studied describe a reaction scheme in which the first reaction is inhibited by the product of the last reaction. The differential equations take the form dS 1 ⧸dt = K⧸( 1 + α(S n) ρ) and dS j⧸dt = g j− 1 S j− 1 −b jS j, j = 2, 3,⋯n . The parameter ϱ is a positive integer and represents the number of molecules of inhibitor required to block the S 1 to S 2 reaction. The equations can be interpreted as a simple model of inhibition of transcription, or they can be interpreted as an inhibited enzyme reaction system in which initial substrate concentration and enzyme concentrations are held constant. The system of simultaneous equations is reduced to a single equation in S n : (p + b 1 )(p + b 2 )⋯(p + b n)S n = d 1 /( 1 + d 2 S ρ n) . Here p is the differentiation operator and d 1 and d 2 are positive constants expressible in terms of α, g j 's, and K. The transfer function block diagram equivalent to this equation is established, and is seen to have closed feedback loop form and to contain a linear block and a nonlinear block. The nonlinear block is replaced by the describing function which is related to the Fourier series of the nonlinear block's output. A study of the system containing the describing function is then developed. It is shown that if ϱ=1, then the describing function analysis indicates, for arbitrary n, that stable limit cycles will not appear if K, α, g j , and b j are positive. Since these constants represents the products of reaction rate constants and concentrations, this requirement is automatically met. The nonexistence of stable limit cycles for ρ=1 holds for all values of n; it is also shown that for n⩽4 unstable limit cycles are also necessarily absent. The extension of the method for larger values of ρ is outlined. Since the 1 (1 + z ρ) nonlinearity frequently appears in biological problems, the describing function will be useful in several areas of research.

Studies on the catalytic mechanism of a serine protease from Streptomyces griseus.

The kinetics of the Streptomyces griseus protease‐3‐catalyzed hydrolysis of p‐nitrophenyl‐acetate have been studied by stopped‐flow techniques with widely varied initial concentrations of enzyme and substrate. The results obtained are consistent with a three‐step mechanism in which there is a rapid equilibration between enzyme and substrate to form a Michaelis complex with a dissociation constant in the order of 10 mM, followed by a moderately rapid formation of an acyl‐enzyme and a rate‐limiting deacylation of this intermediate. Estimated rate constants forthe latter two reaction steps are 15 s−1 and 0.09 s−1, respectively.The presence of a nucleophile such as methanol results in a partitioning of the deacylation process, reflected by a linear dependence of the maximum steady‐state reaction velocity on the concentration of methanol. This observation provides confirmatory evidence for a rate‐limiting deacylation step in the catalytic mechanism.

Identification, hysteresis, and discrimination in enzyme kinetic models

AbstractThree kinetic rate constants and an initial enzyme concentration are estimated in Britton Chance's classical peroxidase model by applying both the Picard iteration‐orthogonal polynomial and stationary state methods to his transient experimental data. Since this model does not describe the hysteresis exhibited by the data, more complex models are examined in order to account for this behavior. From a study of this hysteresis phenomena which is inherent to the structure of consecutive reactions, it is found that in addition to discriminating between mechanisms much useful information about the history of enzyme induction can be observed from the direction, shape, and area of the hysteresis loop.

The pH-dependence of rates of individual steps in ficin catalysis.

The kinetics of the ficin‐catalysed hydrolysis of benzoylglycine p‐nitrophenyl ester have been studied at different pH values with widely varying initial concentrations of enzyme and substrate. The time‐courses of proton release and p‐nitrophenol release were followed. The failure to observe a lag period for p‐nitrophenol release employing a stopped‐flow spectrophotometer leads to a minimum value for the rate constant for the formation of the E · S complex of 5 × 105 M−1 sec−1. Evidence is presented for the formation of E · S being a pseudo‐equilibrium process. The results are consistent with a three‐step mechanism involving an acyl‐enzyme intermediate. Time‐courses of reactions with [E0] ∼ [S0] were independent of wavelength in the range 291 to 400 nm so that it is unlikely that an oxazolinone is formed as an intermediate. The pH‐dependencies have been determined for the dissociation constant of the E · S complex (Ks) as well as for the individual rate constants associated with the catalytic steps (k+2 and k+3). pH profiles of k+2/Ks implicate ionising groups of pKa values 4.3 and 8.58 in the free enzyme (25 °C, I= 0.1). The pH dependency of k+2 (measured directly at pH values below neutrality) implicates an ionising group in the catalytic step with pKa∼ 5.8. The change in the value of Ks with pH is in accord with this being identical to the group with pK 4.3 in the free enzyme. The value of k+3 does not vary significantly between pH 3.9 and 6.6, from which it is deduced that the group of pKa∼ 5.8 in the E · S complex undergoes a downward shift in pKa by at least 2 units on formation of the acyl‐enzyme intermediate. The release of protons concomitant with acyl‐enzyme formation (pH 5 and [E0] ∼ [S0]) is consistent with such a pKa shift. At neutral pH values the k+3 step is rate limiting in catalysis whereas at pH 3.9 k+2 becomes rate limiting. This change in rate‐limiting step with pH illustrates the danger in the assumption that kcatversus pH profiles for thiol protease action on substrates with good leaving groups are equivalent to k+3versus pH profiles.

Antithrombin

SummaryAn evaluation of the mode of action of antithrombin in the temporary inhibition of purified 3.7 S bovine thrombin was made according to traditional enzyme inhibition theory. Using enzyme clotting activity and concentration of active sites synonymously, it was observed that the binding of antithrombin to thrombin followed a second order reaction that could be distinguished into an essentially irreversible phase and a slower, potentially reversible phase. The level of steady state enzyme inhibition depended upon the ratio of the initial concentrations of enzyme to antithrombin. In addition, there occurred a rapid enhancement of enzyme esterolytic activity during the concomitant loss in clotting activity. This enhancement was also observed for acetylated thrombin which had no proteolytic activity. Under high concentrations of antithrombin, this enhancement subsequently deteriorated. A working hypothesis, including equations, for a mutual depletion system is presented to account for the known parameters of enzyme inhibition by antithrombin. We compared the neutralization of thrombin C with autoprothrombin C and found that each enzyme responds to antithrombin according to similar kinetic relationships.