Kinetic behavior of slowly equilibrating association-dissociation enzyme systems]

The shape of the plots of product accumulation versus time (t) has been analysed for slowly equilibrating association-dissociation enzyme systems of the types 2p in equilibrium P (P is enzyme oligomer which is able to dissociate reversibly forming two identical halves p) and M in equilibrium M2 in equilibrium M2 in equilibrium... (M is monomer which has two association sites overlapping with active sites). It is assumed that the rate of equilibration between oligomeric forms is comparable with the rate of over-all enzymatic reaction and that substrate-oligomer complexes are in rapid equilibrium with free components. It has been shown that characteristic feature of kinetic behavior of slowly equilibrating association-dissociation enzyme systems is that the value of tau depends on enzyme concentration (tau is the intercept on t-axis for linear asymptota of the curve of product concentration versus time at t leads to infinity).     

Kinetic analysis of urea-inactivation of beta-galactosidase in the presence of galactose

The effect of galactose on the inactivation of purified beta-galactosidase from the black bean, Kestingiella geocarpa, in 5 M urea at 50 degrees C and at pH 4.5, was determined. Lineweaver-Burk plots of initial velocity data in the presence and absence of urea and galactose were used to determine the relevant K(m) and V(max) values, with p-nitrophenyl beta-D-galactopyranoside (PNPG) as substrate, S. The inactivation data were analysed using the Tsou equation and plots. Plots of ln([P](infinity) - [P](t) ) against time in the presence of urea yielded the inactivation rate constant, A. Plots of A vs [S] at different galactose concentrations were zero order showing that A was independent of [S]. Plots of [P](infinity) vs [S] were used to determine the mode of inhibition of the enzyme by galactose, and slopes and intercepts of the 1/[P](infinity) vs. 1/[S] yielded k(+0) and k '(+0), the microscopic rate constants for the free enzyme and the enzyme-substrate complex, respectively. Plots of k(+0) and k '(+0) vs. galactose concentrations showed that galactose protected the free enzyme and not the enzyme-substrate complex against urea inactivation via a noncompetitive mechanism at low galactose concentrations and a competitive pattern of inhibition at high galactose concentrations. The implication of the different modes of inhibition in protecting the free enzyme was discussed.     

Fluorescence monitoring of the conformational change in alpha 2-macroglobulin induced by trypsin under second-order conditions: the macroglobulin acts both as a substrate and a competitive inhibitor of the protease

The reaction of bovine pancreatic trypsin with human plasma alpha(2)-macroglobulin (alpha(2)M) was studied at 25 degrees C, using equimolar mixtures of E and I in 50 mM potassium phosphate buffer, pH 7. The conformational change in alpha(2)M was monitored through the increase in protein fluorescence at 320 nm (exc lambda, 280 nm). At [alpha(2)M](0) =[E](0) =11.5-200 nM, the fluorescence change data fit the integrated second-order rate equation, (F(infinity) -F(0) )/(F(infinity) -F(t) )=1+k(i,obsd) [alpha(2)M](0) t, indicating that cleavage of the bait region in alpha(2)M was the rate-determining step. The apparent rate constant (k(i,obsd)) was found to be inversely related to reactant concentration. The kinetic behavior of the system was compatible with a model involving reversible, nonbait region binding of E to alpha(2)M, competitively limiting the concentration of E available for bait region cleavage. The intrinsic value of k(i) was (1.7+/-0.24) x 10(7) M(-1) s(-1).K(p), the inhibitory constant associated with peripheral binding, was estimated to be in the submicromolar range. The results of the present study point to a potential problem in interpreting kinetic data relating to protease-induced structural changes in macromolecular substrates. If there is nonproductive binding, as in the case of trypsin and alpha(2)M, and the reactions are monitored under pseudo first-order conditions ([S](0) >[E](0) ), an intrinsically second-order process (such as the rate-limiting bait region cleavage in alpha(2)M) may become kinetically indistinguishable from an intrinsically first-order process (e.g. rate-limiting conformational change). Hence an excess of one component over the other should be avoided in kinetic studies addressing such systems.     

An explicit solution for progress curve analysis in systems characterized by endogenous substrate production

The Lambert W function was used to explicitly relate substrate concentration S, to time t, and the kinetic parameters V (m), K (m), and R in the modified Michaelis-Menten equation that accounts for endogenous substrate production. The applicability of this explicit formulation for kinetic parameter estimation by progress curve analysis was demonstrated using a combination of synthetic and experimental substrate depletion data. Synthetic substrate depletion data were generated using S (0) values of 1, 2, and 3 μM and V (m), K (m), and R values of 1.0 μM h(-1), 1.0 μM, and 0.1 μM h(-1), respectively, and contained 5% normally distributed error. Experimental data were obtained from two previously published studies on hydrogen depletion in four experimental systems. In all instances, experimental data were well described by the explicit solution presented in this study. Differential equation solution and iterative S estimation are eliminated with the explicit solution approach, thereby simplifying progress curve analysis in systems characterized by endogenous substrate production.     

Characterization of hydroxyl radical-induced damage after sparsely and densely ionizing irradiation

The extent of hydroxyl radical mediated cell inactivation was measured for a variety of particle beams ranging from 8.5 Me V/u neon ions to 570 Me V/u argon ions. In general, the fraction of the total radiosensitivity caused by OH decreases from close to 60 per cent at low ionization density or low linear energy transfer (low LET) to close to 25 per cent at high LET for aerobically irradiated mammalian cells. The extent of OH induced cell lethality can be explained in terms of LET infinity only for low energy or low atomic number particles where fragmentations and complicated track structures do not contaminate the characteristic particle LET. For example, at a calculated LET infinity of 100 ke V/micron, the OH mediated fraction of the total radiation damage is about 25 per cent for low energy carbon but close to 40 per cent for high energy carbon ions. For low energy charged nuclei of approximately the same energy, as the 5.4-13.4 MeV/u He, Li, C and Ne ions in this report, there is a predictable diminution of the OH mediated effect with increasing LET infinity; however, the biological effect cannot be predicted accurately from calculated LET infinity values for high energy particle irradiation, nor indeed from a variety of low energy charged particles of quite different energies (incident velocities). This illustrates the unsuitability of using LET as a unifying parameter, except under specific circumstances. As more is learned about the energy deposition for energized charged particles in terms of track structure (core and penumbra), it may be possible to characterize the radiobiological data with a better physical parameter than LET infinity.     

Simultaneous estimation of T(G2+M), T(S), and T(pot) using single sample dynamic tumor data from bivariate DNA-thymidine analogue cytometry

BACKGROUND: Estimating the duration of S phase (T(S) ) and the potential doubling time (T(pot) ) from a single time measurement of the movement of cells using bivariate cytometry is common. However, these estimates require an assumption of the duration of G2 + M (T(G2+M) ). Inspection of the measured dynamic quantities, relative movement [RM(t)], fractions of labeled divided and undivided cells (f(lu)(t) and f(ld)(t)) suggests that T(G2+M), T(S), and T(pot) can be determined simultaneously. METHODS: An equation connecting the growth of the cell population, time, and the dynamic quantities was determined. The equation cannot be solved analytically, but accurate approximations can be used to find T(pot). From this result, the value of T(G2+M) can be determined from f(ld)(t), and T(S) can be determined from RM(t). RESULTS: Kinetic parameters obtained from single time estimates using the new method compared to those obtained from the analysis of multiple time-point measurements of MCa-K and MCa-4 murine tumors are shown to be in close agreement. Moreover, estimates of T(G2+M) in MCa-4 tumors, treated with paclitaxel, provide extra information on the changes in T(G2+M). When applied to the rat R3327-G prostate tumor model following androgen ablation, a correlation analysis of the T(pot) values obtained by the new and previous single time-point methods demonstrates that the rank order from shortest to longest T(pot) values are largely preserved. CONCLUSIONS: The new procedure makes direct estimation of T(G2+M) possible from single time-dynamic measurements. The results from previous studies on T(S) and T(pot) are largely unchanged, but extra information is now available.     

Modeling pulmonary and CNS O(2) toxicity and estimation of parameters for humans.

The power expression for cumulative oxygen toxicity and the exponential recovery were successfully applied to various features of oxygen toxicity. From the basic equation, we derived expressions for a protocol in which PO(2) changes with time. The parameters of the power equation were solved by using nonlinear regression for the reduction in vital capacity (DeltaVC) in humans: %DeltaVC = 0.0082 x t(2)(PO(2)/101.3)(4.57), where t is the time in hours and PO(2) is expressed in kPa. The recovery of lung volume is DeltaVC(t) = DeltaVC(e) x e(-(-0.42 + 0.00379PO(2))t), where DeltaVC(t) is the value at time t of the recovery, DeltaVC(e) is the value at the end of the hyperoxic exposure, and PO(2) is the prerecovery oxygen pressure. Data from different experiments on central nervous system (CNS) oxygen toxicity in humans in the hyperbaric chamber (n = 661) were analyzed along with data from actual closed-circuit oxygen diving (n = 2,039) by using a maximum likelihood method. The parameters of the model were solved for the combined data, yielding the power equation for active diving: K = t(2) (PO(2)/101.3)(6.8), where t is in minutes. It is suggested that the risk of CNS oxygen toxicity in diving can be derived from the calculated parameter of the normal distribution: Z = [ln(t) - 9.63 +3.38 x ln(PO(2)/101.3)]/2.02. The recovery time constant for CNS oxygen toxicity was calculated from the value obtained for the rat, taking into account the effect of body mass, and yielded the recovery equation: K(t) = K(e) x e(-0.079t), where K(t) and K(e) are the values of K at time t of the recovery process and at the end of the hyperbaric oxygen exposure, respectively, and t is in minutes.     

Yield per recruit of the pacu Piaractus mesopotamicus (Holmberg, 1887) in the pantanal of Mato Grosso do Sul, Brazil.

Among the several fish species comercially exploited at the Pantanal of Mato Grosso do Sul, the "pacu" (Piaractus mesopotamicus) stands as one of the most important. Information regarding its exploitation level is necessary for the proper management of its stocks. Between 1996 and 1997 data on total length of the pacu were collected on a monthly basis from specimens caught by professional and sport fishers in the municipality of Corumbá. These data were used to estimate growth parameters and to assess the exploitation level for this species, applying the Beverton and Holt yield per recruit model. Length frequency analysis, carried out with the software FISAT (ELEFAN), was used to estimate growth parameters: 1996: L(infinity) = 87.20 cm; K = 0.34 year(-1); phi(')=3.41; C = 0.74; WP = 0.81; Longevity = 8.40 years; and 1997: L(infinity) = 86.50 cm; K = 0.34 year(-1); phi(')=3.40; C = 0.60; WP = 0.80; Longevity = 8.40 years. The value for t(0) is -0.363 years for mean values of L(infinity) and k. The weight-length relationship, calculated from data derived from experimental fisheries carried out in 1999 and 2000, is described by the equation: W = 0.048LF(2.835). Estimated mortalities and survival rates were: 1996: Z = 1.51 year(-1); M = 0.62 year(-1); F = 0.89 year(-1); S = 21.9%; and 1997: Z = 1.65 year(-1); M = 0.63 year(-1); F = 1.02 year(-1); S = 19.1%. The yield per recruit analysis showed the following values: F(Present) = 0.96 year(-1); F(max) = 0.67 year(-1) ; F(0.1) = 0.51 year(-1) (for L(c) = 26.7 cm). These results suggest that the pacu is overexploited in the area, so that restrictive measures are in need to manage the pacu fisheries.     

Hypothesis: cyclic AMP turnover in S49 cells

The fractional turnover constant (ke) of cAMP in S49 lymphoma cells stimulated by epinephrine was essentially identical to the decay constant for cAMP in these cells. This was in sharp distinction to the situation in the human diploid lung fibroblast WI-38, in which ke was much lower in hormone stimulated cells. In this study we report a new method for the determination of cAMP turnover. The method was based on the assumption that for tritium label to be incorporated into cAMP on treatment of cells with [3H]-adenine, the label must first pass through ATP. An equation relating the rate of change in cAMP specific radioactivity with cAMP and ATP specific radioactivities was thereby determined. The equation was expressed in a form that gave a linear graphical plot with the fractional turnover constant as the slope of the line.     

Effect of electric field on erythrocyte sedimentation rate. II. Dependence on electric current

We measured the electric current dependence of sedimentation curves of swine erythrocytes in a saline solution at the volume fraction of erythrocytes H = 0.091 and 0.220. The sedimentation curve fitted well to the exponential type equation l = a[1-exp(-bt)] at the upward initial electric current I0 = 0.50 mA, 1.01 mA and 1.50 mA, where l is the length of the medium layer at time t, and a and b are phenomenological parameters. The initial slope v0 of sedimentation curve was enhanced from 0.68 mm/hr at I0 = 0 mA to 2.85 mm/hr, 3.87 mm/hr and 5.50 mm/hr at I0 = 0.50 mA, 1.01 mA and 1.50 mA, respectively, for H = 0.220. We also made sedimentation measurements of erythrocytes in their own plasma at H = 0.220 and 0.316. Sedimentation curves coincided with the sigmoidal type equation l = l infinity/[1 + (t50/t)beta] at I0 = 0 mA and 0.50 mA, where l infinity is l at t----infinity, t50 is the time when the plasma level falls to l infinity/2 and beta is a constant. The maximum slope vmax of sedimentation curve increased from 13.29 mm/hr at I0 = 0 mA to 18.65 mm/hr at I0 = 0.50 mA for H = 0.220.     

Formation of bacterial colonies in successive time intervals

By enumerating colonies on a plate in successive equal short intervals of time, we found that the number of colonies formed in individual intervals varied at random and their distribution was approximated by a Poisson series. Based on the result, we derived the equation of colony formation (CF equation). This equation describes the relationship between the cumulative number of colonies and incubation time: N(t) = N infinity (1 - exp[-lambda(t - tr)]) where N(t) is the number of colonies at time t. N infinity, lambda, and tr are parameters, expressing the expected number of colonies on a plate at infinite incubation time, the probability of the occurrence of colony formation in a unit of time, and a retardation time, respectively.     

Formation of bacterial colonies in successive time intervals.

By enumerating colonies on a plate in successive equal short intervals of time, we found that the number of colonies formed in individual intervals varied at random and their distribution was approximated by a Poisson series. Based on the result, we derived the equation of colony formation (CF equation). This equation describes the relationship between the cumulative number of colonies and incubation time: N(t) = N infinity (1 - exp[-lambda(t - tr)]) where N(t) is the number of colonies at time t. N infinity, lambda, and tr are parameters, expressing the expected number of colonies on a plate at infinite incubation time, the probability of the occurrence of colony formation in a unit of time, and a retardation time, respectively.     

Electrodiffusion of ions approaching the mouth of a conducting membrane channel.

The movement of ions in the aqueous medium as they approach the mouth (radius a) of a conducting membrane channel is analyzed. Starting with the Nernst-Planck and Poisson equations, we derive a nonlinear integrodifferential equation for the electric potential, phi(r), a less than or equal to r less than infinity. The formulation allows deviations from charge neutrality and dependence of phi(r) on ion flux. A numerical solution is obtained by converting the equation to an integral equation that is solved by an iterative method for an assumed mouth potential, combined with a shooting method to adjust the mouth potential until the numerical solution agrees with an asymptotic expansion of the potential at r-a much greater than lambda (lambda = Debye length). Approximate analytic solutions are obtained by assuming charge neutrality (Läuger, 1976) and by linearizing. The linear approximation agrees with the exact solution under most physiological conditions, but the charge-neutrality solution is only valid for r much greater than lambda and thus cannot be used unless a much greater than lambda. Families of curves of ion flux vs. potential drop across the electrolyte, phi(infinity)-phi (a), and of permeant ion density at the channel mouth, n1(a), vs. flux are obtained for different values of a/lambda and S = a d phi/dr(a). If a much greater than lambda and S = O, the maximum flux (which is approached when n1(a)----0) is reduced by 50% compared to the value predicted by the charge-neutrality solution. Access resistance is shown to be a factor a/[2 (a + lambda)] times the published formula (Hille, 1968), which was derived without including deviations from charge neutrality and ion density gradients and hence does not apply when there is no counter-ion current. The results are applied to an idealized diffusion-limited channel with symmetric electrolytes. For S = O, the current/voltage curves saturate at a value dependent on a/lambda; for S greater than O, they increase linearly for large voltage.     

Estimation by gas chromatography-mass spectrometry with selected ion monitoring of urinary excretion rates of 3 alpha-androstanediol during/after i.v. administration of 13C-labelled testosterone in man

To study in vivo the conversion of testosterone (T) into its metabolites, dihydro-testosterone (DHT) and 5 alpha-androstane-3 alpha, 17 beta diol (3 alpha-Diol) the urinary excretion rates of these steroids were determined by mass spectrometry in 6 healthy men during/after the i.v. infusion (t = 4 h) of 20 mg [13C]testosterone. In addition, plasma concentrations of T, DHT and 3 alpha-Diol were determined by radioimmunoassay. During steady state conditions at the end of the 4-h infusion of [13C]T the increase in the plasma concentrations of T from, basal, 405 +/- 140 ng/dl to 4205 +/- 804 ng/dl was paralleled by an increase in the plasma concentrations of DHT to 106.4 +/- 62.5 ng/dl) (basal: 30.8 +/- 21.8 ng/dl), and of 3 alpha-Diol to 32.2 +/- 12.5 ng/dl (basal: 12.5 +/- 13.9 ng/dl). Plasma concentrations of T, DHT and 3 alpha-Diol then returned to basal concentrations within 24 hours. Using mass-spectrometry we found a cumulative renal excretion of 13C-labelled T of 15.6 +/- 9.6 micrograms/24 h, equivalent to 0.08 +/- 0.05% of the infused amount (20 mg) of [13C]T. Whereas urinary excretion of [13C]DHT was below the level of detection by mass-spectrometry the cumulative excretion of [13C]3 alpha-Diol was 67.7 +/- 19.9 micrograms/24 hours which is equivalent to 0.3 +/- 0.1% of the infused dose of 13C-labelled testosterone. These data suggest that the determination of urinary 3 alpha-Diol by mass-spectrometry during/after the infusion of stable-labelled testosterone represents an alternative to the use of radioactive label for turnover studies.     

High affinity binding of paclitaxel to human serum albumin.

Paclitaxel, a very potent antitumor agent is a hydrophobic molecule with low aqueous solubility. Its currently used formula (Taxol) contains the drug in a 1 : 1 (v/v) mixture of ethanol and Cremophor EL. To minimize vehicle-related toxicity, we developed a novel, water-soluble formulation in which paclitaxel is bound noncovalently to human serum albumin. For this purpose, studies of the paclitaxel-albumin binding equilibrium were performed. Paclitaxel dissolved in ethanol was added to the aqueous solution of human serum albumin. Precipitated paclitaxel was removed and unbound drug was separated by ultrafiltration. Paclitaxel concentration was measured by RP-HPLC. Binding data were evaluated based both on the Scatchard plot and the general binding equation describing binding equilibria with the stepwise stoichiometric binding constants. The Scatchard plot was found to be curvilinear with a slight positive slope of the final part. Parameters of high affinity specific binding were determined from the initial part of the curve (nsp = 1.3 and Ksp = 1.7 x 10(6) M(-1)). Stoichiometric binding constants were estimated by fitting the general binding equation to the experimental data (K1 = 2.4 x 10(6) M(-1) and K2 = 1.0 x 10(5) M(-1)). Saturation of the protein with paclitaxel, similarly to other ligands of albumin, could not be reached. The greatest observed value of r (number of paclitaxel molecules bound to one albumin molecule) was 6.6.     

Intracellular ice formation during the freezing of hepatocytes cultured in a double collagen gel.

During freezing, intracellular ice formation (IIF) has been correlated with loss in viability for a wide variety of biological systems. Hence, determination of IIF characteristics is essential in the development of an efficient methodology for cryopreservation. In this study, IIF characteristics of hepatocytes cultured in a collagen matrix were determined using cryomicroscopy. Four factors influenced the IIF behavior of the hepatocytes in the matrix: cooling rate, final cooling temperature, concentration of Me2SO, and time in culture prior to freezing. The maximum cumulative fraction of cells with IIF increased with increasing cooling rate. For cultured cells frozen in Dulbecco's modified Eagle's medium (DMEM), the cooling rate for which 50% of the cells formed ice (B50) was 70 degrees C/min for cells frozen after 1 day in culture and decreased to 15 degrees C/min for cells frozen after 7 days in culture. When cells were frozen in a 0.5 M Me2SO + DMEM solution, the value of B50 decreased from 70 to 50 degrees C/min for cells in culture for 1 day and from 15 to 10 degrees C/min for cells in culture for 7 days. The value of the average temperature for IIF (TIIF) for cultured cells was only slightly depressed by the addition of Me2SO when compared to the IIF behavior of other cell types. The results of this study indicate that the presence of the collagen matrix alters significantly the IIF characteristics of hepatocytes. Thus freezing studies using hepatocytes in suspension are not useful in predicting the freezing behavior of hepatocytes cultured in a collagen matrix. Furthermore, the weak effect of Me2SO on IIF characteristics implies that lower concentrations of Me2SO (0.5 M) may be just as effective in preserving viability. Finally, the value of B50 measured in this study indicates that cooling rates nearly an order of magnitude faster than those previously investigated could be used for cryopreservation of the hepatocytes in a collagen gel.     

An experimental study of some indigenous drugs with special reference to hydraulic permeability

The effect of commonly used indigenous drugs for hepatic disorders i.e. Tinospora cordifolia, (Guduchi/Amrita), Andrographis paniculata (Kalmegha), Picrorhiza kurroa (Kutki), Phyllantnus niruri (Bhoomyamalaki) and Berberis aristata (Daruharidra) was tested on the hydraulic permeability of water in the presence of bile salt through a transport cell model. The data on hydraulic permeability were calculated as t (time). JV = Lp x AP, where Lp = hydraulic conductivity and AP is the pressure difference. It was observed that the value of controlled hydraulic permeability (0.49 x 10(-8) M3 S(-1) N(-1)) decreased in the presence of indigenous drugs and bile salt. The results suggest that these drugs might have the cell membrane stabilizing property which may lead to prevention of the toxic effect of bile salts in various hepatic disorders.     

Steady-state fluorescence polarization data in membranes. Resolution into physical parameters by an extended Perrin equation for restricted rotation of fluorophores

An extended Perrin equation is derived applicable to the restricted rotation of fluorophores. The equation results in a relation between time-resolved (r infinity) and steady-state fluorescence anisotropy (rs) data. This relation contains a parameter m, which expresses the difference between rotational diffusion in a lipid membrane and that in an isotropic reference oil having the same rs value. The relation is in agreement with rs, r infinity literature data for a variety of artificial and biological membranes labeled with various probes. Cholesterol and fatty acyl unsaturation affect the value of m, but temperature does not. The results indicate that, as far as fluorescence depolarization is concerned, either liposomes of saturated phospholipids without cholesterol or liposomes of unsaturated phospholipids containing cholesterol are good model systems for biological membranes. The accuracy of estimating order parameters or rotational diffusion constants from rs data is discussed. The formalism described here introduces a novel way of applying Arrhenius plots and allows for an unambiguous interpretation of rs data.     

The time course of hydrolysis of a beta-lactam antibiotic by intact gram-negative bacteria possessing a periplasmic beta-lactamase.

An equation is derived from first principles for describing the change in concentration with time of a beta-lactam antibiotic in the presence of intact Gram-negative bacteria possessing a beta-lactamase located in the periplasmic space. The equation predicts a first-order decline in beta-lactam concentration of the form [S] = [Si]e lambda t, where [S] is the exogenous concentration of beta-lactam, [Si] is the value of [S] at time zero, t is the time from mixing of cells and antibiotic and lambda (less than 0) is the decay constant. The value of lambda is exactly described by the theory in terms of experimentally measurable quantities. Quantitative data concerning cephaloridine hydrolysis by intact cells of Haemophilus influenzae agreed well with the theory, as did data concerning the uptake of 2-nitrophenyl galactoside by intact cells of Escherichia coli. Cephalosporin C hydrolysis by intact cells of Pseudomonas aeruginosa did not progress as predicted by the theory. The theory is applicable to any substrate which is acted on by an enzyme that is located solely in the periplasmic space and that obeys the Michaelis-Menten equation of enzyme kinetics.