Current–voltage–time records of ion translocating enzymes

Membrane currents, as non-linear functions of membrane voltage, V, and time, t, can be recorded quickly by triangular V protocols. From the differences, dI(V,t), of these relationships upon addition of a putative substrate of a charge-translocating membrane protein, the I(V,t) relationships of the transporter itself can be determined. These relationships likely comprise a steady-state component, I_a(V), of the active transporter, and a dynamic component, p_a(V,t), of its V- and time-dependent activity, p_a. Here, the steady-state component is modeled by a central reaction cycle, which senses a fraction _tr of the total V, whereas 1–_tr can be assigned to an inner and outer pore section with _i and _o, respectively (_i+_tr+_o = 1). For the enzymatic cycle, fast binding/debinding is assumed, plus V-sensitive and -insensitive reaction steps which may become rate limiting for charge translocation. At given substrate concentrations, I_a(V) is defined by eight independent system parameters, including a coefficient for the barrier shape of charge translocation. In ordinary cases, the behavior of p_a(V,t) can be described by two rate constants (for activation and inactivation) and their respective V-sensitivity coefficients. Here, the effects of the individual system parameters on I(V,t) from triangular V-clamp experiments are investigated systematically. The results are illustrated by panels of typical curve shapes for non-gated and gated transporters to enable a first classification of mechanisms. We demonstrate that all system parameters can be determined fairly well by fitting the model to experimental data of known origin. Applicability of the model to channels, pumps and cotransporters is discussed.     

On the mechanism of a 60-Hz electric field induced growth reduction of mammalian cellsin vitro

Data on 60-Hz electric field (EF) induced reduction in growth rate of plant roots have strongly supported the hypothesis that the effect is related to an EF-induced transmembrane potential (V ⁱ _m). An investigation was undertaken to determine if this hypothesis is also applicable to 60-Hz EF-induced reductions in growth rate of mammalian cells in vitro. Human lymphoblastic (RPMI 1788) and human carcinoma (HeLa) cells were selected for study, the former having a relatively small diameter (11.2 m), and the latter having a relatively large diameter (15.4 tm). The 60-Hz EFs ranged from 430–1200 V/m in the culture medium. The growth rate of RPMI 1788 cells after 4-days was depressed by about 42% at a 60-Hz EF of 1000–1200 V/m with a response threshold occurring at 950 V/m; theV ⁱ _m at the response threshold was 8 mV There was no 60-Hz EF-induced effect on HeLa cell growth rate of aV ⁱ _m of 8 mV (60-Hz EF=700 V/m); a statistically significant effect was achieved atV ⁱ _m of 11 mV (950 V/m). The data support the hypothesis that above a threshold 60-Hz EF,V ⁱ _m acts as the initial signal leading to growth rate reductions.     

Anchorage-dependent animal cell culture by using a porous microcarrier

CHO-K1 cells were cultured by using a porous microcarrier. The effects of microcarrier concentration and agitation rate on cell growth in porous microcarrier cultures were investigated. The specific growth rate of 0.041 h^–1 in porous microcarrier cultures was independent of both microcarrier concentration and agitation rate. By estimating the total surface area occupied by cells from the maximum cell number, it was found that not all the surface area of the porous microcarrier was utilizable for cell growth.The maximum cell number decreased with increasing the microcarrier concentration and the agitation rate. From this result, it was also found that not all the cells grown on the interior surface of the porous microcarrier were protected against mechanical damage due to agitation. The protection capacity of the porous microcarrier was estimated to be 300 cells/carrier. The direct gas sparging into the culture broth in porous microcarrier cultures improved the cell density without mechanical damage to animal cells.List of Symbols d m microcarrier diameter - d _i m impeller diameter - d _p m mean pore diameter - n _i s^–1 agitation rate - p Pa pressure difference - v m/s velocity of microcarrier - v _p m/s average velocity flowing through cyclinder - Pa · s viscosity of medium - angle measured from stagnant point - Pa average shear stress - Pa shear stress distribution     

An Unbalanced Nested Model with Random Effects Having Unequal Variances

Consider the model Y_ijk=μ + a_i + b_ij + e_ijk (i=1, 2,…, t; j=1,2,…, B_i; k=1,2…,n_ij), where μ is a constant and a¹,b_ij and e_ijk are distributed independently and normally with zero means and variances σ²_ad_ij and σ², respectively, where it is assumed that the d_i's and d_ij's are known. In this paper procedures for estimating the variance components (σ², σ²_a and σ²_b) and for testing the hypothesis σ²_b = 0 and σ²_a = 0 are presented. In the last section the mixed model y_ijk, where x_ijkkm are known constants and β_m's are unknown fixed effects (m = 1, 2,…,p), is transformed to a fixed effect model with equal variances so that least squares theory can be used to draw inferences about the β_m's.     

Packed-bed immobilized enzyme reactors for complex processes

Utilization of enzymic reactors for biotechnological-biomedical applications is currently developing at a sustained pace.Our present study concentrates on development of procedures for describing the performance of devices where enzyme-catalyzed reactions between two substrates take place, and for the rational design and optimization of the reactors considered. Within this context, an analytical model was developed for immobilized enzyme packed-bed reactors; it takes into account internal diffusion limitations for the cosubstrates, and hydrodynamic backmixing effects. In order to overcome the complex mathematical problems involved, the compartmental analysis approach was employed.Using this model, performance was simulated for various configurations of the enzymic unit, i.e. from a continuously operated stirred tank reactor (CSTR) to an essentially plug flow type. In addition, an experimental method is described for quantitatively assessing the backmixing effects prevailing in the reactor.The procedures established also provide the ground for further developments, particularly for systems where, in parallel to the enzymic reaction, additional processes (e. g. complexation) take place.List of Symbols C _j,i mM Concentration of substrate j in the pores of stage - iD _j cm²/s Internal (pore) diffusion coefficient of substrate j; defined in Eq. (7) - D _e cm²/s Axial dispersion diffusion coefficient - D _j, cm²/s cm²/s Bulk diffusion coefficient for substrate j - E mM Enzyme concentration inside the catalytic pores - J _j,immol/s/cm² Net flux of substrate j taking place from the bulk of stage i into the corresponding pores; defined in Eq. (6) - K _m,1, K _m,2 mM Michaelis-Menten constants for cosubstrates 1 and 2, respectively - k s ^–1 Catalytic constant - k _s cm/s Catalytic constant - n Total number of elementary stages in the reactor - Q cm³/s Volumetric flow rate throught the reactor - r cm Radius of the pore - R _j,i mM/s Reaction rate of substrate j in stage i, in terms of volumetric units - S cm² Internal surface of a pore - S _j,0 mM Concentration of substrate j in the reactor feed - S _j,i–1, S _j,i mM Concentration of substrate j in the bulk phase leaving stages i — 1 and i, respectivley - V _i cm³ Total volume of stage i (bulk phase + pore phase + inert solid carrier) - V cm³ Total volume of the reactor - V _m ^* mmol/s/cm² Maximal reaction rate in terms of surface units; defined in Eq. (8) - V _m mM/s Maximal reaction rate in terms of volumetric units; defined in Eq. (8) - V _p cm³ Volume of one pore - y cm Axial coordinate of the pores - y ₀ cm Depth of the pores - Z cm Axial coordinate of the reactor - Z ₀ cm Length of the reactor - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - Ratio between the radius of the enzyme molecule and the radius of the pore (dimensionless) - V₁ Dimensionless parameter; defined in Eq. (21) - v₂ Dimensionless parameter; defined in Eq. (21) - Q Volumetric packing density of catalytic particles (dimensionless) - Ø Porosity of the catalytic particles (dimensionless) - Ø Dimensionless concentration of substrate j in pores of stage i; defined in Eq. (16) - _j,i-1,_j,i Dimensionless concentration of substrate j in the bulk phase of stage i; defined in Eq. (18) - Dimensionless position; defined in Eq. (16) - ² s² Variance; defined in Eq. (33) - Mean residence time in the reactor; defined in Eq. (33)     

Using a Normal Approximation to Test for the Binomial Distribution

The commonly used method to test for the binomial distribution is the x²-test. In this paper, we introduce an alternative method to test for the binomial distribution. Suppose N is the number of sample groups with n individuals each, x_ij is the jth sample in ith group, a Bernoulli variable with parameter and VVI=s²/[m(1 - m)/n]. Then it is well know that the asymptotic distribution of the statistic (N - 1) VVI is x²(N - 1) under the hypothesis p₁ = p₂ = … = p_N. Here we find that VVI has an asymptotic normal distribution N(1, 2(1 - 1/n)/(N - 1)). Unlike the x²-statistic, the variance of the normal test statistic is a function of n. This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples.     

Basolateral membrane potential and conductance in frog skin exposed to high serosal potassium

Summary In studies of apical membrane current-voltage relationships, in order to avoid laborious intracellular microelectrode techniques, tight epithelia are commonly exposed to high serosal K concentrations. This approach depends on the assumptions that high serosal K reduces the basolateral membrane resistance and potential to insignificantly low levels, so that transepithelial values can be attributed to the apical membrane. We have here examined the validity of these assumptions in frog skins (Rana pipiens pipiens). The skins were equilibrated in NaCl Ringer's solutions, with transepithelial voltageV _t clamped (except for brief perturbations V _t) at zero. The skins were impaled from the outer surface with 1.5m KCl-filled microelectrodes (R _el>30 M). The transepithelial (short-circuit) currentl _i and conductanceg _t=–I _t/V _t, the outer membrane voltageV _o (apical reference) and voltage-divider ratio (F _o=V _o/V _t), and the microelectrode resistanceR _el were recorded continuously. Intermittent brief apical exposure to 20 m amiloride permitted estimation of cellular (c) and paracellular (p) currents and conductances. The basolateral (inner) membrane conductance was estimated by two independent means: either from values ofg _i andF _o before and after amiloride or as the ratio of changes (–I _c/V _i) induced by amiloride. On serosal substitution of Na by K, within about 10 min,I _c declined andg _t increased markedly, mainly as a consequence of increase ing _p. The basolateral membrane voltage (V _i(=–V _o) was depolarized from 75±4 to 2±1 mV [mean±sem (n=6)], and was partially repolarized following amiloride to 5±2 mV. The basolateral conductance increased in high serosal K, as estimated by both methods. Essentially complete depolarization of the basolateral membrane and increase in its conductance in response to high [K] were obtained also when the main serosal anion was SO₄ or NO₃ instead of Cl. On clampingV _t over the range 0 to +125 mV in K₂SO₄-depolarized skins, the quasi-steady-stateV _o V _t relationship was linear, with a mean slope of 0.88±0.03. The above results demonstrate that, in a variety of conditions, exposure to high serosal K results in essentially complete depolarization of the basolateral membrane and a large increase in its conductance.     

Convenient experimental determination of adsorption isotherms in a Hydrophobic Interaction Chromatography system

Summary HPLC was combined with a packable microbore guard column to obtain the adsorption isotherm of lysozyme in a Hydrophobic Interaction Chromatography system. The equipment configuration enabled isotherm determination of the protein on a relatively low pressure chromatographic media (TosoHaas 650M Phenyl).Notation C_m,i is the mobile phase concentration of protein. (M/L³ _(liquid)) - C_m,0 =0 - C_s,i is the stationary phase concentration of protein. It is the concentration of protein on the chromatographic media. (M/L³ _(solid)) - C_s,0 =0 - M,L is the dimensions mass and length - V_r,i is the retention volume of the peak front that corresponds to a mobile phase protein on the concentration C_m,i. (L³ _(liquid)) - i i is a counter that is used to keep track of C_m, C_s, and V_r.For example, i=1 in the term C_m,i denotes the first, and lowest, mobile phase protein concentrations are described by higher values of i. - V_d is the system dead volume. It consists of all of the system volume that the mobile phase "sees" or contacts, includingchromatographic media interparticle and pore volume. (L³ _liquid) - V_s the stationary phase volume. V_s is the nonporous bead volume. For porous beads, V_s is the bead volume - the porevolume. (L³ _(solid)) - V_e is the empty column volume. (L³ _liquid) - V_m is the packed column mobile phase volume and consists of the pore volume and the excluded volume. (L³ _(liquid)) - V_{e system} is the empty column system volume. (L³ _(liquid)) - V_frit the volume of mobile phase that fills the column frits. (L³ _(liquid)) - V_woc the system volume without the column connected. (L³ _(liquid))     

The problem of nonstationary ion fluxes in excitable membranes

Time-dependent electrodiffusion through a membrane is analysed within a simple model treating the boundary-layers in a consistent manner. It is shown that time-independent reversal potentials for the ion fluxes exist only under steady-state conditions. We argue that this result holds very generally. Therefore nonstationary effects like ion storage and depletion inside the membrane should not contribute to the phenomena of excitability.Glossary of Symbols A _mv [V] functional cf. Equation (3) - C membrane capacitance - d one half the thickness of the membrane - F[V] functional cf. Equation (1) - g _i electrochemical potential inside membrane - g _i electrochemical potentials outside membrane at x ±d, respectively - i (index) refers to i-th ionic species - J electric current across membrane - j = j ^} = j ^< current density measured by external electrodes - j _i (x) current density inside membrane in x-direction - j _i ^inst(x) instantaneous current density - J _i ^stat steady-state current density - k Boltzmann constant - m (index) is used in Sec. 2 to denote the independent diffusion currents - n ^< ionic strength of electrolyte at x = - - n _i density of ions inside membrane - n _i density of ions outside membrane at x = ±, respectively - Q charge per unit area of boundary layers at x ± d, respectively - Q ₀ fixed charge per unit area of membrane - q elementary charge - q _i ionic charges - T temperature - it time - V membrane potential (= (-)-()) - V _i Nernst potential - V potential drops inside boundary layers (can be neglected, see Appendix II) - V ^± potential steps at x = ± d, cf. Equation (29) - V ₀ = V ^–-V ⁺ - w _i activation energy inside membrane - x spatial coordinate perpendicular to membrane - y, z spatial coordinates parallel to membrane - dielecric constant - ₀ dielectric constant of electrolyte solution ( 80) - _m dielectric constant of membrane ( 5) - (x) electrostatic potential - charge density of boundary layers - ⁰ fixed charge density inside membrane - spatial average, cf. Equation (12)     

Multivariate Probability in Terms of Marginal Probability and Correlation Coefficient

This paper is motivated by a practical problem relating to student performance in a number of subjects of equal standing. Its mathematical formulation is to find an approximation to a multivariate probability of the form Pr {X₁⩾a, X₂⩾a, …, X_N⩾a} for arbitrary a and N, in terms of p = Pr {X₁⩾a} and q = Corr (X_i, X_j), i≠j, where X_i, i = 1, …, N are exchangeable random variables with mean 0 and variance unity.     

A modified unstructured mathemathical model for the penicillin G fed-batch fermentation

Summary In this paper, an updated unstructured mathematical model for the penicillin G fed-batch fermentation is proposed, in order to correct some physical and biochemical shortcomings in the model of Heijnen et al. (1979,Biotechnol. Bioeng.,21, 2175–2201) and the model of Bajpai and Reuß (1980,J. Chem. Tech. Biotechnol.,30, 332–344). Its main features are the consistency for all values of the variables, and the ability to adequately describe different metabolic conditions of the mould. The model presented here can be considered as the translation of the latest advances in the biochemical knowledge of the penicillin biosynthesis.Nomenclature t time (h) - S amount of substrate in broth (g) - X amount of cell mass in broth (g) - P amount of product in broth (g) - V fermentor volume (L) - F input substrate feed rate (L/hr) - C _s S/V substrate concentration in broth (g/L) - C _x X/V cell mass concentration in broth (g/L) - C _P P/V product concentration in broth (g/L) - s _F substrate concentration in feed stream (g/L) - E _m parameter related to the endogenous fraction of maintenance (g/L) - E _p parameter related to the endogenous fraction of production (g/L) - K _x Contois saturation constant for substrate limitation of biomass production (g/g DM) - K _s Monod saturation constant for substrate limitation of biomss production (g/L) - K _p saturation constant for substrate limitation of product formation (g/L) - K _i substrate inhibition constant for product formation (g/L) - m _s maintenance constant (g/g DM hr) - k _h penicillin hydrolysis or degradation constant (hr^–1) - Y _x/s cell mass on substrate yield (g DM/g) - Y _p/s product on substrate yield (g/g) - specific substrate consumption rate (g/g DM hr) - specific growth rate (hr^–1) - _substr specific substrate to biomass conversion rate (hr^–1) - _x maximum specific substrate to biomass conversion rate (hr^–1) - specific production rate (g/g DM hr) - _p specific production constant (g/g DM hr)     

Modelling of enzyme hydrolysis of maltose in a single pellet of immobilized biocatalyst

The reversible hydrolysis of maltose to glucose by immobilized glucoamylase entrapped in spherical solid particles is studied theoretically. For this purpose a known kinetic model taking into account these reversible reactions and the competitive synthesis of iso-maltose was adopted. The mass transfer limitations in the bulk liquid and in the pores of the particles containing the enzyme are considered, using Fick's law. On the basis of mathematical modelling the optimum conditions for biocatalyst performance are established. An appropriate combination of particle size and initial substrate concentration may lead to reduction of undesirable mass transfer resistance and therefore product inhibition and to an improved selectivity of the biocatalyst with respect of glucose formation.List of Symbols C _i kmoles/m³ current concentration ofi-th component along the radius - C _oi kmoles/m³ bulk concentration ofi-th component - C _i ^* kmoles/m³ concentrations ofi-th component on the pellet surface - D _si ,D _i m²/s internal and molecular diffusion coefficient ofi-th component - W _M kmoles/m³·s reaction rate of maltose hydrolysis - W _IM kmoles/m³·s reaction rate of iso-maltose formation - W _G kmoles/m³·s reaction rate of glucose production - R ₀ m pellet radius - r m current radius of the pellet - t s time coordinate - r ₀ ratio of the time step to the square of the radial coordinate - Re Reynolds number =w·R/v - Sc Schmidt number =v/D - Bi Biot number = R/D - A _j ,B, C _j coefficients in the system of linear equations, Eq. (8) - X _i dimensionless degree of transformation - NR number of independent reactions - N number of division sections of the pellet radius - G kmoles/m³ concentration of glucose - M kmoles/m³ concentration of maltose - IM kmoles/m³ concentration of isomaltose - K _m kmoles/m³ Michaelis constant - V _max kmoles/m³·s maximum reaction rate in Eq. (6) - K _i kmoles/m³ inhibition constant - K _1eq ,K _2eq equilibrium constants in Eq. (6) - , h steps along the time and radial coordinate in the pellet - m/s mass transfer coefficient - dimensionless radius of the pellet - computation accuracy Indices i number of reaction component - j index along the radius of the pellet - k index along the time coordinate This work was accomplished with thanks to the financial support of the Bulgarian National Fund for Scientific Investigations —Grant No. MU-1-BE/93.     

Sampling bias in estimating Design II variance components with S1 families

Summary The use of several S₁ individuals to represent an S₀ individual permits the use of a Design II mating scheme for plants with only one pistillate flower per plant. Estimates of additive (V _A ) and dominance (V _D ) variance from this mating scheme will be biased upwards, when a small number (10) of individuals of each S₁ line are used. This bias can be computed, and the additive and dominance estimates can be corrected. Of particular interest is the observation that the additive genetic variance contributes to bias in estimates of V _D . When S₀ plants are non inbred and their selfedprogeny (S₁ lines) are used to represent them in developing families for use in the Design II, where m₁ is the number of individuals used to represent an S₁ line in developing half sib-families and m₂ is the number of individuals used to represent the S₁ line in making up full sib-families. For example, in a 3×3 Design II, with about 10 individuals used to represent each S₁ line in each cross, m₂ = 10 and m₁ = 30. When m₁ = m₂ = 1, and Joint contribution from Department of Agronomy, University of Nebraska 68583, and the S. S. Cameron Laboratory, Werribee, Victoria 3030, Australia. Published as paper No. 7395, Journal Series     

The Cytochrome cbo from the Obligate Methylotroph Methylobacillus flagellatus KT Is a Cytochrome c Oxidase

The cbo-type oxidase of Methylobacillus flagellatus KT was purified to homogeneity by preparative native gel electrophoresis, and the kinetic properties and substrate specificity of the enzyme were studied. Ascorbate and ascorbate/N,N,N,N-tetramethyl-p-phenylenediamine (TMPD) were oxidized by cytochrome cbo with a pH optimum of 8.3. With TMPD as an electron donor for the cbo-type oxidase, the optimal pH (7.0 to 7.6) was determined from the difference between respiration rates in the presence of ascorbate/TMPD and only ascorbate. The kinetic constants determined at pH 7.0 were as follows: oxidation by the enzyme of reduced TMPD was characterized by K _M = 0.86 mM and V _max = 1.1 mol O₂/(min mg protein), and oxidation of reduced horse heart cytochrome c was characterized by K _M = 0.09 mM and V _max = 0.9 mol O₂/(min mg protein). Cyanide inhibited ascorbate/TMPD–oxidase activity (K _i = 4.5–5.0 M). The soluble cytochrome c _H (12 kDa), partially purified from M. flagellatus KT, was found to serve as a natural electron donor for the cbo-type oxidase.     

Dependence of tetanic hyperpolarization on pump conductance in the cyanide-treatedXenopus node

Prolonged exposure to cyanide leads to a delayed but reversible disappearance of tetanic hyperpolarization in theXenopus node (G. M. Schoepfle,Am. J. Physiol. 231, 1033–1038, 1976). This effect is attributed to a pronounced decline in the absolute values of the ATP and ADP concentrations, such that the ATP-driven ion translocation is no longer possible, regardless of the existing values for (Na)_i, (K)_i and the (ATP)/(ADP) ratio. Mathematically, this would imply a vanishing of a constant pump conductance g_p in the exression for electrogenic pump current densitityJ _p, whereJ _p=g _p (V _m −E _p) in whichV _m is membrane potential andE _p is an ATP-and sodium-dependent e.m.f. Supported by NIH grant NS08802.     

An Unbalanced Two-way Model With Random Effects Having Unequal Variances

Consider the model y_ijk=u ± a_i ± b_i ± c_ij ± e_ijk i=1, 2,…, t; j=1, 2,…b; k=1, 2,…,n_ij where μ is a constant and a_i, b_i, c_ij are distributed independently and normally with zero means and variances Δ₂ Δ2/bd_ij and δ₂ respectively. It is assumed that d_i's, and d_ij's are known (positive) constants (for all i and j). In this paper procedures for estimating the variance components (Δ₂, Δ²_b and Δ²_a) and for testing the hypothesis H_oc:Δ²_c/Δ² = y₃ and H_oa:Δ²_b/Δ² = y₄ (where y₂, y₃, and y₄, are specified constants) are presented. A generalization for the mixed model case is discussed in the last section.     

Additive and testcross genetic variances in crosses among recombinant inbreds

 Breeders desire populations with a high mean performance and a large genetic variance. Theory and methods are lacking for predicting additive variance (V _A ) and testcross variance (V _T ) in biparental populations. Breeders have unsuccessfully attempted to predict V _A based on the coefficient of coancestry ( f ) or molecular-marker similarity between parents. In this paper, we derive the expected values of V _A and V _T in biparental populations, examine the variability of V _A among biparental crosses, and discuss how V _A and V _T may be predicted in applied breeding programs. Suppose i is a recombinant inbred derived from the cross between inbreds P ₁ and P ₂, and inbred j is not a direct descendant of i. Let V _A(i,j) be the additive variance in the F₂ of the (i×j) biparental cross. Let V _T(i, j) be the variance among testcrosses of F₂ individuals with a specific unrelated inbred or population. Assuming linkage equilibrium and the absence of epistasis, V _A(i, j) =λV _A(P1, j) +(1−λ) V _A(P2, j) , where λ= parental contribution of P ₁ to i. Similarly, V _T(i, j) = λV _T(P1, j) +(1−λ) V _T(P2, j) . Additive variance in crosses between recombinant inbreds cannot be modelled as a function of  f if, as indicated in the literature, V _A differs among crosses of founder inbreds. If molecular-marker similarity between parents is used as an estimate of f, then a strong linear relationship is likewise not expected between V _A and marker similarity. Differences between the actual and expected λ led to variation in V _A . In applied breeding programs, modelling V _A or V _T in biparental crosses may be feasible with estimates of V _A or V _T in prior crosses and information on λ obtained from molecular-marker data. Received: 23 September 1997 / Accepted: 30 December 1997     

A kinetic analysis of the electrogenic pump ofChara corallina: II. Dependence of the pump activity on external pH

Summary The current-voltage curve of theChara membrane was obtained by applying a slow ramp de- and hyperpolarization by use of voltage clamp. By inhibiting the electrogenic pump with 50m DCCD (dicyclohexylcarbodiimide), theI–V curve approached a steady state within 100 min, which gave thei _d -V curve of the passive diffusion channel. Thei _p -V curve of the electrogenic pump channel was obtained by subtracting the latter from the former. With the increase of external pH, thei _d -V curve showed only a slight change, while thei _p -V curve of the pump channel showed almost a parallel shift, in the hyperpolarizing direction, along the voltage axis in the pH range between 6.5 and 7.5. The sigmoidali _p -V curve in this pH range could be simulated satisfactorily with the five-state model reported previously (U. Kishimoto, N. Kami-ike, Y. Takeuchi & T. Ohkawa,J. Membrane Biol. 80:175–183, 1984) as well as with a lumped two-state model presented in this report. The analysis based on these models suggests that the electrogenic pump of theChara membrane is mainly a 2H⁺/1ATP pump. The forward rate constant in the voltage-dependent step increased with the increase of external pH, while the backward one decreased. On the other hand, the forward rate constant in the voltage-independent step remained almost unchanged with the increase of external pH, while the backward one increased markedly. The pump conductance at the resting membrane potential showed either a slight increase or a decrease with the increase of external pH, depending on the sample. Nevertheless, the pump current showed generally a slight increase with the increase of external pH.     

Role of ionization of the phosphate cosubstrate on phosphorolysis by purine nucleoside phosphorylase (PNP) of bacterial (<Emphasis Type="Italic">E. coli</Emphasis>) and mammalian (human) origin

Kinetics of the reactions of purine nucleoside phosphorylases (PNP) from E. coli (PNP-I, the product of the deoD gene) and human erythrocytes with their natural substrates guanosine (Guo), inosine (Ino), a substrate analogue N(7)-methylguanosine (m⁷Guo), and orthophosphate (P_i, natural cosubstrate) and its thiophosphate analogue (SP_i), found to be a weak cosubstrate, have been studied in the pH range 5–8. In this pH range Guo and Ino exist predominantly in the neutral forms (pK_a 9.2 and 8.8); m⁷Guo consists of an equilibrium mixture of the cationic and zwitterionic forms (pK_a 7.0); and P_i and SP_i exhibit equilibria between monoanionic and dianionic forms (pK_a 6.7 and 5.4, respectively). The phosphorolysis of m⁷Guo (at saturated concentration) with both enzymes exhibits Michaelis kinetics with SP_i, independently of pH. With P_i, the human enzyme shows Michaelis kinetics only at pH ∼5. However, in the pH range 5–8 for the bacterial enzyme, and 6–8 for the human enzyme, enzyme kinetics with P_i are best described by a model with high- and low-affinity states of the enzymes, denoted as enzyme-substrate complexes with one or two active sites occupied by P_i, characterized by two sets of enzyme-substrate dissociation constants (apparent Michaelis constants, K _m1 and K _m2) and apparent maximal velocities (V _max1 and V _max2). Their values, obtained from non-linear least-squares fittings of the Adair equation, were typical for negative cooperativity of both substrate binding (K _m1 < K _m2) and enzyme kinetics (V _max1/K _m1 > V _max2/K _m2). Comparison of the pH-dependence of the substrate properties of P_i versus SP_i points to both monoanionic and dianionic forms of P_i as substrates, with a marked preference for the dianionic species in the pH range 5–8, where the population of the P_i dianion varies from 2 to 95%, reflected by enzyme efficiency three orders of magnitude higher at pH 8 than that at pH 5. This is accompanied by an increase in negative cooperativity, characterized by a decrease in the Hill coefficient from n _H ∼1 to n _H ∼0.7 for Guo with the human enzyme, and to n _H ∼0.7 and 0.5 for m⁷Guo with the E. coli and human enzymes, respectively. Possible mechanisms of cooperativity are proposed. Attention is drawn to the substrate properties of SP_i in relation to its structure.     

Enzyme inhibition by p-cresol and lacticacid in lipase-mediated synthesis of p-cresyl acetate and stearoyl lactic acid: a kinetic study

A detailed kinetic study was carried out to investigate the porcine pancreatic lipase-catalysed esterification reactions of p-cresol–acetic acid and lactic acid–stearic acid. The kinetic data were in agreement with a Ping Pong Bi–Bi mechanism being followed by the enzyme, where inhibition is indicated in the presence of p-cresol and lactic acid in the respective reactions. Mathematical analyses of experimentally observed initial rates yielded various kinetic parameters, K _m(p-cresol) = 0.1, K _{m(acetic acid)} = 0.54, K _{m(lactic acid)} = 0.059 M, K _{m(stearic acid)} = 0.04 M, V _{max(p-cresol–acetic acid)} = 13.2(h^–1), V _{max(lactic acid–stearic acid)} = 0.00163 M/h, K _i(p-cresol) = 0.59 and K _{i(lactic acid)} = 0.079 M. The K _m and K _i values of p-cresol and lactic acid observed in the respective reactions showed both the competitive nature of binding between the substrates p-cresol and acetic acid on the one hand and lactic acid and stearic acid on the other and the inhibitory nature of p-cresol and lactic acid.