Permeability properties of cell-to-cell channels: Kinetics of fluorescent tracer diffusion through a cell junction

Summary We have analyzed the intracellular and cell-to-cell diffusion kinetics of fluorescent tracers in theChironomus salivary gland. We use this analysis to investigate whether membrane potential-induced changes in junctional permeability are accompanied by changes in cell-to-cell channel selectivity. Tracers of different size and fluorescence wavelength were coinjected into a cell, and the fluorescence was monitored in this cell and an adjacent one. Rate constants,k _j , for cell-to-cell diffusion were derived by compartment model analysis, taking into account (i) cell-to-cell diffusion of the tracers; (ii) their loss from the cells; (iii) their binding (sequestration) to cytoplasmic components; and (iv) their relative mobility to cytoplasm, as determined separately on isolated cells. In cell pairs, we compared a tracer'sk _j with the electrical cell-to-cell conductance,g _j .At cell membrane resting potential, thek _j 's ranged 3.8–9.2×10^–3 sec^–1 for the small carboxyfluorescein (mol wt 376) to about 0.4×10^–3 sec^–1 for a large fluorescein-labeled sugar (mol wt 2327). Cell membrane depolarization reversibly reducedg _j andk _j for a large and a small tracer, all in the same proportion. This suggests that membrane potential controls the number of open channels, rather than their effective pore diameter or selectivity. From the inverse relation between tracer mean diameter and relativek _j we calculate an effective, permeation-limiting diameter of approximately 29 Å for the insect cell-to-cell channel. Intracellular diffusion was faster than cell-to-cell diffusion, and it was not solely dependent on tracer size. Rate constants for intracellular sequestration and loss through nonjunctional membrane were large enough to become rate-limiting for cell-to-cell tracer diffusion at low junctional permeabilities.     

Kinetic analysis of biphasic protein modification reactions cooperative effects

A mathematical treatment of protein modification reactions is presented, and it is shown thai in these cases protein modification is described by a summation of exponential functions of reaction time, the number of exponentials being equal to the number of modified protein species. It is shown that in cases of protein modification cooperativity, there is a strict dependence of the coefficients of the multiexponential modification equation on the constants of the same equation. The conditions necessary for a reduction of a multiexponential protein modification equation to one of a summation of two exponentials only are examined. The possible formulae for the coefficients of a two-exponential-summation equation, used to describe the modification of protein models with two, three or four modifiable residues (as well as some aspects of models with five and six modifiable residues) per protein molecule are derived. It is seen that the number of such coefficients is severely limited. The most frequently obtained formula for the lower stoichiomelric coefficient of a 'wo-exponential-summation equation is Ak_a/(k_a-k_b). where k_b and k_b are the constants of the two exponentials of the equation, and A is a constant. The value most frequently arrived at for A is (n?1)/n, where n is the number of modifiable residues per protein molecule, while values such as 1/n, or a/n (where a is an integer, and also where a < n) are also possible. In most of the cooperative protein modification models worked out, k_a is identical with k_n, viz., k_a is identical with the rate constant for the first stoichiometric protein modification.     

On the theory of blood-tissue exchanges: I. Fundamental equations

A mathematical analysis of the absorption of an inert gas by a heterogeneous system ofn phases, e.g., a limb consisting ofn tissues, is presented. The total uptake of gas, ϕ(t), up to timet is given in terms of arterial concentration, cardiac delivery, blood volume, and the volume, permeability, and partition coefficient of each tissue. The theory predicts how the uptake curve should change in shape under a variety of physiological conditions, and how from the numerical values of the constants the values of certain tissue constants, e.g. permeabilities, may be obtained. The material in this article should be construed only as the personal opinion of the writers and not as representing the opinion of the Navy Department officially.     

Contributions of binding and catalytic rate constants to evolutionary modifications inKm of NADH for muscle-type (M4) lactate dehydrogenases

Summary The apparent Michaelis constant (K _m) of NADH for muscle-type (M₄ isozyme) lactate dehydrogenases (LDHs) is highest, at any given temperature of measurement, for LDHs of cold-adapted vertebrates (Table 1). However, these interspecific differences in theK _m of NADH are not due to variations in LDH-NADH binding affinity. Rather, theK _m differences result entirely from interspecific variation in the substrate turnover constant (k _cat) (Fig. 1; Table 2). This follows from the fact that theK _m of NADH is equal tok _cat divided by the on constant for NADH binding to LDH,k ₁, so that interspecific differences ink _cat, combined with identical values fork ₁ among different LDH reactions, make the magnitude of theK _m of NADH a function of substrate turnover number. The temperature dependence of theK _m of NADH for a single LDH homologue is the net result of temperature dependence of bothk _cat andk ₁ (Figs. 3 and 4). Temperature independentK _m values can result from simultaneous, and algebraically offsetting, increases ink _cat andk ₁ with rising temperature. Salt-induced changes in theK _m of NADH also may be due to simultaneous perturbation of bothk _cat andk ₁ (Table 3). These findings are discussed from the standpoint of the evolution of LDH kinetic properties, particularly the interspecific conservation of catalytic and regulatory functions, in differently-adapted species.     

The isomerization of D-glucose into D-fructose catalyzed by whole-cell immobilized glucose isomerase. The dependence of the intrinsic rate of reaction on substrate concentration,pH, and temperature

The relation between the intrinsic rate of the glucose-fructose isomerization catalyzed by whole-cell immobilized glucose isomerase and the substrate concentration can be described with the kinetic model The numerical values of k₁, k_?1, k₂, and k_?2 have been determined from low-conversion experiments starting from pure glucose or fructose solutions, and are presented as a function of pH and temperature. The difference between the overall chemical reaction rate determined in high-conversion experiments and that calculated from the individual k₁, k_?1, k₂, and k_?2 values is less than 10%.     

A three-state MWC analysis of oxygenation in tench (Tinca tinca) hemoglobin

Summary Oxygen equilibria in tench hemoglobin were analysed according to a three-state MWC model. In addition to theT andR states of the traditionally used two-state model, the three-state model introduces an additional state, theS state, when organic phosphates bind to theT-structure hemoglobin. Under conditions covering natural red cell pH values and nucleoside triphosphate-hemoglobin ratios, it was possible to closely fit experimental data to the three-state equation with constant values of the association constantsK _R ,K _T , andK _S , and with only the allosteric constantsL andM varying with effector conditions. Thus, in contrast to a twostate analysis of oxygen equilibria, the three-state analysis was consistent with the basic assumption of the MWC model, that heterotropic ligands only affect allosteric constants and not association constants. The temperature-dependence of the three-state parameter values showed that in the presence of nucleoside triphosphate the dominance of theS state over theT state was most pronounced at low temperatures. Furthermore, the numerical values of the enthalpy and entropy change of oxygenation were lower in theS state than in theT andR states, and the enthalpy and entropy change for the allostericSR transition were much larger than for theTR transition.Abbreviations Hb hemoglobin - Y fractional O₂ saturation - ATP adenosine triphosphate     

Kinetic characteristics of interaction of conotoxin with N-type Ca2+ channels in rat hippocampal neurons

The binding and unbinding constants describing interaction of ω-CTx-GVIA with N-type Ca²⁺ channels were calculated based on the time course of the blocking action of the toxin. The experiments were carried out on pyramidal neurons freshly dissociated from theCA3 region of the rat hippocampus using a “concentration-clamp” technique and a patch-clamp technique in the whole-cell configuration. The bindingk ₁ and unbindingk ₋₁ constants were evaluated as 0.32 (μM·sec)⁻¹ and 0.004 sec⁻¹, respectively. The dissociation constantK _D kinetically derived from the ratiok ₋₁/k ₁ was 0.012 μM. These values allow us to interpret the apparent “irreversibility” of the toxin action.     

MINQUE and ANOVA Estimator for One-way Classification - a Risk Comparison

For the one-way classification in unbalanced case MINQUEstimator for components of variance are given in a more explicit form than it is done in the paper from C. R. RAO (1971). By means of the risk functions we compare MINQUE and ANOVA estimator. For given n_j-patterns angular ranges in the positive quadrant are given where MINQUE is better than ANOVA estimator. A special n_j-pattern and one parameter δ₀ is found for which MINQUE is uniformly better than ANOVA. Limit values are given for MINQUE for δ₀ = ∞ and δ₀ = 0 and their relations to the ANOVA estimator are considered. The coincidence between MINQUE and ANOVA for balanced case is verified. Extensive numerical studies for real data are carried out which stimulated the search for a fixpoint δ as a point for which the distance to the initial parameter δ₀ is as small as possible.     

Bayesian image processing of data from constrained source distributions—I. non-valued,uncorrelated and correlated constraints

A series of Bayesian image processing algorithms which incorporate various classes ofa priori source information in treating data which obeys Poisson and Gaussian statistics is derived using maximum entropy considerations. The standard maximum likelihood equations are shown to be a special case of Bayesian image processing when thea priori information about a source distribution φ _j is solely that a non-vanishing probability for each element value φ _j exists only in some finite interval,a _j ≤φ _j ≤φ _j . Bayesian image processing equations for thea priori source information that all φ _j are finite -∞<φ _j <∞ and each φ _j distribution has a defined mean φ _j and a defined variance σ _j are derived. The Bayesian image processing equations are also derived when thea priori source information is that all φ _j ≥0 and that each φ _j distribution has a defined mean φ _j and a defined variance σ _j . The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods.     

Use of glucose oxidase system in measuring aeration capacity of fermentors. Comparison of the dynamic and steady-state methods of kla measurement

A steady-state method for k_la determination has been presented using the Michaelis–Menten two-substrate kinetic equation for oxidation of glucose in the presence of the enzymes glucose oxidase and excess catalase. The conditions have been specified where spontaneous hydrolysis of lactone is sufficiently rapid, thus eliminating inhibitory action of lactone on the oxidation. In glucose oxidase-free batches, the k_la values were determined using various modification of the dynamic method. The dynamic methods in which gas interchange was effected without interrupting aeration and agitation of the batch yielded erroneously lower k_la values as compared to the results of steady-state methods if the measured k_la value was higher than 0.03 s^?1. The values yielded by the dynamic method in which the gas interchange was effected at the same time with turning on aeration and agitation of the batch agreed with values resulting from the steady-state method provided that the measured k_la values were lower than 0.08^?1 and the simultaneous interfacial transport of nitrogen and oxygen had been taken into account in the evaluation. At k_la values higher than 0.08 ^?1, this modification of the dynamic method also yielded lower k_la values as compared with the outcome of the steady-state method. The experiments performed do not, however, allow one to decide unambiguously on the whether these lower k_la values are due to failure of the adopted model to describe adequately the dynamic behavior of the system or whether they are true values differing from those yielded by the steady-state method on account of different physical properties of compared batches.     

Urea interactions with protein groups: A volumetric study

We determined the partial molar volumes and adiabatic compressibilities of N‐acetyl amino acid amides, N‐acetyl amino acid methylamides, N‐acetyl amino acids, and short oligoglycines as a function of urea concentration. We analyze these data within the framework of a statistical thermodynamic formalism to determine the association constants for the reaction in which urea binds to the glycyl unit and each of the naturally occurring amino acid side chains replacing two waters of hydration. Our determined association constants, k, range from 0.04 to 0.39M. We derive a general equation that links k with changes in free energy, ΔG_tr, accompanying the transfer of functional groups from water to urea. In this equation, ΔG_tr is the sum of a change in the free energy of cavity formation, ΔΔG_C, and the differential free energy of solute–solvent interactions, ΔΔG_I, in urea and water. The observed range of affinity coefficients, k, corresponds to the values of ΔΔG_I ranging from highly favorable to slightly unfavorable. Taken together, our data support a direct interaction model in which urea denatures a protein by concerted action via favorable interactions with a wide range of protein groups. Our derived equation linking k to ΔG_tr suggests that ΔΔG_I and, hence, the net transfer free energy, ΔG_tr, are both strongly influenced by the concentration of a solute used in the experiment. We emphasize the need to exercise caution when two solutes differing in solubility are compared to determine the ΔG_tr contribution of a particular functional group. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 866–879, 2010.     

An attempt to apply ligand field theory to positronium reactions with 3d complexes

Positronium, Ps, the bound state between an electron, e, and a positron, c⁺, may have two spin states: theortho,o-Ps, and thepara,p-Ps, states, which differ for the spin orientation of the two particles. The two types of Ps atoms may be inter-converted by collision with paramagnetic compounds, such as several3d complexes. By investigating about 90 complexes of V^II, Cr^II, Cr^III, Mn^II, Fe^II, Co^II and Ni^II as a function of temperature, it was found that the rate constants k_CR of theo-Ps intop-Ps conversion reactions, CR, are linearly correlated to the delocalization β of metal electrons caused by the ligands. Therefore, if β known, k_CR may be estimated andvice versa. This suggests a new method for the experimental determination of β. The rate constants of the Ps oxidation reactions by Co^III complexes were also investigated and discussed. The paper is preceded by four sections dealing with: 1) the positron and positronium formation; 2) the positron annihilation modes; 3) the methods for measuring the Ps rate constants and establishing the Ps reaction types; 4) the application of the Smoluchowski equation to Ps reactions. Moreover, an attempt is made to ascertain the standard electrochemical potential of Ps atoms. The positron reactions and the formation of positronides are also taken into consideration. Presentata nella seduta del 13 dicembre 2002 dal Socio F. Calderazzo.     

Comparison of the relative and k0 methods for the standardization of NAA with stable low-flux reactors

Thek ₀ standardization method was Actapted for NAA with stable low-flux reactors where flux monitors are not needed. The modifiedk ₀ method offers the convenience of the use of libraries of sensitivity constants. It was compared to the relative method for 52 elements using a SLOWPOKE reactor and 6 counting geometries. The sensitivity constants determined fromk ₀ values were found to be as accurate or more accurate than those measured with standards. NAA with this modifiedk ₀ method should be accurate to 3% for light elements and 5% for heavy elements.     

Multivariate Homogeneity Testing Using an Extended Concept of Nearest Neighbors

Given independent multivariate random samples {X_ij: j = 1, …, n_i} from F_i, for i = 1,2, a test is desired for H₀: F₁ = F₂ against general alternatives. Consider the k · (n₁ + n₂) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let S_k be the proportion of these choices in which the point and neighbor are in the same sample. Schilling (1986) proposed S_k as a test statistic, but did not indicate how to determine k. We suggest as test statistic W = N Σ kS_k, which we show is equivalent to a sum of N Wilcoxon rank sums, and also to a sum of two two-sample U-statistics of degrees (1, 2) and (2, 1). Simulation with multivariate normal data suggests that our test is generally more powerful than Schilling's test using k = 1, 2, or 3. We illustrate its use with Fisher's iris data.     

Determination of thermodynamic functions from scanning calorimetry data. II. For the system that includes self-dissociation / association process

The basic relations between the molar fractions and the scanning calorimetry data for the system that includes self-dissociation/association process such as are presented, where m_i is the stoichiometric coefficient of the ith state A_i. The relations are described for each state j as where f_j(T) is the molar fraction function of state j and ΔH_j(T) is the difference enthalpy function of the system referred to the state j, which can be obtained by scanning calorimetry; R is the gas constant; and T is the absolute temperature. By these relations, scanning calorimetry data can be deconvoluted in order to determine the thermodynamic functions by means of single and double deconvolution. The concentration dependence of the data is analyzed by a method presented in this paper. The nonlinear least squares fitting method for the determination of the functions is discussed. For an example of the application of this method to the actual scanning calorimetry data, thermodynamic data of multistate thermal transition of Vibrio parahaemolyticus hemolysin are analyzed.     

Theory of transport in linear biological systems: II. Multiflux problems

If in a multiflux system theith flux is given by the integral equation, , the corresponding equation in the Laplace transforms is Γ _i = Σ _j W _ij Γ _j +M _i -the entire system having the matrix formulaion, [I−W]Γ=M. The general solution of this equation and its physical interpretation are discussed. Explicit solutions are given for the general mammillary and catenary systems and for some capillary exchange problems. The theory is applied to the integrated from of the fundamental continuity equation to give equations for total quantity of material in the various “compartments.” If the compartments are uniformly mixed, the integral equation treatment is shown to be mathematically equivalent to the usual differential equation formulation.     

On Mechanism of Interaction of Organophosphorus Inhibitors with Cholinesterases of Different Origin

A study is carried out as a development of A.P. Brestkin's concept of mechanism of irreversible inhibition of cholinesterases (ChE) by organophosphorus inhibitors (OPI) with taking into account reversibility of the first stage of this reaction, which has made it possible to determine individual constants of separate stages of the process. For the first time, a comparative study is performed on horse blood serum BuChE, human erythrocyte AChE, and ChE of optical ganglia of Pacific squid Todarodes pacificus. Besides, the OPI set is enlarged essentially due to use of some highly specific inhibitors of each of the enzymes. To evaluate the cholinesterase activity, chromogenic indophenol esters are used as substrates. For each of the studied ChE, differences in sensitivity to the studied OPI are realized only in values of the kinetic constant of formation of the enzyme-inhibitor complex (k ₅), whereas the rate constants of dissociation of this complex to initial components (ChE and OPI) (k _–5) and of process of its transformation into phosphorylated ChE (k ₆) are close to each other by the values, values of these constants k _–5 and k ₆ for different enzymes also being similar. Some statements about the molecular mechanism of the cholinesterase catalysis are formulated. It is suggested that the revealed elements of similarity of different ChE are realized in the work of the catalytic machine of active centers of the enzymes.     

Enhanced oxygen transfer rates in fermentation using soybean oil-in-water dispersions

Summary The effect of soybean oil on the volumetric oxygen transfer coefficient during the cultivation ofAerobacter aerogenes cells is presented. For our aeration-agitation conditions (0.278 vvm and 500 rpm), it has been demonstrated that the use 19% (v/v) of soybean oil enabled a 1.85-fold increase of thek _l a coefficient (calculated on a per liter aqueous phase basis). For smaller volumetric oil fractions,k _L a increased linearly with the oil loading. Because of the oxygen-vector properties of soybean oil, this oil is able to significantly increase thek _L a of a bioreactor.Nomenclature C^*, C saturation and actual dissolved oxygen concentrations respectively (g/m³) - K_La volumetric oxygen transfer coefficient (h^–1) - K_La_initial k _La measured before the oil addition (h^–1) - M_O2 molar mass of oxygen (dalton) - N oxygen transfer rate (g/m³. h) - P_O2. P_N2 partial pressures ofO ₂ andN ₂ in the gas (atm) - P_H2OT partial pressure of water in air at the temperatureT (atm) - P_T total pressure (atm) - Q₀ volumetric flow rate of outlet air before seeding (m³/h) - Sp spreading coefficient (dynes/cm) - T absolute temperature of outlet gas (K) - V_i volume of the liquidi in the fermentor (m³) - V_M molar volume at 273 K and 1 atm (m³/mole) - _ij interfacial tension betweeni andj componants (dynes/cm) - _v volumetric fraction of the oil (v/v) - G gas - O oil - W water - i inlet - o outlet     

On the use of non-linear regression with the logistic equation for changes with time of percentage root length colonized by arbuscular mycorrhizal fungi

For the regression of sigmoid-shaped responses with time t of colonization C of roots by arbuscular mycorrhizal fungi, C=C _p/1+[e ^−k(t−ti) ] is the most useful form of the logistic equation. At the time of inflection t _i the slope is maximal and directly proportional to the product of the colonization plateau C _p and the abruptness k of the curve. Coefficient k has a high value when the curve rises abruptly following and preceding long shallow phases. The logistic equation has a curve that is symmetrical about t _i such that C=C _p/2 at inflection. Although the logistic equation can generate a good fit to many data sets for changes in colonization with time, there are cases that are not sigmoid and the logistic equation does not apply. For sigmoid curves, the lag in the development of colonization is directly related to both t _i and k but not to the plateau and not to the value of the maximum slope. Higher values of k or t _i reflect longer lag. When considered alone, t _i and k do not fully summarize the lag in colonization, and so a numerical method to combine them is presented here which allows lag to be compared between curves. In this method, the lag is evaluated by calculating the time during early colonization when the slope equals half of the value of the maximum slope. In summary, use of the logistic equation for regression of sigmoid curves of colonization with time allows numerical comparison between curves of the lag, the period of steep ascent, and the plateau. The logistic equation does not model directly the fundamental processes at work in the development of the mycorrhizae. Instead, it can be used as described here to gain insight into the colonization process by comparing the dynamics of that colonization for different species under various conditions. Accepted: 20 October 2000     

Disintegration of yeast Saccharomyces cerevisiae in the vertical perl mill with a bell-shaped impeller

Investigation of disintegration of yeast Saccharomyces cerevisiae in the laboratory batch perl mill with a bell-shaped impeller was carried out. The number of non-damaged cells, changing in time was determined using hemocytometer (Thom's chamber).To describe kinetics of the disintegration process the differential equation was applied: where N _p the number of non-damaged cells in the sample, [number of cells/ml] t time, [s] m,k constants.The effect of three operating parameters: rotation frequency of the impeller shaft n, filling of the mill with disintegrating elements (ballotini) S _k and the initial concentration of yeast cells in the suspension C ₀ on the process of disintegration was analyzed.For S _k =0.5, m=1 and dependence of constant k on the rotation frequency of the impeller and suspension concentration were obtained. For S _k =0.6 and 0.7 the values of m were higher than 1. The effect of rotation frequency of the impeller and filling of the mill, with ballotini on constant k and exponent m was determined.List of Symbols a, b constants - a ₁, b ₁, c ₁, d ₁ constants - C ₀ initial concentration of suspension g/ml - C concentration of cell suspension g/ml - k constant disintegration rate 1/s; N ₀ ^1-m /s - m variable in the equation - N ₀ initial number of cells no. of cells/ml - N _p number of non-damaged cells no. of cells/ml - r process rate g/ml·s - X(t) disintegration degree % - , variables in the equation - z variable in the equation - S _k degree of filling the mill with disintegrating elements