Curve fitting approach for measurement of cellular osmotic properties by the electrical sensing zone method. I. Osmotically inactive volume

We have investigated the confounding effects of dynamic range limitations on measurement of the osmotically inactive volume using electrical sensing zone instruments (e.g., Coulter counters), and propose an improved approach to parameter estimation. The conventional approach for analysis of cell size distributions measured by such particle sizing instruments requires data truncation: the mean cell volume is computed after exclusion of data below a specified lower bound (typically chosen to remove artifacts due to small-volume noise) and above an upper bound (typically governed by instrument limitations). The osmotically inactive volume is then estimated from a Boyle–van’t Hoff plot of the averaged volume data obtained after exposure to various solution osmolalities. We demonstrate that systematic exclusion of data in the conventional approach introduces bias that results in erroneously high estimates of the osmotically inactive volume fraction. To minimize this source of error, we have devised a new algorithm based on fitting a bimodal distribution model to the non-truncated volume data. In experiments with mouse insulinoma (MIN6) cells, the osmotically inactive volume fraction was estimated to be 0.15 ± 0.01 using the new method, which was significantly smaller than the estimate of 0.37 ± 0.02 obtained using the conventional method (p < 0.05). In silico experiments indicated that the parameter estimate obtained by the new method was accurate within 5%, whereas the error associated with the conventional approach was approximately 150%. Parametric analysis was used to elucidate the sensitivity of errors to variations in instrument dynamic range and cell volume distribution width.     

Curve fitting approach for measurement of cellular osmotic properties by the electrical sensing zone method. II. Membrane water permeability

In a companion paper, we demonstrated that dynamic range limitations can confound measurement of the osmotically inactive volume using electrical sensing zone instruments (e.g., Coulter counters), and presented an improved parameter estimation method in which a lognormal function was fit to the cell volume distribution to allow extrapolation beyond the bounds of the data. Presently, we have investigated the effect of dynamic range limitations on measurement of the cell membrane water permeability (L_p), and adapted the lognormal extrapolation method for estimation of L_p from transient volume data. An alternative strategy (the volume limit adjustment method, in which the measured isotonic volume distribution is used to generate model predictions for curve fitting, and the bounds of the dynamic range are adjusted such that extrapolation is not required) was also developed. The performance of these new algorithms was compared to that of a conventional parameter estimation method. The best-fit L_p values from in vitro experiments with mouse insulinoma (MIN6) cells differed significantly for the different parameter estimation techniques (p < 0.001). Using in silico experiments, the volume limit adjustment method was shown to be the most accurate (relative error 0.4 ± 3.2%), whereas the conventional method underestimated L_p by 19 ± 2% for MIN6 cells. Parametric analysis revealed that the error associated with the conventional method was sensitive to the dynamic range and the width of the volume distribution. Our initial implementation of the lognormal extrapolation method also yielded significant errors, whereas accuracy of this algorithm improved after including a normalization scheme.     

A novel method for the determination of electrical potentials across cellular membranes. I. Theoretical considerations and mathematical approach

A new method for the determination of electrical potentials across cellular membranes has been developed. In order to determine the membrane potential, cells were incubated in buffer solutions with increasing concentrations of KCl. Parallel experiments were performed with buffer solutions which additionally contained valinomycin. After sedimentation of the cells, the membrane potential was calculated from data which were obtained by simply measuring the wet mass, the dry mass and the potassium content of cell pellets by atomic absorption spectroscopy.     

EPR method for the measurement of cellular sulfhydryl groups.

An EPR method that can measure the concentration of sulfhydryl groups in intact cells has been developed using a specially designed stable nitroxyl biradical. The biradical, RS-SR, contains a disulfide bond and readily undergoes thiol-disulfide exchange reactions with thiols resulting in a characteristic EPR spectrum which can be analyzed to provide a quantitative measure of sulfhydryl groups. The data obtained from the EPR method are in good agreement with those obtained from the conventional optical method using Ellman's reagent. The advantages of the EPR method are that the measurement can be carried out on intact cells or any other highly colored, absorbing and/or scattering solutions and the sensitivity is such that only a few cells (approximately 100) are needed for each quantitative measurement.     

Criteria for set point estimation in the volume clamp method of blood pressure measurement.

When blood pressure is measured in the finger using the volume clamp method the value at which the vascular volume is clamped is of crucial importance. Since the discovery of the method, several criteria of finding a correct set point have been elaborated: 1. The volume oscillations reach their maximum amplitude at cuff pressure equalling mean blood pressure. 2. The form of the diastolic portion of volume pulsations changes if the cuff pressure moves around the mean blood pressure. 3. The set point can be positioned at one third of the arterial volume. 4. The dynamic vascular compliance (DVC) may be continuously measured as the instantaneous amplitude of vascular volume oscillations is elicited by a relatively small and rapid vibration of the cuff pressure. The shape of the DVC pulse characteristically depends on the transmural pressure (TP): at negative TP (cuff pressure exceeding the blood pressure) it shows a distinct positive systolic peak, at positive TP the polarity of the DVC pulse is reversed. In contrast to the first three ways to find the set point, the last one may operate even in closed-loop performance, i.e. during the blood pressure measurement.     

Breath-by-breath measurement of the volume displaced by diaphragm motion.

To develop an accurate method to measure the volume displaced by diaphragm motion (DeltaVdi) breath by breath, we compared DeltaVdi measured by a previously evaluated biplanar radiographic method (Singh B, Eastwood PR, and Finucane KE. J Appl Physiol 91: 1913-1923, 2001) at several lung volumes during vital capacity inspirations in 10 healthy and nine hyperinflated subjects with 1) DeltaVdi measured from the same chest X-rays by two previously described uniplanar methods (Petroll WM, Knight H, and Rochester DF. J Appl Physiol 69: 2175-2182, 1990; Verschakelen JA, Deschepper K, and Demendts M. J Appl Physiol 72: 1536-1540, 1992) and a proposed method that considered actual cross-sectional shape of the rib cage and spinal volume (DeltaVdi(S)); and 2) DeltaVdi(S) measured by lateral fluoroscopy in the same 10 healthy subjects. Relative to biplanar DeltaVdi, DeltaVdi(S) values from lateral chest X-rays and fluoroscopy were not different, whereas DeltaVdi values of Petroll et al. and Verschakelen et al. were increased by (means +/- SD) 1.98 +/- 1.59 and 1.16 +/- 0.82 liters, respectively (both P < 0.001). During quiet breathing, DeltaVdi(S) by lateral fluoroscopy was 66 +/- 16% of tidal volume and similar to that between functional residual capacity and one-half inspiratory capacity by the biplanar radiographic method. We conclude that accurate breath-by-breath measurements of DeltaVdi can be made by using lateral fluoroscopy.     

A quantitative method for the measurement of cellular guanosine triphosphate pool specific activities

Studies on quantitation of RNA synthesis in eucaryotic cells have frequently used adenosine as the radioactively labeled precursor, largely because of the convenience of the firefly luciferin-luciferase assay in measuring ATP pool specific activity (1,2). This could result in some difficulties if the addition of poly(A) to the 3′ OH end of RNA represents a significant portion of total incorporation, as is the case in sea-urchin embryos (3). In addition, in some cases, the ATP pool may be large enough to prevent the use of adenosine as an effective labeling agent. Hence, a simple and sensitive method for the determination of the specific activity of the other nucleic acid precursor pools would be of value.Although the crystalline luciferase is specific for ATP, extracts of firefly lanterns most commonly used for quantitating ATP (4–9) also exhibit activity with other ribonucleoside triphosphates, adenosine tetraphosphate, ADP, and the deoxyribonucleoside triphosphates. This activity is due to the presence of contaminating enzymes such as nucleoside 5′-diphosphate kinase and adenylate kinase which catalyze the formation of ATP from these nucleotides and trace amounts of ADP, also present in the extracts (10–13). Recently, Manandhar and Van Dyke (14) have reported a procedure for quantitating picomole levels of GTP with a crude extract of firefly lanterns. In the present study, we have adapted their procedure to develop an assay for GTP pool specific activity in Xenopus laevis oocytes microinjected with [8-³H]GTP. Our assay may be extended to the analysis of any nucleoside triphosphate pool, provided that an adequate chromatography system is available for the separation of the extracted nucleotides.     

A method for the in situ measurement of the electrical quantities in frog skin

A method allowing the measurement of the electrical quantities related to the physiological functions of the frog skin in situ is presented. The method allows the performance of several experiments on the same pithed animal, which remains alive for a number of days. The preparation is very stable, and the electric potential difference and short-circuit current values are higher than in isolated skin. The theory of measurement and the possible systematic errors are discussed. The possibilities of the method are evaluated on comparing the pH and temperature dependence of the electrical quantities in situ with previous measurements on isolated skin.     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. II. Effects of osmotic perturbation

The effects of osmotic perturbation on the dielectric behavior of cultured rat basophilic leukemia (RBL-1) cells were examined. Cells exposed to osmolalities (pi) of 145-650 mosmolal showed dielectric dispersions of the following characteristics: Permittivity increment delta epsilon(= epsilon l - epsilon h where epsilon l and epsilon h refer to the low- and high-frequency limit values) for a fixed volume concentration increased with pi; gross permittivity behavior was apparently of a typical Cole-Cole type; however, frequency dependence of conductivity was undulant and could be simulated by a superposition of two separate Cole-Cole type dispersions; separation of these subdispersions along the frequency axis was an increasing function of pi, and so was conductivity increment in the high-frequency region. As examined by light microscopy, the cells were spherical in spite of imposed anisotonic stresses and behaved as osmometers at 200-410 mosmolal. When normalized by dividing by number (not volume) concentration, delta epsilon remained relatively constant irrespective of pi. Apparent membrane capacities (Cm), analyzed by applying a single-shell model, increased systematically from a hypotonic value of approx. 1 microF/cm2 up to 5 microF/cm2 at 650 mosmolal. This increase was interpreted as due to increased cellular 'surface/volume' ratios that were confirmed by scanning electron microscopy. Cole-Cole's beta parameter, which culminated around 0.9 for isotonic cells and declined to approx. 0.8 for anisotonic cells, did not parallel the broadening of cell volume distribution but appeared to reflect changes in the intracellular conductivity caused by the anisotonic challenge. The results indicate that the dispersion method can probe changes in surface morphology as well as subcellular organelles' constitution of living cells.