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.     

Topography of cell-glass apposition revealed by total internal reflection fluorescence of volume markers

We have developed a new method based on total internal reflection fluorescence to map the shape of the region between glass and the lower surface of a living cell spread upon it. Fluorescently labeled nonadsorbing volume marker molecules that cannot penetrate into the cell are locally stimulated so that they fluoresce only very near the glass/medium interface. The total fluorescence intensity at any point beneath the cell depends on the cell-to-glass separation. Focal contacts appear as dark areas owing to dye exclusion, whereas when the gap exceeds approximately 150 nm, fluorescence asymptotes to the bright background level. Our technique provides greater contrast than does interference reflection microscopy and is free from errors due to cytoplasmic thickness and refractive index inhomogeneities arising from cytoplasmic inclusions. We have shown that sufficiently large molecules suffer steric exclusion from regions accessible to small molecules, which gives new information about lateral penetrability in the apposition region.     

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.     

An Investigation of Errors in Direct Counts of Aquatic Bacteria by Epifluorescence Microscopy, with Reference to a New Method for Dyeing Membrane Filters

A number of methods for observing freshwater bacteria by epifluorescence (incident light fluorescence) microscopy are examined. The suitability of each method for quantitative studies using black membrane filters is assessed. In spite of inadequacies it was considered that the use of acridine-based fluorochromes provided the best available estimate of the bacterial population. The errors which may arise when these stains are used were examined and it was noted that small changes in methodology could cause significant differences in the results obtained. The largest errors were associated with changes in volume of sample filtered and the pore size of the membrane used. A procedure for sample treatment is suggested and a new method for dyeing membrane filters is given which allows the use of 0·22-μm pore size membranes of the cellulose ester and polycarbonate type.     

Cellular dimensions affecting the nucleocytoplasmic volume ratio

Although it has long been appreciated that larger eukaryotic cells have larger nuclei, little is known about how this size relationship is maintained. Here we describe a method for measuring the aqueous volume ratio of nucleus to cytoplasm, two compartments which are interconnected via the pores in the nuclear envelope. We then use that method to identify proportional cellular dimensions in variously treated cells and in different cell types. Cells were scrape loaded with a mixture of fluorescent dextrans: Texas red dextran, average mol wt = 10,000 (TRDx10), and fluorescein isothiocyanate dextran, average mol wt = 70,000 (FDx70). After introduction into the cytoplasmic space, the TRDx10 distributed into both the nucleus and cytoplasm, whereas the FDx70 was restricted to cytoplasm, due to size exclusion by the nuclear pores. The aqueous nucleocytoplasmic volume ratio (RN/C) was determined by measuring, from fluorescence images of spread cells, total cellular fluorescence of each of the two probes and the fluorescence ratio of those probes in the cytoplasm. RN/C was unaffected by the measurement procedure or by varying temperatures between 23 degrees and 37 degrees C. Loading excess unlabeled dextrans had little effect on RN/C, with the single exception that high concentrations of large dextrans could lower RN/C in endothelial cells. Expanding intracellular membranous compartments of macrophages by phagocytosis of latex beads decreased RN/C. Expanding the same compartment by pinocytosis of sucrose, which nearly doubled total cell volume, had little effect on RN/C, indicating that nuclear volume was more closely linked to the cytoplasmic volume, exclusive of vesicular organelles, than to total cell volume. RN/C was the same in mononucleate and binucleate endothelial cells. Finally, measurements of RN/C in murine bone marrow-derived macrophages, bovine aortic endothelial cells, Swiss 3T3 fibroblasts, PtK2 cells, and CV-1 cells revealed that nuclear volume scaled allometrically with cell volume. The allometric relationship indicated that cell volume was proportional to nuclear surface area.     

A Monte Carlo simulation of the determination of mean particle volume using the Cavalieri estimator

BACKGROUND: A common morphometric problem is the determination of an estimate of the size of biological particles obtained from measurements made on a sample of profiles observed in sections. Results are reported typically in terms of mean caliper diameter or mean volume of the particle. METHODS: We have investigated the use of the Cavalieri estimator for obtaining estimates of mean particle volume using a Monte Carlo simulation. Samples of spherical and ellipsoidal particles were generated by computer and serially sectioned at a fixed mean thickness with a small, imposed random variation. The area of each profile was determined and the volume of the particle was calculated according to the Cavalieri estimator. The influence on the estimate of the mean particle volume and its 95% confidence interval was evaluated for several variables: the shape of the particles, the standard deviation of the particle volume in the population, the section thickness, and the standard deviation of the section thickness. RESULTS: The results obtained with the Cavalieri estimator correspond favorably with those obtained with previously reported alternative methods. This leads to a recommendation for the strong consideration for the use of the Cavalieri estimator in cases in which it is technically feasible to obtain at least three sections through the individual particles. Graphs are provided, which relate the confidence interval for the mean volume to the number of particles measured.     

The volume and hydration of the Cryptococcus neoformans polysaccharide capsule

We present a new method to measure capsule size in the human fungal pathogen Cryptococcus neoformans that avoids the limitations and biases inherent in India ink measurements. The method is based on the use of gamma-radiation, which efficiently releases the capsule from the cell. By comparing the volume of irradiated and non-irradiated cells, one can accurately estimate the relative size of the capsule per cell. This method was also used to obtain an estimate of the capsule weight and water content. The C. neoformans capsule is a highly hydrated structure in all the conditions measured. However, after capsule enlargement, the amount of capsular polysaccharide significantly increases, suggesting a that capsule growth has a high energy cost for the cell.     

Determination of bacterial cell volume with the Coulter Counter.

Two methods were used to determine mean volumes of cells of Escherichia coli B/rA in both stationary- and exponential-phase cultures, i.e., electronic measurement with a Coulter Counter-Analyzer system and biophysical measurement of the total volume and number of cells in sedimented cell pellets. Within experimental errors, the methods gave the same mean cell volumes.     

Additional Circular Systematic Sampling Methods

Several systematic sampling methods have been used to estimate the population mean when size of the population is a multiple of sample size. Among these, only few methods have been extended and used to estimate mean of the population when its size is not a multiple of sample size. In this paper, new methods called balanced circular systematic sampling and centered circular systematic sampling are introduced by extending balanced systematic sampling method and centered systematic sampling method respectively. These methods are compared with circular systematic sampling using average variance of corrected sample means for populations exhibiting approximate linear and parabolic trends. The suggested methods are found suitable to estimate the population mean.     

Measurement errors in line transect surveys where detectability varies with distance and size

When using bivariate line transect methods to estimate the biomass density of a tightly clustered biological population, it is generally assumed that both the perpendicular distance from the trackline to the cluster and the cluster size, or biomass, are measured without error. This is unlikely to be the case in practice. In this article, assuming additive mean zero errors in distance and multiplicative errors in size, we develop an estimator of density that corrects for these errors. We use the method of moments for the case of gamma cluster size, randomly placed transect lines, and the generalized exponential detection function. We derive results that show that it may not be necessary to correct for errors in distance or size when the distance and size estimates are not biased. When the size estimates are biased, the biomass density estimate has approximately the same bias as the size estimates. The work is illustrated in the context of annual aerial surveys for juvenile southern bluefin tuna in the Great Australian Bight.     

Accuracy of cancellous bone volume fraction measured by micro-CT scanning

Volume fraction, the single most important parameter in describing trabecular microstructure, can easily be calculated from three-dimensional reconstructions of micro-CT images. This study sought to quantify the accuracy of this measurement. One hundred and sixty human cancellous bone specimens which covered a large range of volume fraction (9.8-39.8%) were produced. The specimens were micro-CT scanned, and the volume fraction based on Archimedes' principle was determined as a reference. After scanning, all micro-CT data were segmented using individual thresholds determined by the scanner supplied algorithm (method I). A significant deviation of volume fraction from method I was found: both the y-intercept and the slope of the regression line were significantly different from those of the Archimedes-based volume fraction (p < 0.001). New individual thresholds were determined based on a calibration of volume fraction to the Archimedes-based volume fractions (method II). The mean thresholds of the two methods were applied to segment 20 randomly selected specimens. The results showed that volume fraction using the mean threshold of method I was underestimated by 4% (p = 0.001), whereas the mean threshold of method II yielded accurate values. The precision of the measurement was excellent. Our data show that care must be taken when applying thresholds in generating 3-D data, and that a fixed threshold may be used to obtain reliable volume fraction data. This fixed threshold may be determined from the Archimedes-based volume fraction of a subgroup of specimens. The threshold may vary between different materials, and so it should be determined whenever a study series is performed.     

Estimation of intracellular fluid volume of L cells

Dilution of ¹⁴C-sucrose solution by intracellular fluid released as a result of ultracentrifugation was used to estimate the intracellular fluid volume of L cells. Consistent relationships to total cell volume as estimated by use of an electronic particle counter were obtained. Expressed as a percentage of total cell volume, the mean value plus or minus the S.D. for 6 experiments was 72.8 ± 0.9.     

Calibration and application of an intra-articular force transducer for the measurement of patellar tendon graft forces: an in situ evaluation.

The objective of this study was to evaluate two calibration methods for the "Arthroscopically Implantable Force Probe" (AIFP) that are potentially suitable for in vivo use: (1) a direct, experimentally based method performed by applying a tensile load directly to the graft after it is harvested but prior to implantation (the "pre-implantation" technique), and (2) an indirect method that utilizes cadaver-based analytical expressions to transform the AIFP output versus anterior shear load relationship, which may be established in vivo, to resultant graft load (the "post-implantation" technique). The AIFP outputs during anterior shear loading of the knee joint using these two calibration methods were compared directly to graft force measurements using a ligament cutting protocol and a 6 DOF load cell. The mean percent error (actual-measured)/(actual)* 100) associated with the pre-implantation calibration ranged between 85 and 175 percent, and was dependent on the knee flexion angle tested. The percent error associated with the post-implantation technique was evaluated in two load ranges: loads less than 40 N, and loads greater than 40 N. For graft force values greater than 40 N, the mean percent errors inherent to the post-implantation calibration method ranged between 20 and 29 percent, depending on the knee flexion angle tested. Below 40 N, these errors were substantially greater. Of the two calibration methods evaluated, the post-implantation approach provided a better estimate of the ACL graft force than the pre-implantation technique. However, the errors for the post-implantation approach were still high and suggested that caution should be employed when using implantable force probes for in vivo measurement of ACL graft forces.     

Quantitative studies on ultrathin sections of bacteria infected with bacterio phage

A quantitative relationship has been established between the number of particles, for example bacteriophages, counted in ultrathin sections of bacteria and the total number present in the whole bacterial cells. The factor F relating particles counted per section with the total number of these particles per entire bacterium could be arrived at by two methods, which proved to give results in close agreement. The first involves knowledge of the average volume of a bacterial section in proportion to the average volume of a whole bacterium; if the mean number of appearances of the same particle on consecutive sections is also known, F may then be calculated. The thickness of sections and, therefore, their volume, as well as the average number of times a single particle is sectioned could be learned by examination of serial sections. By counting the relative number of T2 phage particles which had been intersected once or twice, and relating this proportion to the known phage dimensions, the thickness of the sections was determined to be about 400 A. The second measurement of F could be made in a particular case of late phage development where the number of particles per cell was countable or titratable directly in the bacterial lysate, this number being compared with the number seen in sections of the bacteria just before lysis. The different sources of errors are discussed. The statistical error is under 20 per cent, while the systematic errors are higher and cannot yet be indicated precisely. After a very cautious estimation of the upper limits, we can state, however, that the counts made with this method are certainly reliable to well within a factor of two.     

A novel method for measuring dynamic changes in cell volume.

Many cell types regulate their volume in response to extracellular tonicity changes through a complex series of adaptive mechanisms. Several methods that are presently used to measure cell volume changes include Coulter counters, fluorescent techniques, electronic impedance, and video microscopy. Although these methods are widely used and accepted, there are limitations associated with each technique. This paper describes a new method to measure changes in cell volume based on the principle that fluid flow within a rigid system is well determined. For this study, cos-7 cells were plated to line the inner lumen of a glass capillary and stimulated to swell or shrink by altering the osmolarity of the perfusing solution. The cell capillary was connected in series with a blank reference capillary, and differential pressure changes across each tube were monitored. The advantages of this method include 1) ability to continuously monitor changes in volume during rapid solution changes, 2) independence from cell morphology, 3) presence of physiological conditions with cell surface contacts and cell-cell interactions, 4) no phototoxic effects such as those associated with fluorescent methods, and 5) ability to report from large populations of cells. With this method, we could detect the previously demonstrated enhanced volume regulation of cells overexpressing the membrane phosphoprotein phospholemman, which has been implicated in osmolyte transport.     

Parametric analysis of volume distributions of Schizosaccharomyces pombe and other cells

Time-lapse photomicrographic data have been obtained on mating strains of the yeast Schizosaccharomyces pombe to evaluate the effect of the variability of the patterns of cell cycle behavior on population structure. These have been used to design a computer model which accepts volume distribution data from exponential cultures of a cell and yields estimates of the mean and standard deviation of daughter cell volume and telophase cell volume, as well as a stop-grow point, and the degree of cell volume doubling. Given a cell population's volume distribution and a volume distribution from a subpopulation, the program will estimate the mean age and display how the age is distributed in the subpopulation. Several cell types have been examined.     

The propagation of errors in long-term measurements of land-atmosphere fluxes of carbon and water

For surface fluxes of carbon dioxide, the net daily flux is the sum of daytime and nighttime fluxes of approximately the same magnitude and opposite direction. The net flux is therefore significantly smaller than the individual flux measurements and error assessment is critical in determining whether a surface is a net source or sink of carbon dioxide. For carbon dioxide flux measurements, it is an occasional misconception that the net flux is measured as the difference between the net upward and downward fluxes (i.e. a small difference between large terms). This is not the case. The net flux is the sum of individual (half-hourly or hourly) flux measurements, each with an associated error term. The question of errors and uncertainties in long-term flux measurements of carbon and water is addressed by first considering the potential for errors in flux measuring systems in general and thus errors which are relevant to a wide range of timescales of measurement. We also focus exclusively on flux measurements made by the micrometeorological method of eddy covariance. Errors can loosely be divided into random errors and systematic errors, although in reality any particular error may be a combination of both types. Systematic errors can be fully systematic errors (errors that apply on all of the daily cycle) or selectively systematic errors (errors that apply to only part of the daily cycle), which have very different effects. Random errors may also be full or selective, but these do not differ substantially in their properties. We describe an error analysis in which these three different types of error are applied to a long-term dataset to discover how errors may propagate through long-term data and which can be used to estimate the range of uncertainty in the reported sink strength of the particular ecosystem studied.     

Dye exclusion artifact in flow cytometers

BACKGROUND: Cells exclude their own volume of dye solution in the sample flow which carries them through the flow chamber of the flow cytometer, thereby affecting the otherwise constant signal arising from the fluorescence of this solution. Under certain conditions, this phenomenon may significantly influence the fluorescence signal of the cells. MATERIALS AND METHODS: Using the slit scan technique, we studied this phenomenon as observed for monodisperse polystyrene particles in fluorescein solution. RESULTS: The measurements show that dye solution accumulates just in front of the particle and just behind it, with a relative void in between. This phenomenon is most likely caused by the rapid constriction of the flow as it enters the orifice of the nozzle or flow chamber, giving rise to a pulse of fluorescence which adds to that of the particle or cell itself. The magnitude of this artifact depends on the design and dimensions of the nozzle/flow chamber as well as on the rate of sample flow. CONCLUSIONS: The dye exclusion artifact may affect measurements of cells when they are in a dye solution having a fluorescence per unit volume which is significant compared to that of the cells, especially at low sample flow rates.     

A probabilistic method to estimate gait kinetics in the absence of ground reaction force measurements

Human joint torques during gait are usually computed using inverse dynamics. This method requires a skeletal model, kinematics and measured ground reaction forces and moments (GRFM). Measuring GRFM is however only possible in a controlled environment. This paper introduces a probabilistic method based on probabilistic principal component analysis to estimate the joint torques for healthy gait without measured GRFM. A gait dataset of 23 subjects was obtained containing kinematics, measured GRFM and joint torques from inverse dynamics in order to obtain a probabilistic model. This model was then used to estimate the joint torques of other subjects without measured GRFM. Only kinematics, a skeletal model and timing of gait events are needed. Estimation only takes 0.28 ms per time instant. Using cross-validation, the resulting root mean square estimation errors for the lower-limb joint torques are found to be approximately 0.1 Nm/kg, which is 6–18% of the range of the ground truth joint torques. Estimated joint torque and GRFM errors are up to two times smaller than model-based state-of-the-art methods. Model-free artificial neural networks can achieve lower errors than our method, but are less repeatable, do not contain uncertainty information on the estimates and are difficult to use in situations which are not in the learning set. In contrast, our method performs well in a new situation where the walking speed is higher than in the learning dataset. The method can for example be used to estimate the kinetics during overground walking without force plates, during treadmill walking without (separate) force plates and during ambulatory measurements.     

Fluvo-metricell, a combined cell volume and cell fluorescence analyzer.

A new flow through instrument that simultaneously measures cell volume (resistance pulse technique) and cell fluorescence in the same orifice will be described. The fluorescence pulses of the hydrodynamically focussed cells are picked up by the optics via the axial direction (principle of Dittrich and Goehde, Z Naturforsch 24b:360, 1969). There is no coordination problem between the fluorescence and the resistance pulses to be observed because a new type of transducer is used. The electronic system provides gating of one or two parameter histograms. Function tests are performed with the incorporated two-parameter test spectrum generator. Different examples of using the instrument in practice are shown. The volume that may be measured with an orifice of 70 micron diameter ranges between 4 and 1400 micron3 (1:350). Coefficients of variation of the fluorescence below 2% are measured.