Estimation of the physical properties of neurons and glial cells using dielectrophoresis crossover frequency

We successfully determine the ranges of dielectric permittivity, cytoplasm conductivity, and specific membrane capacitance of mouse hippocampal neuronal and glial cells using dielectrophoresis (DEP) crossover frequency (CF). This methodology is based on the simulation of CF directly from the governing equation of a dielectric model of mammalian cells, as well as the measurements of DEP CFs of mammalian cells in different suspension media with different conductivities, based on a simple experimental setup. Relationships between the properties of cells and DEP CF, as demonstrated by theoretical analysis, enable the simultaneous estimation of three properties by a straightforward fitting procedure based on experimentally measured CFs. We verify the effectiveness and accuracy of this approach for primary mouse hippocampal neurons and glial cells, whose dielectric properties, previously, have not been accurately determined. The estimated neuronal properties significantly narrow the value ranges available from the literature. Additionally, the estimated glial cell properties are a valuable addition to the scarce information currently available about this type of cell. This methodology is applicable to any type of cultured cell that can be subjected to both positive and negative dielectrophoresis.     

The dielectric permittivity at radio frequencies and the bruggeman probe: novel techniques for the on-line determination of biomass concentrations in plant cell cultures

A novel technique is described for the measurement of the volume fraction of biomass in a suspension by the simultaneous measurement of the conductivity of a suspension containing cells and of the medium in which the cells are suspended. The presence of non-conducting particulate matter in a suspension will cause the conductivity of a suspension to be decreased relative to that of the medium in which the particles are suspended. A simple equation (the Bruggeman equation) describes the relationship between the volume fraction of non-conducting particulate matter and the decrease in conductivity. The accuracy of this method for the determination of the biomass concentration of plant cells (Festuca arundinacea) in culture was shown. The method was successfully applied to the on-line determination of biomass concentrations during the growth of F. arundinacea cultures, and gave good agreement with biomass levels as determined from measurements of the radio-frequency dielectric permittivity of such cultures.     

Dielectric spectroscopy as a novel and convenient tool for the study of the shear sensitivity of plant cells in suspension culture.

Plant cell suspensions of different species and different age were subjected to hydrodynamic stress while following the decline in the volume fraction of intact cells by measuring the permittivity of the cell suspension at radio frequencies. Results were compared with the fresh weight, dry weight, packed cell volume and cell number of the suspensions. At first a rapid decline is seen as the most shear-sensitive cells are broken up, followed by a slower decline as less sensitive cells are broken up. The sensitivity of the cells to shear stress depended strongly on the cell line used but only slightly on their age, older cells being more sensitive. The dependence of the shear sensitivity on the cell line might be an effect of the species investigated, the culturing conditions of the cell line, or both. It was found that cells that grow in a finely dispersed suspension are much less prone to shear stress than is often assumed.     

Characterization of the efficiency of a cell separation process by the extent of elimination of a contaminating cell type

A stepwise approach to the selection of an appropriate technique for a cell separation problem is presented in which the preparative purification of cells is linked to their analytical separation. We have introduced the extent of elimination of a contaminating cell type from the cell type which one chooses to purify, as a separation parameter that characterizes the efficiency of a separation process independently of the relative cell composition of the starting material. In order to compare different separation techniques, a preparative fraction boundary needs to be chosen between the cell types. We defined this boundary in terms of the physical property on which the separation is based such that yield and purity of the isolated cell suspension are optimized simultaneously. With this analytical approach, it was found that a similar elutriation technique separated human and equine mononuclear cells equally well and that the separability of human monocytes and lymphocytes improved when the cells were separated by increasing the limiting sedimentation coefficient value of the elutriation chamber in small increments.     

Quantitative Estimates of Phosphorus Concentrations within Lupinus luteus Leaflets by Means of Electron Probe X-ray Microanalysis

Phosphorus contents of epidermal vacuoles and mesophyll cells of Lupinus lutens leaflets were measured by electron probe x-ray microanalysis of fully hydrated, bulk frozen samples. Quantitation was achieved using standard solutions containing colloidal graphite to simulate cell contents and the derived nonlinear relationship between peak over background ratio and concentration improved the accuracy of the analytical procedure. Inorganic phosphate contents of mesophyll cells were shown to be highly dependent on phosphate nutrition. Comparison with data obtained from conventional analysis leads to the suggestion that in heterogeneous tissues the inorganic phosphate concentrations of the cytoplasm may show greater variation than observed in the cytoplasm of simple plant systems such as cell suspension and root tips.     

Tests for Order Restrictions in Binary Data

In this article, a general procedure is presented for testing for equality of k independent binary response probabilities against any given ordered alternative. The proposed methodology is based on an estimation procedure developed in Hwang and Peddada (1994, Annals of Statistics 22, 67-93) and can be used for a very broad class of order restrictions. The procedure is illustrated through application to two data sets that correspond to three commonly encountered order restrictions: simple tree order, simple order, and down turn order.     

Bivariate cumulative probit model for the comparison of neuronal encoding hypotheses

Understanding the way stimulus properties are encoded in the nerve cell responses of sensory organs is one of the fundamental scientific questions in neurosciences. Different neuronal coding hypotheses can be compared by use of an inverse procedure called stimulus reconstruction. Here, based on different attributes of experimentally recorded neuronal responses, the values of certain stimulus properties are estimated by statistical classification methods. Comparison of stimulus reconstruction results then allows to draw conclusions about relative importance of covariate features. Since many stimulus properties have a natural order and can therefore be considered as ordinal, we introduce a bivariate ordinal probit model to obtain classifications for the combination of light intensity and velocity of a visual dot pattern based on different covariates extracted from recorded spike trains. For parameter estimation, we develop a Bayesian Gibbs sampler and incorporate penalized splines to model nonlinear effects. We compare the classification performance of different individual cell covariates and simple features of groups of neurons and find that the combination of at least two covariates increases the classification performance significantly. Furthermore, we obtain a non‐linear effect for the first spike latency. The model is compared to a naïve Bayesian stimulus estimation method where it yields comparable misclassification rates for the given dataset. Hence, the bivariate ordinal probit model is shown to be a helpful tool for stimulus reconstruction particularly thanks to its flexibility with respect to the number of covariates as well as their scale and effect type.     

Passive electrical properties of the membrane and cytoplasm of cultured rat basophil leukemia cells. I. Dielectric behavior of cell suspensions in 0.01-500 MHz and its simulation with a single-shell model

Frequency dependence of relative permittivity (dielectric constant) and conductivity, or the 'dielectric dispersion', of cultured cells (RBL-1 line) in suspension was measured using a fast impedance analyzer system capable of scanning 92 frequency points over a 10 kHz-500 MHz range within 80 s. Examination of the resulting dispersion curves of an improved reliability revealed that the dispersions consisted of at least two separate components. The low-frequency component (dispersion 1) had a permittivity increment (delta epsilon) of 10(3)-10(4) and a characteristic frequency (fc) at several hundred kHz; for the high-frequency component (dispersion 2), delta epsilon was smaller by a factor of 10(2) and fc = 10-30 MHz. Increments delta epsilon for both components increased with the volume fraction of cell suspension, while fc did not change appreciably as long as the conductivity of suspending medium was fixed. By fitting a model for shelled spheres (the 'single-shell' model) to the data of dispersion 1, the dielectric capacity of the plasma membrane phase (Cm) was estimated to be approx. 1.4 microF/cm2 for the cells in an isotonic medium. However, simulation by this particular shell model failed to reproduce the entire dispersion profile leaving a sizable discrepancy between theory and experiment especially at frequencies above 1 MHz where dispersion 2 took place. This discrepancy could not be filled up even by taking into consideration either the effect of cell size distribution actually determined or that of possible heterogeneity in the intracellular conductivity. The present data strongly indicate the need for a more penetrating model that effectively accounts for the behavior of dispersion 2.     

Rheological properties of mammalian cell culture suspensions: Hybridoma and HeLa cell lines

Data on viscous (eta') and elastic (eta') components of the complex viscosity versus oscillatory angular frequency (0.01 to 4.0 rad/s) with increasing strains were obtained for hybridoma cell (62'D3) and HeLa cell (S3) suspensions in PBS at 0.9 (mL/mL) cell volume fraction using a Weissenberg rheogoniometer equipped with two parallel plate geometry at ambient temperature. Both cell suspensions exhibited shear thinning behavior. From the measured viscoelastic properties, the yield stress was calculated. Hybridoma cell suspension (15 mum as the mean diameter of cells) showed the yield stress at 550 dyne/cm(2) that was 1.8 times higher than the value of HeLa cell suspension (22 mum mean diameter) as measured at the oscillatory angular frequency, 4.0 rad/s. The apparent viscosities of HeLa cell suspension at four concentrations and varying steady shear rate were also determined using the Brookfield rotational viscometer. The yield stress to steady shear test was about 130 dyne/cm(2) for HeLa cell suspension at 0.9 (mL/mL) cell volume fraction. The apparent viscosity was in the range about 1 approximately 1000 Poise depending on the cell concentration and shear rate applied. A modified semiempirical Mooney equation, \documentclass{article}\pagestyle{empty}\begin{document}$ \eta = \eta _0 \exp [K\dot \gamma ;{ - \beta } \phi /(1 - K'\sigma \phi _c /D)] $\end{document} was derived based on the cell concentration, the cell morphology, and the steady shear rate. The beta, shear rate index, was estimated as 0.159 in the range of shear rate, 0.16 to 22.1 s(-1), for the cell volume fractions from 0.6 to 0.9 (mL/mL). In this study, the methods of determining the shear sensitivity and the viscous and the elastic components of mammalian cell suspensions are described under the steady shear field. (c) 1993 John Wiley & Sons, Inc.     

Characterization of structure and properties of bone by spectral measure method

Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical properties and ability to withstand fracture depend on the structural organization of bone as a hierarchical composite. Information about the bone structural parameters is contained in the spectral measure in the Stieltjes integral representation of the effective properties. The method is based on constructing the spectral measure either by calculating it directly from micro-CT images or using measurements of electric or viscoelastic properties over a frequency range. In the present paper, we generalize the Stieltjes representation to the viscoelastic case and show how bone microstructure, in particular, bone volume or porosity, can be characterized by the spectral function calculated using measurements of complex permittivity or viscoelastic modulus. For validation purposes, we numerically simulated measured data using micro-CT images of cancellous bone. Recovered values of bone porosity are in excellent agreement with true porosity estimated from the micro-CT images. We also discuss another application of this method, which allows to estimate properties difficult to measure directly. The spectral measure method based on the derived Stieltjes representation for viscoelastic composites, has a potential for non-invasive characterization of bone structure using electric or mechanical measurements. The method is applicable to sea ice, porous rock, and other composite materials.     

Initial filtration rate and initial clogging in the Hemorheometre

The role of different factors contributing to red cell filterability in the Hemorheometre has been investigated. Although the original method uses a small volume of suspension to determine red cell filterability, the present experiments showed that the results obtained are still significantly affected by filter clogging. Consequently a change in filterability could be due to a change in filter clogging possibly by residual leucocytes. An adaptation of filter chamber and filling method is described, resulting in a simpler and faster measuring procedure. The inaccuracy in measuring low haematocrits contributes significantly to experimental errors. Therefore a definition of red cell filterability based on the red cell count (instead of haematocrit) of the suspension is suggested.     

Numerical characterization of diffusion-based extraction in cell-laden flow through a microfluidic channel

Cells are routinely cryopreserved in dimethyl sulfoxide (DMSO), a cryoprotective agent, for medical applications. Infusion of a DMSO-laden cell suspension results in adverse patient reactions, but current DMSO extraction processes result in significant cell losses. A diffusion-based numerical model was employed to characterize DMSO extraction in fully developed channel flow containing a wash stream flowing parallel to a DMSO-laden cell suspension. DMSO was allowed to diffuse across cell membranes as well as across the channel depth. A variety of cases were considered with the ultimate goal of characterizing the optimal geometry and flow conditions to process clinical volumes of cell suspension in a reasonable time (2-3 ml/min). The results were dependent on four dimensionless parameters: depth fraction of the DMSO-laden stream, Peclet number, cell volume fraction in the DMSO-laden stream, and cell membrane permeability parameter. Smaller depth fractions led to faster DMSO extraction but channel widths that were not practical. Higher Peclet numbers led to longer channels but smaller widths. For the Peclet values and channel depths considered (>or=500 microm) and appropriate permeability values, diffusion across cell membranes was significantly faster than diffusion across the channel depth. Cell volume fraction influenced the cross-stream diffusion of DMSO by limiting the fluid volume fraction available in the contaminant stream but did not play a significant role in channel geometry or operating requirements. The model was validated against preliminary experiments in which DMSO was extracted from suspensions of B-lymphoblast cells. The model results suggest that a channel device with practical dimensions can remove a sufficient level of contaminant within a mesoscale volume of cells in the required time.     

Geometric confinement influences cellular mechanical properties I -- adhesion area dependence

Interactions between the cell and the extracellular matrix regulate a variety of cellular properties and functions, including cellular rheology. In the present study of cellular adhesion, area was controlled by confining NIH 3T3 fibroblast cells to circular micropatterned islands of defined size. The shear moduli of cells adhering to islands of well defined geometry, as measured by magnetic microrheometry, was found to have a significantly lower variance than those of cells allowed to spread on unpatterned surfaces. We observe that the area of cellular adhesion influences shear modulus. Rheological measurements further indicate that cellular shear modulus is a biphasic function of cellular adhesion area with stiffness decreasing to a minimum value for intermediate areas of adhesion, and then increasing for cells on larger patterns. We propose a simple hypothesis: that the area of adhesion affects cellular rheological properties by regulating the structure of the actin cytoskeleton. To test this hypothesis, we quantified the volume fraction of polymerized actin in the cytosol by staining with fluorescent phalloidin and imaging using quantitative 3D microscopy. The polymerized actin volume fraction exhibited a similar biphasic dependence on adhesion area. Within the limits of our simplifying hypothesis, our experimental results permit an evaluation of the ability of established, micromechanical models to predict the cellular shear modulus based on polymerized actin volume fraction. We investigated the "tensegrity", "cellular-solids", and "biopolymer physics" models that have, respectively, a linear, quadratic, and 5/2 dependence on polymerized actin volume fraction. All three models predict that a biphasic trend in polymerized actin volume fraction as a function of adhesion area will result in a biphasic behavior in shear modulus. Our data favors a higher-order dependence on polymerized actin volume fraction. Increasingly better experimental agreement is observed for the tensegrity, the cellular solids, and the biopolymer models respectively. Alternatively if we postulate the existence of a critical actin volume fraction below which the shear modulus vanishes, the experimental data can be equivalently described by a model with an almost linear dependence on polymerized actin volume fraction; this observation supports a tensegrity model with a critical actin volume fraction.     

A membrane model describing the effect of temperature on the water conductivity of erythrocyte membranes at subzero temperatures

Thermodynamic models show that the loss of intracellular water from human erythrocytes during freezing depends heavily upon the water conductivity of the erythrocyte membrane. These calculations, which are based on the simple extrapolation of ambient conductivity data to subzero temperatures, show that more than 95% of cell water is transferable during freezing, whereas experiments show that at least 20% of cell water is retained. A study of the effects of different published values for the membrane water conductivity on cell water retained during freezing shows that this discrepancy may be a consequence of the simple extrapolation procedure.For a homogeneous membrane system, absolute reaction rate theory was used to develop a surface-limited permeation model that includes the resistance to the flow of water not only through the interior region of the membrane but also across possible rate-limiting barriers at the solution-membrane interfaces. The model shows that it is unlikely that a single ratelimiting process dominates water transport in the red cell as it is being cooled from ambient to subzero temperatures. The effective membrane conductivity at subzero temperatures could possibly be much lower than a simple extrapolation of existing data would predict. With the aid of this model analytical predictions of intracellular water during freezing are more consistent with experimental observations.     

On the thermal stability of DNA in solution of mixed solvents

The study of the changes in UV absorbance of DNA solutions in water/dioxane and water/ethylene glycol mixture at different concentrations shows that the thermal denaturation of DNA is sensitive to the electrical permittivity of the media and the water content. At relative low concentrations of co-solvent the dominant feature is the electrical permittivity. When water content is lower than a critical value, the electrical permittivity is no longer the determinant of the denaturation temperature but the partial volume fraction of water. The critical water content is about 0.69 partial volume fraction of water.     

Aggregation and disaggregation kinetics of human blood platelets: Part I. Development and validation of a population balance method.

Hydrodynamic shear stress of sufficient intensity is known to cause platelet activation and aggregation and to alter the effects of biochemical platelet agonists and antagonists. In this work, a population balance equation (PBE) model is developed for analysis of platelet aggregation and disaggregation kinetics under the influence of a shear field. The model incorporates both aggregation and disaggregation by splitting and/or erosion mechanisms. This paper, the first of a series of three, deals with the formulation, simplification, and validation of the PBE and with the estimation of parameters involved in the PBE. These population parameters include collision efficiency, void fraction (related to the particle collision diameter), and the breakage rate coefficient. The platelet particle size distribution is determined experimentally, both initially and at some later times. The PBE can then be used to match satisfactorily the observed particle histograms, by appropriate choice of parameters of the model as functions of time, platelet size, and magnitude of physical or chemical stimuli. Besides providing information on adhesive forces and on the rates of aggregation and disaggregation, these parameters infer the physical properties of platelets and platelet aggregates. These properties are of potential value in increasing our understanding of the processes involved in thrombotic disease and/or therapy. A numerical procedure for solving the PBE is validated by application to simple cases for which analytical solutions are available. The model is applied to analysis of experiments, and parameter sensitivity studies are used to order the importance of the parameters and to reduce the complexity of the model. The simplified model is shown to give good agreement with experimental observations.     

Estimation of flattening coefficient for absorption and circular dichroism using simulation

The absorbance and circular dichroism (CD) of suspensions is lower than if the same amount of chromophore were uniformly distributed throughout the medium. Several mathematical treatments of this absorption flattening phenomenon have been presented using various assumptions and approximations. This article demonstrates an alternative simulation approach that allows relaxation of assumptions. On current desktop computers, the algorithm runs quickly with enough particles and light paths considered to get answers that are usually accurate to better than 3%. Results from the simulation agree with the most popular analytical model for 0.01 volume fraction of particles, showing that the extent of flattening depends mainly on the absorbance through a particle diameter. Unlike previous models, the simulation can show that flattening is significantly lower when volume fraction increases to 0.1 but is higher when the particles have a size distribution. The simulation can predict the slope of the nearly linear relationship between flattening of CD and the absorbance of the suspension. This provides a method to correct experimental CD data where volume fraction and particle size are known.     

Ligand-receptor interaction rates in the presence of convective mass transport.

The rate of binding of a ligand to receptors on the cell surface can be diffusion limited. We analyze the kinetics of binding, diffusion-limited in a stationary liquid, in the presence of convective mass transport. We derive a formula that expresses the reaction kinetics in terms of the mass transfer coefficient. A moderately transport-limited kinetics is not readily recognizable from the shape of the binding curve and may lead to erroneous estimates of the rate coefficients. We apply our results to practically important cases: a cell suspension in a stirred volume of liquid and a confluent cell colony under a laminar stream. Using typical numbers characterizing the ligand-receptor interactions, we show that stirring and perfusion can be important factors determining the reaction rates. With the confluent colony, the early reaction kinetics requires a different treatment, and we provide it for the case of low receptor occupancy. We show that, even with a fast perfusion, a cell monolayer can transiently generate a zone of depletion of the ligand, and that would affect the early stages of the reaction. Our results are expressed in a simple analytical form and can be used for the design and interpretation of experimental data.     

Periodic cell aggregation in suspensions of Dictyostelium discoideum

Abstract. Periodic activities of Dictyostelium discoideum can be observed in cell suspension as two types of oscillations in the light-scattering properties, spike-shaped and sinusoidal. Responses of suspended cells to applied chemoattractants are also reflected by transient changes in light scattering. Alterations in the light-scattering properties are due to structural changes such as changes in cell shape and/or changes in the size of cell aggregates. Therefore, changes in the aggregation state during autonomous oscillations and during attractant-induced responses were investigated. In order to be able to withdraw multiple samples and larger sample volumes from optically monitored cell suspensions, a photometer comprising glass fiber optics immersable in a cell suspension was constructed. Samples were fixed with formaldehyde and photographed. The aggregation state of the samples was quantified by counting the number of particles (cells and cell aggregates) per volume. Folic acid elicited in suspensions of undifferentiated cells a transient decrease in the number of particles per volume as did cAMP in suspensions of preaggregation cells. Periodic changes in the number of particles per volume occurred synchronously with spike-shaped and sinusoidal oscillations. The relative amplitude of the oscillations in particle number was larger during sinusoids than during spikes. Photographs showed periodic changes in the aggregate size during sinusoidal oscillations. In each cycle, the cell-aggregation phase was followed by a phase of partial disaggregation. The recurring loosening of cell-cell contacts may be relevant for sorting out the different cell types. The potential role of contact site as synchronizer and as constituent of an oscillator is discussed.     

An Eulerian/XFEM formulation for the large deformation of cortical cell membrane

Most animal cells are surrounded by a thin layer of actin meshwork below their membrane, commonly known as the actin cortex (or cortical membrane). An increasing number of studies have highlighted the role of this structure in many cell functions including contraction and locomotion, but modelling has been limited by the fact that the membrane thickness (about 1?μm) is usually much smaller than the typical size of a cell (10-100?μm). To overcome theoretical and numerical issues resulting from this observation, we introduce in this paper a continuum formulation, based on surface elasticity, that views the cortex as an infinitely thin membrane that can resists tangential deformation. To accurately model the large deformations of cells, we introduced equilibrium equations and constitutive relations within the Eulerian viewpoint such that all quantities (stress, rate of deformation) lie in the current configuration. A solution procedure is then introduced based on a coupled extended finite element approach that enables a continuum solution to the boundary value problem in which discontinuities in both strain and displacement (due to cortical elasticity) are easily handled. We validate the approach by studying the effect of cortical elasticity on the deformation of a cell adhering on a stiff substrate and undergoing internal contraction. Results show very good prediction of the proposed method when compared with experimental observations and analytical solutions for simple cases. In particular, the model can be used to study how cell properties such as stiffness and contraction of both cytoskeleton and cortical membrane lead to variations in cell's surface curvature. These numerical results show that the proposed method can be used to gain critical insights into how the cortical membrane affects cell deformation and how it may be used as a means to determine a cell's mechanical properties by measuring curvatures of its membrane.