A simple correlation for predicting effective diffusivities in immobilized cell systems

A simple correlation method has been developed to predict effective diffusivities of small molecules in heterogeneous materials such as immobilized cell systems. This correlation uses a single diffusivity measurement at one cell volume fraction to predict diffusivities for any other volume fraction of cell. The method has been applied to 20 sets of published diffusivity measurements in immobilized cell systems and accurately predicts affective diffusivities of molecules for the full range of cell fractions. It may also be used to predict effective diffusivities in heterogeneous materials in which the diffusivity of a molecule in each phase and the volume fraction of each phase are known. (c) 1996 John Wiley & Sons, Inc.     

Cholesterol-induced variations in the volume and enthalpy fluctuations of lipid bilayers.

The sound velocity and density of suspensions of large unilamellar liposomes from dimyristoylphosphatidylcholine with admixed cholesterol have been measured as a function of temperature around the chain melting temperature of the phospholipid. The cholesterol-to-phospholipid molar ratio xc has been varied over a wide range (0 </= xc </= 0.5). The temperature dependence of the sound velocity number, of the apparent specific partial volume of the phospholipid, and of the apparent specific adiabatic compressibility have been derived from the measured data. These data are particularly discussed with respect to the volume fluctuations within the samples. A theoretical relation between the compressibility and the excess heat capacity of the bilayer system has been derived. Comparison of the compressibilities (and sound velocity numbers) with heat capacity traces display the close correlation between these quantities for bilayer systems. This correlation appears to be very useful as it allows some of the mechanical properties of membrane systems to be calculated from the specific heat capacity data and vice versa.     

Methods for the Large-Scale Cultivation of an Oxytricha (Ciliophora: Hypotrichida)1

ABSTRACT. Oxytricha strains used in biochemical studies have traditionally been grown in unaerated, unagitated culture tubes or Fernbach flasks. These cultures are limited in volume to about one liter and have a very nonuniform distribution of cells, with the majority of the cells at the very top or bottom of the medium. We have found conditions in which Oxytricha can be grown in 50-liter fermentation vats. The cultures grow to a uniform density of about 6000 cells/ml.     

A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

Estimating trophic link density from quantitative but incomplete diet data

The trophic link density and the stability of food webs are thought to be related, but the nature of this relation is controversial. This article introduces a method for estimating the link density from diet tables which do not cover the complete food web and do not resolve all diet items to species level. A simple formula for the error of this estimate is derived. Link density is determined as a function of a threshold diet fraction below which diet items are ignored ("diet partitioning function"). Furthermore, analytic relationships between this threshold-dependent link density and the generality distribution of food webs are established. A preliminary application of the method to field data suggests that empirical results relating link density to diversity might need to be revisited.     

Intraparticle diffusional effects in immobilized cell particles

Summary Immobilized cell technology frequently relies on the entrapment of the biomass in a gel particle, and it is generally observed that mass transfer limitations within the gel particle lead to nonuniform cell distribution. This note addresses the consequence of maintaining a very high cell mass density within a biopolymer particle. We illustrate that conventional effectiveness factor calculations can be used to determine particle sizes which would avoid nonuniform cell growth. The analysis is based on simple Monod kinetics. Special attention is given to near zero order kinetic systems in which the effectiveness factor remains high although the limiting nutrient may be depleted near the center of the particle. Mina Dalili is at the Department of Chemical Engineering, North Carolina State University     

Estimating the Volume Density from Thin Sections

An approximation formula for the determination of the volume density from thin sections is given. It is applicable under very mild conditions on the structure studied and has a good accuracy.     

Brain sizes, surfaces, and neuronal sizes of the cortex cerebri: a stereological investigation of man and his variability and a comparison with some mammals (primates, whales, marsupials, insectivores, and one elephant)

This study deals with the stereological estimation of macroscopic sizes of brain and cortex, i.e., volume, surface, and folding, and of microscopic neuronal sizes, i.e., density, mean size, size distribution, and number of neurons. The results show that the degree of variability in man amounts to about 15%. A decrease in volume of the different gray structures can be observed in man after the age of 65 years. The surface, folding index, and length of convolution do not alter with aging. The comparison with mammals of various sizes allows the conclusion that there is a high correlation to brain size for nearly all macroscopic values. Man and elephant, however, have a cortical surface which is, in comparison with whales, relatively small. In contrast, whales have very small cortices compared with man. At the cytoarchitectonic level, the neuronal density has a correlation to brain size. Contrary to other mammals, the primates and man have a high fraction of small granular neurons, especially in layer 4. The assumption that the number of cortical neurons beneath a given surface area of cortex is the same in all mammals cannot be verified, especially in those with large brains. The allometric connection between brain size and parameters is not valid for all measurements (e.g., thickness of cortex, mean size of neurons, perikaryal size distribution, and glial density). Yet some other measurements are well correlated.     

Rheological properties of mixtures of protein-polysaccharide-dynamic viscoelasticity of blend gels of acylated gelatin, kappa-carrageenan, and agarose

Complex Young's modulus of blend gels of gelatin and kappa-carrageenan or agarose has been measured in order to clarify the protein-polysaccharide interaction in biological systems. The mixture of gelatin and kappa-carrageenan showed phase separation in the intermediate volume fraction of gelatin, and it formed a homogeneous gel when the volume fraction of gelatin is very large or very small. Since the dynamic Young's modulus for blend gels of kappa-carrageenan and gelatin was larger than the calculated one from a theory for dispersed systems, some structural reinforcing must occur. The mixture of agarose and gelatin showed the inverse tendency. It was concluded that the role of electrolytic groups was dominant in dilute gels, while molecular entanglement became more important in concentrated gels.     

Estimation of molecular averages and equilibrium fluctuations in lipid bilayer systems from the excess heat capacity function

It is demonstrated that the bilayer partition function can be numerically obtained from scanning calorimetric data without assuming a particular model for the gel-liquid crystalline transition. From this partition function, the enthalpy, entropy and volume changes accompanying the transition can be calculated. In the limit of very large systems, the method of the grand partition function allows calculation of cluster model distribution functions from which average sizes of gel and liquid-crystal clusters, cluster densities and equilibrium fluctuations are obtained. These results indicate that the main transition in phospholipid bilayers proceeds through the formation of clusters and that these clusters are not static domains but highly fluctuating entities. These fluctuations in cluster size are approximately equal to the average cluster size and give rise to localized density and volume fluctuations. The magnitude of these fluctuations is affected by the radius of curvature of the bilayer and by the addition of small molecular weight compounds to the system.     

培养容器容积对AM真菌生长发育的影响

研究宿主植物栽培容器对丛枝菌根(Arbuscularmycorrhizae,AM)真菌Glomusmosseae生长发育的影响。结果表明:小容积容器的根系密度相对较大,在菌根共生体建立初期,菌根真菌繁殖体与根接触的机会增大,对于菌根真菌的迅速侵染及共生体的迅速建立非常有利,同时还增大了根外菌丝二次侵染的机会,从而使菌根真菌生长发育形成了一个良性循环,最终有利于根外孢子的形成。容器对共生体的影响决不是简单的盆的体积问题,而与其面积和体积之比有关,也和种植密度有密切关系。     

Interrelationships between water and cellular metabolism in Artemia cysts. XI. Density measurements

Cysts of the crustacean Artemia are a useful model for studies on intracellular water because they are capable of essentially complete and reversible desiccation. We have used a variety of techniques on this system, the present work being an attempt to estimate the density of intracellular water (rho w). The density of individual cysts was evaluated from sedimentation velocity. Heptane displacement methods were used to determine the volume of a known mass of cysts, from which the density was calculated. The two methods produce comparable results. It was shown that the densities and water contents of large masses of cysts accurately reflect those of individual cysts. Cyst densities (rho c) were determined over the entire range of water content from 0 to 0.63 weight fraction of water (Wf), and temperature dependence was measured for 0.61 Wf over 2-41 degrees C. The following refer to 25 degrees C. No marked change was detected in rho c until the water content exceeded 0.15 Wf, at which rho c decreased as a linear function of Wf to maximum water content. However, the cyst does not behave ideally in the sense that the densities of the nonaqueous components and added water are not additive as a function of Wf. The partial specific volume of water in cysts at maximum hydration was estimated to be 3% larger than that of pure water. These observations are compared with density measurements on other systems, and with previous findings on the physical properties of water in this system.     

A new formula for estimating oxygen consumption in man and animal.

A formula for estimating oxygen consumption in man and animals using outlet volume flow and oxygen fraction of CO2-free outlet air is derived. The formula is simplified and the error induced is evaluated. Two applications are discussed.     

Studies on polydisperse systems using an air-driven ultracentrifuge: application to phosphatidylcholine vesicles.

A high-speed air-driven ultracentrifuge (Airfuge) has been used to determine the molecular weight and effective specific volume of phosphatidylcholine vesicles. The method used to determine the effective specific volume involved varying the solution density until zero sedimentation of the vesicles occurred. The value obtained for the effective specific volume of 0.9885 ml/g agrees well with previously reported values. The determination of the molecular weight of the vesicles is based on a method in which the fraction of vesicles remaining in an upper fraction of the solution column is compared with the values obtained using standard proteins. The values obtained for the molecular weight of the vesicles range from 1.7 X 10(6) to 2.3 X 10(6) and are in good agreement with results obtained using the analytical ultracentrifuge and with previously reported results. Possible effects due to the polydispersity of the solute are assessed using theoretical calculations and the possibility of using the Airfuge for the study of other polydisperse systems is discussed.     

The role of fabric in the large strain compressive behavior of human trabecular bone

Osteoporosis-related vertebral body fractures involve large compressive strains of trabecular bone. The small strain mechanical properties of the trabecular bone such as the elastic modulus or ultimate strength can be estimated using the volume fraction and a second order fabric tensor, but it remains unclear if similar estimations may be extended to large strain properties. Accordingly, the aim of this work is to identify the role of volume fraction and especially fabric in the large strain compressive behavior of human trabecular bone from various anatomical locations. Trabecular bone biopsies were extracted from human T12 vertebrae (n=31), distal radii (n=43), femoral head (n=44), and calcanei (n=30), scanned using microcomputed tomography to quantify bone volume fraction (BV/TV) and the fabric tensor (M), and tested either in unconfined or confined compression up to very large strains (～70%). The mechanical parameters of the resulting stress-strain curves were analyzed using regression models to examine the respective influence of BV/TV and fabric eigenvalues. The compressive stress-strain curves demonstrated linear elasticity, yielding with hardening up to an ultimate stress, softening toward a minimum stress, and a steady rehardening followed by a rapid densification. For the pooled experiments, the average minimum stress was 1.89 ± 1.77 MPa, while the corresponding mean strain was 7.15 ± 1.84%. The minimum stress showed a weaker dependence with fabric as the elastic modulus or ultimate strength. For the confined experiments, the stress at a logarithmic strain of 1.2 was 8.08 ± 7.91 MPa, and the dissipated energy density was 5.67 ± 4.42 MPa. The latter variable was strongly related to the volume fraction (R(2)=0.83) but the correlation improved only marginally with the inclusion of fabric (R(2)=0.84). The influence of fabric on the mechanical properties of human trabecular bone decreases with increasing strain, while the role of volume fraction remains important. In particular, the ratio of the minimum versus the maximum stress, i.e., the relative amount of softening, decreases strongly with fabric, while the dissipated energy density is dominated by the volume fraction. The collected results will prove to be useful for modeling the softening and densification of the trabecular bone using the finite element method.     

General continuum analysis of transport through pores. II. Nonuniform pores.

A general continuum derivation of the nonelectrolyte (Js) and volume (Jv) flux through a pore whose cross section is a function of axial position (nonuniform) is given. In general, the flux equations cannot be reduced to the same form as for a uniform pore and it is not possible to characterize the pore kinetics by three constants as in the uniform pore case. However, it is shown that under certain conditions, the nonuniform pore equations can be approximated by the uniform pore form and can be characterized by three constants (omega, sigma, Lp). The only condition needed to reduce the Jv equation to the uniform form is that the solution be dilute. The deviation of the Js equation from the uniform form is characterized by an asymmetrical function of Jv whose maximum value is estimated. It is shown that the maximum posible fractional deviation of the Js equation from the uniform form is given by the parameter: 0:5sigmaJv/omegaRT. Since this parameter is less then 0.15 for most membrane studies, the nonuniform Js equation can usually be approximated by the uniform pore form. The general results are illustrated by explicit calculations on several models of nonuniform pores. It is shown, for example, that the "equivalent pore radius" defined in the usual way is a function of the experimental parameter that is measured and is not unique.     

Compressive axial mechanical properties of rat bone as functions of bone volume fraction,apparent density and micro-ct based mineral density

Mechanical testing has been regarded as the gold standard to investigate the effects of pathologies on the structure–function properties of the skeleton. With recent advances in computing power of personal computers, virtual alternatives to mechanical testing are gaining acceptance and use. We have previously introduced such a technique called structural rigidity analysis to assess mechanical strength of skeletal tissue with defects. The application of this technique is predicated upon the use of relationships defining the strength of bone as a function of its density for a given loading mode. We are to apply this technique in rat models to assess their compressive skeletal response subjected to a host of biological and pharmaceutical stimulations. Therefore, the aim of this study is to derive a relationship expressing axial compressive mechanical properties of rat cortical and cancellous bone as a function of equivalent bone mineral density, bone volume fraction or apparent density over a range of normal and pathologic bones.We used bones from normal, ovariectomized and partially nephrectomized animals. All specimens underwent micro-computed tomographic imaging to assess bone morphometric and densitometric indices and uniaxial compression to failure.We obtained univariate relationships describing 71–78% of the mechanical properties of rat cortical and cancellous bone based on equivalent mineral density, bone volume fraction or apparent density over a wide range of density and common skeletal pathologies. The relationships reported in this study can be used in the structural rigidity analysis introduced by the authors to provide a non-invasive method to assess the compressive strength of bones affected by pathology and/or treatment options.     

Quasi-elastic light scattering from migrating chemotactic bands of Escherichia coli.

We report the observation of migrating chemotactic bands of Escherichia coli in a buffer solution. The temporal development of the bacterial density profile is observed by the scattered light intensity as the band migrates through a stationary laser beam. We have made a preliminary analysis of the observed band profile with help of the Keller-Segel theory. The model accounts for only some aspects of the observed time evolution of the density profile. The microscopic motility characteristics of the E. coli in the band are simultaneously studied by photon correlation. The measured correlation functions are analyzed to obtain the spatial dependence of the half-width within the band. A simple analytical model is proposed to account for the contribution of the twiddle motion to the correlation function. By analyzing the correlation function as a superposition of straight-line and twiddle motions, we obtain a satisfactory agreement between the theory and the measured angular dependence of the line shape. As a consequence we are able to extract a parameter beta, which measures the average fraction of twiddling bacteria in the center of the band at a given time.     

Prediction of surface area in polydisperse gas-suspension systems with variable apparent surface tension,viscosity and density

Bubble size distribution was found to be represented by a modified log-normal distribution with 3 parameters. The parameters are simple functions of suspension properties,viz. surface tension, viscosity and density, and a function of superficial gas rate. Correlations are presented, enabling the prediction of the distribution constants (and thus of the bubble size distribution) from the system properties and gas rate. Model translucent systems can be used, having identical apparent system properties as real suspensions in experimental work. A computer algorithm is presented for (i) prediction of bubble size distribution, defining the region of formation of spherical bubbles, (ii) converting particle size distribution into volume distribution, (iii) determining the actual gas volume from a hold-up correlation, and (iv) giving the surface area of the system of a given predicted distribution.