On-line monitoring of cell mass in mammalian cell cultures by acoustic densitometry

Acoustic resonance densitometry (ARD) provides a highly reproducible and stable method for on-line measurement of culture biomass density. The technique provides a direct determination of changes in relative density of culture medium and cell mass. At cell concentrations higher than 10(6) cells mL(-1)this method can replace cell counts and provide a continuous measure of total cell mass. In cultures of hybridomas or U937 human lymphoma cells, the ARD value correlates well with cell number except when the average cell size changes during culture. It is argued that cell mass determined by ARD rather than cell number should be used as the basis for measurements of specific biological activity.     

Growth behavior of number distributed adherent MDCK cells for optimization in microcarrier cultures

An assay for measuring the number of adherent cells on microcarriers that is independent from dilution errors in sample preparation was used to investigate attachment dynamics and cell growth. It could be shown that the recovery of seeded cells is a function of the specific rates of cell attachment and cell death, and finally a function of the initial cell‐to‐bead ratio. An unstructured, segregated population balance model was developed that considers individual classes of microcarriers covered by 1–220 cells/bead. The model describes the distribution of initially attached cells and their growth in a microcarrier system. The model distinguishes between subpopulations of dividing and nondividing cells and describes in a detailed way cell attachment, cell growth, density‐dependent growth inhibition, and basic metabolism of Madin‐Darby canine kidney cells used in influenza vaccine manufacturing. To obtain a model approach that is suitable for process control applications, a reduced growth model without cell subpopulations, but with a formulation of the specific cell growth rate as a function of the initial cell distribution on microcarriers after seeding was developed. With both model approaches, the fraction of growth‐inhibited cells could be predicted. Simulation results of two cultivations with a different number of initially seeded cells showed that the growth kinetics of adherent cells at the given cultivation conditions is mainly determined by the range of disparity in the initial distribution of cells on microcarriers after attachment. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Differential growth of facial primordia in chick embryos: responses of facial mesenchyme to basic fibroblast growth factor (bFGF) and serum in micromass culture

Differential growth of the three major facial primordia, the frontonasal mass, maxilla and mandible, results in a characteristic face shape. Abnormal growth of any of the primordia can lead to facial defects. In order to dissect out the factors that control growth, we developed a functional assay for cell proliferation using micromass culture and defined medium. Cell number was determined over a 4 day period and BrdU incorporation was used to determine the percentage of cells in S-phase. In defined medium, cell number progressively decreases and proliferation is very reduced in cultures of cells from all three primordia. When foetal calf serum was added, frontonasal mass cell number triples, mandible doubles and maxilla increases by half. The number of cells in S-phase increased in every case but the final cell number reflects a balance between proliferation and cell loss from the culture. The addition of basic fibroblast growth factor (bFGF) to defined medium leads to an increase in cell number in the frontonasal mass, while the cell number of mandibular and maxillary cultures is relatively unaffected. The percentage of cells in S-phase is highest in frontonasal mass cultures. Serum and bFGF both increase chondrogenesis in frontonasal mass cultures when compared to defined medium. In contrast in mandibular cultures, serum does not change the amount of cartilage and with bFGF chondrogenesis is reduced. The coordination of the changes in proliferation and differentiation in frontonasal mass cultures suggest that either these two processes are independently stimulated to the same extent or a single subpopulation of cells is stimulated to divide and differentiate into chondrocytes.(ABSTRACT TRUNCATED AT 250 WORDS)     

Modeling mass transfer in hepatocyte spheroids via cell viability, spheroid size, and hepatocellular functions

Hepatocyte aggregation into spheroids attributes to their increased activity, but in the absence of a vascular network the cells in large spheroids experience mass transfer limitations. Thus, there is a need to define the spheroid size which enables maximal cell viability and productivity. We developed a combined theoretical and experimental approach to define this optimal spheroid size. Hepatocyte spheroids were formed in alginate scaffolds having a pore diameter of 100 microm, in rotating T-flasks or spinners, to yield a maximal size of 100, 200, and 600 microm, respectively. Cell viability was found to decrease with increasing spheroid size. A mathematical model was constructed to describe the relationship between spheroid size and cell viability via the oxygen mass balance equation. This enabled the prediction of oxygen distribution profiles and distribution of viable cells in spheroids with varying size. The model describes that no oxygen limitation will take place in spheroids up to 100 microm in diameter. Spheroid size affected the specific rate of albumin secretion as well; it reached a maximal level, i.e., 60 microg/million cells/day in 100-microm diameter spheroids. This behavior was depicted in an equation relating the specific albumin secretion rate to spheroid size. The calculated results fitted with the experimental data, predicting the need for a critical number of viable hepatocytes to gain a maximal albumin secretion. Taken together, the results on mass transport in spheroids and its effects on cell viability and productivity provide a useful tool for the design of 3D scaffolds with pore diameters of 100 microm.     

Recombinant trypsin production in high cell density fed-batch cultures in Escherichia coli

Fed-batch techniques were employed to obtain high cell density cultures (92-100 g DCW/L) of Escherichia coli strain X90 producing a recombinant serine protease, rat anionic trypsin, secreted to the periplasm. The specific growth rate was controlled to minimize growth-inhibiting acetate formation by utilizing an exponential feeding profile determined from mass balance equation. The volumetric yield of recombinant rat anionic trypsin was 56 mg/L, and the final cell density was 92 g DCW/L when the culture was induced in the late logarithmic phase. However, when the culture was induced in the early logarithmic phase, the volumetric yield was 13 mg/L and the final cell density was 14 g DCW/L. Thus, the induction timing is shown to have a significant effect on the final cell density as well as the overall volumetric yield of the recombinant protease. (c) 1993 Wiley & Sons, Inc.     

Growth Pattern and Movement of Epidermal Cells within Leaves of Asphodelus tenuifolius Cav.

The pattern of growth (velocity field) in the intercalary growthzones of monocotyledon leaves can be determined from patternsof cell number density (number per unit length of cell file)and leaf elongation rates using theory based on a cell numberconservation equation. The case where elongation rate is non-steadywhile the pattern of cell number density is steady is discussedand a method for extending calculations into the meristem usingobservations of numbers of mitotic cells is outlined. Applicationof these methods is illustrated using data for epidermal cellsin the first leaf of Asphodelus tenuifolius Cav. During earlyleaf development, leaf elongation rate increased exponentiallybut cell number density and mitotic number density were steady.Cells 0.1 mm from the base of the leaf when leaves were 3.2mm long took 8.3 d to move through the growth zone. In leavesthat were 4 d older, similar cells took 5.1 d to traverse thegrowth zone. Increases in the rates of leaf elongation and ofcell movement appeared to be associated mainly with increasesin total rates of cell production in the epidermal meristem. Asphodelus tenuifolius Cav., Asphodelus fistulosus L., velocity field, meristem, mitotic cell number density, extension-only zone     

Stochastic Gompertz model of tumour cell growth

In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.     

High density culture of insect cells using rational medium design and feeding strategy

The objective of this study is to achieve high density cell culture by a rational medium design and feeding strategy. Insect cell/baculovirus expression system is one of the widely used methods for the production of heterologous proteins in the cell culture domain. Insect cell Spodoptera frugiperda Sf-21 and a recombinant baculovirus with encoded gene for human interleukin-5 were chosen as the model system in this study. A stoichiometric model was established to study the demand of nutrients, including glucose, 20 amino acids, and yeastolate, for the synthesis of cell mass. The coefficients for individual nutrients in the stoichiometric equation governing insect cell growth were determined from the information of cell mass and compositions. Based on the stoichiometric coefficients, the initial and supplemental media for fed-batch cell cultures were designed. The experiments began with the inoculation of Sf-21 cells into a spinner flask with the initial medium, which provided a starting environment for achieving optimum cell growth. This was followed by the periodic feeding of supplemental medium designed by utilizing the stoichiometric equation that governs insect cell growth. With this strategy, it was demonstrated that the Sf-21 cell culture reached a cell density in excess of 1.9᎒⁷ cells/ml. During the cultivation process, the utilization of various nutrients and the production of metabolites were also monitored. Further experiments proved that high concentration of recombinant product (such as human interleukin-5) could be achieved by infecting the high density cells (resulting from the designed medium) with recombinant baculoviruses.     

Stress-sensitive tissue regeneration in viscoelastic biomaterials subjected to modulated tensile strain

This research contribution addresses the mechanochemistry of intra-tissue mass transfer for nutrients, oxygen, growth factors, and other essential ingredients that anchorage-dependent cells require for successful proliferation on biocompatible surfaces. The unsteady state reaction-diffusion equation (i.e., modified diffusion equation) is solved according to the von Kármán-Pohlhausen integral method of boundary layer analysis when nutrient consumption and tissue regeneration are stimulated by harmonically imposed stress. The mass balance with diffusion and stress-sensitive kinetics represents a rare example where the Damköhler and Deborah numbers appear together in an effort to simulate the development of mass transfer boundary layers in porous viscoelastic biomaterials. The Boltzmann superposition integral is employed to calculate time-dependent strain in terms of the real and imaginary components of dynamic compliance for viscoelastic solids that transmit harmonic excitation to anchorage-dependent cells. Rates of nutrient consumption under stress-free conditions are described by third-order kinetics which include local mass densities of nutrients, oxygen, and attached cells that maintain dynamic equilibrium with active protein sites in the porous matrix. Thinner nutrient mass transfer boundary layers are stabilized at shorter dimensionless diffusion times when the stress-free intra-tissue Damköhler number increases above its initial-condition-sensitive critical value. The critical stress-sensitive intra-tissue Damköhler number, above which it is necessary to consider the effect of harmonic strain on nutrient consumption and tissue regeneration, is proportional to the Deborah number and corresponds to a larger fraction of the stress-free intra-tissue Damköhler number in rigid biomaterials.     

Competing tumor cell migration mechanisms caused by interstitial fluid flow

In the seminal work by Swartz and collaborators (Shields et al., 2007) it was discovered that autologously secreted or activated (ECM-bound) chemokine forms local pericellular diffusion gradients skewed by fluid convection, and the cells subsequently chemotact up the flow-directed gradient. However, in (Polacheck et al., 2011) Kamm and collaborators found that there is a competing downstream and upstream migration transport mechanism. Their study showed that both mechanisms are present at the same time and the relative strength of these two stimuli governs the directional bias in migration for a cell population and is a function of cell density, interstitial flow rate, and CCR7 receptor availability. The main objective of this work is to give a possible explanation of these two different concurrent cell migration mechanisms by means of a theoretical model. Relying on multiphase modelling, separate momentum balance equations are formulated, respectively, for the cell phase and the interstitial fluid (IF) phase. In order to represent proteolytic activity and autologous chemotaxis a non-moving ECM component is included, as well as proteases secreted by the cancer cells and chemokine that can be released from ECM. The cell and IF momentum balance equations include cell-ECM and fluid-ECM resistance force terms (i.e., classical Darcy’s equation terms), but also a cell-fluid interaction term that can account for a more indirect effect that fluid-generated stress may have on cancer cells. We illustrate how the cancer cells can work through this term and effectively avoid being pushed in the flow direction, and even create upstream migration by controlling its magnitude and sign. We think of this as the mathematical interpretation of the experimental observation by Kamm and collaborators that the fluid generated matrix adhesion tension on the upstream side of cells activates integrin adhesion complexes, resulting in activation of focal adhesion (FA) proteins. The model predicts that generally the strength of the upstream migration mechanism is sensitive to the cell volume fraction: a lower density of cells is subject to a weaker upstream migration effect; a higher density of cancer cells can more effectively generate upstream migration. This behavior is a result of the nonlinear coupling between cell-ECM, fluid-ECM, and cell-fluid interaction terms that naturally are involved in the mathematical expression for the net cell velocity.     

Modeling the interactions of Lactobacillus curvatus colonies in solid medium: consequences for food quality and safety

The growth process of Lactobacillus curvatus colonies was quantified by a coupled growth and diffusion equation incorporating a volumetric rate of lactic acid production. Analytical solutions were compared to numerical ones, and both were able to predict the onset of interaction well. The derived analytical solution modeled the lactic acid concentration profile as a function of the diffusion coefficient, colony radius, and volumetric production rate. Interaction was assumed to occur when the volume-averaged specific growth rate of the cells in a colony was 90% of the initial maximum rate. Growth of L. curvatus in solid medium is dependent on the number of cells in a colony. In colonies with populations of fewer than 10(5) cells, mass transfer limitation is not significant for the growth process. When the initial inoculation density is relatively high, colonies are not able to grow to these sizes and growth approaches that of broth cultures (negligible mass transfer limitation). In foods, which resemble the model solid system and in which the initial inoculation density is high, it will be appropriate to use predictive models of broth cultures to estimate growth. For a very low initial inoculation density, large colonies can develop that will start to deviate from growth in broth cultures, but only after large outgrowth.     

A new combined differential-discrete cellular automaton approach for biofilm modeling: application for growth in gel beads

The theoretical basis and quantitative evaluation of a new approach for modeling biofilm growth are presented here. Soluble components (e.g., substrates) are represented in a continuous field, whereas discrete mapping is used for solid components (e.g., biomass). The spatial distribution of substrate is calculated by applying relaxation methods to the reaction-diffusion mass balance. A biomass density map is determined from direct integration in each grid cell of a substrate-limited growth equation. Spreading and distribution of biomass is modeled by a discrete cellular automaton algorithm. The ability of this model to represent diffusion-reaction-microbial growth systems was tested for a well-characterized system: immobilized cells growing in spherical gel beads. Good quantitative agreement with data for global oxygen consumption rate was found. The calculated concentration profiles of substrate and biomass in gel beads corresponded to those measured. Moreover, it was possible, using the discrete spreading algorithm, to predict the spatial two- and three-dimensional distribution of microorganisms in relation to, for example, substrate flux and inoculation density. The new technique looks promising for modeling diffusion-reaction-microbial growth processes in heterogeneous systems as they occur in biofilms.     

Modeling the Interactions of Lactobacillus curvatus Colonies in Solid Medium: Consequences for Food Quality and Safety

The growth process of Lactobacillus curvatus colonies was quantified by a coupled growth and diffusion equation incorporating a volumetric rate of lactic acid production. Analytical solutions were compared to numerical ones, and both were able to predict the onset of interaction well. The derived analytical solution modeled the lactic acid concentration profile as a function of the diffusion coefficient, colony radius, and volumetric production rate. Interaction was assumed to occur when the volume-averaged specific growth rate of the cells in a colony was 90% of the initial maximum rate. Growth of L. curvatus in solid medium is dependent on the number of cells in a colony. In colonies with populations of fewer than 10⁵ cells, mass transfer limitation is not significant for the growth process. When the initial inoculation density is relatively high, colonies are not able to grow to these sizes and growth approaches that of broth cultures (negligible mass transfer limitation). In foods, which resemble the model solid system and in which the initial inoculation density is high, it will be appropriate to use predictive models of broth cultures to estimate growth. For a very low initial inoculation density, large colonies can develop that will start to deviate from growth in broth cultures, but only after large outgrowth.     

The efficiency and direction of thymus changes after whole-body exposure of mice to the weak electromagnetic field are determined by the initial status of the thymus

The work presents results of the experimental study on thymus changes developing after whole-body exposure of mice to ultralow power pulse-modulated electromagnetic field (carrying frequency 2.39 GHz, modulating pulses with frequency 4 Hz, duration of impulses 0.025 sec, average power density 60 mW/cm2, absorbed dose 0.086 J/g or 0.172 J/g). It was shown that a percent of the microwave induced increase or decrease of thymus mass and the number of cells in the organ (y) are determined by the initial mass or number of cells in thymus accordingly to equation of linear regression: (yx = 215-2.25x, where x is the thymus mass of control animals (in a range 31-63 mg) and (yx = 178.6-41x, where x is the initial number of cells in thymus (in a range 0.6 x 10(8)-2.6 x 10(8)) reduced by a factor of 10(8).     

Control of microtubule assembly by extracellular matrix and externally applied strain

A number of studies have suggested that externally applied mechanical forces and alterations in the intrinsic cell-extracellular matrix (ECM) force balance equivalently induce changes in cell phenotype. However, this possibility has never been directly tested. To test this hypothesis, we directly investigated the response of the microtubule (MT) cytoskeleton in smooth muscle cells to both mechanical signals and alterations in the ECM. A tensile force that resulted in a positive 10% step change in substrate strain increased MT mass by 34 +/- 10% over static controls, independent of the cell adhesion ligand and tyrosine phosphorylation. Conversely, a compressive force that resulted in a negative 10% step change in substrate strain decreased MT mass by 40 +/- 6% over static controls. In parallel, increasing the density of the ECM ligand fibronectin from 50 to 1,000 ng/cm(2) in the absence of any applied force increased the amount of polymeric tubulin in the cell from 59 +/- 11% to 81 +/- 13% of the total cellular tubulin. These data are consistent with a model in which MT assembly is, in part, controlled by forces imposed on these structures, and they suggest a novel control point for MT assembly by altering the intrinsic cell-ECM force balance and applying external mechanical forces.     

Rate and topography of cell wall synthesis during the division cycle of Salmonella typhimurium.

The rates of synthesis of peptidoglycan and protein during the division cycle of Salmonella typhimurium have been measured by using the membrane elution technique and differentially labeled diaminopimelic acid and leucine. The cells were labeled during unperturbed exponential growth and then bound to a nitrocellulose membrane by filtration. Newborn cells were eluted from the membrane with fresh medium. The radioactivity in the newborn cells in successive fractions was determined. As the cells are eluted from the membrane as a function of their cell cycle age at the time of labeling, the rate of incorporation of the different radioactive compounds as a function of cell cycle age can be determined. During the first part of the division cycle, the ratio of the rates of protein and peptidoglycan synthesis was constant. During the latter part of the division cycle, there was an increase in the rate of peptidoglycan synthesis relative to the rate of protein synthesis. These results support a simple, bipartite model of cell surface increase in rod-shaped cells. Before the start of constriction, the cell surface increased only by cylindrical extension. After cell constriction started, the cell surface increased by both cylinder and pole growth. The increase in surface area was partitioned between the cylinder and the pole so that the volume of the cell increased exponentially. No variation in cell density occurred because the increase in surface allowed a continuous exponential increase in cell volume that accommodated the exponential increase in cell mass. Protein was synthesized exponentially during the division cycle. The rate of cell surface increase was described by a complex equation which is neither linear nor exponential.     

A kinetic model for cell agglutination

A model of concanavalin A (ConA) mediated cell agglutination kinetics is proposed, in which the binding of the lectin, the agglutination of cells and the disintegration of cell clumps are discussed. This resulted in a differential equation, which is solved in terms of the average number of cells per cell clump as a function of time.     

Gompertzian growth pattern correlated with phenotypic organization of colon carcinoma,malignant glioma and non-small cell lung carcinoma cell lines

Abstract. In the current study we present a Gompertzian model for cell growth as a function of cell phenotype using six human tumour cell lines (A-549, NCI-H596, NCI-H520, HT-29, SW-620 and U-251). Monolayer cells in exponential growth at various densities were quantified over a week by sulforhodamine B staining assay to produce cell-growth curves. A Gompertz equation was fitted to experimental data to obtain, for each cell line, three empirical growth parameters (initial cell density, cell-growth rate and carrying capacity – the maximal cell density). A cell-shape parameter named deformation coefficient D (a morphological relationship among spreading and confluent cells) was established and compared by regression analysis with the relative growth rate parameter K described by the Gompertz equation. We have found that coefficient D is directly proportional to the growth parameter K . The fit curve significantly matches the empirical data ( P  < 0.05), with a correlation coefficient of 0.9152. Therefore, a transformed Gompertzian growth function was obtained accordingly to D . The degree of correlation between the Gompertzian growth parameter and the coefficient D allows a new interpretation of the growth parameter K on the basis of morphological measurements of a set of tumour cell types, supporting the idea that cell-growth kinetics can be modulated by phenotypic organization of attached cells.     

Kinetics of cell fusion induced by a syncytia-producing mutant of herpes simplex virus type I.

We have isolated a number of plaque-morphology mutants from a strain of herpes simplex virus type I which, unlike the wild type, cause extensive cell fusion during a productive viral infection. After the onset of fusion, there is an exponential decrease in the number of single cells as a function of time after infection. At a multiplicity of infection (MOI) of 3.8 plaque-forming units per cell, fusion begins 5.3 h after infection with the number of single cells decreasing to 10% of the original number 10.2 h after infection. As the MOI is gradually increased from 0.4 to 8, the onset of fusion occurs earlier during infection. However, when the MOI is increased from 8 to 86, the onset of fusion does not occur any earlier. The rate of fusion is independent of the MOI for an MOI greater than 1. The rate of fusion varies linearly with initial cell density up to 3.5 X 10(4) cells/cm2 and is independent of initial cell density at higher cell concentrations. To assay cell fusion we have developed a smiple quantitative assay using a Coulter counter to measure the number of single cells as a function of time after infection. Data obtained using a Coulter counter are similar to those obtained with a microscope assay.