A model for the growth of multicellular spheroids

Abstract. Based on biological observations and the basic physical properties of tri-dimensional structures, a mathematical expression is derived to relate the growth rate of multicellular spheroids to some easily measurable parameters. This model involves properties both of the individual cells and of the spheroid structure, such as the cell doubling time in monolayer, the rate of cell shedding from the spheroid and the depth of the external rim of cycling cells. The derived growth equation predicts a linear expansion of the spheroid diameter with time. The calculated growth rate for a number of spheroid cell types is in good agreement with experimental data. The model provides a simple and practical view of growth control in spheroids, and is further adapted to include parameters presumably responsible for the growth saturation in large spheroids.     

Radiation cell survival and growth delay studies in multicellular spheroids of small-cell lung carcinoma

The radiation sensitivity of two small-cell lung carcinoma cell lines growing as multicellular spheroids in static culture was determined using clonogenic cell survival and growth delay as endpoints. Growth delay determination suggested that clonogenic cell kill was less than was obtained by direct assay of cell survival. Recovery from potentially lethal damage was assayed in one line (HC12) but was not demonstrable, and clonogenic cell survival decreased with time in treated spheroids with diameters greater than 300 microns which contained a hypoxic cell population. Microscopic examination of the treated spheroids showed the emergence of an abnormal giant-cell population, and the progressive clonogenic cell loss that occurred after treatment was thought to be due to oxygen and nutrient deprivation of the remaining viable cells by this doomed cell population. Correction of the growth delay measurements for changes in cell size and clonogenic cell population allowed correlation of the growth delay and cell survival data.     

Metabolic imaging in multicellular spheroids of oncogene-transfected fibroblasts.

Four rat embryo fibroblast (REF) cell lines with defined oncogenic transformation were used to study the relationship between tumorigenic conversion, metabolism, and development of cell death in a 3D spheroid system. Rat1 (spontaneously immortalized) and M1 (myc-transfected) fibroblasts represent early nontumorigenic transformation stages, whereas Rat1-T1 (T24Ha-ras-transfected Rat1) and MR1 (myc/T24Ha-ras-co-transfected REF) cells express a highly tumorigenic phenotype. Localized ATP, glucose, and lactate concentrations in spheroid median sections were determined by imaging bioluminescence. ATP concentrations were low in the nonproliferating Rat1 aggregates despite sufficient oxygen and glucose availability and lack of lactate accumulation. In MR1 spheroids, a 50% decrease in central ATP preceded the development of central necrosis at a spheroid diameter of around 800 micrometer. In contrast, the histomorphological emergence of cell death at a diameter of around 500 micrometer in Rat1-T1 spheroids coincided with an initial steep drop in ATP. Concomitantly, reduction in central glucose and increase in lactate before cell death were recorded in MR1 but not in Rat1-T1 spheroids. As shown earlier, myc transfection confers a considerable resistance to hypoxia of MR1 cells in the center of spheroids, which is reflected by their capability to maintain cell integrity and ATP content in a hypoxic environment. The data obtained suggest that small alterations in the genotype of tumor cell lines, such as differences in the immortalization process, lead to substantial differences in morphological structure, metabolism, occurrence of cell death, and tolerance to hypoxia in spheroid culture.     

Use of a laser diffraction particle sizer for the measurement of mean diameter of multicellular tumor spheroids

Summary Increasing use is being made of tumor cell lines cultured as cell aggregates (generally referred to as multicellular spheroids) in in vitro radiosensitivity and/or chemosensitivity tests. Conventional procedures for the determination of mean spheroid diameters for the construction of growth delay curves employ a microscope-image analyzer. However, this approach can prove excessively time consuming when large numbers of samples have to be, measured. We have, therefore, been exploring the use of a Laser Diffraction Particle Sizer, the Malvern 2600 long bench model, for the measurement of mean spheroid diameter and size distribution. We report here a direct comparison between measurements carried out by the instrument and under the microscope. Also a comparison of growth curves for six cell lines constructed from measurements by the microscope and by the instrument. A number of factors that might affect the accuracy of spheroid diameter measurement by the instrument have been investigated: The effect of stirring to maintain the spheroids in suspension during measurement. Sampling error due to removal of a series of spheroid samples from culture flasks for measurement. Optimum number of scans to be carried out by the instrument to reach a constant value for mean diameter, and minimum SE of the mean. This research was supported by the Yorkshire Cancer Research Campaign, Horrogate HG1 5LQ, United Kingdom, and by the Hospital Research Fund, Cookridge Hospitatl, Leeds LS16 6QB, United Kingdom.     

Formation of porcine hepatocyte spherical multicellular aggregates (spheroids) and analysis of drug metabolic functions

Porcine hepatocytes are used in the hybrid artificial liver support system that we are developing because of their high level of liver functions in vitro and because human hepatocytes can not be used in Japan for ethical reasons. Spherical multicellular aggregates or spheroids have been found to be effective in vitro for long-term maintenance of liver functions. Therefore, we formed spherical multicellular aggregates (spheroids) of primary porcine hepatocytes using a polyurethane foam (PUF) as a culture substratum and analyzed their drug metabolic functions in vitro. Primary porcine hepatocytes inoculated into the pores of a flat PUF plate (25 × 25 × 1 mm), spontaneously formed spheroids within the range of 100 to 150 μm in diameter 24 to 36 h after inoculation. The formed spheroids were attached to the bottom surface of the PUF pores, and their morphology and viability were maintained for more than 12 days. The P-450 activity in the spheroids of porcine hepatocytes was demonstrated by detecting production of monoethylglycinexylidide from lidocaine. In addition, the conjugation enzyme activity was demonstrated by detecting glucuronidation and sulfation of acetaminophen. These activities were maintained for 12 days at a level twice as high as in the monolayer culture. This result shows that the porcine hepatocyte spheroids formed by using PUF can maintain the drug metabolic functions important in a hybrid artificial liver device. Consequently, culturing porcine hepatocyte spheroids using PUF seems to be promising for development of a hybrid artificial liver. This revised version was published online in August 2006 with corrections to the Cover Date.     

Antiproliferation activity of Devil's club (Oplopanax horridus) and anticancer agents on human pancreatic cancer multicellular spheroids

Devil's club (DC, Oplopanax horridus) is an important medicinal herb of the Pacific Northwest which has significant antiproliferation activity against a variety of human tumor cell lines in vitro. This study compared the antiproliferation activity of DC extract alone, and in combination with chemotherapeutic agents gemcitabine (GEM), cisplatin (CDDP), and paclitaxel (PTX) on human pancreatic cancer PANC-1 3D spheroids and 2D monolayer cells. 3D tumor spheroids were prepared with a rotary cell culture system. PANC-1 3D spheroids were significantly more resistant to killing by DC extract, GEM and PTX compared to 2D cells, with IC₅₀ levels closer to that observed in vivo. DC extract significantly enhanced the antiproliferation activity of CDDP and GEM at some concentrations. The bioactive compound identified as a polyacetylene showed strong antiproliferation activity against PANC-1 2D cells and 3D spheroids with IC₅₀ at 0.73 ± 0.04 and 3.15 ± 0.16 μM, respectively. 3D spheroids and 2D cells differentially expressed a number of apoptosis related genes. Cell cycle analysis showed that the proportion of cells in S phase was increased and in G2/M phase reduced in 3D spheroids compared to 2D cells. DC extract can potentially be used to enhance the activity of chemotherapeutic agents against pancreatic cancer cells. Use of 3D spheroid model for screening of natural products can potentially increase the efficiency in discovering in vivo bioactive compounds.     

Redox-regulation of intrinsic prion expression in multicellular prostate tumor spheroids

The cellular function of the intrinsic prion protein (PrPc) remains largely unknown. In the present study PrPc expression was investigated in multicellular prostate tumor spheroids and was correlated to the intracellular redox state as evaluated using the fluorescent dye 2'7'-dichlorodihydrofluorescein diacetate (H2DCFDA). In small tumor spheroids (diameter 100 +/- 20 microm) reactive oxygen species (ROS) levels were increased as compared with large (diameter 250 +/- 50 microm) spheroids. ROS generation was mediated by the mitochondrial respiratory chain and a NADPH oxidaselike enzyme, because carbonylcyanide-m-chlorophenylhydrazone (CCCP), rotenone, and diphenylene iodonium chloride (DPI) significantly reduced ROS levels. The elevated ROS were correlated to an increased expression of PrPc, Cu/Zn superoxide dismutase (SOD-1), and catalase in small as compared with large spheroids. In large tumor spheroids, PrPc was predominantly expressed in the peripheral cell layers and colocalized with SOD-1 and catalase. Raising intracellular ROS in large tumor spheroids by hydrogen peroxide, menadione, buthionine sulfoximine (BSO), and incubation in glutamine-reduced medium increased PrPc expression. In small spheroids PrPc was downregulated after incubation with the radical scavengers dehydroascorbate (DHA) and vitamin E. Our data indicate that PrPc expression in tumor spheroids is related to the intracellular redox state and may participate in antioxidative defense.     

The effect of combined heat and ultrasound on multicellular tumour spheroids

The effect of combined ultrasound and heat treatments on Chinese hamster multicellular spheroids of varying size was investigated using growth rate, single cell survival and ultrastructural damage as endpoints. Ultrasonic irradiation at 37 degrees C had no effect on the growth rate of 200-730 microns spheroids. Similarly there was no effect on the growth rate of 350 microns spheroids when irradiated during a 60 min exposure to 41.5 degrees C. However, spheroids of 200-700 mm diameter showed growth delay when held at 43 degrees C for 1 h. The effect was enhanced with concomitant ultrasound irradiation but was not dependent on spheroid size. When 200 and 400 microns spheroids held at 43 degrees C for 60 min were irradiated with different ultrasonic intensities a dose-dependent decrease in surviving fraction and a dose-dependent increase in growth delay was obtained. When surviving fraction was plotted as a function of growth delay a good correlation was obtained, suggesting that the combination of heat and ultrasound irradiation does not produce cytostasis in the surviving cells of either 200 or 400 microns spheroids. At the ultrastructural level increased cytoplasmic vacuolation was the only result of ultrasonic irradiation at 37 degrees C. Exposure to 43 degrees C for 60 min was required to elicit thermal damage. This took the form of membrane evagination at the spheroid surface, vacuolation of the cytoplasm, grouping of organelles around the periphery of the nucleus, and fragmentation of the nucleolus. These effects were enhanced with concomitant ultrasonic irradiation but other features were also noted, viz. disaggregation of polyribosomes, dilation of the rough endoplasmic reticulum and blebbing of the nuclear membrane. Damage was independent of spheroid size. These results are in agreement with previous data obtained from single-cell studies. Indicating that there is a non-thermal, non-cavitational component to the cell killing in multicellular spheroids resulting from combined heat and ultrasound treatment.     

Further studies on the hyperphosphorylated form (p40) of the rabies virus nominal phosphoprotein (P)

We investigated possible mechanisms involved in production of a hyperphosphorylated form (p40) of rabies virus P protein, to which two dimensional (2-D) gel electrophoresis was applied. The P gene products produced in Escherichia coli cells could be detected as a single spot of unphosphorylated 37-kDa form (termed as p37-0) in a 2-D gel. The 37-kDa proteins in the virus-infected cells are composed of some phosphorylated forms, including a major p37-1 and more phosphorylated minor forms (e.g., p37-2, p37-3, etc.), but little p37-0 is detected (Eriguchi et al., 2002). When the E. coli -produced P protein analogues were incubated with BHK-21 cell lysates, heparin-sensitive phosphorylation occurred as described previously (Takamatsu et al., 1998), giving an additional 40-kDa spot. However, such a p40-like derivative displayed a little more basic pI value than that of the authentic p40 produced in the infected cells; hence, the former was termed p40-0 (pI=4.78), while the latter, p40-1 (pI=4.73). In contrast, p40 produced in the P cDNAtransfected animal cell was detected at the p40-1 position. In addition, staurosporine did not affect the p40-1 production in virus-infected nor the P cDNA-transfected animal cells, while the agent reduced production of hyperphosphorylated forms of p37, resulting in accumulation of p37-1, but not of p37-0. These results suggest that, although p37-0 may become a substrate for the heparin-sensitive protein kinase (PK) in vitro, only p37-1 is a substrate for p40 production catalyzed by heparin-sensitive PK in animal cells, and staurosporine-sensitive PK is involved in the production of more phosphorylated forms of p37, but not in p37-1 production from p37-0.     

Influence of ionizing radiation on oxygen profiles in different types of multicellular spheroids

Human glioma (U-118 MG and U-138 MG), human colorectal adenocarcinoma (HT-29), human thyroid carcinoma (HTh 7), and hamster embryonic lung (V79-379A) spheroids were irradiated with either single doses of 16 or 40 Gy or fractionated doses of eight times 5 Gy. Oxygen profiles in the spheroids were measured with microelectrodes at different times following irradiation, and these profiles were then compared with the oxygen profiles measured in parallel cultured nonirradiated spheroids. No significant radiation-induced changes in the oxygen profiles were seen in any of the spheroids within the first few days after irradiation. The glioma spheroids did not show any significant increase in oxygen tension even after longer times; however, they were growth inhibited, and the number of S-phase cells was strongly suppressed. Increases in oxygen tension did occur in the HT-29 and V79-379A spheroids but only appeared more than a week after irradiation, when degeneration had started. Histological changes and decrease in diameter were seen in the spheroids that started to degenerate about 5 days after irradiation. Thus radiation doses in the therapeutic range did not, for the spheroids studied, produce rapid increases in the oxygen tension. When a change occurred, it appeared rather late and was probably a consequence of cell degeneration.     

A new,fast and semi-automated size determination method (SASDM) for studying multicellular tumor spheroids

Background  

Considering the width and importance of using Multicellular Tumor Spheroids (MTS) in oncology research, size determination of MTSs by an accurate and fast method is essential. In the present study an effective, fast and semi-automated method, SASDM, was developed to determinate the size of MTSs. The method was applied and tested in MTSs of three different cell-lines. Frozen section autoradiography and Hemotoxylin Eosin (H&E) staining was used for further confirmation.     

Elucidative studies on the generic concept of Senecio (Asteraceae)

VINCENT, P. L. D. & GETLIFFE, F. M., 1992. Elucidative studies on the generic concept of Senecio (Asteraceae) . This paper presents the results of studies of the generic concept of Senecio sensu stricto. The sample of taxa studied consisted of 93 Natal senecios (including seven varieties and two forms), five Cape heterochromous senecios and nine non-southern African senecios, including the type of the genus, S. vulgaris L. Also included in the study were six species from taxonomically closely related genera in the tribe Senecioneae and one Senecio of uncertain taxonomic position. The phenotype of these taxa was investigated with respect to a large number (122) of morphological and micromorphological characters. Six characters were selected as being taxonomically important with respect to elucidating the generic concept of Senecio sensu stricto. The generic concept of Senecio has been provisionally re-circumscribed and the generic status of each of the senecios and non-senecios studied has been tested according to this concept of Senecio sensu stricto sensu Vincent. In the light of this concept of Senecio , the following species are recommended for exclusion from Senecio sensu stricto sensu Vincent: S. cissampelinus, S. transvaalensis, S. syringifolius and S. hockii. The following species are considered to be peripheral to Senecio sensu stricto sensu Vincent: S. tanacetopsis, S. seminiveus, S. medley-woodii, S. tamoides, S. helminthioides, S. barbertonicus, S. brevilorus, S. viminalis, S. radicans and S.fulgens. Before any taxonomic changes are made to the current composition of Senecio , the concept of Senecio sensu stricto sensu Vincent, is being tested on a worldwide sample of the genus.     

Paradoxial changes in the expression of estrogen receptor alpha in breast cancer multicellular spheroids

Multicellular spheroids are excellent models for the analysis of cancer behavior. Just like small avascular tumors, they present a marked zonal heterogeneity which influences gene expression and thus, growth and response to chemotherapy. In the present paper, we sought to analyze the effects of three-dimensional culture in the expression and distribution of estrogen receptor alpha. Using MCF-7 breast cancer cells, we found that multicellular spheroids in estrogen-containing medium presented a paradoxical regulation of estrogen receptor alpha, with a decrease in protein expression and a marked increase in mRNA steady-state levels. Immunohistochemistry showed that only sparse cells in the periphery of the spheroid expressed estrogen receptor, in sharp contrast with progresterone receptor, which was more extensively expressed and HIF-alpha, which was expressed in the central core of the spheroid. This could mean that both hypoxia and ERA activation by estrogen participate in the expression heterogeneity of this hormone receptor in breast cancer These results are important to considerate in the analysis and interpretation of immunohistochemistry of ERA and downstream targets in samples of solid tumors.     

Use of multicellular tumor spheroids to dissect endothelial cell-tumor cell interactions: a role for T-cadherin in tumor angiogenesis

This study addresses establishment of an "in vitro" melanoma angiogenesis model using multicellular tumor spheroids (MCTS) of differentiated (HBL) or undifferentiated (NA8) melanoma cell lines. DNA microarray assay and qRT-PCR indicated upregulation of pro-angiogenic factors IL-8, VEGF, Ephrin A1 and ANGPTL4 in NA8-MCTSs (vs. monolayers) whereas these were absent in MCTS and monolayer cultures of HBL. Upon co-culture with endothelial cell line HMEC-1 NA8-MCTS attract, whereas HBL-MCTS repulse, HMEC-1. Overexpression of T-cadherin in HMEC-1 leads to their increased invasion and network formation within NA8-MCTS. Given an appropriate angiogenic tumor microenvironment, T-cadherin upregulation on endothelial cells may potentiate intratumoral angiogenesis.     

Oscillations in growth of multicellular tumour spheroids: a revisited quantitative analysis

Objectives: Multicellular tumour spheroids (MTS) provide an important tool for study of the microscopic properties of solid tumours and their responses to therapy. Thus, observation of large‐scale volume oscillations in MTS, reported several years ago by two independent groups ( 1 , 2 ), in our opinion represent a remarkable discovery, particularly if this could promote careful investigation of the possible occurrence of volume oscillations of tumours ‘in vivo’. Materials and methods: Because of high background noise, quantitative analysis of properties of observed oscillations has not been possible in previous studies. Such an analysis can be now performed, thanks to a recently proposed approach, based on formalism of phenomenological universalities (PUN). Results: Results have provided unambiguous confirmation of the existence of MTS volume oscillations, and quantitative evaluation of their properties, for two tumour cell lines. Proof is based not only on quality of fitting of the experimental datasets, but also on determination of well‐defined values of frequency and amplitude of the oscillations for each line investigated, which would not be consistent with random fluctuation. Conclusions: Biological mechanisms, which can be directly responsible for observed oscillations, are proposed, which relates also to recent work on related topics. Further investigations, both at experimental and at modelling levels, are also suggested. Finally, from a methodological point of view, results obtained represent further confirmation of applicability and usefulness of the PUN approach.     

Method for the determination of oxygen consumption rates and diffusion coefficients in multicellular spheroids

A method has been developed for the quantitative evaluation of oxygen tension (PO2) distributions in multicellular spheroids measured with O2-sensitive microelectrodes. The experimental data showed that multicellular tumor spheroids in stirred growth media were characterized by a diffusion-depleted zone surrounding the spheroids. This zone was elicited by an unstirred layer of medium next to the spheroid leading to a continuous decrease in the PO2 values from the bulk medium towards the spheroid surface. Theoretical considerations demonstrate that the volume-related O2 consumption rate, Q, in the spheroids can be assessed by measuring the PO2 gradient in the diffusion-depleted zone outside the spheroids. Accordingly, Krogh's diffusion constant, KS, in the spheroids can be determined through measuring the PO2 gradient within the spheroids. The results obtained suggest that multicellular spheroids represent useful in vitro tumor models for the experimental and theoretical analysis of the interrelationship among O2 supply to tumor cells, O2 metabolism in tumors tissue, and the responsiveness of cancer cells to treatment.     

Visualizing the effect of tumor microenvironments on radiation-induced cell kinetics in multicellular spheroids consisting of HeLa cells

In this study, we visualized the effect of tumor microenvironments on radiation-induced tumor cell kinetics. For this purpose, we utilized a multicellular spheroid model, with a diameter of ∼500 μm, consisting of HeLa cells expressing the fluorescent ubiquitination-based cell-cycle indicator (Fucci). In live spheroids, a confocal laser scanning microscope allowed us to clearly monitor cell kinetics at depths of up to 60 μm. Surprisingly, a remarkable prolongation of G2 arrest was observed in the outer region of the spheroid relative to monolayer-cultured cells. Scale, an aqueous reagent that renders tissues optically transparent, allowed visualization deeper inside spheroids. About 16 h after irradiation, a red fluorescent cell fraction, presumably a quiescent G0 cell fraction, became distinct from the outer fraction consisting of proliferating cells, most of which exhibited green fluorescence indicative of G2 arrest. Thereafter, the red cell fraction began to emit green fluorescence and remained in prolonged G2 arrest. Thus, for the first time, we visualized the prolongation of radiation-induced G2 arrest in spheroids and the differences in cell kinetics between the outer and inner fractions.     

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

PurposeTo develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools.MethodsCells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters.ResultsSimulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings.ConclusionsThe model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.     

In situ oxygen consumption rates of cells in V-79 multicellular spheroids during growth

The rate of consumption of oxygen by V-79 cells in multicellular spheroids was measured as a function of the spheroid diameter. In situ consumption was equal to that of exponentially growing cells for spheroids less than 200 micron in diameter. The rate of oxygen consumption decreased for cells in spheroids between 200 and 400 micron diameter to a value one-fourth the initial, then remained constant with further spheroid growth. Comparison of consumption rates for spheroid-derived cells before and after dissociation from the spheroid structure indicated that the spheroid microenvironment accounted for only 20% of the change in oxygen consumption rate. Cell-cell contact, cell packing, and cell volume were not critical parameters. Plateau-phase cells had a fivefold lower rate of oxygen consumption than exponential cells, and it is postulated that the spheroid quiescent cell population accounts for a large part of the intrinsic alteration in oxygen consumption of cells in spheroids. Some other mechanism must be involved in the regulation of cellular oxygen consumption in V-79 spheroids to account for the remainder of the reduction observed in this system.