Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH.

Tumors and multicellular tumor spheroids can develop gradients in oxygen concentration, glucose concentration, and extracellular pH as they grow. In order to calculate these gradients and assess their impact on tumor growth, it is necessary to quantify the effect of these variables on tumor cell metabolism and growth. In this work, the oxygen consumption rates, glucose consumption rates, and growth rates of EMT6/Ro mouse mammary tumor cells were measured at a variety of oxygen concentrations, glucose concentrations, and extracellular pH levels. At an extracellular pH of 7.25, the oxygen consumption rate of EMT6/Ro cells increased by nearly a factor of 2 as the glucose concentration was decreased from 5.5 mM to 0.4 mM. This effect of glucose concentration on oxygen consumption rate, however, was slight at an extracellular pH of 6.95 and disappeared completely at an extracellular pH of 6.60. The glucose consumption rate of EMT6/Ro cells increased by roughly 40% when the oxygen concentration was reduced from 0.21 mM to 0.023 mM and decreased by roughly 60% when the extracellular pH was decreased from 7.25 to 6.95. The growth rate of EMT6/Ro cells decreased with decreasing oxygen concentration and extracellular pH; however, severe conditions were required to stop cell growth (0.0082 mM oxygen and an extracellular pH of 6.60). Empirical correlations were developed from these data to express EMT6/Ro cell growth rates, oxygen consumption rates, and glucose consumption rates, as functions of oxygen concentration, glucose concentration, and extracellular pH. These empirical correlations make it possible to mathematically model the gradients in oxygen concentration, glucose concentration, and extracellular pH in EMT6/Ro multicellular spheroids by solution of the diffusion/reaction equations. Computations such as these, along with oxygen and pH microelectrode measurements in EMT6/Ro multicellular spheroids, indicated that nutrient concentration and pH levels in the inner regions of spheroids were low enough to cause significant changes in nutrient consumption rates and cell growth rates. However, pH and oxygen concentrations measured or calculated in EMT6/Ro spheroids where quiescent cells have been observed were not low enough to cause the cessation of cell growth, indicating that the observed quiescence must have been due to factors other than acidic pH, oxygen depletion, or glucose depletion.     

A reduction in the in situ rates of oxygen and glucose consumption of cells in EMT6/Ro spheroids during growth

The rates of consumption of oxygen and glucose by EMT6/Ro cells in multicellular spheroids were measured at various times during normal growth. In situ spheroid cellular consumption rates were similar to those of exponentially growing single cells up to a spheroid diameter of 150 micron. Further growth resulted in decreases in the rates of both oxygen and glucose consumption which were correlated with the increase in spheroid diameter and cell number. At a diameter of 1300 micron, both rates of cellular consumption had decreased by a factor of 2.5. The rates of consumption per unit of nonnecrotic spheroid volume decreased in a similar manner. Measurements with single cells demonstrated that the rate of oxygen consumption was coupled with glucose concentration, and vice versa. The rates of consumption for cells dissociated from small spheroids indicated that there was some effect of the spheroid environment. As the spheroids grew, however, association in the spheroid structure accounted for a smaller proportion of the total observed reduction in the rates of nutrient consumption. The presence of central necrosis also appeared to have no effect on the rates of consumption of these nutrients. Spheroid-derived cells showed a decrease in cell volume with growth as the cells accumulated in a quiescent state. Measurements with single cells demonstrated that oxygen and glucose consumption were correlated with cell volume and with the development of nonproliferating cells. We conclude that the observed decrease in oxygen and glucose consumption with growth in spheroids is largely due to the progressive accumulation of cells in a quiescent state characterized by an inherently lower cellular rate of nutrient utilization.     

Necrotic core in EMT6/Ro tumour spheroids: Is it caused by an ATP deficit?

Although commonly related to nutrient deprivation, the cause of the formation of the necrotic core in the multicellular tumour spheroids is still a controversial issue. We propose a simple model for the cell ATP production that assumes glucose and lactate as the only fuel substrates, and describes the main reactions occurring in the glycolytic and the oxidative pathways. Under the key assumption that cell death occurs when ATP production falls to a critical level, we formulate a multiscale model that integrates the energy metabolism at the cellular level with the diffusive transport of the metabolites in the spheroid mass. The model has been tested by predicting the measurements of the necrotic radius obtained by Freyer and Sutherland (1986a) in EMT6/Ro spheroids under different concentrations of glucose and oxygen in the culture medium. The results appear to be in agreement with the hypothesis that necrosis is caused by ATP deficit.     

ATP concentrations in multicellular tumor spheroids assessed by single photon imaging and quantitative bioluminescence

To evaluate the interrelationship among the cellular energy status and the development of necrosis in tumor microregions, local ATP concentrations and the extent of necrosis were determined in multicellular tumor spheroids, i.e., in spherical tumor cell aggregates. The spheroids were grown in rotated suspension cultures using EMT6 cells that were derived from a murine mammary sarcoma. The distribution of viable and necrotic cell areas was assessed by histological investigations. The regional distribution of ATP concentrations was measured with a novel technique using quantitative bioluminescence and single photon imaging. This method makes it possible to determine ATP concentrations in absolute terms with a spatial resolution at the level of a single cell. The results show that ATP concentrations in the center of EMT6 spheroids decrease from values of 1.0 to 1.5 mM in small spheroids with 300 microns in diameter to values close to or at the background level in 750 microns spheroids. Necrosis was detectable in spheroids larger than 300 microns, and virtually no spheroid without necrosis was found at sizes larger than 600 microns. Since the emergence of central necrosis precedes the drop in ATP to undetectably low values, the data suggest that energy metabolism is not or not directly involved in the development of necrosis in tumor spheroids under the growth conditions investigated.     

Proliferation-associated oxygen consumption and morphology of tumor cells in monolayer and spheroid culture.

The oxygen consumption rate, proliferative activity, and morphology of EMT6/Ro mouse mammary sarcoma cells in monolayer and multicellular spheroid culture have been investigated in a comparative study. During the transition of monolayer cells from the exponential into the plateau growth phase, there is a distinct decrease in the cellular volume that is associated with a corresponding decrease in the proliferative and respiratory activity of the cells. The decline in cell volume is mainly due to a decrease in the content of cytoplasm, whereas the size of the nucleus is only slightly reduced. A concomitant decrease in the number of mitochondria per cell obviously accounts for the reduction in cellular oxygen uptake. Despite a continuous decrease of cell proliferation from the surface to interior regions of EMT6 spheroids reflected by a gradient in tritiated thymidine labeling, volume-related oxygen consumption is rather uniform in viable regions of these aggregates. The finding can be explained by the results of the morphometric evaluation showing a uniform volume density of mitochondria, i.e., of oxygen-consuming sites within these spheroids.     

Parameter estimation and determinability analysis applied to Drosophila gap gene circuits

Background

Our objective was to discover in silico axioms that are plausible representations of the operating principles realized during characteristic growth of EMT6/Ro mouse mammary tumor spheroids in culture. To reach that objective we engineered and iteratively falsified an agent-based analogue of EMT6 spheroid growth. EMT6 spheroids display consistent and predictable growth characteristics, implying that individual cell behaviors are tightly controlled and regulated. An approach to understanding how individual cell behaviors contribute to system behaviors is to discover a set of principles that enable abstract agents to exhibit closely analogous behaviors using only information available in an agent's immediate environment. We listed key attributes of EMT6 spheroid growth, which became our behavioral targets. Included were the development of a necrotic core surrounded by quiescent and proliferating cells, and growth data at two distinct levels of nutrient.

Results

We then created an analogue made up of quasi-autonomous software agents and an abstract environment in which they could operate. The system was designed so that upon execution it could mimic EMT6 cells forming spheroids in culture. Each agent used an identical set of axiomatic operating principles. In sequence, we used the list of targeted attributes to falsify and revise these axioms, until the analogue exhibited behaviors and attributes that were within prespecified ranges of those targeted, thereby achieving a level of validation.

Conclusion

The finalized analogue required nine axioms. We posit that the validated analogue's operating principles are reasonable representations of those utilized by EMT6/Ro cells during tumor spheroid development.     

Increased thermoresistance developed during growth of small multicellular spheroids

Mammalian cells growing as multicell spheroids, an in vitro model of tumor microregions, have been shown previously to be more resistant than single cells from monolayer cultures to killing by ionizing radiation, hyperthermia, ultrasound, and chemotherapeutic drugs. Although the mechanisms by which cells in spheroids acquire these increased resistances are unknown, available evidence has indicated that intercellular contact mediates the process for ionizing radiation. This investigation was undertaken to evaluate the role of intercellular contact produced during growth of small spheroids on the sensitivity of EMT6/Ro mouse mammary tumor cells to moderate hyperthermia. Increased thermoresistance developed in small spheroids (approximately 70 micron diameter, 25 cells/spheroid), as measured by colony formation, after exposures to different temperatures in the range of 37 to 45 degrees C for periods less than or equal to 2 hr and at 42.5 degrees C for less than or equal to 8 hr. Experiments were performed to determine the relative contributions to this increased thermoresistance of 1) the extent of intercellular contact in spheroids of different cellular multiplicities, 2) differences in membrane damage influenced by trypsin heat treatment sequence, and 3) physiological changes associated with growth of cells as spheroids in suspension compared to monolayer culture. Treatment with trypsin prior to heating sensitized cells to killing by hyperthermia but did not account for the differential thermoresistance between cells from spheroids and monolayers. Spheroid multiplicity in the range of 1.16 to 76.2 cells/spheroid had no significant effect on cell survival after hyperthermia. However, cells grown in spinner suspension culture were more thermoresistant than cells from monolayer cultures and nearly as thermoresistant as cells in spheroids. From these data we conclude that the greater thermoresistance of EMT/Ro cells in spheroids is the result of cellular physiological changes associated with growth in suspension and is not mediated by intercellular contact.     

Two-Dimensional Diffusion Limited System For Cell Growth

Abstract. A new cell system, designed to supplement multicellular spheroids as tumour analogues, was analysed theoretically and experimentally. This 'sandwich' system is a single layer of cells, subject to self-created gradients of nutrients and metabolic products. Due to these gradients the sandwich system develops a border of viable cells and an inner region of necrotic cells corresponding to the viable rim and the necrotic center of a spheroid. However, sandwiches differ from spheroids in several ways. All the cells in the sandwich can be microscopically viewed during the entire experiment. In sandwiches there is no three-dimensional cell to cell contact. Also, the gradients are less steep in our sandwich system, so the width of the viable region in a sandwich is about 10 times as large as the width of the viable rim in a spheroid. Indeed, in sandwiches the experimenter has some control over the steepness of the gradients and thus can vary the width of this viable border. We used DNA labelling studies and flow cytometry along with visual observation to analyse the system. Our experiments show that the observed cell necrosis, similar to that found in spheroids, is due to diffusion limitations. the results are consistent with the idea that oxygen deprivation stops cell cycling and, when extreme and prolonged, leads to necrosis. the possibility that substances other than oxygen are involved is not excluded by the data. the data also suggests that in the final, near-equilibrium state the average overall oxygen consumption rate for the viable sandwich population may be about one-quarter of that for an exponentially growing population of the same cell line.     

Migration and internalization of cells and polystyrene microspheres in tumor cell spheroids

The movement and internalization of ³H-labelled cells and of inert polystyrene microspheres within multicellular spheroids has been examined through histological sectioning and autoradiography. EMT6 and RIF-1 spheroids were cultured in spinner flasks for approx. 2.5 weeks. At this time, ³H-labelled cells and/or microspheres were allowed to adhere to the spheroid surface. Microspheres, ³H-labelled RIF-1 monolayer cells and ³H-labelled EMT6 monolayer cells were observed to move centripetally as a wave into EMT6 spheroids. In contrast, ³H-labelled trypsinized RIF-1 and EMT6 spheroid cells became mixed with the other non-labelled spheroid cells in homotypic RIF-1 and EMT6 spheroids, respectively. Reduction of spheroid growth by maintaining the spheroids at room temperature and by treatment with 2500 rads irradiation did not prohibit the internalization of ³H-labelled EMT6 cells and microspheres in EMT6 spheroids.     

Shedding of mitotic cells from the surface of multicell spheroids during growth

During the growth of EMT6/Ro mammary tumor multicell spheroids, a large number of cells are shed into the suspension medium. The rate of cell shedding was 218 cells per square millimeter of spheroid surface per hour, or up to 1.5% of the total spheroid cell content per hour. Shed cells had a clonogenic capacity equal to that of exonential monolayer cultures and were further characterized by volume distribution, mitotic index, flow cytoflurometry, and autoradiography. The results indicated that cells are released from the spheroid surface at mitosis, presumably due to a loosening of the cell-to-cell attachment during this cycle phase. These mitotic cells, when placed in monolayer culture, attached and grew synchronously with a cell cycle time of about 13 hours. Shed cells kept in suspension culture had a similar cell cycle time, but these cells reaggregated immediately after mitosis. The results indicated that cell shedding and reaggregation both occur near the time of mitosis and are intrinsic factors regulating the initiation and subsequent growth of multicell spheroids. Although these studies were done with spheroids cultured in vitro, shedding of mitotic cells may play an important role in the in vivo process of metastasis.     

Hypoxic fraction and binding of misonidazole in EMT6/Ed multicellular tumor spheroids

Misonidazole has been shown to bind selectively to hypoxic cells in tissue culture and to cells which are presumed to be chronically hypoxic in EMT6 spheroids and tumors. Thus it has considerable potential as a marker of hypoxic cells in vivo. To further evaluate this potential EMT6/Ed spheroids were used to quantitate misonidazole binding under conditions which resulted in hypoxic fractions between 0 and 1. Hypoxic fractions were quantitated using radiation survival curves. A doubling of the oxygen in the gas phase to 40% was required to fully oxygenate all chronically hypoxic cells. The patterns of binding of 14C-labeled misonidazole determined by autoradiography were consistent with the regions of radiobiological hypoxia as predicted by oxygen diffusion theory. The overall uptake of 3H-labeled misonidazole by spheroids correlated well with the hypoxic fraction, although binding to aerobic cells and necrotic tissue contributed appreciably to the total label in the spheroids. It is concluded that misonidazole is an excellent marker of hypoxia in EMT6/Ed spheroids at the microscopic level, and the total amount bound per spheroid provides a potentially useful measure of the hypoxic fraction.     

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.     

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.     

The radiation response of hypoxic cells in EMT6 spheroids in suspension culture does model data from EMT6 tumors

Radiation survival curves of EMT6/Ed spheroids have been obtained under conditions which eliminate changes in oxygen concentration between growth and irradiation. These curves show a high-dose, resistant component which is nearly parallel to the curves obtained when spheroids were irradiated under nitrogen. Thus EMT6 spheroids appear to model accurately the radiation responses of EMT6 tumors. In contrast, when spheroids were grown to relatively high density (300-400 spheroids per 250-ml spinner flask), then separated into several flasks for irradiation, an increase in oxygen concentration in the medium occurred which fully oxygenated the previously hypoxic cells. The two causes for the oxygen depletion in sealed growth flasks were quantitated. Depletion of total oxygen in the flask occurred, and, more importantly, oxygen consumption kept the growth medium well below equilibrium with the oxygen in the gas phase. Smaller but similar effects on oxygen concentration were found in flasks containing V79 spheroids.     

Effect of cytochalasin B, nocodazole and irradiation on migration and internalization of cells and microspheres in tumor cell spheroids

The effect of cytochalasin B (CB), nocodazole, and irradiation on the adherence and internalization of 3H-labeled EMT6 spheroid-derived single cells and inert microspheres in unlabeled, intact EMT6 multicellular spheroids has been examined. CB inhibited adhesion and internal migration, whereas nocodazole did not stop adhesion but did prevent later internalization. Treatment of labeled cells with 5, 15 and 25 Gy 250 kV X-rays before adherence did not effect their adherence or later internalization. The same radiation treatments administered to the spheroids either immediately before or after the introduction of unirradiated single cells did not affect adherence, but the depths reached by labeled cells and microspheres were reduced largely because of the consequent reduction in spheroid growth. Microsphere size (9, 15, or 25 microns) and surface charge (negative, or non-ionic) had minimal, if any, effect on the adherence and internalization of these particles.     

Cytophotometric measurement of the cellular DNA content of [3H]thymidine-labelled spheroids. Demonstration that some non-labelled cells have S and G2 DNA content

Spheroids from the V279-171b and MCa-11 cell lines were incubated continuously for 24 hr in [3H]thymidine for labelling of the outer cells of the viable rim. The spheroids were dispersed into single cells, and the DNA content of photomapped cells was measured by absorption cytophotometry. Autoradiographs were then prepared from which we ascertained cellular labelling. For spheroids of both cell lines, we found a larger proportion of cells with a G0/G1 DNA content among the non-labelled inner spheroid cells than among the labelled outer cells (P less than 0.001). This block of non-labelled spheroid cells in G0/G1 was not a cell cycle perturbation caused by the isotope for the MCa-11 spheroids. Approximately 8% of non labelled MCa-11 spheroid cells had S/G2 DNA content, suggesting that non-cycling cells in spheroids may be blocked in S and G2 as well as in the G0/G1 phase of the cell cycle.     

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.     

Formulation and numerical simulations of a continuum model of avascular tumor growth

In this paper we present a continuum mathematical model for a multicellular spheroid that mimics the micro-environment within avascular tumor growth. The model consists of a coupled system of non-linear convection-diffusion-reaction equations. This system is solved using a previously developed conservative Galerkin characteristics method. In the model considered, there are three cell types: the proliferative cells, the quiescent non-dividing cells which stay in the G₀ phase of the cell cycle and the necrotic cells. The model includes viable cell diffusion, diffusion of cellular material and the removal of necrotic cells. We assume that the nutrients diffuse passively and are consumed by the proliferative and quiescent tumor cells depending on the availability of resources (oxygen, glucose, etc.). The numerical simulations are performed using different sets of parameters, including biologically realistic ones, to explore the effects of each of these model parameters on reaching the steady state. The present results, taken together with those reported earlier, indicate that the removal of necrotic cells and the diffusion of cellular material have significant effects on the steady state, reflecting growth saturation, the number of viable cells, and the spheroid size.     

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.