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.     

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.     

Modeling of self-organized avascular tumor growth with a hybrid cellular automaton

Pattern formation in multicellular spheroids is addressed with a hybrid lattice-gas cellular automaton model. Multicellular spheroids serve as experimental model system for the study of avascular tumor growth. Typically, multicellular spheroids consist of a necrotic core surrounded by rings of quiescent and proliferating tumor cells, respectively. Furthermore, after an initial exponential growth phase further spheroid growth is significantly slowed down even if further nutrient is supplied. The cellular automaton model explicitly takes into account mitosis, apoptosis and necrosis as well as nutrient consumption and a diffusible signal that is emitted by cells becoming necrotic. All cells follow identical interaction rules. The necrotic signal induces a chemotactic migration of tumor cells towards maximal signal concentrations. Starting from a small number of tumor cells automaton simulations exhibit the self-organized formation of a layered structure consisting of a necrotic core, a ring of quiescent tumor cells and a thin outer ring of proliferating tumor cells.     

Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids

In order to determine the role of micromilieu in tumour spheroid growth, a mathematical model was developed to predict EMT6/Ro spheroid growth and microenvironment based upon numerical solution of the diffusion/reaction equation for oxygen, glucose, lactate ion, carbon dioxide, bicarbonate ion, chlorine ion and hydrogen ion along with the equation of electroneutrality. This model takes into account the effects of oxygen concentration, glucose concentration and extracellular pH on cell growth and metabolism. Since independent measurements of EMT6/Ro single cell growth and metabolic rates, spheroid diffusion constants, and spinner flask mass transfer coefficients are available, model predictions using these parameters were compared with published data on EMT6/Ro spheroid growth and micro-environment. The model predictions of reduced spheroid growth due to reduced cell growth rates and cell shedding fit experimental spheroid growth data below 700 microns, but overestimated the spheroid growth rate at larger diameters. Predicted viable rim thicknesses based on predicted near zero glucose concentrations fit published viable rim thickness data for 1000 microns spheroids grown at medium glucose concentrations of 5.5 mM or less. However, the model did not accurately predict the onset of necrosis. Moreover, the model could not predict the observed decreases in oxygen and glucose metabolism seen in spheroids with time, nor could it predict the observed growth plateau. This suggests that other unknown factors, such as inhibitors or cell-cell contact effects, must also be important in affecting spheroid growth and cellular metabolism.     

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.     

The migration of cells in multicell tumor spheroids

A mathematical model is proposed to explain the observed internalization of microspheres and 3H-thymidine labelled cells in steady-state multicellular spheroids. The model uses the conventional ideas of nutrient diffusion and consumption by the cells. In addition, a very simple model of the progress of the cells through the cell cycle is considered. Cells are divided into two classes, those proliferating (being in G1, S, G2 or M phases) and those that are quiescent (being in G0). Furthermore, the two categories are presumed to have different chemotactic responses to the nutrient gradient. The model accounts for the spatial and temporal variations in the cell categories together with mitosis, conversion between categories and cell death. Numerical solutions demonstrate that the model predicts the behavior similar to existing models but has some novel effects. It allows for spheroids to approach a steady-state size in a non-monotonic manner, it predicts self-sorting of the cell classes to produce a thin layer of rapidly proliferating cells near the outer surface and significant numbers of cells within the spheroid stalled in a proliferating state. The model predicts that overall tumor growth is not only determined by proliferation rates but also by the ability of cells to convert readily between the classes. Moreover, the steady-state structure of the spheroid indicates that if the outer layers are removed then the tumor grows quickly by recruiting cells stalled in a proliferating state. Questions are raised about the chemotactic response of cells in differing phases and to the dependency of cell cycle rates to nutrient levels.     

Multicell spheroids as a model for cell kinetic studies

Cells growing in tissue culture as three-dimensional, multicellular aggregates called 'spheroids' typically show a decreasing growth fraction and development of quiescent subpopulations as the spheroids enlarge. Kinetic studies in a number of spheroid systems have indicated that the primary reason for the tumour-like growth is a progressive decrease in growth fraction, with only a modest elongation of cell cycle time in larger spheroids. In this paper, the cellular growth kinetics for spheroids of V79 Chinese hamster lung cells are reviewed, and the regrowth kinetics of cells resuming growth after recovery from quiescent regions of the spheroids are described. Further, the role of regrowth/repopulation in determining the spheroid response to anti-tumour cytotoxics is explored, with particular emphasis on treatment with cisplatin and etoposide. By separating the effects of cytotoxicity and regrowth in the overall spheroid response to anti-neoplastic drugs, it is suggested that 'drug resistance' in tumours can be a kinetic as well as a genetic problem.     

Invited review Multicell spheroids as a model for cell kinetic studies

Abstract. Cells growing in tissue culture as three-dimensional, multicellular aggregates called 'spheroids' typically show a decreasing growth fraction and development of quiescent subpopulations as the spheroids enlarge. Kinetic studies in a number of spheroid systems have indicated that the primary reason for the tumour-like growth is a progressive decrease in growth fraction, with only a modest elongation of cell cycle time in larger spheroids. In this paper, the cellular growth kinetics for spheroids of V79 Chinese hamster lung cells are reviewed, and the regrowth kinetics of cells resuming growth after recovery from quiescent regions of the spheroids are described. Further, the role of regrowth/repopulation in determining the spheroid response to anti-tumour cytotoxics is explored, with particular emphasis on treatment with cisplatin and etoposide. By separating the effects of cytotoxicity and regrowth in the overall spheroid response to anti-neoplastic drugs, it is suggested that 'drug resistance' in tumours can be a kinetic as well as a genetic problem.     

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.     

Decreased mitochondrial function in quiescent cells isolated from multicellular tumor spheroids

Cells in the inner region of multicellular spheroids markedly reduce their oxygen consumption rate, presumably in response to their stressful microenvironment. To determine the mechanism behind this metabolic adaptation, we have investigated relative mitochondrial mass and mitochondrial function in cells isolated from different regions of tumor spheroids by using a combination of mitochondrial-specific fluorescent stains and flow cytometric analysis. Uptake of rhodamine 123 (R123) is driven by the mitochondrial membrane potential and thus reflects mitochondrial activity. Uptake of 10-nonyl-acridine orange (NAO) reflects total mitochondrial mass independently of activity because this compound binds to cardiolipin in the inner mitochondrial membrane. NAO fluorescence per unit cell volume only decreased 10–20% for cells from the inner spheroid region compared with those near the surface. There was greater than a twofold reduction in R123 fluorescence in the inner region cells, however. Thus, tumor cells in spheroids alter their rate of respiration predominately by downregulating mitochondrial function as opposed to degradation of mitochondria. There was a correlation between R123 staining per unit cell volume and the growth fraction of the cells from spheroids, but not for monolayer cultures. We also show a linear correlation between R123 staining and the rate of oxygen consumption for both monolayer- and spheroid-derived cells. After separating the inner region cells from the spheroid and replating them in monolayer culture, the R123 uptake recovered to normal levels prior to entry of the cells into S-phase. This reduction in mitochondrial function in quiescent cells from spheroids can explain the long period required for these cells to re-enter the cell cycle and may have important implications for the regulation of tumor cell oxygenation in vivo. J. Cell. Physiol. 176:138–149, 1998. Published 1998 Wiley-Liss, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Novel fluid shear‐based dissociation device for improved single cell dissociation of spheroids and cell aggregates

Biological industries commonly rely on bioreactor systems for the large‐scale production of cells. Cell aggregation, clumping, and spheroid morphology of certain suspension cells make their large‐scale culture challenging. Growing stem cells as spheroids is indispensable to retain their stemness, but large spheroids (>500 µm diameter) suffer from poor oxygen and nutrient diffusion, ultimately resulting in premature cell death in the centers of the spheroids. Despite this, most large‐scale bioprocesses do not have an efficient method for dissociating cells into single cells, but rely on costly enzymatic dissociation techniques. Therefore, we tested a proof‐of‐concept fluid shear‐based mechanical dissociator that was designed to dissociate stem cell spheroids and aggregates. Our prototype was able to dissociate cells while retaining high viability and low levels of apoptosis. The dissociator also did not impact long‐term cell growth or spheroid formation. Thus, the dissociator introduced here has the potential to replace traditional dissociation methods. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 34:293–298, 2018     

Dynamics of cell kinetic parameters during 9L spheroid growth

Cell population kinetics were followed in 9L tumour spheroids as they grew from aggregates of about 80 micron in diameter to over 800 micron. The kinetic parameters measured were cell cycle time, spheroid-doubling time, and growth fraction; from these the cell loss factor phi was calculated. The rate of cell shedding from the surface was also measured, so that the contribution of shedding to the overall cell loss could be evaluated. The major findings include significant elongation of the cell cycle, a low rate of cell death in spheroids below 500 micron in diameter, and a relatively high GF in large spheroids. The results also indicated that 9L spheroid kinetic parameters may be strongly influenced by the culture methodology.     

Regrowth kinetics of cells from different regions of multicellular spheroids of four cell lines

A basic understanding of the recruitment of quiescent tumor cells into the cell cycle would be an important contribution to tumor biology and therapy. As a first step in pursuing this goal, we have investigated the regrowth kinetics of cells from different regions in multicellular spheroids of rodent and human origin. Cells were isolated from four different depths within the spheroids using a selective dissociation technique. The outer cells were proliferating and resumed growth after replating with a 0-8-hour lag period, similar to cells from exponentially growing monolayers. With increasing depth of origin, the lag periods prior to regrowth increased to 2-3 times the monolayer doubling time; cells from plateau-phase monolayers showed a lag period of 1-1.5 times the doubling period. After resuming growth, all cells of a given cell line grew with the same doubling time and achieved the same confluency level. The inner spheroid cells and cells from plateau-phase monolayers had reduced clonogenic efficiencies. The inner cells were initially 1.5-3 times smaller than the outer cells, but began to increase in volume within 4 hours of replating. The fractions of S-phase cells were greatly decreased with increasing depth of origin in the spheroids; there were long delays prior to S-phase recovery after plating, to a maximum of 1-1.5 times the normal doubling time. These results suggest that those quiescent cells from spheroids and monolayers which are able to reenter the cell cycle are predominantly in the G1-phase. However, quiescent cells from the innermost spheroid region require approximately twice as long to enter normal cell cycle traverse as cells from plateau-phase monolayers. The selective dissociation method can isolate very pure populations of proliferating and quiescent cells in a rapid and nonperturbing manner; this system will be valuable in further characterizing quiescent cells from spheroids.     

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.     

Automated selective dissociation of cells from different regions of multicellular spheroids

Summary In this report we describe a new apparatus which has been developed for the automated selective dissociation of multicellular spheroids into fractions of viable cells from different locations in the spheroid. This device is based on the exposure of spheroids to a 0.25% solution of trypsin under carefully controlled conditions, such that the cells are released from the outer spheroid surface in successive layers. Study of the spheroid size, number of cells per spheroid, and sections through the spheroid with increasing exposure to trypsin demonstrate the effectiveness of this technique. The technique has been successfully used on spheroids from five different cell lines over a wide range of spheroid diameters. We also present data detailing the effect of varying the dissociation temperature, the mixing speed, the trypsin concentration, and the number of spheroids being dissociated. The new apparatus has several advantages over previous selective dissociation methods and other techniques for isolating cells from different regions in spheroids, including: a) precise control over dissociation conditions, improving reproducibility; b) short time to recover cell fractions; c) ability to isolate large numbers of cells from many different spheroid locations; d) use of common, inexpensive laboratory equipment; and e) easy adaptability to new cell lines or various spheroid sizes. Applications of this method are demonstrated, including the measurement of nutrient consumption rates, regrowth kinetics, and radiation survivals of cells from different spheroid regions. This work was supported by grants CA-36535, CA-22585, and RR-02845 from the National Institutes of Health, Bethesda, MD, the National Flow Cytometry Resource (NIH grant RR-01315), and by the Department of Energy, Washington, DC.     

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.     

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.     

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.