Multicell Spheroid Research Articles

A computational modeling approach for predicting multicell spheroid patterns based on signaling-induced differential adhesion.

Physiological and pathological processes including embryogenesis and tumorigenesis rely on the ability of individual cells to work collectively to form multicell patterns. In these heterogeneous multicell systems, cell-cell signaling induces differential adhesion between cells that leads to tissue-level patterning. However, the sensitivity of pattern formation to changes in the strengths of signaling or cell adhesion processes is not well understood. Prior work has explored these issues using synthetically engineered heterogeneous multicell spheroid systems, in which cell subpopulations engage in bidirectional intercellular signaling to regulate the expression of different cadherins. While engineered cell systems provide excellent experimental tools to observe pattern formation in cell populations, computational models of these systems may be leveraged to explore more systematically how specific combinations of signaling and adhesion parameters can drive the emergence of unique patterns. We developed and validated two- and three-dimensional agent-based models (ABMs) of spheroid patterning for previously described cells engineered with a bidirectional signaling circuit that regulates N- and P-cadherin expression. Systematic exploration of model predictions, some of which were experimentally validated, revealed how cell seeding parameters, the order of signaling events, probabilities of induced cadherin expression, and homotypic adhesion strengths affect pattern formation. Unsupervised clustering was also used to map combinations of signaling and adhesion parameters to these unique spheroid patterns predicted by the ABM. Finally, we demonstrated how the model may be deployed to design new synthetic cell signaling circuits based on a desired final multicell pattern.

Cell Kinetics and Repopulation During Multifraction Irradiation of Spheroids: Implications for Clinical Radiotherapy.

T here seems to be little question that development of a predictive assay that could reliably forecast the response of individual tumors to treatment would be of tremendous value to practicing oncologists. However, exactly what type of information is needed in such an assay is less certain. For example, is the determinant of success the inherent sensitivity of the majority, or that of a minority of the tumor cells? Because treatment "failure" is typically recognized by the regrowth or continued growth of the tumor mass, what is the role of cell kinetics in that process? Perhaps of most pressing importance, can predictive assays lead to alternate, hopefully superior, forms of treatment? While measuring tumor cell sensitivity to both radiation and drugs has become fashionable in recent years, correlations between in vitro sensitivity analyses and eventual patient outcome have generally been found only between tumor types, but not between individual tumors of a certain type. This suggests that factors in addition to inherent sensitivity must be considered. Analyzing patterns of failure can often be useful in this regard; in a provocative article analyzing outcomes for patients with head and neck cancer, Withers et al I reached the rather alarming conclusion that treatments lasting more than 4 weeks required a dose escalation of 0.6 Gy/extension day to retain the same probability of cure. More general reviews 2-4 similarly argue for a dose increase of 0.3 to 0.7 Gy/day of treatment for treatment extensions beyond 4 weeks. These results strongly' implicate time as a critical factor for successful treatments. However, identifying a clinical problem is considerably easier than resoMng it. For example, does the repopulation seen at later times during therapy indicate that cells are cycling more rapidly, that more cells are in cycle, that fewer clonogenic cells are "lost," or combinations of the above? When does repopulation actually"accelerate"? Perhaps of greater immediate importance, can reliable and unambiguous methods of measurement be developed for tumor cell kinetics, and when should they be used? Alternatively, can repopulation rate or potential be predicted? Clearly', several philosophical and practical limitations combine to inhibit addressing these questions in the most relevant system, the human cancer patient. At least one tumor model system is available, however, in which many relevant and highly detailed studies can be pursued: the multicell spheroid model. 5,6 It is of particular note that the spheroid system can be easily maintained in long-term culture, allowing large numbers of virtually identical "tumors" to be propagated and reproducibly tested, without host factors complicating the response. 7,8 Every cell of the system potentially contributes to the net response, and of particular importance, each cell can be recovered and assessed. The intent of this article is to examine the role of cell kinetics when spheroids are treated with multifraction protocols. In addition to multifraction radiation treatments, multiple drug exposures will be briefly explored. From the design of these studies, we have been able to address not only the role of pretreatment cell kinetics, but also factors controlling changes of those kinetic properties during, and in response to, the therapeutic manipulations.

Stresses in growing soft tissues

Biochemical processes of tissue growth lead to production of new proteins, cells, and other material particles at the microscopic level. At the macroscopic level, growth is marked by the change of the tissue shape and mass. In addition, the appearance of the new material particles is generally accompanied by deformation and, consequently, stresses in the surrounding material. Built upon a microscopic toy-tissue model mimicking the mechanical processes of mass supply, a simple phenomenological theory of tissue growth is used in the present work for explaining residual stresses in arteries and studying stresses around growing solid tumors/multicell spheroids. It is shown, in particular, that the uniform volumetric growth can lead to accumulation of residual stresses in arteries because of the material anisotropy. This can be a complementary source of residual stresses in arteries as compared to the stresses induced by non-uniform tissue growth. It is argued that the quantitative assessment of the residual stresses based on in vitro experiments may not be reliable because of the essential stress redistribution in the tissue samples under the cutting process. Concerning the problem of tumor growth, it is shown that the multicell spheroid or tumor evolution depends on elastic properties of surrounding tissues. In good qualitative agreement with the experimental in vitro observations on growing multicell spheroids, numerical simulations confirm that stiff hosting tissues can inhibit tumor growth.

A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues II: Solutions to the Biphasic Equations for a Multicell Spheroid

This is the second paper in the series A Mixture Theory for the Genesis of Residual Stresses in Growing Tissues. While the first paper in the series elaborated a general formulation for such a theory, the present paper develops a simple biphasic model of residual stress evolution in a growing multicell spheroid comprising a linear-elastic cellular phase and an inviscid interstitial fluid. Both isotropic and anisotropic growth are considered in this study, highlighting the necessity to incorporate stress relaxation in order to predict an evolution of stresses over a period of growth. The solutions to the biphasic equations are juxtaposed with the corresponding solutions to the single phase equations, illuminating the approximate nature of the single phase formulation for growing tissues. Moreover, the analysis demonstrates the significance of both interphase drag and the stress-relaxation characteristics of the solid phase in distinguishing between the single phase and multiphase paradigms.

The role of stress in the growth of a multicell spheroid.

Rather recent experimental results demonstrate the non-negligible role of mechanical stress in the growth of a multicell spheroid. In this paper we discuss a theoretical framework for volumetric growth suitable for modeling the growth of soft tissues exhibiting the properties of a solid. After a proper kinematic decomposition, balance equations for mass, momentum and energy are discussed together with constitutive relationships. The mathematical model is then applied to avascular tumor growth. We show by numerical simulation that, under assumption of spherical symmetry, the mathematical model is able to reproduce the experimental data with a satisfying qualitative agreement.

Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures

In this paper we adapt an avascular tumour growth model to compare the effects of drug application on multicell spheroids and on monolayer cultures. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death generates volume changes described by a velocity field. The drug is modelled as an externally applied, diffusible material capable of killing cells, both linear and Michaelis–Menten kinetics for drug action on cells being studied. Numerical solutions of the resulting system of partial differential equations for the multicell spheroid case are compared with closed form solutions of the monolayer case, particularly with respect to the effects on the cell kill of the drug dosage and of the duration of its application. The results show an enhanced survival rate in multicell spheroids compared to monolayer cultures, consistent with experimental observations, and indicate that the key factor determining this is drug penetration. An analysis of the large time tumour spheroid response to a continuously applied drug at fixed concentration reveals up to three stable large time solutions, namely the trivial solution (i.e. a dead tumour), a travelling wave (continuously growing tumour) and a sublinear growth case in which cells reach a pseudo-steady-state in the core. Each of these possibilities is formulated and studied, with the bifurcations between them being discussed. Numerical solutions reveal that the pseudo-steady-state solutions persist to a significantly higher drug dose than travelling wave solutions.

On the mechanics of a growing tumor

In this paper we study tumor growth within the framework of Continuum Mechanics, considering a tumor as a specific case of a growing soft tissue. Using the notion of multiple natural configurations we introduce a mechanical description that splits volumetric growth and mechanical response into two separate contributions. Growth is described as an increase of the mass of the particles of the body and not as an increase of their number. As tumor growth strongly depends upon the availability of nutrients and on the presence of chemical signals, such as growth factors, their diffusion through the growing material is introduced in the description. The model is then applied to describe the homogeneous growth inside a rigid cylinder, a model mimicking the growth of a ductal carcinoma, and to the growth of a multicell spheroid fed by a non-homogeneous diffusion of nutrients. In the latter case residual stresses are generated because the non-uniform distribution of nutrients leads to inhomogeneous growth.

Modelling the Internalization of Labelled Cells in Tumour Spheroids

In this paper a mathematical model is developed to describe the migration of labelled particles within a multicell spheroid. In the model, spatial variations in cell proliferation and death create an internal velocity field which leads to redistribution of the labelled and unlabelled cells. By applying a range of numerical and analytical techniques to the model equations, it is possible to show that, whilst the speed with which the labelled cells migrate through the tumour is independent of the type of cells that are labelled, their limiting distribution depends crucially on whether inert polystyrene microspheres or live tumour cells are labelled. These predictions are shown to be in good qualitative agreement with independent experimental results.

Effects of vascularization on lymphocyte/tumor cell dynamics: Qualitative features

By adapting a pre-existing model to include the effects of Vascularization within a tumor or multicell spheroid, a predator-prey system describing the cell populations of a solid tumor and reactive lymphocytes is formulated. The paper serves as a review of the minimal deterministic approach to tumor-host immune system interactions while examining, in a qualitative manner, the modifications to the dynamics induced by a simple representation of the vascularized tumor. In addition, the possibility of limit-cycle behavior is studied by regarding each of six parameters present in the model as a bifurcation parameter. Thus, in principle, well-defined and periodic oscillations in both lymphocyte and tumor cell populations may occur under appropriate circumstances; whether or not such oscillations are sustainable by the host, and their stability, amplitude and period depend on aquisition of more quantitative information concerning the relevant parameter ranges.

Nonlinear diffusion of a growth inhibitory factor in multicell spheroids

A mathematical model is presented for the production of a growth inhibitory factor (GIF) within a multicell spheroid. The model is based on the assumption that the GIF diffuses within the spheroid in a nonlinear spatially dependent manner. This is in contrast with previous models, in which the nonlinearity was assumed in the production team. The results of the new model are compared with those of previous models and with experimental data.

β-Galactosidase Activity in Transfected Ltk- Cells is Differentially Regulated in Monolayer and in Spheroid Cultures

We have investigated whether three-dimensional cultivation of cells to multicell spheroids influences the expression of a transfected gene. Ltk- cells (mouse fibroblasts, thymidine kinase negative) have been transfected with a bacterial lacZ gene which was coupled to a β-actin promoter. The transfected cells synthesize β-galactosidase, a cytoplasmic enzyme which can easily be stained for histology with 5-bromo-4-chloro-3-indoxyl β-D-galactoside and for cytometry with fluorescein di(β-D-galactopyranoside). As we have shown with monolayer cells, β-galactosidase is produced independently of cell density, medium condition, and cell cycle. In multicell spheroids, however, the portion of producing cells was reduced from ∼98% to ∼2% within a week. This reduction is also independent of cell density, medium condition, and cell cycle. Nonproducing multicell spheroid cells, however, regained their ability to synthesize β-galactosidase within a few days when the cells were recultivated as monolayers. Since the lacZ gene was not lost, its expression might have been regulated by its β-actin promoter. We, therefore, investigated whether the endogenous synthesis of β-actin was similarly regulated. A correlation between the distinct reduction in β-galactosidase-producing cells and filamentous or total actin concentration was not unequivocally observed.

On the concentration profile of a growth inhibitory factor in multicell spheroids

A mathematical model is presented for the production of a growth inhibitory factor (GIF) within a multicell spheroid. The main assumption of the model is that the GIF is produced by cells within the spheroid in some prescribed nonlinear, spatially dependent manner. Given that the diffusion of the GIF is known to take place over a much shorter time scale than that of spheroid growth, the steady-state profile of the GIF in various spheroids of differing radii is examined and theoretical results are compared with actual experimental data.

Cell kinetics and repopulation during multifraction irradiation of spheroids: Implications for clinical radiotherapy

T here seems to be little question that development of a predictive assay that could reliably forecast the response of individual to treatment would be of tremendous value to practicing oncologists. However, exactly what type of information is needed in such an assay is less certain. For example, is the determinant of success the inherent sensitivity of the majority, or that of a minority of the tumor cells? Because treatment is typically recognized by the regrowth or continued growth of the tumor mass, what is the role of cell kinetics in that process? Perhaps of most pressing importance, can predictive assays lead to alternate, hopefully superior, forms of treatment? While measuring tumor cell sensitivity to both radiation and drugs has become fashionable in recent years, correlations between in vitro sensitivity analyses and eventual patient outcome have generally been found only between tumor types, but not between individual of a certain type. This suggests that factors in addition to inherent sensitivity must be considered. Analyzing patterns of failure can often be useful in this regard; in a provocative article analyzing outcomes for patients with head and neck cancer, Withers et al I reached the rather alarming conclusion that treatments lasting more than 4 weeks required a dose escalation of 0.6 Gy/extension day to retain the same probability of cure. More general reviews 2-4 similarly argue for a dose increase of 0.3 to 0.7 Gy/day of treatment for treatment extensions beyond 4 weeks. These results strongly' implicate time as a critical factor for successful treatments. However, identifying a clinical problem is considerably easier than resoMng it. For example, does the repopulation seen at later times during therapy indicate that cells are cycling more rapidly, that more cells are in cycle, that fewer clonogenic cells are lost, or combinations of the above? When does repopulation actuallyaccelerate? Perhaps of greater immediate importance, can reliable and unambiguous methods of measurement be developed for tumor cell kinetics, and when should they be used? Alternatively, can repopulation rate or potential be predicted? Clearly', several philosophical and practical limitations combine to inhibit addressing these questions in the most relevant system, the human cancer patient. At least one tumor model system is available, however, in which many relevant and highly detailed studies can be pursued: the multicell spheroid model. 5,6 It is of particular note that the spheroid system can be easily maintained in long-term culture, allowing large numbers of virtually identical tumors to be propagated and reproducibly tested, without host factors complicating the response. 7,8 Every cell of the system potentially contributes to the net response, and of particular importance, each cell can be recovered and assessed. The intent of this article is to examine the role of cell kinetics when spheroids are treated with multifraction protocols. In addition to multifraction radiation treatments, multiple drug exposures will be briefly explored. From the design of these studies, we have been able to address not only the role of pretreatment cell kinetics, but also factors controlling changes of those kinetic properties during, and in response to, the therapeutic manipulations.

Cell and Environment Interactions in Tumor Microregions: The Multicell Spheroid Model

Abnormal vascularization of malignant tumors is associated with the development of microregions of heterogeneous cells and environments. Experimental models such as multicell spheroids and a variety of new techniques are being used to determine the characteristics of these microregions and to study the interactions of the cells and microenvironments. The special cellular microecology of tumors influences responsiveness to therapeutic agents and has implications for future directions in cancer research.

On the analysis of oxygen diffusion and reaction in biological systems

An analysis of oxygen diffusion and reaction in multiregion biological systems is presented. This analysis considers a time-dependent flux boundary condition and oxygen consumption governed by Michaelis-Menten kinetics. The mathematical problem is developed in a uniform fashion, so as to include both the single cell and anisotropic systems with distinct regions which are characteristic of either a multicell spheroid or a tumor mass. Both transient and steady-state solutions are obtained, based on orthogonal collocation. Literature results on single-cell analysis are corroborated, and detailed transient solutions are presented for the oxygenation of a multicell spheroid, and for systemic oxygenation of both small and large tumors.

Oxygen Diffusion Distance and Development of Necrosis in Multicell Spheroids

The multicell spheroid in vitro tumor model was used to study the effects of diffusion limitations of metabolites on the development of necrosis in a tumor-like environment. Chinese hamster V79-171b cells were grown in suspension as multicellular spheroids in different oxygen or glucose concentrations to diameters where they developed central necrosis surrounded by an outer rim of viable cells. The range of oxygen concentrations used in the gas phase was 1 to 20.3%, in equilibrium with complete nutrient medium. For each oxygen concentration the thickness of the rim of viable cells was determined from measurements of histological sections. The square of the thickness of the viable rims of spheroids grown at different oxygen concentrations between 5 and 20.3% increased linearly with the theoretically derived oxygen diffusion distance, showing that the oxygen diffusion distance is a main factor controlling, either directly or indirectly, the development of necrosis in this concentration range. The data were interpreted as meaning spheroids grown at more than 5% O/sub 2/ contain a very small proportion of cells which were severely hypoxic or anoxic. The viable rim thickness was relatively less affected during growth at less than 5% oxygen, implying that an unknown mechanism controls the formationmore » of necrosis when the oxygen diffusion distance is less than approximately 80 ..mu..m. Although alterations in the glucose concentration had some effect on viable rim thickness at these low oxygen concentrations, the effect was much less than expected if glucose alone were responsible for controlling viability in this outer region.« less