Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability.

Tumours are subject to external environmental variability. However, in vitro tumour spheroid experiments, used to understand cancer progression and develop cancer therapies, have been routinely performed for the past fifty years in constant external environments. Furthermore, spheroids are typically grown in ambient atmospheric oxygen (normoxia), whereas most in vivo tumours exist in hypoxic environments. Therefore, there are clear discrepancies between in vitro and in vivo conditions. We explore these discrepancies by combining tools from experimental biology, mathematical modelling, and statistical uncertainty quantification. Focusing on oxygen variability to develop our framework, we reveal key biological mechanisms governing tumour spheroid growth. Growing spheroids in time-dependent conditions, we identify and quantify novel biological adaptation mechanisms, including unexpected necrotic core removal, and transient reversal of the tumour spheroid growth phases.

Formation and Growth of Co-Culture Tumour Spheroids: New Compartment-Based Mathematical Models and Experiments.

Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. Therefore, methods to quantitatively characterise and interpret co-culture spheroid growth are of great interest. However, co-culture spheroid growth is complex. Multiple biological processes occur on overlapping timescales and different cell types within the spheroid may have different characteristics, such as differing proliferation rates or responses to nutrient availability. At present there is no standard, widely-accepted mathematical model of such complex spatio-temporal growth processes. Typical approaches to analyse these experiments focus on the late-time temporal evolution of spheroid size and overlook early-time spheroid formation, spheroid structure and geometry. Here, using a range of ordinary differential equation-based mathematical models and parameter estimation, we interpret new co-culture experimental data. We provide new biological insights about spheroid formation, growth, and structure. As part of this analysis we connect Greenspan's seminal mathematical model to co-culture data for the first time. Furthermore, we generalise a class of compartment-based spheroid mathematical models that have previously been restricted to one population so they can be applied to multiple populations. As special cases of the general model, we explore multiple natural two population extensions to Greenspan's seminal model and reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types and the new class of mathematical models provide opportunities for further mathematical and biological insights.

Synchronized oscillations in growing cell populations are explained by demographic noise.

Understanding synchrony in growing populations is important for applications as diverse as epidemiology and cancer treatment. Recent experiments employing fluorescent reporters in melanoma cell lines have uncovered growing subpopulations exhibiting sustained oscillations, with nearby cells appearing to synchronize their cycles. In this study, we demonstrate that the behavior observed is consistent with long-lasting transient phenomenon initiated and amplified by the finite-sample effects and demographic noise. We present a novel mathematical analysis of a multistage model of cell growth, which accurately reproduces the synchronized oscillations. As part of the analysis, we elucidate the transient and asymptotic phases of the dynamics and derive an analytical formula to quantify the effect of demographic noise in the appearance of the oscillations. The implications of these findings are broad, such as providing insight into experimental protocols that are used to study the growth of asynchronous populations and, in particular, those investigations relating to anticancer drug discovery.

A novel mathematical model of heterogeneous cell proliferation.

We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two cellular processes, asymmetric cell division and induced switching between proliferative states, which are important determinants for the heterogeneity of a cell population. As motivation for our model we provide experimental data that illustrate the induced-switching process. Our model consists of a system of two coupled delay differential equations with distributed time delays and the cell densities as functions of time. The distributed delays are bounded and allow for the choice of delay kernel. We analyse the model and prove the nonnegativity and boundedness of solutions, the existence and uniqueness of solutions, and the local stability characteristics of the equilibrium points. We find that the parameters for induced switching are bifurcation parameters and therefore determine the long-term behaviour of the model. Numerical simulations illustrate and support the theoretical findings, and demonstrate the primary importance of transient dynamics for understanding the evolution of many experimental cell populations.

Examining Go-or-Grow Using Fluorescent Cell-Cycle Indicators and Cell-Cycle-Inhibiting Drugs.

The go-or-grow hypothesis states that adherent cells undergo reversible phenotype switching between migratory and proliferative states, with cells in the migratory state being more motile than cells in the proliferative state. Here, we examine go-or-grow in two-dimensional in vitro assays using melanoma cells with fluorescent cell-cycle indicators and cell-cycle-inhibiting drugs. We analyze the experimental data using single-cell tracking to calculate mean diffusivities and compare motility between cells in different cell-cycle phases and in cell-cycle arrest. Unequivocally, our analysis does not support the go-or-grow hypothesis. We present clear evidence that cell motility is independent of the cell-cycle phase and that nonproliferative arrested cells have the same motility as cycling cells.

Mathematical Models for Cell Migration with Real-Time Cell Cycle Dynamics.

The fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the visualization of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore how the cell cycle relates to the location of individual cells, local cell density, and different cellular microenvironments. In particular, FUCCI is used in experimental studies examining cell migration, such as malignant invasion and wound healing. Here we present, to our knowledge, new mathematical models that can describe cell migration and cell cycle dynamics as indicated by FUCCI. The fundamental model describes the two cell cycle phases, G1 and S/G2/M, which FUCCI directly labels. The extended model includes a third phase, early S, which FUCCI indirectly labels. We present experimental data from scratch assays using FUCCI-transduced melanoma cells, and show that the predictions of spatial and temporal patterns of cell density in the experiments can be described by the fundamental model. We obtain numerical solutions of both the fundamental and extended models, which can take the form of traveling waves. These solutions are mathematically interesting because they are a combination of moving wavefronts and moving pulses. We derive and confirm a simple analytical expression for the minimum wave speed, as well as exploring how the wave speed depends on the spatial decay rate of the initial condition.

Real-Time Cell Cycle Imaging in a 3D Cell Culture Model of Melanoma, Quantitative Analysis, Optical Clearing, and Mathematical Modeling.

Aberrant cell cycle progression is a hallmark of solid tumors. Therefore, cell cycle analysis is an invaluable technique to study cancer cell biology. However, cell cycle progression has been most commonly assessed by methods that are limited to temporal snapshots or that lack spatial information. In this chapter, we describe a technique that allows spatiotemporal real-time tracking of cell cycle progression of individual cells in a multicellular context. The power of this system lies in the use of 3D melanoma spheroids generated from melanoma cells engineered with the fluorescent ubiquitination-based cell cycle indicator (FUCCI). This technique, combined with mathematical modeling, allows us to gain further and more detailed insight into several relevant aspects of solid cancer cell biology, such as tumor growth, proliferation, invasion, and drug sensitivity.

Rapid Optical Clearing for Semi-High-Throughput Analysis of Tumor Spheroids.

Tumor spheroids are fast becoming commonplace in basic cancer research and drug development. Obtaining data regarding protein expression within the spheroid at the cellular level is important for analysis, yet existing techniques are often expensive, laborious, use non-standard equipment, cause significant size distortion, or are limited to relatively small spheroids. This protocol presents a new method of mounting and clearing spheroids that address these issues while allowing for confocal analysis of the inner structure of spheroids. In contrast to existing approaches, this protocol provides for rapid mounting and clearing of a large number of spheroids using standard equipment and laboratory supplies. Mounting spheroids in a pH-neutral agarose-PBS gel solution before introducing a refractive-index-matched clearing solution minimizes size distortion common to other similar techniques. This allows for detailed quantitative and statistical analysis where the accuracy of size measurements is paramount. Furthermore, compared to liquid clearing solutions, the agarose gel technique keeps spheroids fixed in place, allowing for the collection of three-dimensional (3D) confocal images. The present article elaborates how the method yields high-quality two- and 3D images that provide information about inter-cell variability and inner spheroid structure.

Designing and interpreting 4D tumour spheroid experiments.

Tumour spheroid experiments are routinely used to study cancer progression and treatment. Various and inconsistent experimental designs are used, leading to challenges in interpretation and reproducibility. Using multiple experimental designs, live-dead cell staining, and real-time cell cycle imaging, we measure necrotic and proliferation-inhibited regions in over 1000 4D tumour spheroids (3D space plus cell cycle status). By intentionally varying the initial spheroid size and temporal sampling frequencies across multiple cell lines, we collect an abundance of measurements of internal spheroid structure. These data are difficult to compare and interpret. However, using an objective mathematical modelling framework and statistical identifiability analysis we quantitatively compare experimental designs and identify design choices that produce reliable biological insight. Measurements of internal spheroid structure provide the most insight, whereas varying initial spheroid size and temporal measurement frequency is less important. Our general framework applies to spheroids grown in different conditions and with different cell types.

A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling.

In vitro tumour spheroids have been used to study avascular tumour growth and drug design for over 50 years. Tumour spheroids exhibit heterogeneity within the growing population that is thought to be related to spatial and temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us to identify the position and cell cycle status of individual cells within the growing spheroid, giving rise to the notion of a four-dimensional (4D) tumour spheroid. We develop the first stochastic individual-based model (IBM) of a 4D tumour spheroid and show that IBM simulation data compares well with experimental data using a primary human melanoma cell line. The IBM provides quantitative information about nutrient availability within the spheroid, which is important because it is difficult to measure these data experimentally.

Fluorescence-Based Quantitative and Spatial Analysis of Tumour Spheroids: A Proposed Tool to Predict Patient-Specific Therapy Response.

Tumour spheroids are widely used to pre-clinically assess anti-cancer treatments. They are an excellent compromise between the lack of microenvironment encountered in adherent cell culture conditions and the great complexity of in vivo animal models. Spheroids recapitulate intra-tumour microenvironment-driven heterogeneity, a pivotal aspect for therapy outcome that is, however, often overlooked. Likely due to their ease, most assays measure overall spheroid size and/or cell death as a readout. However, as different tumour cell subpopulations may show a different biology and therapy response, it is paramount to obtain information from these distinct regions within the spheroid. We describe here a methodology to quantitatively and spatially assess fluorescence-based microscopy spheroid images by semi-automated software-based analysis. This provides a fast assay that accounts for spatial biological differences that are driven by the tumour microenvironment. We outline the methodology using detection of hypoxia, cell death and PBMC infiltration as examples, and we propose this procedure as an exploratory approach to assist therapy response prediction for personalised medicine.

Quantitative analysis of tumour spheroid structure.

Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, tumour spheroids more closely mimic the avascular tumour microenvironment where spatial differences in nutrient availability strongly influence growth. We show that spheroids initiated using significantly different numbers of cells grow to similar limiting sizes, suggesting that avascular tumours have a limiting structure; in agreement with untested predictions of classical mathematical models of tumour spheroids. We develop a novel mathematical and statistical framework to study the structure of tumour spheroids seeded from cells transduced with fluorescent cell cycle indicators, enabling us to discriminate between arrested and cycling cells and identify an arrested region. Our analysis shows that transient spheroid structure is independent of initial spheroid size, and the limiting structure can be independent of seeding density. Standard experimental protocols compare spheroid size as a function of time; however, our analysis suggests that comparing spheroid structure as a function of overall size produces results that are relatively insensitive to variability in spheroid size. Our experimental observations are made using two melanoma cell lines, but our modelling framework applies across a wide range of spheroid culture conditions and cell lines.

Mathematical models incorporating a multi-stage cell cycle replicate normally-hidden inherent synchronization in cell proliferation.

We present a suite of experimental data showing that cell proliferation assays, prepared using standard methods thought to produce asynchronous cell populations, persistently exhibit inherent synchronization. Our experiments use fluorescent cell cycle indicators to reveal the normally hidden cell synchronization, by highlighting oscillatory subpopulations within the total cell population. These oscillatory subpopulations would never be observed without these cell cycle indicators. On the other hand, our experimental data show that the total cell population appears to grow exponentially, as in an asynchronous population. We reconcile these seemingly inconsistent observations by employing a multi-stage mathematical model of cell proliferation that can replicate the oscillatory subpopulations. Our study has important implications for understanding and improving experimental reproducibility. In particular, inherent synchronization may affect the experimental reproducibility of studies aiming to investigate cell cycle-dependent mechanisms, including changes in migration and drug response.

BCL-XL and MCL-1 are the key BCL-2 family proteins in melanoma cell survival.

Malignant melanoma is one of the most difficult cancers to treat due to its resistance to chemotherapy. Despite recent successes with BRAF inhibitors and immune checkpoint inhibitors, many patients do not respond or become resistant to these drugs. Hence, alternative treatments are still required. Due to the importance of the BCL-2-regulated apoptosis pathway in cancer development and drug resistance, it is of interest to establish which proteins are most important for melanoma cell survival, though the outcomes of previous studies have been conflicting. To conclusively address this question, we tested a panel of established and early passage patient-derived cell lines against several BH3-mimetic drugs designed to target individual or subsets of pro-survival BCL-2 proteins, alone and in combination, in both 2D and 3D cell cultures. None of the drugs demonstrated significant activity as single agents, though combinations targeting MCL-1 plus BCL-XL, and to a lesser extent BCL-2, showed considerable synergistic killing activity that was elicited via both BAX and BAK. Genetic deletion of BFL-1 in cell lines that express it at relatively high levels only had minor impact on BH3-mimetic drug sensitivity, suggesting it is not a critical pro-survival protein in melanoma. Combinations of MCL-1 inhibitors with BRAF inhibitors also caused only minimal additional melanoma cell killing over each drug alone, whilst combinations with the proteasome inhibitor bortezomib was more effective in multiple cell lines. Our data show for the first time that therapies targeting specific combinations of BCL-2 pro-survival proteins, namely MCL-1 plus BCL-XL and MCL-1 plus BCL-2, could have significant benefit for the treatment of melanoma.

Decatenation checkpoint-defective melanomas are dependent on PI3K for survival.

Melanoma cell lines are commonly defective for the G2-phase cell cycle checkpoint that responds to incomplete catenation of the replicated chromosomes. Here, we demonstrate that melanomas defective for this checkpoint response are less sensitive to genotoxic stress, suggesting that the defective cell lines compensated for the checkpoint loss by increasing their ability to cope with DNA damage. We performed an siRNA kinome screen to identify kinases responsible and identified PI3K pathway components. Checkpoint-defective cell lines were three-fold more sensitive to small molecule inhibitors of PI3K. The PI3K inhibitor PF-05212384 promoted apoptosis in the checkpoint-defective lines, and the increased sensitivity to PI3K inhibition correlated with increased levels of activated Akt. This work demonstrates that increased PI3K pathway activation is a necessary adaption for the continued viability of melanomas with a defective decatenation checkpoint.

"Humanized" stem cell culture techniques: the animal serum controversy.

Cellular therapy is reaching a pinnacle with an understanding of the potential of human mesenchymal stem cells (hMSCs) to regenerate damaged tissue in the body. The limited numbers of these hMSCs in currently identified sources, like bone marrow, adipose tissue, and so forth, bring forth the need for their in vitro culture/expansion. However, the extensive usage of supplements containing xenogeneic components in the expansion-media might pose a risk to the post-transplantation safety of patients. This warrants the necessity to identify and develop chemically defined or "humanized" supplements which would make in vitro cultured/processed cells relatively safer for transplantation in regenerative medicine. In this paper, we outline the various caveats associated with conventionally used supplements of xenogenic origin and also portray the possible alternatives/additives which could one day herald the dawn of a new era in the translation of in vitro cultured cells to therapeutic interventions.