Multiscale Modeling of Spheroid Tumors: Effect of Nutrient Availability on Tumor Evolution.

Recent years have revealed a large number of complex mechanisms and interactions that drive the development of malignant tumors. Tumor evolution is a framework that explains tumor development as a process driven by survival of the fittest, with tumor cells of different properties competing for limited available resources. To predict the evolutionary trajectory of a tumor, knowledge of how cellular properties influence the fitness of a subpopulation in the context of the microenvironment is required and is often inaccessible. Computational multiscale-modeling of tissues enables the observation of the full trajectory of each cell within the tumor environment. Here, we model a 3D spheroid tumor with subcellular resolution. The fitness of individual cells and the evolutionary behavior of the tumor are quantified and linked to cellular and environmental parameters. The fitness of cells is solely influenced by their position in the tumor, which in turn is influenced by the two variable parameters of our model: cell-cell adhesion and cell motility. We observe the influence of nutrient independence and static and dynamically changing nutrient availability on the evolutionary trajectories of heterogeneous tumors in a high-resolution computational model. Regardless of nutrient availability, we find a fitness advantage of low-adhesion cells, which are favorable for tumor invasion. We find that the introduction of nutrient-dependent cell division and death accelerates the evolutionary speed. The evolutionary speed can be increased by fluctuations in nutrients. We identify a distinct frequency domain in which the evolutionary speed increases significantly over a tumor with constant nutrient supply. The findings suggest that an unstable supply of nutrients can accelerate tumor evolution and, thus, the transition to malignancy.

Development of a scoring function for comparing simulated and experimental tumor spheroids.

Progress continues in the field of cancer biology, yet much remains to be unveiled regarding the mechanisms of cancer invasion. In particular, complex biophysical mechanisms enable a tumor to remodel the surrounding extracellular matrix (ECM), allowing cells to invade alone or collectively. Tumor spheroids cultured in collagen represent a simplified, reproducible 3D model system, which is sufficiently complex to recapitulate the evolving organization of cells and interaction with the ECM that occur during invasion. Recent experimental approaches enable high resolution imaging and quantification of the internal structure of invading tumor spheroids. Concurrently, computational modeling enables simulations of complex multicellular aggregates based on first principles. The comparison between real and simulated spheroids represents a way to fully exploit both data sources, but remains a challenge. We hypothesize that comparing any two spheroids requires first the extraction of basic features from the raw data, and second the definition of key metrics to match such features. Here, we present a novel method to compare spatial features of spheroids in 3D. To do so, we define and extract features from spheroid point cloud data, which we simulated using Cells in Silico (CiS), a high-performance framework for large-scale tissue modeling previously developed by us. We then define metrics to compare features between individual spheroids, and combine all metrics into an overall deviation score. Finally, we use our features to compare experimental data on invading spheroids in increasing collagen densities. We propose that our approach represents the basis for defining improved metrics to compare large 3D data sets. Moving forward, this approach will enable the detailed analysis of spheroids of any origin, one application of which is informing in silico spheroids based on their in vitro counterparts. This will enable both basic and applied researchers to close the loop between modeling and experiments in cancer research.

Assembly of Multi-Spheroid Cellular Architectures by Programmable Droplet Merging.

Artificial multicellular systems are gaining importance in the field of tissue engineering and regenerative medicine. Reconstruction of complex tissue architectures in vitro is nevertheless challenging, and methods permitting controllable and high-throughput fabrication of complex multicellular architectures are needed. Here, a facile and high-throughput method is developed based on a tunable droplet-fusion technique, allowing programmed assembly of multiple cell spheroids into complex multicellular architectures. The droplet-fusion technique allows for construction of various multicellular architectures (double-spheroids, multi-spheroids, hetero-spheroids) in a miniaturized high-density array format. As an example of application, the propagation of Wnt signaling is investigated within hetero-spheroids formed from two fused Wnt-releasing and Wnt-reporter cell spheroids. The developed method provides an approach for miniaturized, high-throughput construction of complex 3D multicellular architectures and can be applied for studying various biological processes including cell signaling, cancer invasion, embryogenesis, and neural development.

Cells in Silico - introducing a high-performance framework for large-scale tissue modeling.

BACKGROUND: Discoveries in cellular dynamics and tissue development constantly reshape our understanding of fundamental biological processes such as embryogenesis, wound-healing, and tumorigenesis. High-quality microscopy data and ever-improving understanding of single-cell effects rapidly accelerate new discoveries. Still, many computational models either describe few cells highly detailed or larger cell ensembles and tissues more coarsely. Here, we connect these two scales in a joint theoretical model. RESULTS: We developed a highly parallel version of the cellular Potts model that can be flexibly applied and provides an agent-based model driving cellular events. The model can be modular extended to a multi-model simulation on both scales. Based on the NAStJA framework, a scaling implementation running efficiently on high-performance computing systems was realized. We demonstrate independence of bias in our approach as well as excellent scaling behavior. CONCLUSIONS: Our model scales approximately linear beyond 10,000 cores and thus enables the simulation of large-scale three-dimensional tissues only confined by available computational resources. The strict modular design allows arbitrary models to be configured flexibly and enables applications in a wide range of research questions. Cells in Silico (CiS) can be easily molded to different model assumptions and help push computational scientists to expand their simulations to a new area in tissue simulations. As an example we highlight a 10003 voxel-sized cancerous tissue simulation at sub-cellular resolution.

Modeling of Wnt-mediated tissue patterning in vertebrate embryogenesis.

During embryogenesis, morphogens form a concentration gradient in responsive tissue, which is then translated into a spatial cellular pattern. The mechanisms by which morphogens spread through a tissue to establish such a morphogenetic field remain elusive. Here, we investigate by mutually complementary simulations and in vivo experiments how Wnt morphogen transport by cytonemes differs from typically assumed diffusion-based transport for patterning of highly dynamic tissue such as the neural plate in zebrafish. Stochasticity strongly influences fate acquisition at the single cell level and results in fluctuating boundaries between pattern regions. Stable patterning can be achieved by sorting through concentration dependent cell migration and apoptosis, independent of the morphogen transport mechanism. We show that Wnt transport by cytonemes achieves distinct Wnt thresholds for the brain primordia earlier compared with diffusion-based transport. We conclude that a cytoneme-mediated morphogen transport together with directed cell sorting is a potentially favored mechanism to establish morphogen gradients in rapidly expanding developmental systems.

Wnt/PCP controls spreading of Wnt/ß-catenin signals by cytonemes in vertebrates.

Signaling filopodia, termed cytonemes, are dynamic actin-based membrane structures that regulate the exchange of signaling molecules and their receptors within tissues. However, how cytoneme formation is regulated remains unclear. Here, we show that Wnt/planar cell polarity (PCP) autocrine signaling controls the emergence of cytonemes, and that cytonemes subsequently control paracrine Wnt/ß-catenin signal activation. Upon binding of the Wnt family member Wnt8a, the receptor tyrosine kinase Ror2 becomes activated. Ror2/PCP signaling leads to the induction of cytonemes, which mediate the transport of Wnt8a to neighboring cells. In the Wnt-receiving cells, Wnt8a on cytonemes triggers Wnt/ß-catenin-dependent gene transcription and proliferation. We show that cytoneme-based Wnt transport operates in diverse processes, including zebrafish development, murine intestinal crypt and human cancer organoids, demonstrating that Wnt transport by cytonemes and its control via the Ror2 pathway is highly conserved in vertebrates.