Cell-based computational modeling of vascular morphogenesis using Tissue Simulation Toolkit

The shapes of elongating gastruloids are consistent with convergent extension driven by a combination of active cell crawling and differential adhesion

Gastruloids have emerged as highly useful in vitro models of mammalian gastrulation. One of the most striking features of 3D gastruloids is their elongation, which mimics the extension of the embryonic anterior-posterior axis. Although axis extension is crucial for development, the underlying mechanism has not been fully elucidated in mammalian species. Gastruloids provide an opportunity to study this morphogenic process in vitro. Here, we measure and quantify the shapes of elongating gastruloids and show, by Cellular Potts model simulations based on a novel, optimized algorithm, that convergent extension, driven by a combination of active cell crawling and differential adhesion can explain the observed shapes. We reveal that differential adhesion alone is insufficient and also directly observe hallmarks of convergent extension by time-lapse imaging of gastruloids. Finally, we show that gastruloid elongation can be abrogated by inhibition of the Rho kinase pathway, which is involved in convergent extension in vivo. All in all, our study demonstrates, how gastruloids can be used to elucidate morphogenic processes in embryonic development.

Digitize your Biology! Modeling multicellular systems through interpretable cell behavior

Cells are fundamental units of life, constantly interacting and evolving as dynamical systems. While recent spatial multi-omics can quantitate individual cells' characteristics and regulatory programs, forecasting their evolution ultimately requires mathematical modeling. We develop a conceptual framework-a cell behavior hypothesis grammar-that uses natural language statements (cell rules) to create mathematical models. This allows us to systematically integrate biological knowledge and multi-omics data to make them computable. We can then perform virtual "thought experiments" that challenge and extend our understanding of multicellular systems, and ultimately generate new testable hypotheses. In this paper, we motivate and describe the grammar, provide a reference implementation, and demonstrate its potential through a series of examples in tumor biology and immunotherapy. Altogether, this approach provides a bridge between biological, clinical, and systems biology researchers for mathematical modeling of biological systems at scale, allowing the community to extrapolate from single-cell characterization to emergent multicellular behavior.

Evolution of selfish multicellularity: collective organisation of individual spatio-temporal regulatory strategies

BACKGROUND

The unicellular ancestors of modern-day multicellular organisms were remarkably complex. They had an extensive set of regulatory and signalling genes, an intricate life cycle and could change their behaviour in response to environmental changes. At the transition to multicellularity, some of these behaviours were co-opted to organise the development of the nascent multicellular organism. Here, we focus on the transition to multicellularity before the evolution of stable cell differentiation, to reveal how the emergence of clusters affects the evolution of cell behaviour.

RESULTS

We construct a computational model of a population of cells that can evolve the regulation of their behavioural state - either division or migration - and study both a unicellular and a multicellular context. Cells compete for reproduction and for resources to survive in a seasonally changing environment. We find that the evolution of multicellularity strongly determines the co-evolution of cell behaviour, by altering the competition dynamics between cells. When adhesion cannot evolve, cells compete for survival by rapidly migrating towards resources before dividing. When adhesion evolves, emergent collective migration alleviates the pressure on individual cells to reach resources. This allows individual cells to maximise their own replication. Migrating adhesive clusters display striking patterns of spatio-temporal cell state changes that visually resemble animal development.

CONCLUSIONS

Our model demonstrates how emergent selection pressures at the onset of multicellularity can drive the evolution of cellular behaviour to give rise to developmental patterns.

Simulating 3D Cell Shape with the Cellular Potts Model

Computer simulations have become a widely used method for the field of mechanobiology. An important question is whether one can predict the shape and forces of cells as a function of the extracellular environment. Different types of models have been described before to simulate cell and tissue shapes in structured environments. In this chapter, we give a brief overview of commonly used models and then describe the Cellular Potts Model, a lattice-based modelling framework, in more detail. We provide a hands-on guide on how to build a model that simulates the shape of a single cell on a micropattern in three dimensions in different open source software packages using the Cellular Potts framework. A simulation is set up with an initial configuration of generalized cells that change shape and position due to an energy function that incorporates cellular volume and surface area constraints as well as interaction energies between the generalized cells.

Implementing computational modeling in tissue engineering: where disciplines meet

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.

Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics

Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with respectively continuous or discontinuous attachment to the ECM, or pivoting behaviour with sustained attachment to the ECM. Moreover, on the long term, lymphocytes either perform a persistent random walk or a Brownian-like movement depending on the ECM composition. How the ECM affects cell motility is still incompletely understood. Here, we integrate essential mechanistic details of the lymphocyte-matrix adhesions and lymphocyte intrinsic cytoskeletal induced cell propulsion into a Cellular Potts model (CPM). We show that the combination of de novo cell-matrix adhesion formation, adhesion growth and shrinkage, adhesion rupture, and feedback of adhesions onto cell propulsion recapitulates multiple lymphocyte behaviours, for different lymphocyte subsets and various substrates. With an increasing attachment area and increased adhesion strength, the cells’ speed and persistence decreases. Additionally, the model predicts random walks with short-term persistent but long-term subdiffusive properties resulting in a pivoting type of motility. For small adhesion areas, the spatial distribution of adhesions emerges as a key factor influencing cell motility. Small adhesions at the front allow for more persistent motility than larger clusters at the back, despite a similar total adhesion area. In conclusion, we present an integrated framework to simulate the effects of ECM proteins on cell-matrix adhesion dynamics. The model reveals a sufficient set of principles explaining the plasticity of lymphocyte motility.

During immunosurveillance, lymphocytes patrol through tissues to interact with cancer cells, other immune cells, and pathogens. The efficiency of this process depends on the kinds of trajectories taken, ranging from simple Brownian walks to Lévy walks. The composition of the extracellular matrix (ECM), a network of macromolecules, affects the formation of cell-matrix adhesions, thus strongly influencing the way lymphocytes move. Here, we present a model of lymphocyte motility driven by adhesions that grow, shrink and rupture in response to the ECM and cellular forces. Compared to other models, our model is computationally light making it suitable for generating long term cell track data, while still capturing actin dynamics and adhesion turnover. Our model suggests that cell motility is affected by the force required to break adhesions and the rate at which new adhesions form. Adhesions can promote cell protrusion by inhibiting retrograde actin flow. After introducing this effect into the model, we found that it reduces the cellular diffusivity and that it promotes stick-slip behaviour. Furthermore, location and size of adhesion clusters determined cell persistence. Overall, our model explains the plasticity of lymphocyte behaviour in response to the ECM.

Artistoo, a library to build, share, and explore simulations of cells and tissues in the web browser

The cellular Potts model (CPM) is a powerful in silico method for simulating biological processes at tissue scale. Their inherently graphical nature makes CPMs very accessible in theory, but in practice, they are mostly implemented in specialised frameworks users need to master before they can run simulations. We here present Artistoo (Artificial Tissue Toolbox), a JavaScript library for building ‘explorable’ CPM simulations where viewers can change parameters interactively, exploring their effects in real time. Simulations run directly in the web browser and do not require third-party software, plugins, or back-end servers. The JavaScript implementation imposes no major performance loss compared to frameworks written in C++; Artistoo remains sufficiently fast for interactive, real-time simulations. Artistoo provides an opportunity to unlock CPM models for a broader audience: interactive simulations can be shared via a URL in a zero-install setting. We discuss applications in CPM research, science dissemination, open science, and education.

Spatial Statistics-Based Image Analysis Methods for the Study of Vascular Morphogenesis

Several studies are available addressing the mechanisms of vascular morphogenesis in order to unravel how cooperative cell behavior can follow from the underlying, genetically regulated behavior of endothelial cells and from cell-to-cell and cell-to-extracellular matrix interactions. From the morphological standpoint several aspects of the process are of interest. They include the way the pattern of vessels fills the available tissue space and how the network grows during the angiogenic process, namely how a main trunk divides into smaller branches, and how branching occurs at different distances from the root point of a vascular tree. A third morphological aspect of interest concerns the spatial relationship between vessels and tissue cells able to secrete factors modulating endothelial cells self-organization, thus influencing vascular rearrangement.In the present chapter image analysis methods allowing for a quantitative characterization of these morphological aspects will be detailed and discussed. They are almost based on concepts derived from the theoretical framework represented by spatial statistics.

Evolution of multicellularity by collective integration of spatial information

At the origin of multicellularity, cells may have evolved aggregation in response to predation, for functional specialisation or to allow large-scale integration of environmental cues. These group-level properties emerged from the interactions between cells in a group, and determined the selection pressures experienced by these cells. We investigate the evolution of multicellularity with an evolutionary model where cells search for resources by chemotaxis in a shallow, noisy gradient. Cells can evolve their adhesion to others in a periodically changing environment, where a cell's fitness solely depends on its distance from the gradient source. We show that multicellular aggregates evolve because they perform chemotaxis more efficiently than single cells. Only when the environment changes too frequently, a unicellular state evolves which relies on cell dispersal. Both strategies prevent the invasion of the other through interference competition, creating evolutionary bi-stability. Therefore, collective behaviour can be an emergent selective driver for undifferentiated multicellularity.

Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues

A main goal of mathematical and computational oncology is to develop quantitative tools to determine the most effective therapies for each individual patient. This involves predicting the right drug to be administered at the right time and at the right dose. Such an approach is known as precision medicine. Mathematical modelling can play an invaluable role in the development of such therapeutic strategies, since it allows for relatively fast, efficient and inexpensive simulations of a large number of treatment schedules in order to find the most effective. This review is a survey of mathematical models that explicitly take into account the spatial architecture of three-dimensional tumours and address tumour development, progression and response to treatments. In particular, we discuss models of epithelial acini, multicellular spheroids, normal and tumour spheroids and organoids, and multi-component tissues. Our intent is to showcase how these in silico models can be applied to patient-specific data to assess which therapeutic strategies will be the most efficient. We also present the concept of virtual clinical trials that integrate standard-of-care patient data, medical imaging, organ-on-chip experiments and computational models to determine personalized medical treatment strategies.

Neural crest streaming as an emergent property of tissue interactions during morphogenesis

A fundamental question in embryo morphogenesis is how a complex pattern is established in seemingly uniform tissues. During vertebrate development, neural crest cells differentiate as a continuous mass of tissue along the neural tube and subsequently split into spatially distinct migratory streams to invade the rest of the embryo. How these streams are established is not well understood. Inhibitory signals surrounding the migratory streams led to the idea that position and size of streams are determined by a pre-pattern of such signals. While clear evidence for a pre-pattern in the cranial region is still lacking, all computational models of neural crest migration published so far have assumed a pre-pattern of negative signals that channel the neural crest into streams. Here we test the hypothesis that instead of following a pre-existing pattern, the cranial neural crest creates their own migratory pathway by interacting with the surrounding tissue. By combining theoretical modeling with experimentation, we show that streams emerge from the interaction of the hindbrain neural crest and the neighboring epibranchial placodal tissues, without the need for a pre-existing guidance cue. Our model suggests that the initial collective neural crest invasion is based on short-range repulsion and asymmetric attraction between neighboring tissues. The model provides a coherent explanation for the formation of cranial neural crest streams in concert with previously reported findings and our new in vivo observations. Our results point to a general mechanism of inducing collective invasion patterns.

Mathematical and Computational Modeling in Complex Biological Systems

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

In silico modeling for tumor growth visualization

BACKGROUND

Cancer is a complex disease. Fundamental cellular based studies as well as modeling provides insight into cancer biology and strategies to treatment of the disease. In silico models complement in vivo models. Research on tumor growth involves a plethora of models each emphasizing isolated aspects of benign and malignant neoplasms. Biologists and clinical scientists are often overwhelmed by the mathematical background knowledge necessary to grasp and to apply a model to their own research.

RESULTS

We aim to provide a comprehensive and expandable simulation tool to visualizing tumor growth. This novel Web-based application offers the advantage of a user-friendly graphical interface with several manipulable input variables to correlate different aspects of tumor growth. By refining model parameters we highlight the significance of heterogeneous intercellular interactions on tumor progression. Within this paper we present the implementation of the Cellular Potts Model graphically presented through Cytoscape.js within a Web application. The tool is available under the MIT license at https://github.com/davcem/cpm-cytoscape and http://styx.cgv.tugraz.at:8080/cpm-cytoscape/ .

CONCLUSION

In-silico methods overcome the lack of wet experimental possibilities and as dry method succeed in terms of reduction, refinement and replacement of animal experimentation, also known as the 3R principles. Our visualization approach to simulation allows for more flexible usage and easy extension to facilitate understanding and gain novel insight. We believe that biomedical research in general and research on tumor growth in particular will benefit from the systems biology perspective.

An in silico study on the role of smooth muscle cell migration in neointimal formation after coronary stenting

Excessive migration and proliferation of smooth muscle cells (SMCs) has been observed as a major factor contributing to the development of in-stent restenosis after coronary stenting. Building upon the results from in vivo experiments, we formulated a hypothesis that the speed of the initial tissue re-growth response is determined by the early migration of SMCs from the injured intima. To test this hypothesis, a cellular Potts model of the stented artery is developed where stent struts were deployed at different depths into the tissue. An extreme scenario with a ruptured internal elastic lamina was also considered to study the role of severe injury in tissue re-growth. Based on the outcomes, we hypothesize that a deeper stent deployment results in on average larger fenestrae in the elastic lamina, allowing easier migration of SMCs into the lumen. The data also suggest that growth of the neointimal lesions owing to SMC proliferation is strongly dependent on the initial number of migrated cells, which form an initial condition for the later phase of the vascular repair. This mechanism could explain the in vivo observation that the initial rate of neointima formation and injury score are strongly correlated.