Plasticity of cancer invasion and metastasis depends on the ability of cancer cells to switch between collective and single cell dissemination, controlled by cadherinmediated cell-cell junctions. In clinical samples, E-cadherin expressing and deficient tumors both invade collectively and metastasize equally, implicating additional mechanisms controlling cell-cell cooperation and individualization. Using spatially defined organotypic culture, intravital microscopy of mammary tumors in mice and in silico modeling, we here identify cell density regulation by 3D tissue boundaries to physically control collective movement irrespective of the composition and stability of cell-cell junctions. Deregulation of adherens junctions, including E-cadherin and p120-catenin, resulted in a transition from coordinated to uncoordinated collective movement along extracellular boundaries, whereas singlecell escape depended on locally free tissue space. These data indicate that cadherins and ECM confinement cooperate to determine unjamming transitions towards step-wise epithelial fluidization and, ultimately, cell individualization.

Cellular decision making allows cells to assume functionally different phenotypes in response to microenvironmental cues, with or without genetic change. It is an open question, how individual cell decisions influence the dynamics at the tissue level. Here, we study spatio-temporal pattern formation in a population of cells exhibiting phenotypic plasticity, which is a paradigm of cell decision making. We focus on the migration/resting and the migration/proliferation plasticity which underly the epithelial-mesenchymal transition and the go or grow dichotomy. We assume that cells change their phenotype in order to minimize their microenvironmental entropy following the LEUP (Least microEnvironmental Uncertainty Principle) hypothesis. In turn, we study the impact of the LEUP-driven migration/resting and migration/proliferation plasticity on the corresponding multicellular spatio-temporal dynamics with a stochastic cell-based mathematical model for the spatio-temporal dynamics of the cell phenotypes. In the case of the go or rest plasticity, a corresponding mean-field approximation allows to identify a bistable switching mechanism between a diffusive (fluid) and an epithelial (solid) tissue phase which depends on the sensitivity of the phenotypes to the environment. For the go or grow plasticity, we show the possibility of Turing pattern formation for the ‘solid’ tissue phase and its relation with the parameters of the LEUP-driven cell decisions.

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective dynamics - understood as population behaviour arising from the interplay of the constituting discrete cells - can be studied with mathematical models. Off- and on-lattice agent-based models allow to analyse the link between individual cell and collective behaviour. Notably, in on-lattice agent-based models known as cellular automata, collective behaviour can not only be analysed through computer simulations, but predicted with mathematical methods. However, classical cellular automaton models fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce a novel on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, we demonstrate that rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental single cell migration data or biophysical laws for individual cell migration. Furthermore, we present elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. Finally, we present a mathematical mean-field analysis of a BIO-LGCA model that allows to predict collective patterns for a particular cell-cell interaction.

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Countries around the world implement nonpharmaceutical interventions (NPIs) to mitigate the spread of COVID-19. Design of efficient NPIs requires identification of the structure of the disease transmission network. We here identify the key parameters of the COVID-19 transmission network for time periods before, during, and after the application of strict NPIs for the first wave of COVID-19 infections in Germany combining Bayesian parameter inference with an agent-based epidemiological model. We assume a Watts–Strogatz small-world network which allows to distinguish contacts within clustered cliques and unclustered, random contacts in the population, which have been shown to be crucial in sustaining the epidemic. In contrast to other works, which use coarse-grained network structures from anonymized data, like cell phone data, we consider the contacts of individual agents explicitly. We show that NPIs drastically reduced random contacts in the transmission network, increased network clustering, and resulted in a previously unappreciated transition from an exponential to a constant regime of new cases. In this regime, the disease spreads like a wave with a finite wave speed that depends on the number of contacts in a nonlinear fashion, which we can predict by mean field theory.

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.

How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarrete et al., eLife 2019), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters of the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes exhibit local coordination and are aligned with the biaxially anisotropic sinusoidal network for blood transport. Our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues and in-vitro organoids.

Metastatic tumor cell invasion into interstitial tissue is a mechanochemical process that responds to tissue cues and further involves proteolytic remodeling of the tumor stroma. How matrix density, tissue guidance and the ability of proteolytic tissue remodeling cooperate and determine decision-making of invading tumor cells in complex-structured three-dimensional (3D) tissue remains unclear. We here developed a collagen-based invasion assay containing a guiding interface of low collagen density adjacent to randomly organized 3D fibrillar lattice and examined the invasion of melanoma cells from multicellular spheroids in response to matrix density, guidance cues and collagenolysis. After 48 hours of culture, two invasion niches developed, (i) sheet-like collective migration along the interface and (ii) single cell- and strand-like invasion into randomly organized 3D matrix. High collagen density impeded migration into the random matrix, whereas migration along a high-density collagen interface was increased compared to the low-density matrix assay. In silico analysis predicted that facilitated interface migration in high-density matrix depended on physical guidance without collagen degradation, whereas migration into randomly organized matrix was strongly dependent on collagenolysis. When tested in 3D culture, inhibition of matrix metalloprotease (MMP)-mediated collagen degradation compromised migration into random matrix in dependence of density, whereas interface-guided migration remained effective. In conclusion, with increasing tissue density, matrix cues bordered by dense matrix, but not randomly organized matrix, support effective MMP-independent migration. This identifies the topology of interstitial tissue a primary determinant of switch behaviors between MMP-dependent and MMP-independent cancer cell invasion.