Cell jamming in a collagen-based interface assay is tuned by collagen density and proteolysis.

Tumor cell invasion into heterogenous interstitial tissues consisting of network-, channel- or rift-like architectures involves both matrix metalloproteinase (MMP)-mediated tissue remodeling and cell shape adaptation to tissue geometry. Three-dimensional (3D) models composed of either porous or linearly aligned architectures have added to the understanding of how physical spacing principles affect migration efficacy; however, the relative contribution of each architecture to decision making in the presence of varying MMP availability is not known. Here, we developed an interface assay containing a cleft between two high-density collagen lattices, and we used this assay to probe tumor cell invasion efficacy, invasion mode and MMP dependence in concert. In silico modeling predicted facilitated cell migration into confining clefts independently of MMP activity, whereas migration into dense porous matrix was predicted to require matrix degradation. This prediction was verified experimentally, where inhibition of collagen degradation was found to strongly compromise migration into 3D collagen in a density-dependent manner, but interface-guided migration remained effective, occurring by cell jamming. The 3D interface assay reported here may serve as a suitable model to better understand the impact of in vivo-relevant interstitial tissue topologies on tumor invasion patterning and responses to molecular interventions.

The impact of tumor associated macrophages on tumor biology under the lens of mathematical modelling: A review.

In this article, we review the role of mathematical modelling to elucidate the impact of tumor-associated macrophages (TAMs) in tumor progression and therapy design. We first outline the biology of TAMs, and its current application in tumor therapies, and their experimental methods that provide insights into tumor cell-macrophage interactions. We then focus on the mechanistic mathematical models describing the role of macrophages as drug carriers, the impact of macrophage polarized activation on tumor growth, and the role of tumor microenvironment (TME) parameters on the tumor-macrophage interactions. This review aims to identify the synergies between biological and mathematical approaches that allow us to translate knowledge on fundamental TAMs biology in addressing current clinical challenges.

Inferring the effect of interventions on COVID-19 transmission networks.

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.

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration.

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.

Cell-cell adhesion and 3D matrix confinement determine jamming transitions in breast cancer invasion.

Plasticity of cancer invasion and metastasis depends on the ability of cancer cells to switch between collective and single-cell dissemination, controlled by cadherin-mediated cell-cell junctions. In clinical samples, E-cadherin-expressing and -deficient tumours both invade collectively and metastasize equally, implicating additional mechanisms controlling cell-cell cooperation and individualization. Here, using spatially defined organotypic culture, intravital microscopy of mammary tumours in mice and in silico modelling, we identify cell density regulation by three-dimensional tissue boundaries to physically control collective movement irrespective of the composition and stability of cell-cell junctions. Deregulation of adherens junctions by downregulation of E-cadherin and p120-catenin resulted in a transition from coordinated to uncoordinated collective movement along extracellular boundaries, whereas single-cell escape depended on locally free tissue space. These results indicate that cadherins and extracellular matrix confinement cooperate to determine unjamming transitions and stepwise epithelial fluidization towards, ultimately, cell individualization.

Molecular Characterization of Astrocytoma Progression Towards Secondary Glioblastomas Utilizing Patient-Matched Tumor Pairs.

Astrocytomas are primary human brain tumors including diffuse or anaplastic astrocytomas that develop towards secondary glioblastomas over time. However, only little is known about molecular alterations that drive this progression. We measured multi-omics profiles of patient-matched astrocytoma pairs of initial and recurrent tumors from 22 patients to identify molecular alterations associated with tumor progression. Gene copy number profiles formed three major subcluters, but more than half of the patient-matched astrocytoma pairs differed in their gene copy number profiles like astrocytomas from different patients. Chromosome 10 deletions were not observed for diffuse astrocytomas, but occurred in corresponding recurrent tumors. Gene expression profiles formed three other major subclusters and patient-matched expression profiles were much more heterogeneous than their copy number profiles. Still, recurrent tumors showed a strong tendency to switch to the mesenchymal subtype. The direct progression of diffuse astrocytomas to secondary glioblastomas showed the largest number of transcriptional changes. Astrocytoma progression groups were further distinguished by signaling pathway expression signatures affecting cell division, interaction and differentiation. As expected, IDH1 was most frequently mutated closely followed by TP53, but also MUC4 involved in the regulation of apoptosis and proliferation was frequently mutated. Astrocytoma progression groups differed in their mutation frequencies of these three genes. Overall, patient-matched astrocytomas can differ substantially within and between patients, but still molecular signatures associated with the progression to secondary glioblastomas exist and should be analyzed for their potential clinical relevance in future studies.

Modelling collective cell motion: are on- and off-lattice models equivalent?

Biological processes, such as embryonic development, wound repair and cancer invasion, or bacterial swarming and fruiting body formation, involve collective motion of cells as a coordinated group. Collective cell motion of eukaryotic cells often includes interactions that result in polar alignment of cell velocities, while bacterial patterns typically show features of apolar velocity alignment. For analysing the population-scale effects of these different alignment mechanisms, various on- and off-lattice agent-based models have been introduced. However, discriminating model-specific artefacts from general features of collective cell motion is challenging. In this work, we focus on equivalence criteria at the population level to compare on- and off-lattice models. In particular, we define prototypic off- and on-lattice models of polar and apolar alignment, and show how to obtain an on-lattice from an off-lattice model of velocity alignment. By characterizing the behaviour and dynamical description of collective migration models at the macroscopic level, we suggest the type of phase transitions and possible patterns in the approximative macroscopic partial differential equation descriptions as informative equivalence criteria between on- and off-lattice models. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Multi-scale analysis and modelling of collective migration in biological systems.

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Stem cell-associated heterogeneity in Glioblastoma results from intrinsic tumor plasticity shaped by the microenvironment.

The identity and unique capacity of cancer stem cells (CSC) to drive tumor growth and resistance have been challenged in brain tumors. Here we report that cells expressing CSC-associated cell membrane markers in Glioblastoma (GBM) do not represent a clonal entity defined by distinct functional properties and transcriptomic profiles, but rather a plastic state that most cancer cells can adopt. We show that phenotypic heterogeneity arises from non-hierarchical, reversible state transitions, instructed by the microenvironment and is predictable by mathematical modeling. Although functional stem cell properties were similar in vitro, accelerated reconstitution of heterogeneity provides a growth advantage in vivo, suggesting that tumorigenic potential is linked to intrinsic plasticity rather than CSC multipotency. The capacity of any given cancer cell to reconstitute tumor heterogeneity cautions against therapies targeting CSC-associated membrane epitopes. Instead inherent cancer cell plasticity emerges as a novel relevant target for treatment.

Whither systems medicine?

New technologies to generate, store and retrieve medical and research data are inducing a rapid change in clinical and translational research and health care. Systems medicine is the interdisciplinary approach wherein physicians and clinical investigators team up with experts from biology, biostatistics, informatics, mathematics and computational modeling to develop methods to use new and stored data to the benefit of the patient. We here provide a critical assessment of the opportunities and challenges arising out of systems approaches in medicine and from this provide a definition of what systems medicine entails. Based on our analysis of current developments in medicine and healthcare and associated research needs, we emphasize the role of systems medicine as a multilevel and multidisciplinary methodological framework for informed data acquisition and interdisciplinary data analysis to extract previously inaccessible knowledge for the benefit of patients.

Patterns of Tumor Progression Predict Small and Tissue-Specific Tumor-Originating Niches.

The development of cancer is a multistep process in which cells increase in malignancy through progressive alterations. Such altered cells compete with wild-type cells and have to establish within a tissue in order to induce tumor formation. The range of this competition and the tumor-originating cell type which acquires the first alteration is unknown for most human tissues, mainly because the involved processes are hardly observable, aggravating an understanding of early tumor development. On the tissue scale, one observes different progression types, namely with and without detectable benign precursor stages. Human epidemiological data on the ratios of the two progression types exhibit large differences between cancers. The idea of this study is to utilize data of the ratios of progression types in human cancers to estimate the homeostatic range of competition in human tissues. This homeostatic competition range can be interpreted as necessary numbers of altered cells to induce tumor formation on the tissue scale. For this purpose, we develop a cell-based stochastic model which is calibrated with newly-interpreted human epidemiological data. We find that the number of tumor cells which inevitably leads to later tumor formation is surprisingly small compared to the overall tumor and largely depends on the human tissue type. This result points toward the existence of a tissue-specific tumor-originating niche in which the fate of tumor development is decided early and long before a tumor becomes detectable. Moreover, our results suggest that the fixation of tumor cells in the tumor-originating niche triggers new processes which accelerate tumor growth after normal tissue homeostasis is voided. Our estimate for the human colon agrees well with the size of the stem cell niche in colonic crypts. For other tissues, our results might aid to identify the tumor-originating cell type. For instance, data on primary and secondary glioblastoma suggest that the tumors originate from a cell type competing in a range of 300 - 1,900 cells.

Arginine Deprivation Therapy: Putative Strategy to Eradicate Glioblastoma Cells by Radiosensitization.

Tumor cells-even if nonauxotrophic-are often highly sensitive to arginine deficiency. We hypothesized that arginine deprivation therapy (ADT) if combined with irradiation could be a new treatment strategy for glioblastoma (GBM) patients because systemic ADT is independent of local penetration and diffusion limitations. A proof-of-principle in vitro study was performed with ADT being mimicked by application of recombinant human arginase or arginine-free diets. ADT inhibited two-dimensional (2-D) growth and cell-cycle progression, and reduced growth recovery after completion of treatment in four different GBM cell line models. Cells were less susceptible to ADT alone in the presence of citrulline and in a three-dimensional (3-D) environment. Migration and 3-D invasion were not unfavorably affected. However, ADT caused a significant radiosensitization that was more pronounced in a GBM cell model with p53 loss of function as compared with its p53-wildtype counterpart. The synergistic effect was independent of basic and induced argininosuccinate synthase or argininosuccinate lyase protein expression and not abrogated by the presence of citrulline. The radiosensitizing potential was maintained or even more distinguishable in a 3-D environment as verified in p53-knockdown and p53-wildtype U87-MG cells via a 60-day spheroid control probability assay. Although the underlying mechanism is still ambiguous, the observation of ADT-induced radiosensitization is of great clinical interest, in particular for patients with GBM showing high radioresistance and/or p53 loss of function. Mol Cancer Ther; 17(2); 393-406. ©2017 AACRSee all articles in this MCT Focus section, "Developmental Therapeutics in Radiation Oncology."

Amoeboid-mesenchymal migration plasticity promotes invasion only in complex heterogeneous microenvironments.

During tissue invasion individual tumor cells exhibit two interconvertible migration modes, namely mesenchymal and amoeboid migration. The cellular microenvironment triggers the switch between both modes, thereby allowing adaptation to dynamic conditions. It is, however, unclear if this amoeboid-mesenchymal migration plasticity contributes to a more effective tumor invasion. We address this question with a mathematical model, where the amoeboid-mesenchymal migration plasticity is regulated in response to local extracellular matrix resistance. Our numerical analysis reveals that extracellular matrix structure and presence of a chemotactic gradient are key determinants of the model behavior. Only in complex microenvironments, if the extracellular matrix is highly heterogeneous and a chemotactic gradient directs migration, the amoeboid-mesenchymal migration plasticity allows a more widespread invasion compared to the non-switching amoeboid and mesenchymal modes. Importantly, these specific conditions are characteristic for in vivo tumor invasion. Thus, our study suggests that in vitro systems aiming at unraveling the underlying molecular mechanisms of tumor invasion should take into account the complexity of the microenvironment by considering the combined effects of structural heterogeneities and chemical gradients on cell migration.

Cell adhesion heterogeneity reinforces tumour cell dissemination: novel insights from a mathematical model.

BACKGROUND: Cancer cell invasion, dissemination, and metastasis have been linked to an epithelial-mesenchymal transition (EMT) of individual tumour cells. During EMT, adhesion molecules like E-cadherin are downregulated and the decrease of cell-cell adhesion allows tumour cells to dissociate from the primary tumour mass. This complex process depends on intracellular cues that are subject to genetic and epigenetic variability, as well as extrinsic cues from the local environment resulting in a spatial heterogeneity in the adhesive phenotype of individual tumour cells. Here, we use a novel mathematical model to study how adhesion heterogeneity, influenced by intrinsic and extrinsic factors, affects the dissemination of tumour cells from an epithelial cell population. The model is a multiscale cellular automaton that couples intracellular adhesion receptor regulation with cell-cell adhesion. RESULTS: Simulations of our mathematical model indicate profound effects of adhesion heterogeneity on tumour cell dissemination. In particular, we show that a large variation of intracellular adhesion receptor concentrations in a cell population reinforces cell dissemination, regardless of extrinsic cues mediated through the local cell density. However, additional control of adhesion receptor concentration through the local cell density, which can be assumed in healthy cells, weakens the effect. Furthermore, we provide evidence that adhesion heterogeneity can explain the remarkable differences in adhesion receptor concentrations of epithelial and mesenchymal phenotypes observed during EMT and might drive early dissemination of tumour cells. CONCLUSIONS: Our results suggest that adhesion heterogeneity may be a universal trigger to reinforce cell dissemination in epithelial cell populations. This effect can be at least partially compensated by a control of adhesion receptor regulation through neighbouring cells. Accordingly, our findings explain how both an increase in intra-tumour adhesion heterogeneity and the loss of control through the local environment can promote tumour cell dissemination. REVIEWERS: This article was reviewed by Hanspeter Herzel, Thomas Dandekar and Marek Kimmel.

CellTrans: An R Package to Quantify Stochastic Cell State Transitions.

Many normal and cancerous cell lines exhibit a stable composition of cells in distinct states which can, e.g., be defined on the basis of cell surface markers. There is evidence that such an equilibrium is associated with stochastic transitions between distinct states. Quantifying these transitions has the potential to better understand cell lineage compositions. We introduce CellTrans, an R package to quantify stochastic cell state transitions from cell state proportion data from fluorescence-activated cell sorting and flow cytometry experiments. The R package is based on a mathematical model in which cell state alterations occur due to stochastic transitions between distinct cell states whose rates only depend on the current state of a cell. CellTrans is an automated tool for estimating the underlying transition probabilities from appropriately prepared data. We point out potential analytical challenges in the quantification of these cell transitions and explain how CellTrans handles them. The applicability of CellTrans is demonstrated on publicly available data on the evolution of cell state compositions in cancer cell lines. We show that CellTrans can be used to (1) infer the transition probabilities between different cell states, (2) predict cell line compositions at a certain time, (3) predict equilibrium cell state compositions, and (4) estimate the time needed to reach this equilibrium. We provide an implementation of CellTrans in R, freely available via GitHub (https://github.com/tbuder/CellTrans).

Accelerated cell divisions drive the outgrowth of the regenerating spinal cord in axolotls.

Axolotls are unique in their ability to regenerate the spinal cord. However, the mechanisms that underlie this phenomenon remain poorly understood. Previously, we showed that regenerating stem cells in the axolotl spinal cord revert to a molecular state resembling embryonic neuroepithelial cells and functionally acquire rapid proliferative divisions (Rodrigo Albors et al., 2015). Here, we refine the analysis of cell proliferation in space and time and identify a high-proliferation zone in the regenerating spinal cord that shifts posteriorly over time. By tracking sparsely-labeled cells, we also quantify cell influx into the regenerate. Taking a mathematical modeling approach, we integrate these quantitative datasets of cell proliferation, neural stem cell activation and cell influx, to predict regenerative tissue outgrowth. Our model shows that while cell influx and neural stem cell activation play a minor role, the acceleration of the cell cycle is the major driver of regenerative spinal cord outgrowth in axolotls.

Model-Based Evaluation of Spontaneous Tumor Regression in Pilocytic Astrocytoma.

Pilocytic astrocytoma (PA) is the most common brain tumor in children. This tumor is usually benign and has a good prognosis. Total resection is the treatment of choice and will cure the majority of patients. However, often only partial resection is possible due to the location of the tumor. In that case, spontaneous regression, regrowth, or progression to a more aggressive form have been observed. The dependency between the residual tumor size and spontaneous regression is not understood yet. Therefore, the prognosis is largely unpredictable and there is controversy regarding the management of patients for whom complete resection cannot be achieved. Strategies span from pure observation (wait and see) to combinations of surgery, adjuvant chemotherapy, and radiotherapy. Here, we introduce a mathematical model to investigate the growth and progression behavior of PA. In particular, we propose a Markov chain model incorporating cell proliferation and death as well as mutations. Our model analysis shows that the tumor behavior after partial resection is essentially determined by a risk coefficient γ, which can be deduced from epidemiological data about PA. Our results quantitatively predict the regression probability of a partially resected benign PA given the residual tumor size and lead to the hypothesis that this dependency is linear, implying that removing any amount of tumor mass will improve prognosis. This finding stands in contrast to diffuse malignant glioma where an extent of resection threshold has been experimentally shown, below which no benefit for survival is expected. These results have important implications for future therapeutic studies in PA that should include residual tumor volume as a prognostic factor.

An Emerging Allee Effect Is Critical for Tumor Initiation and Persistence.

Tumor cells develop different strategies to cope with changing microenvironmental conditions. A prominent example is the adaptive phenotypic switching between cell migration and proliferation. While it has been shown that the migration-proliferation plasticity influences tumor spread, it remains unclear how this particular phenotypic plasticity affects overall tumor growth, in particular initiation and persistence. To address this problem, we formulate and study a mathematical model of spatio-temporal tumor dynamics which incorporates the microenvironmental influence through a local cell density dependence. Our analysis reveals that two dynamic regimes can be distinguished. If cell motility is allowed to increase with local cell density, any tumor cell population will persist in time, irrespective of its initial size. On the contrary, if cell motility is assumed to decrease with respect to local cell density, any tumor population below a certain size threshold will eventually extinguish, a fact usually termed as Allee effect in ecology. These results suggest that strategies aimed at modulating migration are worth to be explored as alternatives to those mainly focused at keeping tumor proliferation under control.

Self-propelled rods exhibit a phase-separated state characterized by the presence of active stresses and the ejection of polar clusters.

We study collections of self-propelled rods (SPR) moving in two dimensions for packing fractions less than or equal to 0.3. We find that in the thermodynamical limit the SPR undergo a phase transition between a disordered gas and a novel phase-separated system state. Interestingly, (global) orientational order patterns-contrary to what has been suggested-vanish in this limit. In the found novel state, the SPR self-organize into a highly dynamical, high-density, compact region-which we call aggregate-which is surrounded by a disordered gas. Active stresses build inside aggregates as a result of the combined effect of local orientational order and active forces. This leads to the most distinctive feature of these aggregates: constant ejection of polar clusters of SPR. This novel phase-separated state represents a novel state of matter characterized by large fluctuations in volume and shape, related to mass ejection, and exhibits positional as well as orientational local order. SPR systems display new physics unseen in other active matter systems.