Publications by authors named "Andreas Deutsch"

51 Publications

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

PLoS Comput Biol 2021 Jun 15;17(6):e1009066. Epub 2021 Jun 15.

Centre for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany.

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.
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http://dx.doi.org/10.1371/journal.pcbi.1009066DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8232544PMC
June 2021

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

Nat Cell Biol 2020 09 24;22(9):1103-1115. Epub 2020 Aug 24.

Department of Cell Biology, Radboud Institute for Molecular Life Sciences, Radboud University Medical Center, Nijmegen, the Netherlands.

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.
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http://dx.doi.org/10.1038/s41556-020-0552-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7502685PMC
September 2020

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

Philos Trans R Soc Lond B Biol Sci 2020 09 27;375(1807):20190377. Epub 2020 Jul 27.

Centre de Recherches sur la Cognition Animale, Centre de Biologie Intégrative, Université de Toulouse, CNRS, UPS, Toulouse, France.

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'.
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http://dx.doi.org/10.1098/rstb.2019.0377DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7423374PMC
September 2020

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

Philos Trans R Soc Lond B Biol Sci 2020 09 27;375(1807):20190378. Epub 2020 Jul 27.

Laboratoire J. A. Dieudonné, Université Côte d'Azur, UMR 7351 CNRS, Parc Valrose, 06108 Nice Cedex 02, France.

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'.
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http://dx.doi.org/10.1098/rstb.2019.0378DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7423376PMC
September 2020

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

Cancers (Basel) 2020 Jun 26;12(6). Epub 2020 Jun 26.

National Center for Tumor Diseases (NCT), Partner Site Dresden, D-01307 Dresden, Germany.

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.
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http://dx.doi.org/10.3390/cancers12061696DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7352509PMC
June 2020

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

Nat Commun 2019 04 16;10(1):1787. Epub 2019 Apr 16.

NorLux Neuro-Oncology Laboratory, Department of Oncology, Luxembourg Institute of Health, L-1526, Luxembourg, Luxembourg.

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.
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http://dx.doi.org/10.1038/s41467-019-09853-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6467886PMC
April 2019

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

Front Oncol 2018 10;8:668. Epub 2019 Jan 10.

Center for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany.

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.
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http://dx.doi.org/10.3389/fonc.2018.00668DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6335293PMC
January 2019

Whither systems medicine?

Exp Mol Med 2018 03 2;50(3):e453. Epub 2018 Mar 2.

Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg, Germany.

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.
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http://dx.doi.org/10.1038/emm.2017.290DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5898894PMC
March 2018

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

Sci Rep 2017 08 23;7(1):9237. Epub 2017 Aug 23.

Center for Information Services and High Performance Computing, Technische Universität Dresden, 01062, Dresden, Germany.

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.
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http://dx.doi.org/10.1038/s41598-017-09300-3DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5569097PMC
August 2017

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

Mol Cancer Ther 2018 02 22;17(2):393-406. Epub 2017 Aug 22.

OncoRay - National Center for Radiation Research in Oncology, Faculty of Medicine and University Hospital Carl Gustav Carus, TU Dresden, and Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany.

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 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.
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http://dx.doi.org/10.1158/1535-7163.MCT-16-0807DOI Listing
February 2018

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

Biol Direct 2017 08 11;12(1):18. Epub 2017 Aug 11.

Center for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Str. 46, Dresden, 01062, Germany.

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.
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http://dx.doi.org/10.1186/s13062-017-0188-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5553611PMC
August 2017

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

Bioinform Biol Insights 2017 16;11:1177932217712241. Epub 2017 Jun 16.

Fakultät Informatik/Mathematik, Hochschule für Technik und Wirtschaft Dresden, Dresden, Germany.

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).
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http://dx.doi.org/10.1177/1177932217712241DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5478290PMC
June 2017

Obituary: Hans Meinhardt (1938-2016).

Bull Math Biol 2017 02 4;79(2):383-388. Epub 2017 Jan 4.

Center for Information Services and High Performance Computing, Technische Universität Dresden, 01062, Dresden, Germany.

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http://dx.doi.org/10.1007/s11538-016-0243-4DOI Listing
February 2017

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

Elife 2016 11 25;5. Epub 2016 Nov 25.

Center for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany.

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.
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http://dx.doi.org/10.7554/eLife.20357DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5182066PMC
November 2016

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

PLoS Comput Biol 2015 Dec 10;11(12):e1004662. Epub 2015 Dec 10.

Zentrum für Informationsdienste und Hochleistungsrechnen (ZIH), Technische Universität Dresden, Dresden, Germany.

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.
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http://dx.doi.org/10.1371/journal.pcbi.1004662DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4675550PMC
December 2015

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

PLoS Comput Biol 2015 Sep 3;11(9):e1004366. Epub 2015 Sep 3.

Center for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany.

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.
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http://dx.doi.org/10.1371/journal.pcbi.1004366DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4559422PMC
September 2015

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

Phys Rev E Stat Nonlin Soft Matter Phys 2015 Jul 27;92(1):012322. Epub 2015 Jul 27.

Université Nice Sophia Antipolis, Laboratoire J.A. Dieudonné, UMR 7351 CNRS, Parc Valrose, F-06108 Nice Cedex 02, France.

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.
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http://dx.doi.org/10.1103/PhysRevE.92.012322DOI Listing
July 2015

Impaired extracellular matrix structure resulting from malnutrition in ovariectomized mature rats.

Histochem Cell Biol 2015 Nov 26;144(5):491-507. Epub 2015 Jul 26.

Laboratory of Experimental Trauma Surgery, Justus-Liebig University, Giessen, Germany.

Bone loss is a symptom related to disease and age, which reflects on bone cells and ECM. Discrepant regulation affects cell proliferation and ECM localization. Rat model of osteoporosis (OVX) was investigated against control rats (Sham) at young and old ages. Biophysical, histological and molecular techniques were implemented to examine the underlying cellular and extracellular matrix changes and to assess the mechanisms contributing to bone loss in the context of aging and the widely used osteoporotic models in rats. Bone loss exhibited a compromised function of bone cells and infiltration of adipocytes into bone marrow. However, the expression of genes regulating collagen catabolic process and adipogenesis was chronologically shifted in diseased bone in comparison with aged bone. The data showed the involvement of Wnt signaling inhibition in adipogenesis and bone loss due to over-expression of SOST in both diseased and aged bone. Further, in the OVX animals, an integrin-mediated ERK activation indicated the role of MAPK in osteoblastogenesis and adipogenesis. The increased PTH levels due to calcium and estrogen deficiency activated osteoblastogenesis. Thusly, RANKL-mediated osteoclastogenesis was initiated. Interestingly, the data show the role of MEPE regulating osteoclast-mediated resorption at late stages in osteoporotic bone. The interplay between ECM and bone cells change tissue microstructure and properties. The involvement of Wnt and MAPK pathways in activating cell proliferation has intriguing similarities to oncogenesis and myeloma. The study indicates the importance of targeting both pathways simultaneously to remedy metabolic bone diseases and age-related bone loss.
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http://dx.doi.org/10.1007/s00418-015-1356-9DOI Listing
November 2015

Analysis of individual cell trajectories in lattice-gas cellular automaton models for migrating cell populations.

Bull Math Biol 2015 Apr 17;77(4):660-97. Epub 2015 Apr 17.

Technische Universität Dresden, Zentrum für Informationsdienste und Hochleistungsrechnen, Nöthnitzer Strasse 46, 01187, Dresden, Germany,

Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also important observables of collective dynamics related to individual cell behavior. In particular, individual cell trajectories are footprints of emergent behavior in populations of migrating cells. Lattice-gas cellular automata (LGCA) have proven successful to model and analyze collective behavior arising from interactions of migrating cells. There are well-established methods to analyze cell density patterns in LGCA models. Although LGCA dynamics are defined by cell-based rules, individual cells are not distinguished. Therefore, individual cell trajectories cannot be analyzed in LGCA so far. Here, we extend the classical LGCA framework to allow labeling and tracking of individual cells. We consider cell number conserving LGCA models of migrating cell populations where cell interactions are regulated by local cell density and derive stochastic differential equations approximating individual cell trajectories in LGCA. This result allows the prediction of complex individual cell trajectories emerging in LGCA models and is a basis for model-experiment comparisons at the individual cell level.
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http://dx.doi.org/10.1007/s11538-015-0079-3DOI Listing
April 2015

Evolutionary game theory: cells as players.

Mol Biosyst 2014 Dec;10(12):3044-65

Fachhochschule Schmalkalden, Faculty of Electrical Engineering, Blechhammer, 98574 Schmalkalden, Germany.

In two papers we review game theory applications in biology below the level of cognitive living beings. It can be seen that evolution and natural selection replace the rationality of the actors appropriately. Even in these micro worlds, competing situations and cooperative relationships can be found and modeled by evolutionary game theory. Also those units of the lowest levels of life show different strategies for different environmental situations or different partners. We give a wide overview of evolutionary game theory applications to microscopic units. In this first review situations on the cellular level are tackled. In particular metabolic problems are discussed, such as ATP-producing pathways, secretion of public goods and cross-feeding. Further topics are cyclic competition among more than two partners, intra- and inter-cellular signalling, the struggle between pathogens and the immune system, and the interactions of cancer cells. Moreover, we introduce the theoretical basics to encourage scientists to investigate problems in cell biology and molecular biology by evolutionary game theory.
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http://dx.doi.org/10.1039/c3mb70602hDOI Listing
December 2014

Evolutionary game theory: molecules as players.

Mol Biosyst 2014 Dec;10(12):3066-74

Friedrich-Schiller-University Jena, Faculty of Biology and Pharmacy, Department of Bioinformatics, Ernst-Abbe-Platz 2, 07743 Jena, Germany.

In this and an accompanying paper we review the use of game theoretical concepts in cell biology and molecular biology. This review focuses on the subcellular level by considering viruses, genes, and molecules as players. We discuss in which way catalytic RNA can be treated by game theory. Moreover, genes can compete for success in replication and can have different strategies in interactions with other genetic elements. Also transposable elements, or "jumping genes", can act as players because they usually bear different traits or strategies. Viruses compete in the case of co-infecting a host cell. Proteins interact in a game theoretical sense when forming heterodimers. Finally, we describe how the Shapley value can be applied to enzymes in metabolic pathways. We show that game theory can be successfully applied to describe and analyse scenarios at the molecular level resulting in counterintuitive conclusions.
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http://dx.doi.org/10.1039/c3mb70601jDOI Listing
December 2014

Autoregressive higher-order hidden Markov models: exploiting local chromosomal dependencies in the analysis of tumor expression profiles.

PLoS One 2014 23;9(6):e100295. Epub 2014 Jun 23.

Center for Information Services and High Performance Computing, Dresden University of Technology, Dresden, Germany.

Changes in gene expression programs play a central role in cancer. Chromosomal aberrations such as deletions, duplications and translocations of DNA segments can lead to highly significant positive correlations of gene expression levels of neighboring genes. This should be utilized to improve the analysis of tumor expression profiles. Here, we develop a novel model class of autoregressive higher-order Hidden Markov Models (HMMs) that carefully exploit local data-dependent chromosomal dependencies to improve the identification of differentially expressed genes in tumor. Autoregressive higher-order HMMs overcome generally existing limitations of standard first-order HMMs in the modeling of dependencies between genes in close chromosomal proximity by the simultaneous usage of higher-order state-transitions and autoregressive emissions as novel model features. We apply autoregressive higher-order HMMs to the analysis of breast cancer and glioma gene expression data and perform in-depth model evaluation studies. We find that autoregressive higher-order HMMs clearly improve the identification of overexpressed genes with underlying gene copy number duplications in breast cancer in comparison to mixture models, standard first- and higher-order HMMs, and other related methods. The performance benefit is attributed to the simultaneous usage of higher-order state-transitions in combination with autoregressive emissions. This benefit could not be reached by using each of these two features independently. We also find that autoregressive higher-order HMMs are better able to identify differentially expressed genes in tumors independent of the underlying gene copy number status in comparison to the majority of related methods. This is further supported by the identification of well-known and of previously unreported hotspots of differential expression in glioblastomas demonstrating the efficacy of autoregressive higher-order HMMs for the analysis of individual tumor expression profiles. Moreover, we reveal interesting novel details of systematic alterations of gene expression levels in known cancer signaling pathways distinguishing oligodendrogliomas, astrocytomas and glioblastomas. An implementation is available under www.jstacs.de/index.php/ARHMM.
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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0100295PLOS
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4067306PMC
November 2015

How does a single cell know when the liver has reached its correct size?

PLoS One 2014 1;9(4):e93207. Epub 2014 Apr 1.

Center for Information Services and High Performance Computing, Technical University Dresden, Dresden, Germany.

The liver is a multi-functional organ that regulates major physiological processes and that possesses a remarkable regeneration capacity. After loss of functional liver mass the liver grows back to its original, individual size through hepatocyte proliferation and apoptosis. How does a single hepatocyte 'know' when the organ has grown to its final size? This work considers the initial growth phase of liver regeneration after partial hepatectomy in which the mass is restored. There are strong and valid arguments that the trigger of proliferation after partial hepatectomy is mediated through the portal blood flow. It remains unclear, if either or both the concentration of metabolites in the blood or the shear stress are crucial to hepatocyte proliferation and liver size control. A cell-based mathematical model is developed that helps discriminate the effects of these two potential triggers. Analysis of the mathematical model shows that a metabolic load and a hemodynamical hypothesis imply different feedback mechanisms at the cellular scale. The predictions of the developed mathematical model are compared to experimental data in rats. The assumption that hepatocytes are able to buffer the metabolic load leads to a robustness against short-term fluctuations of the trigger which can not be achieved with a purely hemodynamical trigger.
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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0093207PLOS
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3972176PMC
December 2015

Change of mechanical vertebrae properties due to progressive osteoporosis: combined biomechanical and finite-element analysis within a rat model.

Med Biol Eng Comput 2014 Apr 12;52(4):405-14. Epub 2014 Feb 12.

Institute for Materials Science and Max Bergmann Center of Biomaterials, Dresden University of Technology, 01062, Dresden, Germany,

For assessing mechanical properties of osteoporotic bone, biomechanical testing combined with in silico modeling plays a key role. The present study focuses on microscopic mechanical bone properties in a rat model of postmenopausal osteoporosis. Female Sprague-Dawley rats were (1) euthanized without prior interventions, (2) sham-operated, and (3) subjected to ovariectomy combined with a multi-deficiencies diet. Rat vertebrae (corpora vertebrae) were imaged by micro-CT, their stiffness was determined by compression tests, and load-induced stress states as well as property changes due to the treatment were analyzed by finite-element modeling. By comparing vertebra stiffness measurements with finite-element calculations of stiffness, an overall microscopic Young's modulus of the bone was determined. Macroscopic vertebra stiffness as well as the microscopic modulus diminish with progression of osteoporosis by about 70 %. After strong initial changes of bone morphology, further decrease in macroscopic stiffness is largely due to decreasing microscopic Young's modulus. The micromechanical stress calculations reveal particularly loaded vertebra regions prone to failure. Osteoporosis-induced changes of the microscopic Young's modulus alter the fracture behavior of bone, may influence bone remodeling, and should be considered in the design of implant materials.
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http://dx.doi.org/10.1007/s11517-014-1140-3DOI Listing
April 2014

Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology.

Bioinformatics 2014 May 17;30(9):1331-2. Epub 2014 Jan 17.

Center for Information Services and High Performance Computing, Technische Universität Dresden, 01062 Dresden, Germany.

Morpheus is a modeling environment for the simulation and integration of cell-based models with ordinary differential equations and reaction-diffusion systems. It allows rapid development of multiscale models in biological terms and mathematical expressions rather than programming code. Its graphical user interface supports the entire workflow from model construction and simulation to visualization, archiving and batch processing.
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http://dx.doi.org/10.1093/bioinformatics/btt772DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3998129PMC
May 2014

Pattern-formation mechanisms in motility mutants of Myxococcus xanthus.

Interface Focus 2012 Dec 3;2(6):774-85. Epub 2012 Oct 3.

Center for Information Services and High Performance Computing (ZIH), Technische Universität Dresden, Zellescher Weg 12, 01069 Dresden, Germany.

Formation of spatial patterns of cells is a recurring theme in biology and often depends on regulated cell motility. Motility of the rod-shaped cells of the bacterium Myxococcus xanthus depends on two motility machineries, type IV pili (giving rise to S-motility) and the gliding motility apparatus (giving rise to A-motility). Cell motility is regulated by occasional reversals. Moving M. xanthus cells can organize into spreading colonies or spore-filled fruiting bodies, depending on their nutritional status. To ultimately understand these two pattern-formation processes and the contributions by the two motility machineries, as well as the cell reversal machinery, we analyse spatial self-organization in three M. xanthus strains: (i) a mutant that moves unidirectionally without reversing by the A-motility system only, (ii) a unidirectional mutant that is also equipped with the S-motility system, and (iii) the wild-type that, in addition to the two motility systems, occasionally reverses its direction of movement. The mutant moving by means of the A-engine illustrates that collective motion in the form of large moving clusters can arise in gliding bacteria owing to steric interactions of the rod-shaped cells, without the need of invoking any biochemical signal regulation. The two-engine strain mutant reveals that the same phenomenon emerges when both motility systems are present, and as long as cells exhibit unidirectional motion only. From the study of these two strains, we conclude that unidirectional cell motion induces the formation of large moving clusters at low and intermediate densities, while it results in vortex formation at very high densities. These findings are consistent with what is known from self-propelled rod models, which strongly suggests that the combined effect of self-propulsion and volume exclusion interactions is the pattern-formation mechanism leading to the observed phenomena. On the other hand, we learn that when cells occasionally reverse their moving direction, as observed in the wild-type, cells form small but strongly elongated clusters and self-organize into a mesh-like structure at high enough densities. These results have been obtained from a careful analysis of the cluster statistics of ensembles of cells, and analysed in the light of a coagulation Smoluchowski equation with fragmentation.
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http://dx.doi.org/10.1098/rsfs.2012.0034DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3499129PMC
December 2012

A general theoretical framework to infer endosomal network dynamics from quantitative image analysis.

Curr Biol 2012 Aug 28;22(15):1381-90. Epub 2012 Jun 28.

Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straβe 38, 01187 Dresden, Germany.

Background: Endocytosis allows the import and distribution of cargo into a series of endosomes with distinct morphological and biochemical characteristics. Our current understanding of endocytic cargo trafficking is based on the kinetics of net cargo transport between endosomal compartments without considering individual endosomes. However, endosomes form a dynamic network of membranes undergoing fusion and fission, thereby continuously exchanging and redistributing cargo. The macroscopic kinetic properties, i.e., the properties of the endosomal network as a whole, result from the collective behaviors of many individual endosomes, a problem so far largely unaddressed.

Results: Here, we developed a general theoretical framework to describe the dynamics of cargo distributions in the endosomal network. We combined the theory with quantitative experiments to study how the macroscopic kinetic properties of the endosomal network emerge from microscopic processes at the level of individual endosomes. We compared our theory predictions to experimental data in which dynamic distributions of endocytosed low-density lipoprotein (LDL) were quantified.

Conclusions: Our theory can quantitatively describe the observed cargo distributions as a function of time. Remarkably, the theory allows determining microscopic kinetic parameters such as the fusion rate between endosomes from still images of cargo distributions at different times of internalization. We show that this method is robust and sensitive because cargo distributions result from an average over many stochastic events in many cells. Our results provide theoretical and experimental support to the "funnel model" of endosome progression and suggest that the conversion of early to late endosomes is the major mode of LDL trafficking.
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http://dx.doi.org/10.1016/j.cub.2012.06.021DOI Listing
August 2012

Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria.

Phys Rev Lett 2012 Mar 28;108(9):098102. Epub 2012 Feb 28.

Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis, UMR CNRS 7351, Parc Valrose, F-06108 Nice Cedex 02, France.

We characterize cell motion in experiments and show that the transition to collective motion in colonies of gliding bacterial cells confined to a monolayer appears through the organization of cells into larger moving clusters. Collective motion by nonequilibrium cluster formation is detected for a critical cell packing fraction around 17%. This transition is characterized by a scale-free power-law cluster-size distribution, with an exponent 0.88±0.07, and the appearance of giant number fluctuations. Our findings are in quantitative agreement with simulations of self-propelled rods. This suggests that the interplay of self-propulsion and the rod shape of bacteria is sufficient to induce collective motion.
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http://dx.doi.org/10.1103/PhysRevLett.108.098102DOI Listing
March 2012

Early embryonic vascular patterning by matrix-mediated paracrine signalling: a mathematical model study.

PLoS One 2011 19;6(9):e24175. Epub 2011 Sep 19.

Department of Applied Mathematics and Institute for Interdisciplinary Mathematics, Faculty of Mathematics, Universidad Complutense de Madrid, Madrid, Spain.

During embryonic vasculogenesis, endothelial precursor cells of mesodermal origin known as angioblasts assemble into a characteristic network pattern. Although a considerable amount of markers and signals involved in this process have been identified, the mechanisms underlying the coalescence of angioblasts into this reticular pattern remain unclear. Various recent studies hypothesize that autocrine regulation of the chemoattractant vascular endothelial growth factor (VEGF) is responsible for the formation of vascular networks in vitro. However, the autocrine regulation hypothesis does not fit well with reported data on in vivo early vascular development. In this study, we propose a mathematical model based on the alternative assumption that endodermal VEGF signalling activity, having a paracrine effect on adjacent angioblasts, is mediated by its binding to the extracellular matrix (ECM). Detailed morphometric analysis of simulated networks and images obtained from in vivo quail embryos reveals the model mimics the vascular patterns with high accuracy. These results show that paracrine signalling can result in the formation of fine-grained cellular networks when mediated by angioblast-produced ECM. This lends additional support to the theory that patterning during early vascular development in the vertebrate embryo is regulated by paracrine signalling.
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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0024175PLOS
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3176223PMC
March 2012
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