RESUMEN
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.
Asunto(s)
Colágeno , Matriz Extracelular , Humanos , Proteolisis , Matriz Extracelular/metabolismo , Invasividad Neoplásica/patología , Colágeno/metabolismo , Movimiento Celular/fisiologíaRESUMEN
Cancer is a significant global health issue, with treatment challenges arising from intratumor heterogeneity. This heterogeneity stems mainly from somatic evolution, causing genetic diversity within the tumor, and phenotypic plasticity of tumor cells leading to reversible phenotypic changes. However, the interplay of both factors has not been rigorously investigated. Here, we examine the complex relationship between somatic evolution and phenotypic plasticity, explicitly focusing on the interplay between cell migration and proliferation. This type of phenotypic plasticity is essential in glioblastoma, the most aggressive form of brain tumor. We propose that somatic evolution alters the regulation of phenotypic plasticity in tumor cells, specifically the reaction to changes in the microenvironment. We study this hypothesis using a novel, spatially explicit model that tracks individual cells' phenotypic and genetic states. We assume cells change between migratory and proliferative states controlled by inherited and mutation-driven genotypes and the cells' microenvironment. We observe that cells at the tumor edge evolve to favor migration over proliferation and vice versa in the tumor bulk. Notably, different genetic configurations can result in this pattern of phenotypic heterogeneity. We analytically predict the outcome of the evolutionary process, showing that it depends on the tumor microenvironment. Synthetic tumors display varying levels of genetic and phenotypic heterogeneity, which we show are predictors of tumor recurrence time after treatment. Interestingly, higher phenotypic heterogeneity predicts poor treatment outcomes, unlike genetic heterogeneity. Our research offers a novel explanation for heterogeneous patterns of tumor recurrence in glioblastoma patients.
Asunto(s)
Neoplasias Encefálicas , Movimiento Celular , Proliferación Celular , Glioblastoma , Fenotipo , Microambiente Tumoral , Humanos , Glioblastoma/genética , Glioblastoma/patología , Proliferación Celular/genética , Microambiente Tumoral/genética , Movimiento Celular/genética , Neoplasias Encefálicas/genética , Neoplasias Encefálicas/patología , Mutación , Heterogeneidad Genética , Biología Computacional , Neoplasias/genética , Neoplasias/patología , Modelos BiológicosRESUMEN
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.
Asunto(s)
Movimiento Celular/fisiología , Modelos Biológicos , Análisis de Sistemas , Fenómenos Biofísicos , Neoplasias de la Mama/patología , Neoplasias de la Mama/fisiopatología , Adhesión Celular/fisiología , Comunicación Celular/fisiología , Biología Computacional , Simulación por Computador , Femenino , Humanos , Invasividad Neoplásica/patología , Invasividad Neoplásica/fisiopatología , Biología de SistemasRESUMEN
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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Astrocitoma/fisiopatología , Neoplasias Encefálicas/fisiopatología , Modelos Biológicos , Modelos Estadísticos , Regresión Neoplásica Espontánea/fisiopatología , Apoptosis/genética , Astrocitoma/patología , Neoplasias Encefálicas/patología , Proliferación Celular/genética , Simulación por Computador , Humanos , Mutación/genética , Regresión Neoplásica Espontánea/patología , Neoplasia ResidualRESUMEN
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.
Asunto(s)
Modelos Biológicos , Procesos Neoplásicos , Microambiente Tumoral/fisiología , Recuento de Células , Movimiento Celular/fisiología , Proliferación Celular/fisiología , Biología Computacional , Simulación por ComputadorRESUMEN
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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Biología de Sistemas/métodos , Modelos Biológicos , Myxococcus xanthus/citología , Programas InformáticosRESUMEN
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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Proteínas de la Matriz Extracelular/metabolismo , Matriz Extracelular/patología , Desnutrición/patología , Osteoporosis/patología , Ovariectomía , Adipogénesis/efectos de los fármacos , Animales , Proteínas Morfogenéticas Óseas/genética , Proteínas Morfogenéticas Óseas/metabolismo , Colágeno , Modelos Animales de Enfermedad , Matriz Extracelular/metabolismo , Proteínas de la Matriz Extracelular/química , Quinasas MAP Reguladas por Señal Extracelular/metabolismo , Femenino , Marcadores Genéticos/genética , Integrinas/metabolismo , Desnutrición/metabolismo , Osteoporosis/metabolismo , Ratas , Ratas Sprague-DawleyRESUMEN
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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Movimiento Celular/fisiología , Modelos Biológicos , Animales , Recuento de Células , Microambiente Celular , Simulación por Computador , Humanos , Conceptos Matemáticos , Procesos EstocásticosRESUMEN
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.
Asunto(s)
Myxococcus/citología , Myxococcus/crecimiento & desarrollo , Análisis por Conglomerados , Recuento de Colonia Microbiana , Movimiento/fisiologíaRESUMEN
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.
Asunto(s)
Macrófagos , Macrófagos Asociados a Tumores , Microambiente Tumoral , Modelos Teóricos , BiologíaRESUMEN
We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node is empty. Here we show that such effects lead to a surprisingly rich variety of self-organized spatial patterns. As particles exhibit an increasingly higher tendency to align to neighbors, they first self-segregate into disordered particle aggregates. Aggregates turn into traffic jams. Traffic jams evolve toward gliders, triangular high density regions that migrate in a well-defined direction. Maximum order is achieved by the formation of elongated high density regions--bands--that transverse the entire system. Numerical evidence suggests that below the percolation density the phase transition associated with orientational order is of first order, while at full occupancy it is of second order.
RESUMEN
We are interested in deciphering the mechanisms for morphogenesis in the Red Sea scleractinian coral Stylophora pistillata with the help of mathematical models. Previous mathematical models for coral morphogenesis assume that skeletal growth is proportional to the amount of locally available energetic resources like diffusible nutrients and photosynthetic products. We introduce a new model which includes factors like dissolved nutrients and photosynthates, but these resources do not serve as building blocks for growth but rather provide some kind of positional information for coral morphogenesis. Depending on this positional information side branches are generated, splittings of branches take place and branch growth direction is determined. The model results are supported by quantitative comparisons with experimental data obtained from young coral colonies.
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Fenómenos Fisiológicos Nutricionales de los Animales , Antozoos/crecimiento & desarrollo , Morfogénesis , Animales , Antozoos/anatomía & histología , Antozoos/genética , Huesos/anatomía & histología , Simulación por Computador , Genotipo , Modelos BiológicosRESUMEN
Invasion of malignant glioma is a highly complex phenomenon involving molecular and cellular processes at various spatio-temporal scales, whose precise interplay is still not fully understood. In order to identify the intrinsic cellular mechanisms of glioma invasion, we study an in vitro culture of glioma cells. By means of a computational approach, based on a cellular automaton model, we compare simulation results to the experimental data and deduce cellular mechanisms from microscopic and macroscopic observables (experimental data). For the first time, it is shown that the migration/proliferation dichotomy plays a central role in the invasion of glioma cells. Interestingly, we conclude that a diverging invasive zone is a consequence of this dichotomy. Additionally, we observe that radial persistence of glioma cells in the vicinity of dense areas accelerates the invasion process. We argue that this persistence results from a cell-cell repulsion mechanism. If glioma cell behavior is regulated through a migration/proliferation dichotomy and a self-repellent mechanism, our simulations faithfully reproduce all the experimental observations.
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Neoplasias Encefálicas/patología , Glioma/patología , Modelos Biológicos , Algoritmos , Movimiento Celular/fisiología , Proliferación Celular , Humanos , Invasividad Neoplásica/fisiopatología , Esferoides Celulares , Células Tumorales CultivadasRESUMEN
Lattice-gas cellular automata (LGCAs) can serve as stochastic mathematical models for collective behavior (e.g. pattern formation) emerging in populations of interacting cells. In this paper, a two-phase optimization algorithm for global parameter estimation in LGCA models is presented. In the first phase, local minima are identified through gradient-based optimization. Algorithmic differentiation is adopted to calculate the necessary gradient information. In the second phase, for global optimization of the parameter set, a multi-level single-linkage method is used. As an example, the parameter estimation algorithm is applied to a LGCA model for early in vitro angiogenic pattern formation.
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Algoritmos , Células , Simulación por Computador , Modelos Biológicos , Neovascularización FisiológicaRESUMEN
The dimorphic yeasts Candida boidinii and Yarrowia lipolytica were applied as model organisms to study mycelial growth. A mathematical model of hybrid cellular automaton type was developed to analyze the impact of different biological assumptions on the predicted development of filamentous yeast colonies. The one-dimensional model described discrete cells and continuous distribution of nutrients. The simulation algorithm accounted for proliferation of cells, diffusion of nutrient, as well as biomass decay and recycling inside the mycelium. Simulations reproduced the spatio-temporal development of C. boidinii colonies when a diffusion-limited growth algorithm based on the growth of pseudohyphal cells was applied. Development of Y. lipolytica colonies could only be reproduced when proliferation was restricted to the colony boundary, and cell decay and biomass recycling were incorporated into the model. The results suggested that cytoplasm, which served as the secondary nutrient resource, had to be translocated inside the hyphal network.
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Candida/crecimiento & desarrollo , Hifa/crecimiento & desarrollo , Modelos Biológicos , Yarrowia/crecimiento & desarrollo , Algoritmos , Candida/metabolismo , División Celular/fisiología , Simulación por Computador , Hifa/metabolismo , Yarrowia/metabolismoRESUMEN
Colony development of the dimorphic yeasts Yarrowia lipolytica and Candida boidinii on solid agar substrates under glucose limitation served as a model system for mycelial development of higher filamentous fungi. Strong differences were observed in the behaviour of both yeasts: C. boidinii colonies reached a final colony extension which was small compared to the size of the growth field. They formed cell-density profiles which steeply declined along the colony radius and no biomass decay processes could be detected. The stop of colony extension coincided with the depletion of glucose from the growth substrate. These findings supported the hypothesis that glucose-limited C. boidinii colonies can be regarded as populations of single cells which grow according to a diffusion-limited growth mechanism. Y. lipolytica colonies continued to extend after the depletion of the primary nutrient resource, glucose, until the populations covered the entire growth field which was accomplished by utilization of mycelial biomass.
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Candida/crecimiento & desarrollo , Hifa/citología , Hifa/crecimiento & desarrollo , Modelos Biológicos , Yarrowia/crecimiento & desarrollo , Agar , Candida/citología , Glucosa/metabolismo , Yarrowia/citologíaRESUMEN
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.
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COVID-19 , Análisis por Conglomerados , Epidemias , HumanosRESUMEN
At the beginning of this special issue of Acta Biotheoretica carrying the above title, we present a brief overview on currently important topics that have been brought up during the last "European Conference on Mathematical and Theoretical Biology" in Edinburgh. After emphasizing the need for a "synthetic biology" also from the side of theory, model building and analysis, we survey most plenary talks of this Conference and a selected series of eigth review articles, which are mainly related to corresponding minisymposia, reflecting the current state of the art and the lively discussion within this interdisciplinary field.
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Matemática , Biología de Sistemas , Animales , Células , Humanos , Modelos BiológicosRESUMEN
Lattice-gas cellular automaton (LGCA) and lattice Boltzmann (LB) models are promising models for studying emergent behaviour of transport and interaction processes in biological systems. In this chapter, we will emphasise the use of LGCA/LB models and the derivation and analysis of LGCA models ranging from the classical example dynamics of fluid flow to clotting phenomena in cerebral aneurysms and the invasion of tumour cells.