Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model

Vega, Rocío; Carretero, Manuel; Travasso, Rui D. M.; Bonilla, L. L.

doi:10.1371/journal.pcbi.1006919

Cited by 30 publications

(43 citation statements)

References 89 publications

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“…Angiogenic sprouting has been extensively studied from a theoretical modelling perspective in numerous physiological and pathological contexts, including tumour growth [ 10 , 16 – 33 ]. Many models [ 18 – 20 , 22 , 24 – 28 , 32 ] fall within the so-called snail-trail paradigm [ 31 ].…”

Section: Introductionmentioning

confidence: 99%

A multiscale model of complex endothelial cell dynamics in early angiogenesis

et al. 2021

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We introduce a hybrid two-dimensional multiscale model of angiogenesis, the process by which endothelial cells (ECs) migrate from a pre-existing vascular bed in response to local environmental cues and cell-cell interactions, to create a new vascular network. Recent experimental studies have highlighted a central role of cell rearrangements in the formation of angiogenic networks. Our model accounts for this phenomenon via the heterogeneous response of ECs to their microenvironment. These cell rearrangements, in turn, dynamically remodel the local environment. The model reproduces characteristic features of angiogenic sprouting that include branching, chemotactic sensitivity, the brush border effect, and cell mixing. These properties, rather than being hardwired into the model, emerge naturally from the gene expression patterns of individual cells. After calibrating and validating our model against experimental data, we use it to predict how the structure of the vascular network changes as the baseline gene expression levels of the VEGF-Delta-Notch pathway, and the composition of the extracellular environment, vary. In order to investigate the impact of cell rearrangements on the vascular network structure, we introduce the mixing measure, a scalar metric that quantifies cell mixing as the vascular network grows. We calculate the mixing measure for the simulated vascular networks generated by ECs of different lineages (wild type cells and mutant cells with impaired expression of a specific receptor). Our results show that the time evolution of the mixing measure is directly correlated to the generic features of the vascular branching pattern, thus, supporting the hypothesis that cell rearrangements play an essential role in sprouting angiogenesis. Furthermore, we predict that lower cell rearrangement leads to an imbalance between branching and sprout elongation. Since the computation of this statistic requires only individual cell trajectories, it can be computed for networks generated in biological experiments, making it a potential biomarker for pathological angiogenesis.

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Section: Introductionmentioning

confidence: 99%

A multiscale model of complex endothelial cell dynamics in early angiogenesis

et al. 2021

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“…To enhance the value of our results, e.g, for studies of metastatic cancer, future works may add cellular mechanisms such as Notch signaling dynamics [ 46 ], models of epithelial/mesenchymal transition and cancer stem cell formation [ 47 , 48 ] to our vertex model. This venue has been successfully followed in studies of angiogenesis [ 49 ].…”

Section: Discussionmentioning

confidence: 99%

“…Promising mechanisms include Notch signaling pathways [ 46 ] and models of the epithelial-mesenchymal transition and cancer stem cell formation [ 47 , 48 ]. Incorporating these cellular mechanisms to our vertex model may pave the way to future progress in this area, much as incorporating the Notch signaling pathway to cellular Potts models helps understanding many aspects of angiogenesis [ 49 ]. Understanding precise biochemical mechanisms influencing cell-cell contact and confluent cellular tissue may help develop therapies for metastatic cancers [ 48 ].…”

Section: Introductionmentioning

confidence: 99%

Tracking collective cell motion by topological data analysis

2020

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By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.

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“…A recent mathematical model of early stage angiogenesis explores the relative importance of mechanical, chemical and cellular cues. Endothelial cells proliferate and move over an extracellular matrix by following external gradients of VEGF, adhesion and stiffness, which are modeled using a cellular Potts model with a finite element description of elasticity [142]. As an early attempt, Bentley et al proposed a hierarchical agent-based model simulating a suggested feedback loop that links VEGF-A tip cell induction with delta-like 4 (Dll4)/notch-mediated lateral inhibition [143].…”

Section: Cell Dynamics Modelsmentioning

confidence: 99%

Angiogenic Networks in Tumors—Insights via Mathematical Modeling

et al. 2020

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Angiogenesis, the formation of a network of blood vessels, is a vital process in the growth of solid tumors as it delivers required nutrients and oxygen. Prior medical studies assert that angiogenesis is influenced by a number of parameters such as endothelial cell migration and proliferation, existence of tumor angiogenesis factors, oxygen, extracellular matrix components, etc. Along with the early developments and findings in the area of tumor angiogenesis, a field of research that has emerged uses mathematical models to interpret and predict the time-course of the crucial factors, as well as new capillary vessel formation, loop formation, and vessel branching. However, most of these early mathematical approaches rely on a small number of parameters; and the characteristics of blood flow, which are significant factors in tumor vessel formation, are neglected. Relatively new integrated models based on the impact of multiple crucial factors and blood flow have seen some success in elucidating the behavior of angiogenesis. Here we review the contributions, opportunities, progress, and challenges of mathematical and computational models for understanding of the tumor-induced angiogenesis, and also consider studies that apply mathematical models to represent blood flow and opportunities for the investigation of therapies and treatments. At the same time, we identify a need for the inclusion of endothelial cell shape and dynamics in models of tumor-induced angiogenesis. Particularly, cell-matrix, cell shape, and cell-cell interaction is necessary for the explanation of blood vessel formation. INDEX TERMS Angiogenesis, mathematical modeling, tumor angiogenesis factor (TAF), endothelial cells (ECs), extracellular matrix (ECM), matrix metalloproteinase MMPs), vascular endothelial growth factor (VEGF), blood flow, vascular adaptation, blood vessel formation, cancer. MOHSEN DORRAKI (Member, IEEE) received the B.Eng. degree in electronics engineering from the Azad University of Birjand, Iran, in 2007, and the M.Sc. degree in electrical engineering from the

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Notch signaling and taxis mechanisms regulate early stage angiogenesis: A mathematical and computational model

Cited by 30 publications

References 89 publications

A multiscale model of complex endothelial cell dynamics in early angiogenesis

A multiscale model of complex endothelial cell dynamics in early angiogenesis

Tracking collective cell motion by topological data analysis

Angiogenic Networks in Tumors—Insights via Mathematical Modeling

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