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A three-dimensional model with two-body interactions for endothelial cells in angiogenesis.

ABSTRACT: We introduce a three-dimensional mathematical model for the dynamics of vascular endothelial cells during sprouting angiogenesis. Angiogenesis is the biological process by which new blood vessels form from existing ones. It has been the subject of numerous theoretical models. These models have successfully replicated various aspects of angiogenesis. Recent studies using particle-based models have highlighted the significant influence of cell shape on network formation, with elongated cells contributing to the formation of branching structures. While most mathematical models are two-dimensional, we aim to investigate whether ellipsoids also form branch-like structures and how their shape affects the pattern. In our model, the shape of a vascular endothelial cell is represented as a spheroid, and a discrete dynamical system is constructed based on the simple assumption of two-body interactions. Numerical simulations demonstrate that our model reproduces the patterns of elongation and branching observed in the early stages of angiogenesis. We show that the pattern formation of the cell population is strongly dependent on the cell shape. Finally, we demonstrate that our current mathematical model reproduces the cell behaviours, specifically cell-mixing, observed in sprouts.

SUBMITTER: Sakai K

PROVIDER: S-EPMC10667370 | biostudies-literature | 2023 Nov

REPOSITORIES: biostudies-literature

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A three-dimensional model with two-body interactions for endothelial cells in angiogenesis.

Sakai Kazuma K Hayashi Tatsuya T Sakai Yusuke Y Mada Jun J Tonami Kazuo K Uchijima Yasunobu Y Kurihara Hiroki H Tokihiro Tetsuji T

Scientific reports 20231123 1

We introduce a three-dimensional mathematical model for the dynamics of vascular endothelial cells during sprouting angiogenesis. Angiogenesis is the biological process by which new blood vessels form from existing ones. It has been the subject of numerous theoretical models. These models have successfully replicated various aspects of angiogenesis. Recent studies using particle-based models have highlighted the significant influence of cell shape on network formation, with elongated cells contr ...[more]

PMID: 37996513

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Project description:Study questionCan primary human uterine microvascular endothelial cells (UtMVECs) be used as a model to study uterine angiogenic responses in vitro that are relevant in pregnancy?Summary answerUtMVECs demonstrated angiogenic responses when stimulated with proangiogenic factors, including sphingosine 1-phosphate (S1P), vascular endothelial growth factor (VEGF), basic fibroblast growth factor (bFGF), physiological levels of wall shear stress (WSS), human chorionic gonadotropin (hCG) and various combinations of estrogen and progesterone.What is known alreadyDuring sprouting angiogenesis, signaling from growth factors and cytokines induces a monolayer of quiescent endothelial cells (ECs) lining the vasculature to degrade the extracellular matrix and invade the surrounding tissue to form new capillaries. During pregnancy and the female reproductive cycle, the uterine endothelium becomes activated and undergoes sprouting angiogenesis to increase the size and number of blood vessels in the endometrium.Study design, size, durationThe study was designed to examine the angiogenic potential of primary human UtMVECs using the well-characterized human umbilical vein EC (HUVEC) line as a control to compare angiogenic potential. ECs were seeded onto three-dimensional (3D) collagen matrices, supplemented with known proangiogenic stimuli relevant to pregnancy and allowed to invade for 24 h. Sprouting responses were analyzed using manual and automated methods for quantification.Participants/materials, setting, methodsRT-PCR, Western blot analysis and immunostaining were used to characterize UtMVECs. Angiogenic responses were examined using 3D invasion assays. Western blotting was used to confirm signaling responses after proangiogenic lipid, pharmacological inhibitor, and recombinant lentiviral treatments. All experiments were repeated at least three times.Main results and the role of chanceAfter ensuring that UtMVECs expressed the proper endothelial markers, we found that UtMVECs invade 3D collagen matrices dose-dependently in response to known proangiogenic stimuli (e.g. S1P, VEGF, bFGF, hCG, estrogen, progesterone and WSS) present during early pregnancy. Invasion responses were positively correlated with phosphorylation of phosphatidylinositol 3-kinase (PI3K)/protein kinase B (Akt) and p42/p44 mitogen-activated protein kinase (ERK). Inhibition of these second messengers significantly impaired sprouting (P < 0.01). Gene silencing of membrane type 1-matrix metalloproteinase using multiple approaches completely abrogated sprouting (P < 0.001). Finally, UtMVECs displayed a unique ability to undergo sprouting in response to hCG, and combined estrogen and progesterone treatment.Large scale dataNot applicable.Limitations, reasons for cautionThe study of uterine angiogenesis in vitro has limitations and any findings many not fully represent the in vivo state. However, these experiments do provide evidence for the ability of UtMVECs to be used in functional sprouting assays in a 3D environment, stimulated by physiological factors that are produced locally within the uterus during early pregnancy.Wider implications of the findingsWe show that UtMVECs can be used reliably to investigate how growth factors, hormones, lipids and other factors, such as flow, affect angiogenesis in the uterus.Study funding/competing interestsThis work was supported by NIH award HL095786 to K.J.B. The authors have no conflicts of interest.

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A three-dimensional model with two-body interactions for endothelial cells in angiogenesis.

Publications

A three-dimensional model with two-body interactions for endothelial cells in angiogenesis.

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