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

Abstract

During angiogenesis, new blood vessels sprout and grow from existing ones. This process plays a crucial role in organ development and repair, in wound healing and in numerous pathological processes such as cancer progression or diabetes. We present here a mathematical model of early stage angiogenesis that permits to explore the relative importance of mechanical, chemical and cellular cues. Endothelial cells proliferate and move over an extracellular matrix by following external gradients of Vessel Endothelial Growth Factor, adhesion and stiffness, which are incorporated to a Cellular Potts model with a finite element description of elasticity. The dynamics of Notch signaling involving Delta-4 and Jagged-1 ligands determines tip cell selection and vessel branching. Through their production rates, competing Jagged-Notch and Delta-Notch dynamics determine the influence of lateral inhibition and lateral induction on the selection of cellular phenotypes, branching of blood vessels, anastomosis (fusion of blood vessels) and angiogenesis velocity. Anastomosis may be favored or impeded depending on the mechanical configuration of strain vectors in the ECM near tip cells. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands. Author SummaryAngiogenesis is the process by which new blood vessels grow from existing ones. This process plays a crucial role in 1 organ development, in wound healing and in numerous pathological processes such as cancer growth or in diabetes. 2Angiogenesis is a complex, multi-step and well regulated process where biochemistry and physics are intertwined: 3 with signaling in vessel cells being driven by both chemical and mechanical mechanisms that result in vascular cell 4 movement, deformation and proliferation. Mathematical models have the ability to bring together these mechanisms 5 in order to explore their relative relevance in vessel growth. In this work, we present a mathematical model of early 6 stage angiogenesis that is able to explore the role of biochemical signaling and tissue mechanics. We use this model to 7 unravel the regulating role of Jagged, Notch and Delta dynamics in vascular cells. These membrane proteins have an 8 important part in determining the leading cell in each neo-vascular sprout. Numerical simulations demonstrate that 9 increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can 10 be compensated by augmenting the production of Delta ligands. 101The section Mathematical Model describes the CPM coupled with the Delta-Notch-Jagged dynamics. In the 102 section Results and Discussion, we present the results of the simulation and how Jagged-1 determines sprouting 103 dynamics. Finally, in the last section we draw the conclusions of the manuscript. 104 Mathematical model 105 The mathematical model consists of a CPM in which the dynamics of the Notch signali...

Integrodifference master equation describing actively growing blood vessels in angiogenesis

“…For example, cellular Potts models directly describe cells that change size and the extracellular matrix by Monte Carlo dynamics coupled to continuum fields for growth factors concentration, elastic fields, etc. (see reviews [22,27] and articles [3,31,32]). It is challenging to deduce dynamics for the active vessel tips from the Monte Carlo cellular dynamics.…”

Anomalous Angiogenesis in Retina

“…Tip cells grow filopodia with many VEGF receptors, pull the other ECs, open a pathway in the ECM, lead the new sprouts, and migrate in the direction of increasing VEGF concentration [17]. Branching of new sprouts occurs as a result of signaling and mechanical cues between neighboring ECs [18][19][20][21]. ECs in growing sprouts alter their shape to form a lumen connected to the initial vessel that is capable of carrying blood [22].…”

“…Here we use a 2D Potts model that includes EC Notch signaling, chemotaxis, haptotaxis and durotaxis [21] to ascertain the influence of these mechanisms on AMD. We consider the simple geometry sketched in Fig.…”

A multiscale model of complex endothelial cell dynamics in early angiogenesis

“…Angiogenesis, the process by which new blood vessels are generated from a pre-existing vascular network, has been extensively investigated in recent years [1][2][3][4][5][6][7][8][9][10]. However, understanding of the complex behaviour of endothelial cells (ECs) during angiogenesis remains incomplete.…”

“…Angiogenic sprouting has been extensively studied from a theoretical modelling perspective in numerous physiological and pathological contexts, including tumour growth [10,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Many models [18-20, 22, 24-28, 32] fall within the so-called snail-trail paradigm [31].…”