Mathematical modelling of vascular development in zebrafish

Modhara, Sunny (2015) Mathematical modelling of vascular development in zebrafish. PhD thesis, University of Nottingham.

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Abstract

The Notch signalling pathway is pivotal in ensuring that the processes of arterial specification, angiogenic sprouting and haematopoietic stem cell (HSC) specification are correctly carried out in the dorsal aorta (DA), a primary arterial blood vessel in developing vertebrate embryos. Using the zebrafish as a model organism, and additional experimental observations from mouse and cell line models to guide mathematical modelling, this thesis aims to better understand the mechanisms involved in the establishment of a healthy vasculature in the growing embryo.

We begin by studying arterial and HSC specification in the zebrafish DA. Mathematical models are used to analyse the dose response of arterial and HSC genes to an input Notch signal. The models determine how distinct levels of Notch signalling may be required to establish arterial and HSC identity. Furthermore, we explore how Delta-Notch coupling, which generates salt-and-pepper patterns, may drive the average gene expression levels higher than their homogeneous levels. The models considered here can qualitatively reproduce experimental observations. Using laboratory experiments, I was able to isolate DA cells from transgenic zebrafish embryos and generate temporal gene expression data using qPCR. We show that it is possible to fit ODE models to such data but more reliable data and a greater number of replicates at each time point is required to make further progress.

The same VEGF-Delta-Notch signalling pathway is involved in tip cell selection in angiogenic sprouting. Using an ODE model, we rigourously study the dynamics of a VEGF-Delta-Notch feedback loop which is capable of amplifying differences betwen cells to form period-2 spatial patterns of alternating tip and stalk cells. The analysis predicts that the feeback strengths of Delta ligand and VEGFR-2 production dictate the onset of patterning in the same way, irrespective of the parameter values used. This model is extended to incorporate feedback from filopodia, growing in a gradient of extracellular VEGF, which are capable of facilitating tip cell selection by amplifying the resulting patterns. Lastly, we develop a PDE model which is able to properly account for VEGF receptor distributions in the cell membrane and filopodia. Receptors can diffuse and be advected due to domain growth, defined by a constitutive law, in this model. Our analysis and simulations predict that when receptor diffusivity is large, the ODE model for filopodia growth is an excellent approximation to the PDE model, but that for smaller diffusivity, the PDE model provides valuable insight into the pattern forming potential of the system.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Owen, M.
Byrne, H.M.
Gering, M.R.
Farcot, E.R.G.
Hodgman, T.C.
Keywords: Mathematical Modelling, Delta-Notch, Juxtacrine Signalling, Lateral Inhibition, Zebrafish, Angiogenic Sprouting, Haematopoietic Stem Cells
Subjects: Q Science > QH Natural history. Biology > QH301 Biology (General)
Q Science > QL Zoology > QL605 Chordates. Vertebrates
Faculties/Schools: UK Campuses > Faculty of Science > School of Biosciences
Item ID: 29125
Depositing User: Modhara, Sunny
Date Deposited: 21 Aug 2015 10:39
Last Modified: 18 Sep 2016 09:25
URI: http://eprints.nottingham.ac.uk/id/eprint/29125

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