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Abstract
Effective regulation of the sonic hedgehog (Shh) signalling pathway is essential for normal development in a wide variety of species. Correct Shh signalling requires the formation of Shh aggregates on the surface of producing cells. Shh aggregates subsequently diffuse away and are recognised in receiving cells located elsewhere in the developing embryo. Various mechanisms have been postulated regarding how these aggregates form and what their precise role is in the overall signalling process. To understand the role of these mechanisms in the overall signalling process, we formulate and analyse a mathematical model of Shh aggregation using nonlinear ordinary differential equations. We consider Shh aggregate formation to comprise of multimerisation, association with heparan sulfate proteoglycans (HSPG) and binding with lipoproteins. We show that the size distribution of the Shh aggregates formed on the producing cell surface resembles an exponential distribution, a result in agreement with experimental data. A detailed sensitivity analysis of our model reveals that this exponential distribution is robust to parameter changes, and subsequently, also to variations in the processes by which Shh is recruited by HSPGs and lipoproteins. The work demonstrates the time taken for different sized Shh aggregates to form and the important role this likely plays in Shh diffusion.
Highlights
The Hedgehog (Hh) family of proteins are fundamental to the organisation and direction of tissue patterning in embryonic development in a wide variety of animal species [1,2,3,4]
The sonic hedgehog (Shh) pathway is vital for normal development in a wide variety of species and its activity is strictly regulated to ensure correct spatiotemporal patterning of numerous developing tissues
Shh signalling requires the formation of Shh aggregates, formed on producing cells via a range of different mechanisms, that diffuse to receiving cells
Summary
The Hedgehog (Hh) family of proteins are fundamental to the organisation and direction of tissue patterning in embryonic development in a wide variety of animal species [1,2,3,4]. Sonic hedgehog (Shh), one isoform of the Hh family, functions in adult organisms, for example in the maintenance of stem cells or wound repair [1]. The generation of Shh protein, its subsequent transport and reception at target cells is a strictly regulated spatiotemporal process. The modified protein is transported to the cell surface where various aggregation mechanisms are utilised to form different size aggregates which diffuse to receiving cells containing the Shh receptor Patched-1 (Ptch) and trigger a signalling cascade. Disruptions to the normal processing of Shh can impede standard dispersal processes and distort gradient formation at critical stages of morphogenesis. This can lead to developmental malformations [4,5,6]
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