2.2.1. Notch signaling kinetics

A one-dimensional AB model recently developed by Loerakker et al. (2018), based on (Sprinzak et al., 2011; Boareto et al., 2015), was adopted to simulate the kinetics of the Notch signaling pathway between VSMCs. Due to symmetry in the vascular wall, a one-dimensional array of VSMCs in radial direction was considered. As endothelial cells line the lumen of coronary arteries, one endothelial cell was modeled to be present on the luminal side of the first VSMC in the one-dimensional array. This endothelial cell provided a constant source of Jagged ligands (J_EC) available for interacting with the Notch receptors on the first VSMC. Other Notch proteins on the endothelial cell were not considered.

For each VSMC, the protein content of Notch, Jagged, Delta, and NICD was tracked over time with a set of ordinary differential equations. This set of equations considered the production and degradation of the proteins, trans-interactions between receptors and ligands of adjacent cells, and cis-interactions between receptors and ligands of the same cell:

Here, Nj, Jj, Dj, and Ij are the Notch, Jagged, Delta, and NICD content of cell j = 1, 2, …, N_c, respectively, with N_c the number of cells based on the vessel wall thickness T₀ and assuming a cell size of 0.01 mm. N_pr, J_pr, and D_pr are the base production rates of Notch, Jagged, and Delta. Parameters k_c and k_t indicate the strength of cis- and trans-interactions, respectively. Degradation of Notch, Jagged, and Delta was assumed to occur at the same rate γ, and the degradation rate of NICD was given by γ_I. The mechanosensitivity of Notch and Jagged was accounted for by multiplying the base production rates with the exponential terms exp(A_NE_θθ,j) and exp(A_JEθθ,j). Here, A_n and A_j are the mechanosensitivity parameters determined in Loerakker et al. (2018), and E_θθ,j is the normal Green-Lagrange strain in circumferential direction in cell j (see equation (23)).

The effects of transactivation on the production of Notch, Jagged, and Delta were included with the following Hill function:

with Λ defining the changes in protein production in response to Notch transactivation (upregulation for Λ > 1, downregulation for Λ < 1, and no change for Λ = 1). The parameter I₀ defines the transition point of the Hill function from convex to concave and the parameter n determines the sensitivity of protein production to the NICD content. Polarized clustering of Jagged, the preferential positioning of Jagged ligands on the abluminal side of the VSMCs, was considered in the model of Loerakker et al. (2018) but not included here. It had only minor effects and was therefore neglected, similar to Ristori et al. (2020).