A novel mathematical model for studying the dynamics of endothelium #

Pradeep Keshavanarayana, Fabian Spill

11:30 Wednesday in 3Q68.

Part of the Blood and blood vessels session.

Abstract #

Several life-threatening diseases such as cancer, atherosclerosis, and Covid-19 exhibit a common trait – leaking blood vessels. A specific type of cells called Endothelial cells form an inner lining of the blood vessels. These cells form bonds with neighbouring cells that can open and close resulting in dynamically varying gap sizes, thereby regulating permeability. Diseased conditions change the homeostasis either by affecting the gap size or the frequency of opening of the gaps, and pathogens make use of these gaps to spread to tissues. But how the coupled mechano-chemical stimuli affect endothelial permeability is still not understood completely.

One of the proteins involved in regulating cell-cell bonds is VE-Cadherin. They are located on the cell-membrane and forms a homophilic bond with VE-Cadherin from the neighbouring cell. Downstream, they are connected to the actin-cytoskeleton, which is responsible for maintaining mechanical equilibrium of the cell. Thus, the actin cytoskeleton-VE-Cadherin link is essential for regulating mechanical equilibrium of the monolayer.

We have developed a continuum level mathematical model to study the dynamics of such gap formation. Taking inspiration from contact mechanics, we model VE-Cadherin bonds as cohesive surface with damage following a traction-separation law. Actin cytoskeleton follows the tensegrity principle and is coupled with microtubules following a non-linear material model. Cells are modelled in 3D and hence we can study the behaviour of micro-vessels, which are hard to study experimentally. We use finite element scheme to solve the coupled mechano-chemical system of equations.

It was found that micro-vessels exhibit higher permeability than its planar monolayer counterparts. In-silico studies showed that permeability of micro-vessels increase with the stiffness of the extracellular matrix. Interestingly, it is found that shear between cells is responsible for variation in permeability between bi-cellular and tri-cellular junctions, which explains the endothelial phenotype dependent differences observed. Simulations also show that permeability is higher in those regions of micro-vessels with high shear stress fluctuations, matching the observations that atherosclerotic plaques are usually formed in regions where the blood flow is disturbed. Thus, the novel mathematical modelling framework is capable of simulating already known observations along with developing several testable hypotheses.