Computational modeling of chemotactic signaling and aggregation of microglia around implantation site during deep brain stimulation

It is well established that prolonged electrical stimulation of brain tissue causes massive release of ATP in the extracellular space. The released ATP and the products of its hydrolysis, such as ADP and adenosine, become the main elements mediating chemotactic sensitivity and motility of microglial cells via subsequent activation of P2Y_2,12 as well as A3A and A2A adenosine receptors. The size of the sheath around the electrode formed by the microglial cells is an important criterion for the optimization of the parameters of electrical current delivered to brain tissue. Here, we study a purinergic signaling pathway underlying the chemotactic motion of microglia towards the implanted electrode during deep brain stimulation. We present a computational model describing formation of a stable aggregate around the implantation site due to the joint chemo-attractive action of ATP and ADP together with a mixed influence of extracellular adenosine. The model was built in accordance with the classical Keller-Segel approach and includes an equation for the cells’ density as well as equations describing the hydrolysis of extracellular ATP via successive reaction steps ATP →ADP →AMP →adenosine. The results of our modeling allowed us to reveal the dependence of the width of the encapsulating layer around the electrode on the amount of ATP released due to permanent electrical stimulation. The dependences of the aggregates’ size on the parameter governing the nonlinearity of interaction between extracellular adenosine and adenosine receptors are also analyzed.