A theoretical study of the role of conformational properties of transepithelial ion pumps on aqueous humor production

Abstract

Purpose :
Intraocular pressure, resulting from the balance of aqueous humor (AH) production and drainage, is the only approved treatable risk factor in glaucoma. AH production is determined by the concurrent function of ion pumps and aquaporins in the ciliary processes but their individual contribution is difficult to characterize experimentally. In this work, we propose a mathematical model to investigate the role of conformational properties of Na⁺-K⁺, Ca²⁺-Na⁺, Cl^--HCO₃^- and Na⁺-H⁺ ion pumps on AH production.

Methods :
Ion pump function is modeled by coupling a velocity-extended electrochemical module for ion motion and an electrochemically driven fluid module for AH flow. Time-dependent simulations are conducted to study ion pump features as a function of (1) permanent electric charge density over the channel pump surface; (2) osmotic gradient coefficient; (3) stoichiometric ratio between ion pump currents at channel inlet and outlet.

Results :
Fig. 1 shows the steady-state electric potential V along the channel axis Z. Potential drop is due only to the electric field generated by permanent surface charge density. Despite remarkably different profiles of V inside the channel, the predicted transmembrane potential V_m=V(Z=10nm)-V(Z=0nm) is for all pumps in good agreement with the range [-2.7, -2.3] mV experimentally measured on monkeys. Fig. 2 shows the steady-state AH velocity along Z. Fluid motion is due only to electric pressure exerted by the ions. Model predicts a positive AH flow in all channel length for Na⁺-K⁺ and Ca²⁺-Na⁺ pumps, a positive AH flow in the central region for Cl^--HCO₃^- pump and AH flow inversion at Z=6.5nm for Na⁺-H⁺ pump.

Conclusions :
The proposed mathematical model allowed us to simulate the four main ion pumps involved in AH production. Predicted transepithelial potential and AH flow are in good agreement with measured data and biophysical intuition. Results support adopting the theoretical tool as a virtual laboratory to verify conjectures, compare different scenarios and complement the indispensable animal model in patient-specific therapy design.

This is an abstract that was submitted for the 2018 ARVO Annual Meeting, held in Honolulu, Hawaii, April 29 - May 3, 2018.

 

Fig. 1. Spatial distribution of electric potential along channel axis. Blue: K⁺-Na⁺ pump. Black: Ca²⁺-Na⁺ pump. Green: Cl^--HCO₃^- pump. Red: H⁺-Na⁺ pump.

 

Fig. 2. Spatial distribution of AH velocity along channel axis. Blue: K⁺-Na⁺ pump. Black: Ca²⁺-Na⁺ pump. Green: Cl^--HCO₃^- pump. Red: H⁺-Na⁺ pump.