Theoretical investigation of Na+/K+-ATPase activity regulation on aqueous humor production

Abstract

Purpose :
Na+/K+-ATPase plays a major role in the electrochemical equilibrium across the ciliary epithelium (CE). Clinical data demonstrate reducing pump activity through Na+/K+-ATPase inhibitors such as nitric oxide-donating prostaglandin may help reduce intraocular pressure (IOP), an established risk factor for glaucoma. In this investigation we estimate optimal levels of Na+/K+-ATPase inhibitors using a mathematical model of the impact of Na+/K+-ATPase activity regulation on aqueous humor production (AHP).

Methods :
AHP is described by the iterative solution of the coupled interaction between electrodiffusion of Na+, Cl- and K+ and AH fluid motion through a compartment scheme of the CE including ciliary capillary (CC), stroma, pigmented (PE) and nonpigmented (NPE) cells, lateral intercellular spaces (LIS) and posterior and anterior chambers connected to the episcleral vein (EV) through an outflow facility conductance. A gap junction separates PE and NPE and a tight junction separates the two LIS. Ion transport is modeled by passive membrane transporters and active Na+/K+-ATPase pump. Cell electroneutrality is enforced by a fixed intracellular negative charge. Simulations are performed under short circuit conditions and hydrostatic pressures of 25 and 8 mmHg in CC and EV.

Results :
Fig. 1 shows the predicted AH volumetric flow rate Q_AH (VFR) as a function of the adimensional ratio γ = [ATP]/Ksat, [ATP] being the intracellular ATP concentration and Ksat=1μM the half-saturation constant, for several values of the maximum activation pump flux density Jmax. Results indicate that for sufficiently high Jmax, there exists a (different) range of γ for which Q_AH decreases with respect to the reference value 2.5 μL/min. Fig. 2 shows the percent variation ΔQ_AH with respect to baseline conditions (γ=0, ‘*’) as a function of Jmax, for several values of γ. Results indicate that maximum Na+/K+-ATPase impact on VFR reduction is of 8%.

Conclusions :
Model predictions suggest that a marked inhibition of ATPase activity (γ <<1) does not significantly reduce AHP. Conversely, modeling demonstrates that allowing an intermediate level of pump activity (for [ATP]=5Ksat) maximizes AHP reduction. These results demonstrate potential ability of mathematical virtual laboratories to assist clinicians in optimizing IOP lowering medications.

This abstract was presented at the 2022 ARVO Annual Meeting, held in Denver, CO, May 1-4, 2022, and virtually.

 

Fig. 1: Q_AH as a function of γ and Jmax

 

Fig. 2: ΔQ_AH as a function of Jmax and γ