A Theoretical Approach for the Electrochemical Characterization of Ciliary Epithelium
Abstract
:1. Introduction
- the flow of ions through ion transporters and the combined effect of channels and pumps (membrane scale level);
- the overall contribution to AH production by a single cell of the ciliary epithelium (cellular scale level);
- the hydrostatic and oncotic pressure effects (eye scale level).
1.1. The Multiscale Architecture of Aqueous Humor Production
- (a)
- the macroscopic scale. This is the level of observation corresponding to the eye globe and its characteristic length is in the order of centimeters;
- (b)
- the cellular scale. This is the level of observation corresponding to the PEC/NPEC couplet and its characteristic length is in the order of tens of microns (i.e., );
- (c)
- the membrane scale. This is the level of observation corresponding to the membrane of the NPEC and its characteristic length is in the order of tens of nanometers (i.e., ).
1.2. Ciliary Epithelium and Aqueous Humor Production
- Convective delivery of water, ions, proteins, and metabolic fuel by the ciliary circulation;
- Ultrafiltration of water and ions (driven by oncotic and hydrostatic pressure gradients) and diffusion of larger molecules from the capillaries into the stroma (driven by concentration gradients);
- Active ionic secretion into the basolateral space between the NPE cells which promotes water flow down the resulting osmotic gradient.
- : volumetric flow rate of aqueous humor due to the difference between the hydrostatic pressure in the ciliary capillaries and the hydrostatic pressure in the posterior chamber assumed to be equal to the intraocular pressure (IOP)
- : volumetric flow rate of aqueous humor due to the difference between the oncotic pressure in the ciliary capillaries and the oncotic pressure in the posterior chamber
1.3. Active Secretion of Aqueous Humor
- Proteins are practically absent inside the CE cells. As a consequence, HCO is the main responsible for maintaining the pH of the cells within physiological values (between 7.21 and 7.4, see [27]);
- The Na/K-ATPase pump (shortly, Na/K pump) is essential to set the cell off its electrochemical balance and create a driving force for the secretion of AH. Studies show that inhibiting this pump results in blocking AH secretion (see [28])
1.4. Connecting AH Flow, Ocular Physiology, and Pathology: The Role of Mathematical Modeling
- A1
- verify that the value of the predicted transepithelial potential difference is physiologically correct;
- A2
- verify that the values of the predicted intracellular ion concentrations are physiologically correct;
- A3
- verify that the value of the predicted NPE transmembrane potential difference is physiologically correct.
2. Results
2.1. Model 0
- Na-K-Cl symporter;
- K uniporter.
- Na-K pump;
- K uniporter;
- Cl uniporter.
2.2. Model 1
- Na-K-Cl symporter;
- K uniporter;
- Cl-HCO antiporter;
- Na-H antiporter.
- Na-K pump;
- K uniporter;
- Cl uniporter;
- Cl-HCO antiporter.
2.3. Verification of Model Predictions against Experimental Data
- transepithelial potential difference (in mV);
- intracellular concentrations of Na, K, and Cl (in mM);
- NPE transmembrane potential difference (in mV).
2.3.1. Results for Model 0
2.3.2. Results for Model 1
3. Discussion
3.1. Discussion of the Predictions of Model 0
3.2. Discussion of the Predictions of Model 1
3.3. Comparison between Model 0 and Model 1
- the configuration of ion exchangers and the biochemical reactions mediated by the carbonic anhydrase enzyme strongly influence the prediction of intracellular ion concentrations and transmembrane potentials;
- Model 1 provides better estimates of intracellular concentrations than predicted by Model 0;
- the transmembrane potentials estimated by Models 0 and 1 are both within the same order of magnitude as those measured experimentally, but not exactly within the experimental range.
4. Materials and Methods
4.1. Model Assumptions
- each pair of neighboring PE and NPE cells are considered as a single unit (referred to as the PE–NPE cell couplet) rather than two distinct compartments;
- ion transporters have uniform spatial distribution along the CE;
- the unit has a fixed volume;
- gap junctions within PE and NPE cells are neglected.
4.2. Mathematical Model
- electric potential at the S side and in the I region;
- ion concentrations in the I region,
- the electric potentials and ;
- the ion concentrations , , and .
- the electric potentials and ;
- the ion concentrations , , , , and ;
- the concentrations and .
4.3. Numerical Solution and the Issue of Electroneutrality
4.4. Models for Ion Fluxes
4.4.1. Uniporters
4.4.2. Antiporters and Symporters
4.4.3. Pumps
4.5. Model for Water Flux
5. Conclusions and Perspectives
- ion exchanger configuration and intracellular biochemical reactions strongly influence the model prediction of intracellular ion concentrations and transmembrane potentials;
- one of the two configurations predicts sodium and potassium intracellular concentrations and transmembrane potential much more accurately than the other;
- predicted transmembrane potentials are within the same order of magnitude as those measured experimentally, but not exactly within the experimental range.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
CE | Ciliary Epithelium |
AH | Aqueous Humor |
IOP | Intraocular Pressure |
PE | Pigmented Epithelial Cells |
NPE | Nonpigmented Epithelial Cells |
S | Stroma |
P | Posterior Chamber |
I | Intracellular region of cell couplet |
cAMP | Cyclic adenosine monophosphate |
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Parameter | Value | Units |
---|---|---|
25 | ||
15 | ||
− | ||
20 | ||
147 | ||
145 |
Study | Species | Transporter/Channel | Localization |
---|---|---|---|
[31] | Human | Gap junctions | Lateral surface of PE/NPE |
Apical junction of PE/NPE | |||
[32] | Human | Na/K ATPase | Basolateral membrane of NPE |
K channel | Basolateral membrane of NPE | ||
[33] | Human | AQP1 | NPE |
[34] | Human | Na/K/2Cl cotransporter | Basolateral membrane of NPE |
[35] | Human | ENaC | Unspecified |
[36] | Bovine | Cl/HCO exchanger | Basolateral membrane of PE |
[37] | Bovine | Ca dependent K channel | Basolateral membrane of NPE |
cAMP activated Cl channel | Basolateral membrane of NPE | ||
[38] | Bovine | Cl dependent Na/HCO cotransporter | Basolateral membrane of PE |
[39] | Bovine | Na/H+ exchanger | Basolateral membrane of PE |
[40] | Bovine | Na/K ATPase (alpha 1, 2, and 3 isoforms) | Basolateral membrane of NPE |
[41] | Bovine | Na/K ATPase (alpha 1 and beta 1 isoforms) | Basolateral membrane of PE |
[42] | Bovine | Na/K/2Cl cotransporter | Basolateral surface of PE |
[43] | Bovine | Na/H+ exchanger | Basolateral membrane of PE |
Cl/HCO exchanger | Basolateral membrane of PE | ||
[44] | Porcine | Na/K ATPase (alpha 1, 2, and 3 isoforms) | Basolateral membrane of NPE |
Tight junctions | Lateral membrane of NPE | ||
[45] | Porcine | Na/K/2Cl cotransporter | Basolateral membrane of PE |
Cl/HCO exchanger | Basolateral membrane of PE | ||
Cl channel | Basolateral membrane of NPE | ||
[46] | Porcine | Swelling activated K channel | PE basolateral membrane |
[47] | Porcine | Hemichannels | Basolateral membrane of NPE |
[48] | Porcine | Na/K exchanger | Basolateral membrane of NPE |
[49] | Murine | APQ4 | Basolateral membrane of NPE |
[50] | Murine | Glutamate transporter | Basolateral membrane of NPE |
Glutamine transporter | Basolateral membrane of NPE | ||
[51] | Murine | TRPV4 channel | NPE |
[52] | Murine | Inwardly rectifying K channel | NPE |
[53] | Leporine | Na/K/2Cl cotransporter | Basolateral membrane of NPE |
[54] | Rabbit | Na/K ATPase (alpha 2 and beta 3 isoforms) | Basolateral membrane of NPE |
[55] | Porcine | Cx isoforms | Gap junctions between PE and NPE cells |
[56] | Rabbits | Na/K ATPase (alpha 2 isoform) | Basolateral membrane of NPE |
[57] | Bovine | Na/K/2Cl cotransporter | Basolateral membrane of PE |
Cl/HCO and Na/H+ exchangers | Basolateral membrane of PE | ||
Cl Channel | Basolateral membrane of NPE | ||
[58] | Rabbits | Na/K/2Cl cotransporter | Basolateral membrane of PE |
Cl/HCO exchanger | Basolateral membrane of PE | ||
Cl channel | Basolateral membrane of NPE |
Quantity | Model Prediction | Reference Range | Species | Bibliographical Source |
---|---|---|---|---|
mV | mV | Humans | [63] | |
75 mM | mM | Rabbit | [64] | |
55 mM | mM | Rabbit | [64] | |
10 mM | mM | Rabbit | [64] | |
mV | mV | Shark | [29] |
Quantity | Model Prediction | Reference Range | Species | Bibliographical Source |
---|---|---|---|---|
mV | mV | Humans | [63] | |
15.59 mM | mM | Rabbit | [64] | |
132.09 mM | mM | Rabbit | [64] | |
3.97 mM | mM | Rabbit | [64] | |
mV | mV | Shark | [29] |
i | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
species | Na | K | Cl | H | HCO | CO | HCO |
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Sacco, R.; Guidoboni, G.; Jerome, J.W.; Bonifazi, G.; Marazzi, N.M.; Verticchio Vercellin, A.C.; Lang, M.S.; Harris, A. A Theoretical Approach for the Electrochemical Characterization of Ciliary Epithelium. Life 2020, 10, 8. https://doi.org/10.3390/life10020008
Sacco R, Guidoboni G, Jerome JW, Bonifazi G, Marazzi NM, Verticchio Vercellin AC, Lang MS, Harris A. A Theoretical Approach for the Electrochemical Characterization of Ciliary Epithelium. Life. 2020; 10(2):8. https://doi.org/10.3390/life10020008
Chicago/Turabian StyleSacco, Riccardo, Giovanna Guidoboni, Joseph W. Jerome, Giulio Bonifazi, Nicholas M. Marazzi, Alice C. Verticchio Vercellin, Matthew S. Lang, and Alon Harris. 2020. "A Theoretical Approach for the Electrochemical Characterization of Ciliary Epithelium" Life 10, no. 2: 8. https://doi.org/10.3390/life10020008