Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmot
Our mathematical model of epithelial transport (Larsen et al. Acta Physiol. 195:171–186, 2009) is extended by equations for currents and conductance of apical SGLT2. With independent variables of the physiological parameter space, the model reproduces int
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Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model Erik Hviid Larsen and Jens Nørkær Sørensen Contents 1 Introduction 2 Description of the Minimalistic Model 2.1 Functional Organization of Proximal Tubule Epithelium 2.2 Solute Flux Equations 2.3 Water Flux Equations 2.4 Compliant Model and Volumes of Intraepithelial Compartments 2.5 Electrical-Circuit Analysis 2.6 Nomenclature and Sign Conventions 2.7 Numerical Methods 2.8 Choice of Independent Variables 2.9 Geometrical Dimensions and Units of Physical Quantities 3 Results 3.1 General Features 3.2 A Component of Na+ Uptake Bypasses the Pump 3.3 Inhibition of the Na+/K+ Pump 3.4 Effect of Adding Glucose 3.5 Blocking Water Channels of Apical Membrane 3.6 Volume Response of the Epithelium to a Luminal Osmotic Pulse 3.7 Uphill Water Transport and Intraepithelial Water Fluxes 3.8 Isosmotic Transport 4 Discussion 4.1 The Coupling Between Active Sodium Transport and Fluid Uptake 4.2 Eliminating the Osmotic Permeability of Apical Membrane 4.3 Transepithelial Osmotic Permeability Versus Osmotic Permeability of Individual Membranes 4.4 Truly Isosmotic Transport
E. H. Larsen (*) Department of Biology, University of Copenhagen, Copenhagen, Denmark e-mail: [email protected] J. N. Sørensen Department of Wind Energy, Technical University of Denmark, Lyngby, Denmark e-mail: [email protected]
E. H. Larsen and J. N. Sørensen 5 Additional Information Appendix 1: Nomenclature Appendix 2: Independent Variables References
Abstract Our mathematical model of epithelial transport (Larsen et al. Acta Physiol. 195:171–186, 2009) is extended by equations for currents and conductance of apical SGLT2. With independent variables of the physiological parameter space, the model reproduces intracellular solute concentrations, ion and water fluxes, and electrophysiology of proximal convoluted tubule. The following were shown: 1. Water flux is given by active Na+ flux into lateral spaces, while osmolarity of absorbed fluid depends on osmotic permeability of apical membranes. 2. Following aquaporin “knock-out,” water uptake is not reduced but redirected to the paracellular pathway. 3. Reported decrease in epithelial water uptake in aquaporin-1 knock-out mouse is caused by downregulation of active Na+ absorption. 4. Luminal glucose stimulates Na+ uptake by instantaneous depolarization-induced pump activity (“cross-talk”) and delayed stimulation because of slow rise in intracellular [Na+]. 5. Rate of fluid absorption and flux of active K+ absorption would have to be attuned at epithelial cell level for the [K+] of the absorbate being in the physiological range of interstitial [K+]. 6. Following unilateral osmotic perturbation, time course of water fluxes between intraepithelial compartments provides physical explanation for the transepithelial osmotic permeability being orders of magnitude smaller than cell membranes’ osmotic permeability. 7. Fluid absorption is always hyperosmotic to bath. 8. Deviation from
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