The papers in this volume arose out of the workshop Membrane Transport and Renal Physiology, which was conducted as part of the IMA 1998-1999 program year, Mathematics in Biology. The workshop brought together physiologists, biophysicists, and applied mathematicians who share a common interest in solute and water transport in biological systems, especially in the integrated function of the kidney. Solute and water transport through cells involves fluxes across two cell membranes, usually via specialized proteins that are integral membrane components. By means of mathematical representations, transport fluxes can be related to transmembrane solute concentrations and electrochemical driving forces. At the next level of functional integration, these representations can serve as key components for models of renal transcellular transport. Ultimately, simulations can be developed for transport-dependent aspects of overall renal function. Workshop topics included solute fluxes through ion channels, cotransporters, and metabolically-driven ion pumps; transport across fiber-matrix and capillary membranes; coordinated transport by renal epithelia; the urine concetrating mechanism; and intra-renal hemodynamic control. This volume will be of interest to biological and mathematical scientists who would like a view of recent mathematical efforts to represent membrane transport and its role in renal function.

Ion Channel Fluxes.- Ionic energetics in narrow channels.- The physical basis of ion channel kinetics: the importance of dynamics.- The use of streaming potential measurements to characterize biological ion channels.- Cotransporter Fluxes.- A kinetic model for secondary active transport.- Asymmetry of the AE1 anion exchange system: implications for modeling the physiological rates of chloride-bicarbonate exchange.- Epithelial ion transport: perspectives on a working mechanism of the sodium pump.- Epithelial Transport.- Assessing homeostatic properties of epithelial cell models: application to kidney proximal tubule.- Fiber Matrix Theory / Capillary Membrane Transport.- Limitations in the application of fiber-matrix models to glomerular basement membrane.- Transport of macromolecules across the peritoneum.- The Urine Concentrating Mechanism.- Urinary concentrating mechanism.- Urine concentrating mechanism: measured permeability values in medullary nephron segments and urea transport processes.- Transport processes in the microcirculation of the renal medulla.- Mathematical models of the mammalian urine concentrating mechanism.- Lactate accumulation in kidney inner medulla: a vasa recta model.- Renal Hemodynamics and Tubuloglomerular Feedback.- Kidney-specific responses of myogenic autoregulation to inhibition of nitric oxide synthase.- TGF gain and effector mechanism: technical and theoretical considerations.- Analysis of generative and dissipative flow-dependent mechanisms in tubuloglomerular feedback.- A reduced model for nephron flow dynamics mediated by tubuloglomerular feedback.- Dynamic model of nephron-nephron interaction.- List of workshop participants.