workshop will bring together physiologists and applied mathematicians
who share a common interest in solute and water transport
and its role in integrated renal function. Topics will include
fiber-matrix theory, membrane transport, renal epithelial
transport, the urine concentrating mechanism, and renal hemodynamic
control. The workshop will seek to facilitate communication
and cooperation among participants who may not be aware of
each other's research and will provide an introduction to
these topics for other biological and mathematical scientists.
Fundamental to the operation of the kidney is the transport
of water and solutes through and around cells. The pathways
through the cells involve transit across two cell membranes.
This membrane transport is often via specialized protein transporters
resident within the membrane: ion channels, solute-specific
facilitated transporters, or metabolically driven ion pumps.
For each of these, there is substantial experimental investigation
within the physiology and biophysics communities to characterize
the transport dynamics and develop a mathematical theory of
its function. These mathematical descriptions constitute the
building blocks for models of epithelial transport. The fundamental
unit of the kidney is the nephron, a cylinder lined by specialized
epithelia which change axially. Hemodynamic control mechanisms
enable distal nephron segments to control delivery of fluid
by using renal arterial tone to modulate proximal fluid entry.
Thus, the questions which relate to whole kidney function are
those of interacting epihelia in a special geometry, both axially
along the nephron and between apposed nephron segments. Consequently,
mathematical models of integrated renal function consist of
systems of ordinary or partial differential equations, which
are solved numerically or from which qualitative information
is extracted through analysis.