Workshop 5: The Kidney: Cellular, Tubular, and Vascular Physiology

(February 19,2007 - February 23,2007 )

Organizers


Harold Layton
Mathematics, Duke University
Leon Moore
Physiology and Biophysics, SUNY
S. Randall Thomas
Univ Evrey Val l-Agora
Alan Weinstein
Physiology and Biophysics, Cornell University

The kidney controls the volume and composition of extracellular fluid and participates in the regulation of blood pressure. Its regulatory function can be understood in terms of the action of resident vascular and epithelial cells. The functional unit of the kidney is the nephron, a long epithelial tubule with attendant vasculature. The kidney processes blood in two basic steps: (1) an ultrafiltrate of blood plasma is formed in specialized vascular capillaries and this fluid enters the renal tubule; (2) the renal tubules transform the ultrafiltrate into urine by means of differential transport of solutes and water through the tubule epithelial cells. These two processes influence each other: the ultrafiltration rate impacts tubule function, and tubule transport can modulate ultrafiltration. Both processes are influenced by body fluid composition, and by neural and hormonal signals that impact on the kidney.

The workshop will focus on the application of mathematical models to elucidate renal function in the context of new experimental methods and data. Physiologists, biophysicists, modelers, and mathematicians will present recent work and discuss current controversies and emerging issues. Topics may include: the regulation of ion channels in renal tubular cells, the regulation of renal hemodynamics, tubular-vascular interactions, new insights into the urine concentrating mechanism, new analytical methods, international computational initiatives, and web-based modeling resources.

Accepted Speakers

Phillip Darwin Bell
School of Medicine, University of Alabama at Birmingham
Ki Chon
Biomedical Engineering, State University of New York
Erik Ilsø Christensen
Cell Biology, Aarhus University
William Dantzler
Physiology, University of Arizona
Aurélie Edwards
Chemical and Biological Engineering, Tufts University
Ian Forster
Institute for Physiology , University of Zurich
Peter Harris
Physiology , University of Melbourne
Niels-Henrik Holstein-Rathlou
Medical Physiology, University of Copenhagen
Peter Jordan
Chemistry, Brandeis University
Mark Knepper
Laboratory of Kidney & Electrolyte Metabolism, National Institutes of Health
Anita Layton
Mathematics, Duke University
Harold Layton
Mathematics, Duke University
Donald Loo
Physiology, University of California, Los Angeles
Rodger Loutzenhiser
Pharmacology & Therapeutics, University of Calgary
Mariano Marcano
Mathematics, University of Puerto Rico
Donald Marsh
Biomedical Center, Brown University
Leon Moore
Physiology and Biophysics, SUNY
Thomas Pallone
Division of Nephrology, Rm. N3W143, University of Maryland at Baltimore
Thomas Pannabecker
Physiology, University of Arizona
Benoit Roux
Pediatrics, Biochemistry & Molecular Biology, University of Chicago
Jeff Sands
Renal Division, Emory University
Jurgen Schnermann
National Institutes of Health
Mark Schumaker
Mathematics, Washington State University
S. Randall Thomas
Univ Evrey Val l-Agora
Alan Verkman
Department of Medicine & Physiology, University of California-San Francisco
Sheldon Weinbaum
Biomedical & Mechanical Engineering, City University of New York (CUNY)
Alan Weinstein
Physiology and Biophysics, Cornell University
Geoffrey Williamson
Electrical and Computer Engineering , Illinois Institute of Technology
Monday, February 19, 2007
Time Session
09:15 AM
10:00 AM
Peter Jordan - Gating Ion Channels: the Interplay of Structure and Theory

Important features of ion channel gating can be reliably studied by coupling theory with high-resolution atomic level structures of channel forming peptides. New methods for tracking ion channels' low frequency deformational modes are applied to analyze gating in two systems: gramicidin and KcsA. In both the lowest frequency normal mode (NM) is the crucial mode that initiates transition between open and closed states. Tracking these NMs reveals each channel's gating mechanism. Gramicidin dissociates via relative opposed monomer rotation and simultaneous lateral displacement. WT KcsA does not open. When the cytoplasmic GLUs are protonated KcsA opens via a complex set of motions initiated near the smoke hole of the "tepee" and propagating to the "glycine hinge," ultimately adopting a structure reminiscent of MthK. In both systems NM structure changes as the system evolves; the gating mechanisms are not simple, exhibiting complex backbone realignments and side chain reorganizations.

11:15 AM
12:00 PM
Mark Schumaker - Framework models of ion permeation

Framework models are designed to incorporate information from molecular dynamics simulations of ion channels in order to calculate their conductance properties on much longer time scales than can be achieved by the simulations. They provide a comparison between the simulations and conductance data. This talk describes three different steady state framework models. The single particle model was originally developed by Levitt, and describes a channel whose pore can be occupied by only one ion at a time. It has been used to model Na+ conduction through gramicidin. Transport is described by a Smoluchowski equation with non-local boundary conditions enforcing the single occupancy constraint. The Grotthuss conduction model describes proton conduction through gramicidin. It incorporates potentials of mean force for proton occupation and water reorientation calculated by Pomes and Roux. Model parameters were optimized against an extensive set of conductance data taken by Busath and his colleagues. Berneche and Roux developed a framework model for conduction through the narrow pore of the KcsA potassium channel, using a potential of mean force for occupation of the pore by two or three potassium ions. Finally, the problem of constructing time-dependent framework models is addressed.

01:30 PM
02:15 PM
Donald Loo - Conformational Dynamics of SGLT1 during Na+/glucose Cotransport

Glucose is actively transported across the apical membrane of proximal tubular cells by Na+/glucose cotransporters (SGLT's). SGLT1, the model for this class of transporter, functions by an alternating access mechanism via a series of conformational changes induced by substrate-binding and membrane voltage. We have examined the conformations of human SGLT1 mutant G507C (expressed in Xenopus oocytes) during sugar transport using simultaneous electrical and optical measurements. The mutant exhibited similar kinetics as wild-type SGLT1, and labeling of Cys507 by tetramethylrhodamine-6-maleimide had no effect on function. We recorded changes in presteady-state currents (charge movement) and fluorescence in response to rapid-jumps in membrane potential in the presence and absence of glucose. Simulations based on an 8-state kinetic model for SGLT1 indicate that external sugar increases the occupancy probability of inward-facing conformations at the expense of outward-facing conformations. The simulations predict, and we have observed experimentally, that presteady-state currents are blocked by saturating sugar, but not the changes in fluorescence. Thus the conformational change associated with the rate-limiting step is electroneutral: at maximal inward Na+/sugar cotransport (saturating voltage and external Na+ and sugar concentrations), it is the slow release of Na+ from the internal surface of SGLT1.

02:15 PM
03:00 PM
Ian Forster - Electrogenic phosphate transport across renal epithelia: mechanistic insights from experiments and simulations

The reabsorption of inorganic phosphate (Pi) across the brush border membrane of renal proximal tubule epithelia is essential for Pi homeostasis. Uphill Pi transport across the apical membrane is secondary-active, driven by the electrochemical gradient of Na+. Transport is mediated by members of the SLC34 solute carrier family (type II Na+/Pi cotransporters, NaPi-II). NaPi-IIa, responsible for up to 80% of Pi reabsorption in the mammalian kidney, operates with a stoichiometry of 3Na+:H2PO42- and +1 charge is translocated per cycle. Expression of cloned NaPi-II transporters in Xenopus oocytes has allowed the transport mechanism to be characterized by means of tracer uptake, electrophysiology and voltage clamp fluorometry. These studies have yielded both steady-state and presteady-state kinetic information.


I will show how we have used experimental data to build a kinetic model that describes the main transport features. We propose a kinetic scheme that involves the ordered binding/debinding of substrates, consistent with an alternating access carrier model. The transport cycle comprises a sequence of partial reactions between 8 states, corresponding to unique conformations of the protein. Electrogenicity arises from the voltage-dependent reorientation of mobile charges of the empty carrier and one Na+ binding partial reaction, which we model as single transitions involving the movement of lumped charged species over single energy barriers. Model simulations have allowed us to quantitate rate constants for the partial reactions and distinguish between different binding order schemes.

Tuesday, February 20, 2007
Time Session
08:30 AM
09:15 AM
Thomas Pallone - Vasoactivity and ion channel architecture of the descending vasa recta wall

The renal medulla is supplied with blood flow by efferent arterioles of juxtamedullary glomeruli. Efferent arterioles form descending vasa recta (DVR) that penetrate the outer medulla of the kidney in vascular bundles. DVR in vascular bundles give rise to ascending vasa recta (AVR) in the inner medulla that flow in a countercurrent manner to return blood to the renal cortex. Modulation of medullary blood flow has been tied to urinary concentration and regulation of salt excretion by the kidney. As such, control of medullary blood flow and its regional distribution to the outer and inner medulla has been of considerable interest.


DVR 12 - 15 micron vessels to which contractility is imparted by smooth muscle remnants called pericytes. Much controversy has surrounded the ion channel architecture of the afferent and efferent circulations of the kidney. The roles of voltage gated calcium channels and membrane potential changes in vasoconstriction has been uncertain. To test their roles, we have isolated DVR by microdissection and performed patch clamp experiments on the pericytes and endothelium. The data shows that vasoactive agonists depolarize the pericyte cell membrane through a combination of calcium dependent chloride channel activation and potassium channel deactivation. Several classes of potassium channels are involved. Voltage gated calcium channel activity can be demonstrated in the pericytes, and, surprisingly, fast voltage gated sodium channels yield prominent currents. Finally, we have demonstrated that both pericytes and endothelial cells are electrically coupled via gap junctions. The pericytes appear to be weakly coupled while the endothelium forms low resistance syncytium. My talk will describe our current knowledge of the channel architecture of the DVR wall and compare it to that of other renal arteriolar segments.

09:15 AM
10:00 AM
Aurélie Edwards - Modification of Cytosolic Calcium Signaling by Subplasmalemmal Microdomain in Outer Medullary Pericytes

Contractility of resistance vessels is regulated by variation of intracellular Ca2+ concentration in both endothelium and smooth muscle. To investigate the hypothesis that Na+ concentration in subplasmalemmal microdomains regulates Ca2+ concentrations in cellular microdomains ([Ca]md), cytosol ([Ca]cyt), and sarcoplasmic reticulum (SR, [Ca]sr), we modeled transport events in those compartments. The model accounts for major classes of ion channels, Na+/Ca2+ exchange (NCX) and the distributions of Na+/K+-ATPase a1 and a2 isoforms in the plasma membrane.  Ca2+ release from SR stores is assumed to occur via ryanodine (RyR) and inositol tris phosphate (IP3R) receptors.  The model shows that requisite existence of a significant Na+ concentration difference between the cytosol ([Na]cyt) and microdomains ([Na]md) necessitates restriction of intercompartmental diffusion.  Accepting the latter, the model predicts resting ion concentrations that are compatible with experimental measurements, and temporal changes in [Ca]cyt similar to those observed upon NCX inhibition.  An important role for NCX in the regulation of Ca2+ signaling is verified.  In the resting state, NCX operates in "forward mode", with Na+ entry and Ca2+ extrusion from the cell.  NCX translates variations in Na+/K+-ATPase activity into changes in [Ca]md, [Ca]sr and [Ca]cyt. Taken together, the model simulations verify the feasibility of the central hypothesis that modulation of [Na]md can influence both the loading of Ca2+ into SR stores and [Ca2+]cyt variation.

10:30 AM
11:15 AM
Sheldon Weinbaum - A new view of the Starling hypothesis and the role of pericytes in the temporal regulation of microvascular exchange

N/A

01:45 PM
02:30 PM
S. Randall Thomas - Overview of Physiome: QKDB, ontology needs, European & International funding

In the interest of developing a global approach to biomedical data integration and interpretation, the Renal Physiome effort is exploring possibilities for multiscale modeling and simulation explicitly targeting questions of physiopathology. To this end, the first resource that has been developed is a quantitative kidney database (QKDB) to provide centralized access to measured parameter values, anatomical features, and functional characteristics at all scales from membrane transporters to the whole organ, both in human, when available, and in animal models. An interactive World-Wide-Web interface to legacy mathematical models at all levels of kidney physiology is also underway. Integral to the project is the development of ontologies, necessary to resolve issues of semantic ambiguity, consistency of descriptions, relational descriptions, and the like, and to enable integration with related resources in other fields. I will present current Physiome efforts internationally, will mention funding opportunities in this direction, and will give an indication of how the renal research community can participate in this communal effort.

02:30 PM
03:00 PM
Peter Harris - The Virtual Kidney: Progress with a 3D anatomical interface, model repository and grid portal for distributed computing

A 3D "virtual kidney" interface has been developed for access to experimental data and parameter values abstracted within the Quantitative Kidney Database (QKDB) described by S Randall Thomas and to a repository of mathematical models of kidney function. At the gross anatomy level a translucent 3D reconstruction of a rat kidney shows contours of the renal capsule, inner and outer medullas, and the ureter, as well as renal arteries and veins to several levels of branching. Within the kidney are superficial and juxtamedullary nephrons. Using the mouse buttons the user can rotate the kidney, display or hide individual structures, and zoom in on any portion. Selection of a structure provides a link to the search facility of QKDB and thence to relevant parameter values and extracts from the literature.


A menu lists the repository of mathematical models, such as segmental (e.g., proximal or distal tubule) or medullary transport models, which may be run on the local machine or, via a Grid Portal (KidneyGrid), simultaneously on several remote machines. The use of a grid resource broker demonstrates the ability to compose, schedule, monitor and visualize the results of the simulation and simplifies the development of application, credential and resource management while decoupling the launch platform from the underlying grid middleware.


The simulation results (e.g., solute concentrations or local flow rates) are visible on the virtual kidney structures as scaled colour gradients, thus allowing a visual and quantitative appreciation of the effects of simulated parameter changes. A separate panel shows x-y plots of the results. The underlying models are implemented via CellML descriptions and are consistent, as far as possible, with standards and ontologies being developed for other organs under the Physiome initiative.


Work done in collaboration with S Randall Thomas, Andrew Lonie, Bill Appelbe, Belinda May, Peter Hunter, Raj Buyya and Xingchen Chu.

03:30 PM
04:30 PM
Robert Moss - A Preliminary Model for Studying the Interactions Between Nephrons

Our aim is to simulate the behaviour of clusters of nephrons and to understand how this behaviour arises from the activities of individual tubule segments. Further, we aim to create models that are capable of predicting kidney function and the effects of renal disease. Ultimately, we are interested in investigating the behaviour of the kidney at a level of abstraction that is relevant to clinicians.


We approach the problem of renal modelling by assuming that the kidney is a complex network and applying techniques from Dynamical Networks (a form of Graph Automata) and methods from Statistical Mechanics and Machine Learning.


We present a model of the nephron as a Graph Automata, where each node models a tubule segment, and difference equations model solute transport between tubule segments, the surrounding renal fluid, and peritubular capillaries. This network will form the basis of multi-nephron models, allowing us to study interactions and patterns of behaviour across groups of nephrons. Our current system of simple transport equations makes simulation of large clusters of nephrons computationally tractable.


The model, though simple and still incomplete, is able to construct and maintain a salt gradient in the medullary fluid, and to regulate water and sodium reabsorption in response to ADH levels. The model also allows us to introduce stochastic failures into the nodes to mimic the onset of renal diseases (such as scar tissue in Bowman's Capsule) and so facilitate the analysis of the effects that diseased nephrons have on neighbouring nephrons.

Wednesday, February 21, 2007
Time Session
08:30 AM
09:15 AM
William Dantzler - Three-dimensional functional reconstructions of vascular and tubular structures of inner medulla

Mammalian kidneys are capable of producing urine substantially more concentrated than the plasma, thereby helping to conserve water. In part, this process involves generation, within the inner medulla, of an osmotic gradient that increases axially from cortex to papilla tip. In the simplest models, generation of this osmotic gradient involves countercurrent multiplication by the loops of Henle of a small lateral osmotic pressure difference between their ascending and descending limbs. In the outer medulla (OM), this model appears to be essentially correct with the lateral difference between the limbs generated by active sodium transport out of the thick ascending limb. However, in the inner medulla (IM), which makes up ~75% of the length of the medulla (rat IM ? 5mm) and which generates the steepest osmotic gradient, the process of gradient generation, although probably involving some form of countercurrent multiplication, is not understood. In an attempt to understand how three-dimensional functional relations between structures in the IM might contribute to this process, we began a total digital reconstruction of the functional three-dimensional architecture of vasculature and nephron segments in rat renal IM from physical serial sections of resin-embedded tissue. Segments of descending vasa recta (DVR), ascending vasa recta (AVR), descending thin limb (DTL), ascending thin limb (ATL), and collecting duct (CD) were identified with antibodies against segment-specific proteins associated with solute and water transport (UT-B, PV-1, AQP1, ClC-K1, and AQP2, respectively, for the above segments) by indirect immunofluorescence. Reconstructions of the central region of the IM through the first 3 mm below the OM-IM border revealed the following major features: 1) DTLs with their loops within 1 mm below the OM-IM border have no detectable AQP1; 2) DTLs with loops below 1 mm from the OM-IM border express AQP1 for the first 40% of their length below the border, but fail to express AQP1 for the remaining 60%; 3) Expression of ClC-K1 begins abruptly with a prebend segment in the DTL, which is always ~150-200 ?m in length regardless of the total length of the loop, and continues uniformly throughout the ATL; 4) clusters of coalescing CDs form the organizing motif for the IM; 5) DTLs and DVR are arranged outside the CD clusters; 6) ATLs and AVR are nearly uniformly distributed transversely across the entire inner medulla outside of and within CD clusters; 7) ATLs that lie closest to the center of the CD clusters arise from the shortest DTLs, whereas ATLs that lie at the periphery or outside of the clusters arise from longer DTLs; 8) DVR and AVR outside CD clusters appear sufficiently juxtaposed to permit good countercurrent exchange; 9) within CD clusters, about four AVR closely abut each CD, surrounding it in a highly symmetrical fashion covering about 54% of the CD surface area and apparently permitting rapid removal of water reabsorbed from collecting ducts; 10) AVR abutting each CD and the ATLs within CD clusters form repeating nodal interstitial spaces bordered by a CD on one side, one or more ATLs on the opposite side, and one AVR on each of the other two sides. These relationships may be highly significant for both establishing and maintaining the inner medullary osmotic gradient.

09:15 AM
09:45 AM
Thomas Pannabecker - Quantitative Analyses of Nephron and Blood Vessel Architecture in the Renal Inner Medulla

Urine concentration by the mammalian kidney is important for fluid and solute homeostasis. The renal inner medulla (IM) plays an important role in producing concentrated urine. As nephrons and blood vessels enter the medulla, traverse, and then exit the IM, returning to the cortex, they exchange fluid and solutes with neighboring structures in a precisely organized fashion. Appropriate fluid and solute exchange relies on specific membrane transporters that exist along the axis of the nephron or vessel. The efficient exchange from one structure to another is also affected by the distance fluid and solutes move between compartments, the number of target compartments that exist within a defined space, as well as physicochemical properties of interstitial space. Our three-dimensional (3D) digital reconstruction of the IM has shown that collecting duct (CD) clusters form the organizing motif around which nephron segments and blood vessels are arranged in a repeating fashion from the base of the IM to the tip of the papilla. In order to understand more fully the manner by which the architectural arrangements and axial protein distribution enable the concentrating mechanism to proceed efficiently, we are conducting quantitative analyses to determine precise spatial relationships among and between nephrons and blood vessels. Three-dimensional architecture of vasculature and nephron segments in rat renal inner medulla (IM) was assessed with digital reconstructions from physical sections of resin-embedded medullae. Segments of descending vasa recta (DVR), ascending vasa recta (AVR), descending thin limb (DTL), ascending thin limb (ATL), and CD were identified with antibodies against segment-specific proteins associated with solute and water transport (UT-B, PV-1, AQP1, ClC-K1, and AQP2) by indirect immunofluorescence. The ratio of ATL:CD total peritubular surface area declines by about 50% in the last 2 mm of the papilla compared to the first 3 mm; this results from both decreased ATL and slightly increased CD total peritubular surface areas. Water and urea delivery by CDs to interstitium in this region could be influenced by increased tubular surface area as well as by increased CD water and urea permeability. Individual CDs 0.5 to 2 mm from the papilla tip have up to 80% greater circumference than individual CDs 1.4 mm from the IM base.  In the final 500 mm CD circumference rises at a markedly steeper rate reaching as much as 200% or more of those CDs nearer the IM base. Return of water to the general circulation from these deep papillary CDs appears to be facilitated, in part, by a 150% increase in the number of AVR closely abutting these CDs. Consequently, the average fractional CD surface area abutting AVR is 0.61, about the same as that (0.54) for the smaller CDs that lie near the IM base. Interstitial nodal compartments, bounded by CDs, ATLs, and AVR, surround CDs in the upper 3 mm of the IM. Fewer ATLs exist in the final 1 mm as there are fewer loops and the number of these nodal arrangements is therefore reduced. However, the tips of those loops reaching this area have bends with 50 to 100% greater lateral lengths than the bends of loops near the IM base. This may be significant for solute movement out of the loop bends.

10:15 AM
10:45 AM
Erik Ilsø Christensen - Reconstruction of the mouse nephron and distribution of AQP-1 and UT-A2

Renal function is crucially dependent on renal microstructure providing the basis for the mechanisms that control the transport of water and solutes between filtrate and plasma and the urinary concentration. This study provides, detailed information on mouse renal architecture, including the spatial course of the tubules, lengths of different segments of nephrons, histotopography of tubules and vascular bundles, epithelial ultrastructure at well-defined positions along Henle's loop and the distal convolution of nephrons, and the exact distribution of AQP-1 and the urea transporter UT-A2. Three-dimensional reconstruction of 200 nephrons and collecting ducts was performed on aligned digital images, obtained from 2.5-mu m-thick serial sections of mouse kidneys. Important new findings include: (1) A tortuous course of the descending thin limbs of long-looped nephrons and a winding course of the thick ascending limbs of short-looped nephrons contribute to a 27% average increase in the lengths of the corresponding segments, (2) the thick-walled tubules incorporated in the central part of the vascular bundles in the inner stripe of the outer medulla were identified as thick ascending limbs of long-looped nephrons, and (3) three types of short-looped nephron bends were identified related to the length and the position of the nephron and its corresponding glomerulus. The ultrastructure of the tubule segments was identified and correlated to the localization of AQP-1 and UT-A2. Our new findings suggest important implications for renal transport mechanisms that should be considered when evaluating the segmental distribution of water and solute transporters within the normal and diseased kidney.


Work done in collaboration with Xiao-Yue Zhai.

01:30 PM
02:00 PM
Jeff Sands - Vasopressin regulation of the UT-A1 renal urea transporter

Urea transport, mediated by the UT-A1 and/or UT-A3 urea transporters, is important for the production of concentrated urine. Vasopressin rapidly increases urea transport in rat terminal inner medullary collecting ducts (IMCDs). UT-A1 is expressed in the apical plasma membrane of inner medullary collecting ducts (IMCDs). The localization of UT-A3 is controversial: it is apical in rat but basolateral in mice. Two mechanisms have been identified by which vasopressin may rapidly increase urea permeability in rat IMCDs: 1) increases in UT-A1 phosphorylation; and 2) increases in UT-A1 plasma membrane accumulation. The fold-increase in urea transport following vasopressin is larger than the fold-increase in either UT-A1 phosphorylation or plasma membrane accumulation alone. This suggests that vasopressin increases urea permeability through increases in both UT-A1 accumulation and phosphorylation.


Vasopressin also stimulates urea flux, UT-A1 phosphorylation, and UT-A1 apical plasma membrane accumulation in UT-A1-MDCK cells, an MDCK cell line that we stably transfected with UT-A1. Vasopressin acts through a cAMP pathway in both rat IMCDs and UT-A1-MDCK cells. However, in UT-A1-MDCK cells, a protein kinase A (PKA) inhibitor only inhibits 50% of the cAMP-stimulated urea flux. This suggests that urea flux is stimulated by both PKA-dependent and PKA-independent cAMP pathways.


Vasopressin also regulates UT-A1 long-term. UT-A1 protein abundance increases in the inner medulla of Brattleboro rats, which lack vasopressin, that are given vasopressin for 12 days. Similarly, reducing endogenous vasopressin in a normal rat by 14 days of water diuresis reduces UT-A1 protein abundance. In contrast, giving vasopressin to Brattleboro rats for only 5 days does not increase UT-A1 protein abundance. UT-A1 promoter activity is increased by hypertonicity through a tonicity enhancer (TonE) element, but lacks a cAMP response element (CRE) and cAMP does not increase promoter activity. The promoters of NKCC2/BSC1 and AQP2 do have CREs. This suggests that vasopressin initially increases the transcription of NKCC2/BSC1(and AQP2), which increases inner medullary osmolality. The increase in inner medullary osmolality then activates UT-A1 transcription, accounting for the delayed increase in UT-A1 protein abundance.


In summary, vasopressin regulates UT-A1: 1) acutely by increasing UT-A1 phosphorylation and plasma membrane accumulation; 2) through both PKA-dependent and PKA-independent cAMP pathways; and 3) long-term by changes in protein abundance in response to increases in inner medullary osmolality. Support: NIDDK and AHA.

02:00 PM
02:30 PM
Alan Verkman - Chemical 'knock-out' by small-molecules to probe components of the urinary concentrating system

Phenotype analysis of transgenic mice lacking various components of the urinary concentrating system, such as aquaporins, urea transporters and the V2 receptor, have provided useful information on their role in generating a concentrating urine. Selective small-molecule inhibitors of these proteins have potential utility for chemical knock-out studies that are not confounded by compensatory changes in transgenic mice, as well as for development of clinical therapies. We have established a small molecule discovery program with high-throughput screening, a collection of >300,000 drug-like chemicals, and pharmacology/small animal testing resources. The program has been successful in identifying small-molecule CFTR activators and inhibitors for therapy of cystic fibrosis and secretory diarrheas, and recently, for identification of nanomolar potency inhibitors of urea transporter UT-B, the V2 receptor, and cyclic nucleotide signaling. Small-molecule modulators of protein function are likely to have great utility in post-genomic renal physiology.

02:30 PM
03:00 PM
Mark Knepper - Analysis of cell signaling networks using proteomics methods and ODE-based modeling

Based on general ordinary differential equations describing mass balance in the cell that incorporate global signaling mechanisms seen in all cells, we can identify four fundamental processes that are common to all signaling pathways: a) changes in protein abundance; b) changes in post-translational modifications including phosphorylation, nitrosylation, acylation, and ubiquitylation; c) changes in cellular location including cytosol-to-membrane translocation and cytosol-to-nucleus translocation; and d) changes in binding of proteins to other proteins and lipids. We are developing quantitative approaches to tandem mass spectrometry to measure each of these changes globally across the proteome of an individual cell type. For example, we have recently published the IVICAT method for non-radioactive isotope labeling of peptides and the neutral loss scanning technique for quantification of protein phosphorylation. These methods have been employed to analyze the signaling response of the inner medullary collecting duct cell to vasopressin. The differential equations can be converted to a graphical analysis of protein-protein interaction through use of the Jacobian matrix to define graph edges.

03:30 PM
04:00 PM
Mariano Marcano - Optimization Problems and Algorithms for Mathematical Models of Renal Systems

N/A

Thursday, February 22, 2007
Time Session
08:45 AM
09:20 AM
Roland Blantz - The Tubular Vascular Relationship of TGF: Is there a Metabolic Contribution to this Connection?

Kidney blood flow is highly regulated and maintained relatively constant via highly efficient autoregulation of blood flow and glomerular filtration and complex interactions of neurohumoral vasoconstrictor and vasodilator influences.   Increases in kidney blood flow obligate an increase in filtered load or GFR which in turn obligates tubular reabsorption, which in turn requires expenditures of ATP and oxygen.  Therefore, in contrast to other organs, increases in blood flow to the kidney both create a supply and a demand.  For these reasons the regulation of filtered load or GFR must be finely coordinated with tubular reabsorption.  This is achieved by the tubuloglomerular feedback system, based at the macula densa and juxtaglomerular apparatus.    The mediators of this TGF system are ATP and adenosine, a product of AMP.  Since these substances are important products critical to metabolism it suggests an important metabolic link to regulation of blood flow and GFR.  The TGF system does not remain static but adapts with time and physiologic conditions, such that the relationship between macula densa Na delivery/reabsorption and GFR is reset and temporally adapts.  These conditions include normal growth, changes in Na intake, reductions in nephron mass and persistent changes in reabsorption proximal to the macula densa.  Modulators of TGF temporal adaptation have been defined and includes NO derived from NOS-1, angiotensin II and COX-2 products.


Oxygen consumption (QO2) by the kidney is directly, and possibly linearly, related to Na reabsorption (TNa).  However, recent studies have suggested that the metabolic efficiency of Na reabsorption can change rather dramatically in normal and pathophysiologic conditions.  In chronic conditions and, specifically, certain forms of hypertension AII has been suggested to increase oxygen consumption relative to Na transport.  We have shown that NO (specifically NO derived from NOS-1) can act to suppress kidney oxygen consumption.  Blockers of NOS-1 dramatically increase QO2 and QO2 /TNa   both in vivo and in vitro in freshly harvested proximal tubules.  Inhibitors of carbonic anhydrase also increase QO2 /TNa   in vivo and in vitro by promoting active and preventing passive Na reabsorption.  The kidney in early diabetes exhibits hyperfiltration and kidney growth, in major part due to increased reabsorption in the proximal tubule which effectively deactivates TGF leading to functional increases in GFR.  NOS-1 is constitutively increased in the diabetic kidney from sources outside the macula densa and acts as a functional brake on increased oxygen consumption.  However the diabetic kidney does not undergo normal TGF temporal adaptation, primarily due to an inability of NOS-1 activity to change appropriately.  Although blockade of AII does not alter oxygen consumption in normal kidneys, application of angiotensin II receptor blockers in models of 5/6th nephrectomy, a model of chronic kidney disease, dramatically reduces elevated values for QO2 /TNa observed in this model.  These studies suggest that endogenous regulators of the relationship between kidney blood flow/GFR and tubular reabsorption are linked to kidney metabolism.  Modulators of the adaptive behavior of TGF systems also act to modify kidney oxygen consumption and the metabolic efficiency of tubular reabsorption.  Therefore the TGF influences critical to kidney function and metabolism involve regulation of both metabolic supply and demand. 


 

09:20 AM
10:00 AM
Jurgen Schnermann - NKCC2 Isoforms and TGF signaling

N/A

01:45 PM
02:15 PM
Rodger Loutzenhiser - Systolic Pressure is the Dominant Signal in Autoregulation

Elevated blood pressure (hypertension) is a leading cause of glomerular injury and kidney disease. By adjusting pre-glomerular resistance in response to pressure elevations, the myogenic response of the afferent arteriole is thought to play a major role in protecting the kidney from such injury. Indeed, when myogenic reactivity is impaired, not only is the autoregulation of renal blood flow less efficient, but the susceptibility of the kidney to hypertensive injury is greatly enhanced. Blood pressure presents to the kidney as a complex oscillating signal. The systolic blood pressure, being the highest pressure attained and the most frequent oscillation within this signal, is intrinsically the most damaging component and clinical studies demonstrate that systolic hypertension is most closely linked to renal injury. The renal myogenic response appears to be uniquely suited to protect against elevations in this signal. We have found that, in the rat, pressure increases initiate a rapid afferent arteriolar vasoconstriction within 200-300 ms. When pressure is reduced, vasodilation is initiated after a much longer delay (~1 s). Moreover, high-speed video studies show that vasoconstrictor responses initiated by short pressure pulses (< 300 ms) continue during this delay in relaxation. Experimental and modeling approaches demonstrate that these features allow the afferent arteriole to sense and adjust steady-state myogenic tone in response to the rapidly oscillating systolic blood pressure signal, thereby attenuating the transmission of pressure transients to the glomerulus. Studies of the mechanisms underlying the unusual myogenic kinetics of this vessel implicate an important role of the release of calcium from the sarcoplasmic reticulum (SR, an internal calcium store) and the involvement of SR calcium channels (ryanodine receptors). Our findings suggest a model of the myogenic response that involves both a sustained membrane depolarization, causing the activation of voltage-gated calcium entry, and a cyclic stretch-induced release of SR calcium in response to the oscillating systolic blood pressure signal.

02:15 PM
02:45 PM
Geoffrey Williamson - Simulation Studies of Dynamic Models for Renal Autoregulation

Renal autoregulation (AR) is the vasoconstriction and dilation of the renal microvasculature in response to changes in systemic blood pressure (BP) that maintains renal blood flow (RBF), glomerular filtration rate, and the glomerular capillary pressure approximately constant. This regulatory effect is believed to simultaneously insulate renal function from variations in BP and to protect glomerular capillaries from hypertensive injury. The dynamics of renal AR informs one about the operational characteristics of its underlying mechanisms and potentially enables the study of AR in vivo. These dynamics have been investigated using spectral analysis of RBF and BP recordings, time-frequency analysis of RBF recordings, and the fitting of exponential curves to the RBF and the afferent arteriolar diameter (AAD) time responses following step changes in pressure. We developed simple dynamic models for the myogenic mechanism of renal AR that take BP waveforms as inputs and produce RBF or AAD waveforms as outputs. Simulation studies of model behavior when driven by BP waveforms measured in rats and by various test waveforms provide insight into the interpretation of results of the various analysis techniques. We have used these models to connect alterations in AR response that are observed during experimental interventions to characteristics of the AR dynamics. In particular, changes in model parameters related to AR strength cause effects similar to those from AR impairment via calcium channel blockers, and changes in parameters related to AR capacity match effects from impairments after renal mass reduction. Our models also enable simulation of (myogenic-based) AR when triggered either by mean or by systolic pressure changes. Empirical observations of AAD responses in the hydronephrotic kidney, when presented with a variety of pressure waveforms, are better matched by model behavior with AR triggered by systolic pressure.

03:15 PM
03:45 PM
Armin Just - Evidence for a third and fourth regulatory mechanism in renal blood flow autoregulation

Autoregulation of renal blood flow (RBF) is mediated by two major mechanisms: a fast myogenic response (MR, <10 s) and slower tubuloglomerular feedback (TGF, 10-40 s). However, it is unclear whether additional mechanisms are involved. To separate the mechanisms and analyze their kinetics, we studied autoregulatory responses to a rapid step increase of renal artery pressure (RAP) in rats and mice. RAP was reduced 20 mmHg for 60 s and then rapidly released.


After the increase in RAP, renal vascular resistance (RVR) briefly fell for < 0.5 s but then quickly rose to an autoregulatory efficiency of 36% within the first 7-10 s in rats. After a brief delay, a secondary rise of RVR began at 10 s, further improving autoregulation to 75% at 40 s. RVR then slowly further rose from 40 s to 120 s to a final level of 94%. Results were similar in mice. Based on these kinetics, the initial response likely reflects MR and the secondary response TGF; the slowest component indicates a third regulatory mechanism substantially slower than TGF. Inhibition of “classical” TGF by furosemide enhanced the initial MR, reduced the secondary component of autoregulation by ~60%, and eliminated the tertiary one. Doubling of the dose of furosemide did not further affect the secondary component or the diuretic effect. In mice, genetically deficient for A1 adenosine receptors (A1AR), which are known to lack TGF, the primary and the tertiary components were unaltered, but the secondary one was reduced ~50%. When furosemide was given to A1AR-deficient mice, the primary component was followed by a small secondary one, while the tertiary component was eliminated. Exactly the same time course was observed during furosemide in wild-type mice. These results indicate that: 1) the fastest component likely reflects MR and contributes at least 40% as it is also responsible for overcoming the initial passive reduction of RVR, 2) part of the secondary response is mediated by classical TGF, i.e., mediated by A1AR and inhibited by furosemide, and contributes ~40% to autoregulation, 3) a third regulatory mechanism exists that is sensitive to furosemide, but not mediated by A1AR, and contributes ~20%, 4) the remnant response between 10 and 40 s during furosemide resembles the kinetics of classical TGF, but is distinct in that it is resistant to the employed doses of furosemide and not dependent on the presence of A1AR.


We conclude that in rats and mice, in addition to well characterized MR and TGF, a third mechanism contributes to RBF autoregulation that is slower than classical TGF and independent of A1AR but sensitive to furosemide. In addition, a fourth mechanism seems to exist resembling classical TGF in response time but differing in being independent of A1AR and insensitive to furosemide.

03:45 PM
04:15 PM
Ki Chon - Insights from Time-Varying Spectral Analysis

Renal autoregulatory mechanisms are not only characterized by their dynamic nature, but the nature of their dynamics varies over time, leading to transient signals. These time-varying dynamics are often nonlinear and have different time scale oscillations (fast and slow), with each oscillation exhibiting its own transient dynamics. Our recent application of high-resolution, time-varying spectral and transfer function methods has revealed substantial differences between hypertensive and normotensive rats in the dynamics of the two principal autoregulatory mechanisms, tubuloglomerular feedback (TGF) and the myogenic mechanism. Despite the major progress made, the fundamental determinants that underlie differences in the renal autoregulatory dynamics between normotensive and hypertensive rats remain unresolved. For example, it remains to be determined why either time-invariant or time-varying spectral densities associated with hypertensive rats are more complicated than those of normotensive rats. A recent modeling study by Layton and Moore have predicted this in part due to the TGF system exhibiting multi-stability which can result in rapid switching between the dynamic modes which can consequently lead to a complicated spectral behavior. We will provide preliminary data from SHR that are consistent with the prediction of the Layton and Moore TGF model, including TGF waveform shape, switching between multiple stable modes of TGF oscillation, increased parameter variability relative to controls, and the presence of low frequency modulation of the TGF system. In addition, we will show data using time-varying nonlinear methods that complicated and additional spectral peaks associated with SHR arise because of nonlinear interactions between the autoregulatory mechanisms.


Work done in collaboration with Kin Siu and Leon C. Moore.

Friday, February 23, 2007
Time Session
08:45 AM
09:15 AM
Niels-Henrik Holstein-Rathlou - Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats

N/A

09:15 AM
09:45 AM
Donald Marsh - Routes to chaos in nephron blood flow regulation: nephron synchronization and ensemble formation

Tubular pressure recordings in normotensive rats reveal a regular oscillation due tubuloglomerular feedback (TGF) operating at 20-40 mHz and a smaller faster oscillation due to the myogenic mechanism operating at 100-200 mHz. The TGF fluctuation is irregular in hypertensive rats, and takes on characteristics of deterministic chaos. We have used simulations to test two hypotheses about the mechanism of the bifurcation. In the first we used a spatially extended model of the nephron, cast as two-point nonlinear boundary value problem. The model solves for flow rate of tubular fluid, tubular pressure, and tubular NaCl concentration as functions of time and distance. The tubule wall is compliant and reabsorbs NaCl and water in accordance with the known behavior of a cortical renal tubule. The initial flow is glomerular filtration rate, the initial NaCl concentration is the plasma value, and the outflow pressure is determined by the operation of a pressure dependent resistance in the distal tubule. Glomerular capillary pressure is governed by the operation of an afferent arteriolar model that simulates membrane currents and PD, myosin light chain phosphorylation, and the operation of a contractile mechanism and an elastic element. The afferent arteriolar model receives input from TGF. We investigated whether the coefficient coupling TGF and the myogenic mechanism can serve as a bifurcation parameter. It does, and within a range of values known to include the increase of this parameter seen in hypertension.


Nephrons signal to each other over the vascular wall; the strength of this signalling increases 3-fold in hypertension. We developed a model that includes a single cortical radial artery, and 22 nephrons, of which 14 are cortical; of the remaining 8, 4 are short medullary nephrons, 3 intermediate length, and 1 a longer length medullary nephron. The nephron models are a 3rd order set of ODE's that predict tubular pressure and arteriolar diameter, with a 3rd order lag to simulate the various physical delays that occur in transmitting a change in proximal tubular outflow into a signal that reaches the afferent arteriole via TGF. The model does not have an independent myogenic component. Cortical nephrons synchronize at a single frequency, but the medullary nephrons cluster at frequencies incommensurate with the cortical frequency. The result is that cortical nephrons operating at normal blood pressure and normal vascular coupling, develop quasiperiodic dynamics, a well known route to chaos. The simulation shows that medullary nephrons operate in a chaotic mode even when arterial pressures and coupling coefficients are normal, and the chaotic domain increases to include cortical nephrons as the arterial blood pressure and the vascular coupling strength are made to increase.


The results of these simulations suggest that there is more than one possible cause of the bifurcation to chaos that has been observed. The simulated synchronization, whether in normotensive or hypertensive states, provides the possibility that nephrons could react to perturbations in arterial pressure as an organized ensemble. The formation of a chaotic state, however, can lead to reduced synchronization despite the increase of coupling strength, because such states are inherently more likely to become desynchronized. The functional significance of synchronization and of its reduction in hypertension, remain to be understood.

10:15 AM
10:45 AM
Anita Layton - Multistable Dynamics Mediated by Tubuloglomerular Feedback in a Model of Coupled Nephrons

To help elucidate the causes of irregular tubular flow oscillations found in the nephrons of spontaneously hypertensive rats (SHR), we have conducted a bifurcation analysis of a mathematical model of two nephrons that are coupled through their tubuloglomerular feedback (TGF) systems. This investigation was motivated by a modeling study which predicts that NaCl backleak from a nephron's thick ascending limb permits multiple stable oscillatory states that are mediated by TGF (Am. J. Physiol. Renal Physiol. 291: F79-F97, 2006). In that study, a characteristic equation obtained via linearization from a single-nephron model having NaCl backleak, in conjunction with numerical solutions of the full, nonlinear model equations for two and three coupled neph rons, was used in the formulation of a comprehensive, multifaceted hypothesis for the emergence of complex dynamics in SHR. In the present study we have derived a characteristic equation for a model of an arbitrary number of mutually coupled nephrons having NaCl backleak. Analysis of that characteristic equation for the case of two coupled nephrons has revealed a number of parameter regions having the potential for differing stable dynamic states. Numerical solutions of the full equations for two model nephrons exhibit a number of differing behaviors in these regions. Some behaviors are markedly irregular and exhibit a degree of spectral complexity that is consistent with physiologic experiments in SHR. Effects of coupling and irregular oscillations on fluid and NaCl delivery are also discussed.

10:45 AM
11:15 AM
Harold Layton - Harmonics and heterodyning in the tubuloglomerular feedback loop

Spectral frequencies arising from harmonics and from heterodyning have been reported in both experimental and modeling studies. Both harmonic and heterodyne frequencies have been attributed to the nonlinear properties of the tubuloglomerular (TGF) loop. However, the detailed mechanisms by which particular renal components generate harmonic and heterodyne frequencies have not been elucidated. Elementary mathematics can be used to show that signal transduction in a model of the thick ascending limb, of tubular flow rate to NaCl concentration at the macula densa, can, in principle, produce infinite series of both harmonic and heterodyne frequencies. Other nonlinear processes (e.g., the sigmoidal TGF response at the juxtaglomerular apparatus) can also introduce harmonic and heterodyne frequencies. Harmonic and heterodyne frequencies may be important components of the complex power spectra which arise from the irregular oscillations that are found in intratubular pressure records obtained from spontaneously hypertensive rats.


Supported by NIH Grant DK-42091 and NSF Grant DMS-0340654.


Collaborators: Anita Layton, Bruce Pitman, Paula Grajdeanu, Kevin Kesseler, Leon Moore, and Lauren Shareshian

11:15 AM
11:45 AM
Leon Moore - Sources of complexity in a model of the TGF system

The talk will consider evidence for multi-stability of the TGF system, primarily from spontaneously hypertensive rats (SHR). The use of time-varying spectral analysis of time series generated by a mathematical model of the TGF system to identify sources of complexity will then be described. Finally, we will present evidence that simple models of TGF in three coupled nephrons can generate dynamics consistent with deterministic chaos.

Name Affiliation
Gonzalez, Maria maria.gonzalez@ul.ie Mathematics , University of Limerick
Aguda, Baltazar bdaguda@gmail.com MBI - Long Term Visitor, Bioinformatics Institute, Singapore
Arendshorst, William School of Medicine, University of North Carolina, Chapel Hill
Bankir, Lise bankir@renalphy.com INSERM Unite 652
Bayram , Saziye bayrams@buffalostate.edu Mathematics, Buffalo State College
Bell, Phillip Darwin bellpd@musc.edu School of Medicine, University of Alabama at Birmingham
Benziane, Boubacar boubacar.benziane@ibisc.fr IBISC, FRE 2873 CNRS
Best, Janet jbest@mbi.osu.edu
Bidani , Anil abidani@lumc.edu Loyola University
Blantz , Roland rblantz@ucsd.edu Department of Medicine, University of California, San Diego
Braam , Branko branko.braam@ualberta.ca Division of Nephrology and Immunology, University of Alberta
Chen, Jing jchen@math.duke.edu Chemical and Biological Engineering, Tufts University
Chon , Ki ki.chon@sunysb.edu Biomedical Engineering, State University of New York
Christensen, Erik Ils eic@ana.au.dk Cell Biology, Aarhus University
Cupples , Will wcupples@uvic.ca Dept of Biology, University of Victoria
Dantzler, William dantzler@email.arizona.edu Physiology, University of Arizona
Dembele, Bassidy bdembele@mbi.osu.edu MBI - Long Term Visitor, Howard University
Ditlevsen , Susanne sudi@pubhealth.ku.dk Department of Biostatistics, University of Copenhagen
Djordjevic, Marko mdjordjevic@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Edwards , Aurlie Chemical and Biological Engineering, Tufts University
Enciso, German German_Enciso@hms.harvard.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Forster , Ian iforster@access.unizh.ch Institute for Physiology , University of Zurich
Grajdeanu, Paula pgrajdeanu@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Green, Ed egreen@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Harris, Peter pjharris@unimelb.edu.au Physiology , University of Melbourne
Hartvigsen, Gregg hartvig@geneseo.edu MBI-Long Term Visitor, University at Buffalo (SUNY)
Hegarty, Alan alan.hegarty@ul.ie Mathematics and Statistics , University of Limerick
Holstein-Rathlou , Niels-Henrik nhhr@mfi.ku.dk Medical Physiology, University of Copenhagen
Jamison , Rex rjamison@leland.stanford.edu nephrology, Stanford University
Jordan, Peter jordan@brandeis.edu Chemistry, Brandeis University
Just, Armin just@med.unc.edu Dept. of Cell & Molecular Physiology , University of North Carolina, Chapel Hill
Kao, Chiu-Yen kao.71@osu.edu MBI - Long Term Visitor, The Ohio State University
Kim, Yangjin ykim@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Kleinstreuer, Nicole nck20@student.canterbury.ac.nz Centre for Bioengineering, University of Canterbury
Knepper , Mark knep@helix.nih.gov Laboratory of Kidney & Electrolyte Metabolism, National Institutes of Health
Kriz , Wilhelm wilhelm.kriz@urz.uni-heidelberg.de Institut für Anatomie und Zellbiologie, INF 307
Layton, Anita alayton@math.duke.edu Mathematics, Duke University
Layton, Harold layton@math.duke.edu Mathematics, Duke University
Loo , Donald dloo@mednet.ucla.edu Physiology, University of California, Los Angeles
Lou, Yuan lou@math.ohio-state.edu MBI - Long Term Visitor, The Ohio State University
Loutzenhiser, Rodger rloutzen@ucalgary.ca Pharmacology & Therapeutics, University of Calgary
Marcano, Mariano mmarcano@uprr.pr Mathematics, University of Puerto Rico
Marsh , Donald marsh@ash.biomed.brown.edu Biomedical Center, Brown University
Moore, Leon leon.moore@sunysb.edu Physiology and Biophysics, SUNY
Moss, Robert rgm@csse.unimelb.edu.au Melbourne School of Population and Global Health, The University of Melbourne
Nevai, Andrew anevai@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Nieves-Gonzalez, Aniel aniegon@ams.sunysb.edu Applied Mathematics and Statistics, SUNY
Oster, Andrew aoester@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Pallone , Thomas tpallone@medicine.umaryland.edu Division of Nephrology, Rm. N3W143, University of Maryland at Baltimore
Pannabecker, Thomas pannabec@u.arizona.edu Physiology, University of Arizona
Pitman , Bruce pitman@buffalo.edu Department of Mathematics , University at Buffalo (SUNY)
Rempe, Michael mrempe@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Roux, Benoit roux@uchicago.edu Pediatrics, Biochemistry & Molecular Biology, University of Chicago
Sands, Jeff jeff.sands@emory.edu Renal Division, Emory University
Schafer , James jschafer@uab.edu Physiology and Biophysics, University of Alabama at Birmingham
Schnermann, Jurgen jsch@starpower.net National Institutes of Health
Schugart, Richard richard.schugart@wku.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Schumaker, Mark schumake@math.wsu.edu Mathematics, Washington State University
Shareshian , Lauren lauren@math.duke.edu Mathematics Department , Duke University
Siu, Kin Lung volario22@aol.com Biomedical Engineering, SUNY
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Stigler, Brandy bstigler@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Stynes, Jeanne jeanne.stynes@cit.ie Computing, Cork Institute of Technology
Sun, Shuying ssun@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Szomolay, Barbara b.szomolay@imperial.ac.uk Mathematical Biosciences Institute (MBI), The Ohio State University
Thomas, Evelyn ethomas@mbi.osu.edu MBI - Long Term Visitor, Howard University
Thomas, S. Randall srthomas@lami.univ-evry.fr Univ Evrey Val l-Agora
Tian, Paul tianjj@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Vallon , Volker vvallon@ucsd.edu Departments of Medicine and Pharmacology, University of California, San Diego
Verkman , Alan Alan.Verkman@ucsf.edu Department of Medicine & Physiology, University of California-San Francisco
Wang, Ying wang@math.ohio-state.edu Department of Mathematics, The Ohio State University
Weinbaum, Sheldon weinbaum@ccny.cuny.edu Biomedical & Mechanical Engineering, City University of New York (CUNY)
Weinstein, Alan alan@nephron.med.cornell.edu Physiology and Biophysics, Cornell University
Williamson, Geoffrey williamson@iit.edu Electrical and Computer Engineering , Illinois Institute of Technology
Yip, Daniel dyip@health.usf.edu Molecular Pharmacology and Physiology, University of South Florida
The Tubular Vascular Relationship of TGF: Is there a Metabolic Contribution to this Connection?

Kidney blood flow is highly regulated and maintained relatively constant via highly efficient autoregulation of blood flow and glomerular filtration and complex interactions of neurohumoral vasoconstrictor and vasodilator influences.   Increases in kidney blood flow obligate an increase in filtered load or GFR which in turn obligates tubular reabsorption, which in turn requires expenditures of ATP and oxygen.  Therefore, in contrast to other organs, increases in blood flow to the kidney both create a supply and a demand.  For these reasons the regulation of filtered load or GFR must be finely coordinated with tubular reabsorption.  This is achieved by the tubuloglomerular feedback system, based at the macula densa and juxtaglomerular apparatus.    The mediators of this TGF system are ATP and adenosine, a product of AMP.  Since these substances are important products critical to metabolism it suggests an important metabolic link to regulation of blood flow and GFR.  The TGF system does not remain static but adapts with time and physiologic conditions, such that the relationship between macula densa Na delivery/reabsorption and GFR is reset and temporally adapts.  These conditions include normal growth, changes in Na intake, reductions in nephron mass and persistent changes in reabsorption proximal to the macula densa.  Modulators of TGF temporal adaptation have been defined and includes NO derived from NOS-1, angiotensin II and COX-2 products.


Oxygen consumption (QO2) by the kidney is directly, and possibly linearly, related to Na reabsorption (TNa).  However, recent studies have suggested that the metabolic efficiency of Na reabsorption can change rather dramatically in normal and pathophysiologic conditions.  In chronic conditions and, specifically, certain forms of hypertension AII has been suggested to increase oxygen consumption relative to Na transport.  We have shown that NO (specifically NO derived from NOS-1) can act to suppress kidney oxygen consumption.  Blockers of NOS-1 dramatically increase QO2 and QO2 /TNa   both in vivo and in vitro in freshly harvested proximal tubules.  Inhibitors of carbonic anhydrase also increase QO2 /TNa   in vivo and in vitro by promoting active and preventing passive Na reabsorption.  The kidney in early diabetes exhibits hyperfiltration and kidney growth, in major part due to increased reabsorption in the proximal tubule which effectively deactivates TGF leading to functional increases in GFR.  NOS-1 is constitutively increased in the diabetic kidney from sources outside the macula densa and acts as a functional brake on increased oxygen consumption.  However the diabetic kidney does not undergo normal TGF temporal adaptation, primarily due to an inability of NOS-1 activity to change appropriately.  Although blockade of AII does not alter oxygen consumption in normal kidneys, application of angiotensin II receptor blockers in models of 5/6th nephrectomy, a model of chronic kidney disease, dramatically reduces elevated values for QO2 /TNa observed in this model.  These studies suggest that endogenous regulators of the relationship between kidney blood flow/GFR and tubular reabsorption are linked to kidney metabolism.  Modulators of the adaptive behavior of TGF systems also act to modify kidney oxygen consumption and the metabolic efficiency of tubular reabsorption.  Therefore the TGF influences critical to kidney function and metabolism involve regulation of both metabolic supply and demand. 


 

Insights from Time-Varying Spectral Analysis

Renal autoregulatory mechanisms are not only characterized by their dynamic nature, but the nature of their dynamics varies over time, leading to transient signals. These time-varying dynamics are often nonlinear and have different time scale oscillations (fast and slow), with each oscillation exhibiting its own transient dynamics. Our recent application of high-resolution, time-varying spectral and transfer function methods has revealed substantial differences between hypertensive and normotensive rats in the dynamics of the two principal autoregulatory mechanisms, tubuloglomerular feedback (TGF) and the myogenic mechanism. Despite the major progress made, the fundamental determinants that underlie differences in the renal autoregulatory dynamics between normotensive and hypertensive rats remain unresolved. For example, it remains to be determined why either time-invariant or time-varying spectral densities associated with hypertensive rats are more complicated than those of normotensive rats. A recent modeling study by Layton and Moore have predicted this in part due to the TGF system exhibiting multi-stability which can result in rapid switching between the dynamic modes which can consequently lead to a complicated spectral behavior. We will provide preliminary data from SHR that are consistent with the prediction of the Layton and Moore TGF model, including TGF waveform shape, switching between multiple stable modes of TGF oscillation, increased parameter variability relative to controls, and the presence of low frequency modulation of the TGF system. In addition, we will show data using time-varying nonlinear methods that complicated and additional spectral peaks associated with SHR arise because of nonlinear interactions between the autoregulatory mechanisms.


Work done in collaboration with Kin Siu and Leon C. Moore.

Reconstruction of the mouse nephron and distribution of AQP-1 and UT-A2

Renal function is crucially dependent on renal microstructure providing the basis for the mechanisms that control the transport of water and solutes between filtrate and plasma and the urinary concentration. This study provides, detailed information on mouse renal architecture, including the spatial course of the tubules, lengths of different segments of nephrons, histotopography of tubules and vascular bundles, epithelial ultrastructure at well-defined positions along Henle's loop and the distal convolution of nephrons, and the exact distribution of AQP-1 and the urea transporter UT-A2. Three-dimensional reconstruction of 200 nephrons and collecting ducts was performed on aligned digital images, obtained from 2.5-mu m-thick serial sections of mouse kidneys. Important new findings include: (1) A tortuous course of the descending thin limbs of long-looped nephrons and a winding course of the thick ascending limbs of short-looped nephrons contribute to a 27% average increase in the lengths of the corresponding segments, (2) the thick-walled tubules incorporated in the central part of the vascular bundles in the inner stripe of the outer medulla were identified as thick ascending limbs of long-looped nephrons, and (3) three types of short-looped nephron bends were identified related to the length and the position of the nephron and its corresponding glomerulus. The ultrastructure of the tubule segments was identified and correlated to the localization of AQP-1 and UT-A2. Our new findings suggest important implications for renal transport mechanisms that should be considered when evaluating the segmental distribution of water and solute transporters within the normal and diseased kidney.


Work done in collaboration with Xiao-Yue Zhai.

Three-dimensional functional reconstructions of vascular and tubular structures of inner medulla

Mammalian kidneys are capable of producing urine substantially more concentrated than the plasma, thereby helping to conserve water. In part, this process involves generation, within the inner medulla, of an osmotic gradient that increases axially from cortex to papilla tip. In the simplest models, generation of this osmotic gradient involves countercurrent multiplication by the loops of Henle of a small lateral osmotic pressure difference between their ascending and descending limbs. In the outer medulla (OM), this model appears to be essentially correct with the lateral difference between the limbs generated by active sodium transport out of the thick ascending limb. However, in the inner medulla (IM), which makes up ~75% of the length of the medulla (rat IM ? 5mm) and which generates the steepest osmotic gradient, the process of gradient generation, although probably involving some form of countercurrent multiplication, is not understood. In an attempt to understand how three-dimensional functional relations between structures in the IM might contribute to this process, we began a total digital reconstruction of the functional three-dimensional architecture of vasculature and nephron segments in rat renal IM from physical serial sections of resin-embedded tissue. Segments of descending vasa recta (DVR), ascending vasa recta (AVR), descending thin limb (DTL), ascending thin limb (ATL), and collecting duct (CD) were identified with antibodies against segment-specific proteins associated with solute and water transport (UT-B, PV-1, AQP1, ClC-K1, and AQP2, respectively, for the above segments) by indirect immunofluorescence. Reconstructions of the central region of the IM through the first 3 mm below the OM-IM border revealed the following major features: 1) DTLs with their loops within 1 mm below the OM-IM border have no detectable AQP1; 2) DTLs with loops below 1 mm from the OM-IM border express AQP1 for the first 40% of their length below the border, but fail to express AQP1 for the remaining 60%; 3) Expression of ClC-K1 begins abruptly with a prebend segment in the DTL, which is always ~150-200 ?m in length regardless of the total length of the loop, and continues uniformly throughout the ATL; 4) clusters of coalescing CDs form the organizing motif for the IM; 5) DTLs and DVR are arranged outside the CD clusters; 6) ATLs and AVR are nearly uniformly distributed transversely across the entire inner medulla outside of and within CD clusters; 7) ATLs that lie closest to the center of the CD clusters arise from the shortest DTLs, whereas ATLs that lie at the periphery or outside of the clusters arise from longer DTLs; 8) DVR and AVR outside CD clusters appear sufficiently juxtaposed to permit good countercurrent exchange; 9) within CD clusters, about four AVR closely abut each CD, surrounding it in a highly symmetrical fashion covering about 54% of the CD surface area and apparently permitting rapid removal of water reabsorbed from collecting ducts; 10) AVR abutting each CD and the ATLs within CD clusters form repeating nodal interstitial spaces bordered by a CD on one side, one or more ATLs on the opposite side, and one AVR on each of the other two sides. These relationships may be highly significant for both establishing and maintaining the inner medullary osmotic gradient.

Modification of Cytosolic Calcium Signaling by Subplasmalemmal Microdomain in Outer Medullary Pericytes

Contractility of resistance vessels is regulated by variation of intracellular Ca2+ concentration in both endothelium and smooth muscle. To investigate the hypothesis that Na+ concentration in subplasmalemmal microdomains regulates Ca2+ concentrations in cellular microdomains ([Ca]md), cytosol ([Ca]cyt), and sarcoplasmic reticulum (SR, [Ca]sr), we modeled transport events in those compartments. The model accounts for major classes of ion channels, Na+/Ca2+ exchange (NCX) and the distributions of Na+/K+-ATPase a1 and a2 isoforms in the plasma membrane.  Ca2+ release from SR stores is assumed to occur via ryanodine (RyR) and inositol tris phosphate (IP3R) receptors.  The model shows that requisite existence of a significant Na+ concentration difference between the cytosol ([Na]cyt) and microdomains ([Na]md) necessitates restriction of intercompartmental diffusion.  Accepting the latter, the model predicts resting ion concentrations that are compatible with experimental measurements, and temporal changes in [Ca]cyt similar to those observed upon NCX inhibition.  An important role for NCX in the regulation of Ca2+ signaling is verified.  In the resting state, NCX operates in "forward mode", with Na+ entry and Ca2+ extrusion from the cell.  NCX translates variations in Na+/K+-ATPase activity into changes in [Ca]md, [Ca]sr and [Ca]cyt. Taken together, the model simulations verify the feasibility of the central hypothesis that modulation of [Na]md can influence both the loading of Ca2+ into SR stores and [Ca2+]cyt variation.

Electrogenic phosphate transport across renal epithelia: mechanistic insights from experiments and simulations

The reabsorption of inorganic phosphate (Pi) across the brush border membrane of renal proximal tubule epithelia is essential for Pi homeostasis. Uphill Pi transport across the apical membrane is secondary-active, driven by the electrochemical gradient of Na+. Transport is mediated by members of the SLC34 solute carrier family (type II Na+/Pi cotransporters, NaPi-II). NaPi-IIa, responsible for up to 80% of Pi reabsorption in the mammalian kidney, operates with a stoichiometry of 3Na+:H2PO42- and +1 charge is translocated per cycle. Expression of cloned NaPi-II transporters in Xenopus oocytes has allowed the transport mechanism to be characterized by means of tracer uptake, electrophysiology and voltage clamp fluorometry. These studies have yielded both steady-state and presteady-state kinetic information.


I will show how we have used experimental data to build a kinetic model that describes the main transport features. We propose a kinetic scheme that involves the ordered binding/debinding of substrates, consistent with an alternating access carrier model. The transport cycle comprises a sequence of partial reactions between 8 states, corresponding to unique conformations of the protein. Electrogenicity arises from the voltage-dependent reorientation of mobile charges of the empty carrier and one Na+ binding partial reaction, which we model as single transitions involving the movement of lumped charged species over single energy barriers. Model simulations have allowed us to quantitate rate constants for the partial reactions and distinguish between different binding order schemes.

The Virtual Kidney: Progress with a 3D anatomical interface, model repository and grid portal for distributed computing

A 3D "virtual kidney" interface has been developed for access to experimental data and parameter values abstracted within the Quantitative Kidney Database (QKDB) described by S Randall Thomas and to a repository of mathematical models of kidney function. At the gross anatomy level a translucent 3D reconstruction of a rat kidney shows contours of the renal capsule, inner and outer medullas, and the ureter, as well as renal arteries and veins to several levels of branching. Within the kidney are superficial and juxtamedullary nephrons. Using the mouse buttons the user can rotate the kidney, display or hide individual structures, and zoom in on any portion. Selection of a structure provides a link to the search facility of QKDB and thence to relevant parameter values and extracts from the literature.


A menu lists the repository of mathematical models, such as segmental (e.g., proximal or distal tubule) or medullary transport models, which may be run on the local machine or, via a Grid Portal (KidneyGrid), simultaneously on several remote machines. The use of a grid resource broker demonstrates the ability to compose, schedule, monitor and visualize the results of the simulation and simplifies the development of application, credential and resource management while decoupling the launch platform from the underlying grid middleware.


The simulation results (e.g., solute concentrations or local flow rates) are visible on the virtual kidney structures as scaled colour gradients, thus allowing a visual and quantitative appreciation of the effects of simulated parameter changes. A separate panel shows x-y plots of the results. The underlying models are implemented via CellML descriptions and are consistent, as far as possible, with standards and ontologies being developed for other organs under the Physiome initiative.


Work done in collaboration with S Randall Thomas, Andrew Lonie, Bill Appelbe, Belinda May, Peter Hunter, Raj Buyya and Xingchen Chu.

Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats

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Gating Ion Channels: the Interplay of Structure and Theory

Important features of ion channel gating can be reliably studied by coupling theory with high-resolution atomic level structures of channel forming peptides. New methods for tracking ion channels' low frequency deformational modes are applied to analyze gating in two systems: gramicidin and KcsA. In both the lowest frequency normal mode (NM) is the crucial mode that initiates transition between open and closed states. Tracking these NMs reveals each channel's gating mechanism. Gramicidin dissociates via relative opposed monomer rotation and simultaneous lateral displacement. WT KcsA does not open. When the cytoplasmic GLUs are protonated KcsA opens via a complex set of motions initiated near the smoke hole of the "tepee" and propagating to the "glycine hinge," ultimately adopting a structure reminiscent of MthK. In both systems NM structure changes as the system evolves; the gating mechanisms are not simple, exhibiting complex backbone realignments and side chain reorganizations.

Evidence for a third and fourth regulatory mechanism in renal blood flow autoregulation

Autoregulation of renal blood flow (RBF) is mediated by two major mechanisms: a fast myogenic response (MR, <10 s) and slower tubuloglomerular feedback (TGF, 10-40 s). However, it is unclear whether additional mechanisms are involved. To separate the mechanisms and analyze their kinetics, we studied autoregulatory responses to a rapid step increase of renal artery pressure (RAP) in rats and mice. RAP was reduced 20 mmHg for 60 s and then rapidly released.


After the increase in RAP, renal vascular resistance (RVR) briefly fell for < 0.5 s but then quickly rose to an autoregulatory efficiency of 36% within the first 7-10 s in rats. After a brief delay, a secondary rise of RVR began at 10 s, further improving autoregulation to 75% at 40 s. RVR then slowly further rose from 40 s to 120 s to a final level of 94%. Results were similar in mice. Based on these kinetics, the initial response likely reflects MR and the secondary response TGF; the slowest component indicates a third regulatory mechanism substantially slower than TGF. Inhibition of “classical” TGF by furosemide enhanced the initial MR, reduced the secondary component of autoregulation by ~60%, and eliminated the tertiary one. Doubling of the dose of furosemide did not further affect the secondary component or the diuretic effect. In mice, genetically deficient for A1 adenosine receptors (A1AR), which are known to lack TGF, the primary and the tertiary components were unaltered, but the secondary one was reduced ~50%. When furosemide was given to A1AR-deficient mice, the primary component was followed by a small secondary one, while the tertiary component was eliminated. Exactly the same time course was observed during furosemide in wild-type mice. These results indicate that: 1) the fastest component likely reflects MR and contributes at least 40% as it is also responsible for overcoming the initial passive reduction of RVR, 2) part of the secondary response is mediated by classical TGF, i.e., mediated by A1AR and inhibited by furosemide, and contributes ~40% to autoregulation, 3) a third regulatory mechanism exists that is sensitive to furosemide, but not mediated by A1AR, and contributes ~20%, 4) the remnant response between 10 and 40 s during furosemide resembles the kinetics of classical TGF, but is distinct in that it is resistant to the employed doses of furosemide and not dependent on the presence of A1AR.


We conclude that in rats and mice, in addition to well characterized MR and TGF, a third mechanism contributes to RBF autoregulation that is slower than classical TGF and independent of A1AR but sensitive to furosemide. In addition, a fourth mechanism seems to exist resembling classical TGF in response time but differing in being independent of A1AR and insensitive to furosemide.

Analysis of cell signaling networks using proteomics methods and ODE-based modeling

Based on general ordinary differential equations describing mass balance in the cell that incorporate global signaling mechanisms seen in all cells, we can identify four fundamental processes that are common to all signaling pathways: a) changes in protein abundance; b) changes in post-translational modifications including phosphorylation, nitrosylation, acylation, and ubiquitylation; c) changes in cellular location including cytosol-to-membrane translocation and cytosol-to-nucleus translocation; and d) changes in binding of proteins to other proteins and lipids. We are developing quantitative approaches to tandem mass spectrometry to measure each of these changes globally across the proteome of an individual cell type. For example, we have recently published the IVICAT method for non-radioactive isotope labeling of peptides and the neutral loss scanning technique for quantification of protein phosphorylation. These methods have been employed to analyze the signaling response of the inner medullary collecting duct cell to vasopressin. The differential equations can be converted to a graphical analysis of protein-protein interaction through use of the Jacobian matrix to define graph edges.

Multistable Dynamics Mediated by Tubuloglomerular Feedback in a Model of Coupled Nephrons

To help elucidate the causes of irregular tubular flow oscillations found in the nephrons of spontaneously hypertensive rats (SHR), we have conducted a bifurcation analysis of a mathematical model of two nephrons that are coupled through their tubuloglomerular feedback (TGF) systems. This investigation was motivated by a modeling study which predicts that NaCl backleak from a nephron's thick ascending limb permits multiple stable oscillatory states that are mediated by TGF (Am. J. Physiol. Renal Physiol. 291: F79-F97, 2006). In that study, a characteristic equation obtained via linearization from a single-nephron model having NaCl backleak, in conjunction with numerical solutions of the full, nonlinear model equations for two and three coupled neph rons, was used in the formulation of a comprehensive, multifaceted hypothesis for the emergence of complex dynamics in SHR. In the present study we have derived a characteristic equation for a model of an arbitrary number of mutually coupled nephrons having NaCl backleak. Analysis of that characteristic equation for the case of two coupled nephrons has revealed a number of parameter regions having the potential for differing stable dynamic states. Numerical solutions of the full equations for two model nephrons exhibit a number of differing behaviors in these regions. Some behaviors are markedly irregular and exhibit a degree of spectral complexity that is consistent with physiologic experiments in SHR. Effects of coupling and irregular oscillations on fluid and NaCl delivery are also discussed.

Harmonics and heterodyning in the tubuloglomerular feedback loop

Spectral frequencies arising from harmonics and from heterodyning have been reported in both experimental and modeling studies. Both harmonic and heterodyne frequencies have been attributed to the nonlinear properties of the tubuloglomerular (TGF) loop. However, the detailed mechanisms by which particular renal components generate harmonic and heterodyne frequencies have not been elucidated. Elementary mathematics can be used to show that signal transduction in a model of the thick ascending limb, of tubular flow rate to NaCl concentration at the macula densa, can, in principle, produce infinite series of both harmonic and heterodyne frequencies. Other nonlinear processes (e.g., the sigmoidal TGF response at the juxtaglomerular apparatus) can also introduce harmonic and heterodyne frequencies. Harmonic and heterodyne frequencies may be important components of the complex power spectra which arise from the irregular oscillations that are found in intratubular pressure records obtained from spontaneously hypertensive rats.


Supported by NIH Grant DK-42091 and NSF Grant DMS-0340654.


Collaborators: Anita Layton, Bruce Pitman, Paula Grajdeanu, Kevin Kesseler, Leon Moore, and Lauren Shareshian

Conformational Dynamics of SGLT1 during Na+/glucose Cotransport

Glucose is actively transported across the apical membrane of proximal tubular cells by Na+/glucose cotransporters (SGLT's). SGLT1, the model for this class of transporter, functions by an alternating access mechanism via a series of conformational changes induced by substrate-binding and membrane voltage. We have examined the conformations of human SGLT1 mutant G507C (expressed in Xenopus oocytes) during sugar transport using simultaneous electrical and optical measurements. The mutant exhibited similar kinetics as wild-type SGLT1, and labeling of Cys507 by tetramethylrhodamine-6-maleimide had no effect on function. We recorded changes in presteady-state currents (charge movement) and fluorescence in response to rapid-jumps in membrane potential in the presence and absence of glucose. Simulations based on an 8-state kinetic model for SGLT1 indicate that external sugar increases the occupancy probability of inward-facing conformations at the expense of outward-facing conformations. The simulations predict, and we have observed experimentally, that presteady-state currents are blocked by saturating sugar, but not the changes in fluorescence. Thus the conformational change associated with the rate-limiting step is electroneutral: at maximal inward Na+/sugar cotransport (saturating voltage and external Na+ and sugar concentrations), it is the slow release of Na+ from the internal surface of SGLT1.

Systolic Pressure is the Dominant Signal in Autoregulation

Elevated blood pressure (hypertension) is a leading cause of glomerular injury and kidney disease. By adjusting pre-glomerular resistance in response to pressure elevations, the myogenic response of the afferent arteriole is thought to play a major role in protecting the kidney from such injury. Indeed, when myogenic reactivity is impaired, not only is the autoregulation of renal blood flow less efficient, but the susceptibility of the kidney to hypertensive injury is greatly enhanced. Blood pressure presents to the kidney as a complex oscillating signal. The systolic blood pressure, being the highest pressure attained and the most frequent oscillation within this signal, is intrinsically the most damaging component and clinical studies demonstrate that systolic hypertension is most closely linked to renal injury. The renal myogenic response appears to be uniquely suited to protect against elevations in this signal. We have found that, in the rat, pressure increases initiate a rapid afferent arteriolar vasoconstriction within 200-300 ms. When pressure is reduced, vasodilation is initiated after a much longer delay (~1 s). Moreover, high-speed video studies show that vasoconstrictor responses initiated by short pressure pulses (< 300 ms) continue during this delay in relaxation. Experimental and modeling approaches demonstrate that these features allow the afferent arteriole to sense and adjust steady-state myogenic tone in response to the rapidly oscillating systolic blood pressure signal, thereby attenuating the transmission of pressure transients to the glomerulus. Studies of the mechanisms underlying the unusual myogenic kinetics of this vessel implicate an important role of the release of calcium from the sarcoplasmic reticulum (SR, an internal calcium store) and the involvement of SR calcium channels (ryanodine receptors). Our findings suggest a model of the myogenic response that involves both a sustained membrane depolarization, causing the activation of voltage-gated calcium entry, and a cyclic stretch-induced release of SR calcium in response to the oscillating systolic blood pressure signal.

Optimization Problems and Algorithms for Mathematical Models of Renal Systems

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Routes to chaos in nephron blood flow regulation: nephron synchronization and ensemble formation

Tubular pressure recordings in normotensive rats reveal a regular oscillation due tubuloglomerular feedback (TGF) operating at 20-40 mHz and a smaller faster oscillation due to the myogenic mechanism operating at 100-200 mHz. The TGF fluctuation is irregular in hypertensive rats, and takes on characteristics of deterministic chaos. We have used simulations to test two hypotheses about the mechanism of the bifurcation. In the first we used a spatially extended model of the nephron, cast as two-point nonlinear boundary value problem. The model solves for flow rate of tubular fluid, tubular pressure, and tubular NaCl concentration as functions of time and distance. The tubule wall is compliant and reabsorbs NaCl and water in accordance with the known behavior of a cortical renal tubule. The initial flow is glomerular filtration rate, the initial NaCl concentration is the plasma value, and the outflow pressure is determined by the operation of a pressure dependent resistance in the distal tubule. Glomerular capillary pressure is governed by the operation of an afferent arteriolar model that simulates membrane currents and PD, myosin light chain phosphorylation, and the operation of a contractile mechanism and an elastic element. The afferent arteriolar model receives input from TGF. We investigated whether the coefficient coupling TGF and the myogenic mechanism can serve as a bifurcation parameter. It does, and within a range of values known to include the increase of this parameter seen in hypertension.


Nephrons signal to each other over the vascular wall; the strength of this signalling increases 3-fold in hypertension. We developed a model that includes a single cortical radial artery, and 22 nephrons, of which 14 are cortical; of the remaining 8, 4 are short medullary nephrons, 3 intermediate length, and 1 a longer length medullary nephron. The nephron models are a 3rd order set of ODE's that predict tubular pressure and arteriolar diameter, with a 3rd order lag to simulate the various physical delays that occur in transmitting a change in proximal tubular outflow into a signal that reaches the afferent arteriole via TGF. The model does not have an independent myogenic component. Cortical nephrons synchronize at a single frequency, but the medullary nephrons cluster at frequencies incommensurate with the cortical frequency. The result is that cortical nephrons operating at normal blood pressure and normal vascular coupling, develop quasiperiodic dynamics, a well known route to chaos. The simulation shows that medullary nephrons operate in a chaotic mode even when arterial pressures and coupling coefficients are normal, and the chaotic domain increases to include cortical nephrons as the arterial blood pressure and the vascular coupling strength are made to increase.


The results of these simulations suggest that there is more than one possible cause of the bifurcation to chaos that has been observed. The simulated synchronization, whether in normotensive or hypertensive states, provides the possibility that nephrons could react to perturbations in arterial pressure as an organized ensemble. The formation of a chaotic state, however, can lead to reduced synchronization despite the increase of coupling strength, because such states are inherently more likely to become desynchronized. The functional significance of synchronization and of its reduction in hypertension, remain to be understood.

Sources of complexity in a model of the TGF system

The talk will consider evidence for multi-stability of the TGF system, primarily from spontaneously hypertensive rats (SHR). The use of time-varying spectral analysis of time series generated by a mathematical model of the TGF system to identify sources of complexity will then be described. Finally, we will present evidence that simple models of TGF in three coupled nephrons can generate dynamics consistent with deterministic chaos.

A Preliminary Model for Studying the Interactions Between Nephrons

Our aim is to simulate the behaviour of clusters of nephrons and to understand how this behaviour arises from the activities of individual tubule segments. Further, we aim to create models that are capable of predicting kidney function and the effects of renal disease. Ultimately, we are interested in investigating the behaviour of the kidney at a level of abstraction that is relevant to clinicians.


We approach the problem of renal modelling by assuming that the kidney is a complex network and applying techniques from Dynamical Networks (a form of Graph Automata) and methods from Statistical Mechanics and Machine Learning.


We present a model of the nephron as a Graph Automata, where each node models a tubule segment, and difference equations model solute transport between tubule segments, the surrounding renal fluid, and peritubular capillaries. This network will form the basis of multi-nephron models, allowing us to study interactions and patterns of behaviour across groups of nephrons. Our current system of simple transport equations makes simulation of large clusters of nephrons computationally tractable.


The model, though simple and still incomplete, is able to construct and maintain a salt gradient in the medullary fluid, and to regulate water and sodium reabsorption in response to ADH levels. The model also allows us to introduce stochastic failures into the nodes to mimic the onset of renal diseases (such as scar tissue in Bowman's Capsule) and so facilitate the analysis of the effects that diseased nephrons have on neighbouring nephrons.

Vasoactivity and ion channel architecture of the descending vasa recta wall

The renal medulla is supplied with blood flow by efferent arterioles of juxtamedullary glomeruli. Efferent arterioles form descending vasa recta (DVR) that penetrate the outer medulla of the kidney in vascular bundles. DVR in vascular bundles give rise to ascending vasa recta (AVR) in the inner medulla that flow in a countercurrent manner to return blood to the renal cortex. Modulation of medullary blood flow has been tied to urinary concentration and regulation of salt excretion by the kidney. As such, control of medullary blood flow and its regional distribution to the outer and inner medulla has been of considerable interest.


DVR 12 - 15 micron vessels to which contractility is imparted by smooth muscle remnants called pericytes. Much controversy has surrounded the ion channel architecture of the afferent and efferent circulations of the kidney. The roles of voltage gated calcium channels and membrane potential changes in vasoconstriction has been uncertain. To test their roles, we have isolated DVR by microdissection and performed patch clamp experiments on the pericytes and endothelium. The data shows that vasoactive agonists depolarize the pericyte cell membrane through a combination of calcium dependent chloride channel activation and potassium channel deactivation. Several classes of potassium channels are involved. Voltage gated calcium channel activity can be demonstrated in the pericytes, and, surprisingly, fast voltage gated sodium channels yield prominent currents. Finally, we have demonstrated that both pericytes and endothelial cells are electrically coupled via gap junctions. The pericytes appear to be weakly coupled while the endothelium forms low resistance syncytium. My talk will describe our current knowledge of the channel architecture of the DVR wall and compare it to that of other renal arteriolar segments.

Quantitative Analyses of Nephron and Blood Vessel Architecture in the Renal Inner Medulla

Urine concentration by the mammalian kidney is important for fluid and solute homeostasis. The renal inner medulla (IM) plays an important role in producing concentrated urine. As nephrons and blood vessels enter the medulla, traverse, and then exit the IM, returning to the cortex, they exchange fluid and solutes with neighboring structures in a precisely organized fashion. Appropriate fluid and solute exchange relies on specific membrane transporters that exist along the axis of the nephron or vessel. The efficient exchange from one structure to another is also affected by the distance fluid and solutes move between compartments, the number of target compartments that exist within a defined space, as well as physicochemical properties of interstitial space. Our three-dimensional (3D) digital reconstruction of the IM has shown that collecting duct (CD) clusters form the organizing motif around which nephron segments and blood vessels are arranged in a repeating fashion from the base of the IM to the tip of the papilla. In order to understand more fully the manner by which the architectural arrangements and axial protein distribution enable the concentrating mechanism to proceed efficiently, we are conducting quantitative analyses to determine precise spatial relationships among and between nephrons and blood vessels. Three-dimensional architecture of vasculature and nephron segments in rat renal inner medulla (IM) was assessed with digital reconstructions from physical sections of resin-embedded medullae. Segments of descending vasa recta (DVR), ascending vasa recta (AVR), descending thin limb (DTL), ascending thin limb (ATL), and CD were identified with antibodies against segment-specific proteins associated with solute and water transport (UT-B, PV-1, AQP1, ClC-K1, and AQP2) by indirect immunofluorescence. The ratio of ATL:CD total peritubular surface area declines by about 50% in the last 2 mm of the papilla compared to the first 3 mm; this results from both decreased ATL and slightly increased CD total peritubular surface areas. Water and urea delivery by CDs to interstitium in this region could be influenced by increased tubular surface area as well as by increased CD water and urea permeability. Individual CDs 0.5 to 2 mm from the papilla tip have up to 80% greater circumference than individual CDs 1.4 mm from the IM base.  In the final 500 mm CD circumference rises at a markedly steeper rate reaching as much as 200% or more of those CDs nearer the IM base. Return of water to the general circulation from these deep papillary CDs appears to be facilitated, in part, by a 150% increase in the number of AVR closely abutting these CDs. Consequently, the average fractional CD surface area abutting AVR is 0.61, about the same as that (0.54) for the smaller CDs that lie near the IM base. Interstitial nodal compartments, bounded by CDs, ATLs, and AVR, surround CDs in the upper 3 mm of the IM. Fewer ATLs exist in the final 1 mm as there are fewer loops and the number of these nodal arrangements is therefore reduced. However, the tips of those loops reaching this area have bends with 50 to 100% greater lateral lengths than the bends of loops near the IM base. This may be significant for solute movement out of the loop bends.

Vasopressin regulation of the UT-A1 renal urea transporter

Urea transport, mediated by the UT-A1 and/or UT-A3 urea transporters, is important for the production of concentrated urine. Vasopressin rapidly increases urea transport in rat terminal inner medullary collecting ducts (IMCDs). UT-A1 is expressed in the apical plasma membrane of inner medullary collecting ducts (IMCDs). The localization of UT-A3 is controversial: it is apical in rat but basolateral in mice. Two mechanisms have been identified by which vasopressin may rapidly increase urea permeability in rat IMCDs: 1) increases in UT-A1 phosphorylation; and 2) increases in UT-A1 plasma membrane accumulation. The fold-increase in urea transport following vasopressin is larger than the fold-increase in either UT-A1 phosphorylation or plasma membrane accumulation alone. This suggests that vasopressin increases urea permeability through increases in both UT-A1 accumulation and phosphorylation.


Vasopressin also stimulates urea flux, UT-A1 phosphorylation, and UT-A1 apical plasma membrane accumulation in UT-A1-MDCK cells, an MDCK cell line that we stably transfected with UT-A1. Vasopressin acts through a cAMP pathway in both rat IMCDs and UT-A1-MDCK cells. However, in UT-A1-MDCK cells, a protein kinase A (PKA) inhibitor only inhibits 50% of the cAMP-stimulated urea flux. This suggests that urea flux is stimulated by both PKA-dependent and PKA-independent cAMP pathways.


Vasopressin also regulates UT-A1 long-term. UT-A1 protein abundance increases in the inner medulla of Brattleboro rats, which lack vasopressin, that are given vasopressin for 12 days. Similarly, reducing endogenous vasopressin in a normal rat by 14 days of water diuresis reduces UT-A1 protein abundance. In contrast, giving vasopressin to Brattleboro rats for only 5 days does not increase UT-A1 protein abundance. UT-A1 promoter activity is increased by hypertonicity through a tonicity enhancer (TonE) element, but lacks a cAMP response element (CRE) and cAMP does not increase promoter activity. The promoters of NKCC2/BSC1 and AQP2 do have CREs. This suggests that vasopressin initially increases the transcription of NKCC2/BSC1(and AQP2), which increases inner medullary osmolality. The increase in inner medullary osmolality then activates UT-A1 transcription, accounting for the delayed increase in UT-A1 protein abundance.


In summary, vasopressin regulates UT-A1: 1) acutely by increasing UT-A1 phosphorylation and plasma membrane accumulation; 2) through both PKA-dependent and PKA-independent cAMP pathways; and 3) long-term by changes in protein abundance in response to increases in inner medullary osmolality. Support: NIDDK and AHA.

NKCC2 Isoforms and TGF signaling

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Framework models of ion permeation

Framework models are designed to incorporate information from molecular dynamics simulations of ion channels in order to calculate their conductance properties on much longer time scales than can be achieved by the simulations. They provide a comparison between the simulations and conductance data. This talk describes three different steady state framework models. The single particle model was originally developed by Levitt, and describes a channel whose pore can be occupied by only one ion at a time. It has been used to model Na+ conduction through gramicidin. Transport is described by a Smoluchowski equation with non-local boundary conditions enforcing the single occupancy constraint. The Grotthuss conduction model describes proton conduction through gramicidin. It incorporates potentials of mean force for proton occupation and water reorientation calculated by Pomes and Roux. Model parameters were optimized against an extensive set of conductance data taken by Busath and his colleagues. Berneche and Roux developed a framework model for conduction through the narrow pore of the KcsA potassium channel, using a potential of mean force for occupation of the pore by two or three potassium ions. Finally, the problem of constructing time-dependent framework models is addressed.

Overview of Physiome: QKDB, ontology needs, European & International funding

In the interest of developing a global approach to biomedical data integration and interpretation, the Renal Physiome effort is exploring possibilities for multiscale modeling and simulation explicitly targeting questions of physiopathology. To this end, the first resource that has been developed is a quantitative kidney database (QKDB) to provide centralized access to measured parameter values, anatomical features, and functional characteristics at all scales from membrane transporters to the whole organ, both in human, when available, and in animal models. An interactive World-Wide-Web interface to legacy mathematical models at all levels of kidney physiology is also underway. Integral to the project is the development of ontologies, necessary to resolve issues of semantic ambiguity, consistency of descriptions, relational descriptions, and the like, and to enable integration with related resources in other fields. I will present current Physiome efforts internationally, will mention funding opportunities in this direction, and will give an indication of how the renal research community can participate in this communal effort.

Chemical 'knock-out' by small-molecules to probe components of the urinary concentrating system

Phenotype analysis of transgenic mice lacking various components of the urinary concentrating system, such as aquaporins, urea transporters and the V2 receptor, have provided useful information on their role in generating a concentrating urine. Selective small-molecule inhibitors of these proteins have potential utility for chemical knock-out studies that are not confounded by compensatory changes in transgenic mice, as well as for development of clinical therapies. We have established a small molecule discovery program with high-throughput screening, a collection of >300,000 drug-like chemicals, and pharmacology/small animal testing resources. The program has been successful in identifying small-molecule CFTR activators and inhibitors for therapy of cystic fibrosis and secretory diarrheas, and recently, for identification of nanomolar potency inhibitors of urea transporter UT-B, the V2 receptor, and cyclic nucleotide signaling. Small-molecule modulators of protein function are likely to have great utility in post-genomic renal physiology.

A new view of the Starling hypothesis and the role of pericytes in the temporal regulation of microvascular exchange

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Simulation Studies of Dynamic Models for Renal Autoregulation

Renal autoregulation (AR) is the vasoconstriction and dilation of the renal microvasculature in response to changes in systemic blood pressure (BP) that maintains renal blood flow (RBF), glomerular filtration rate, and the glomerular capillary pressure approximately constant. This regulatory effect is believed to simultaneously insulate renal function from variations in BP and to protect glomerular capillaries from hypertensive injury. The dynamics of renal AR informs one about the operational characteristics of its underlying mechanisms and potentially enables the study of AR in vivo. These dynamics have been investigated using spectral analysis of RBF and BP recordings, time-frequency analysis of RBF recordings, and the fitting of exponential curves to the RBF and the afferent arteriolar diameter (AAD) time responses following step changes in pressure. We developed simple dynamic models for the myogenic mechanism of renal AR that take BP waveforms as inputs and produce RBF or AAD waveforms as outputs. Simulation studies of model behavior when driven by BP waveforms measured in rats and by various test waveforms provide insight into the interpretation of results of the various analysis techniques. We have used these models to connect alterations in AR response that are observed during experimental interventions to characteristics of the AR dynamics. In particular, changes in model parameters related to AR strength cause effects similar to those from AR impairment via calcium channel blockers, and changes in parameters related to AR capacity match effects from impairments after renal mass reduction. Our models also enable simulation of (myogenic-based) AR when triggered either by mean or by systolic pressure changes. Empirical observations of AAD responses in the hydronephrotic kidney, when presented with a variety of pressure waveforms, are better matched by model behavior with AR triggered by systolic pressure.