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1

Electronic Resource

Glucose Transport in a Model of the Rat Proximal Tubule Epithelium (1985)

WEINSTEIN, ALAN M.

Oxford, UK : Blackwell Publishing Ltd

Annals of the New York Academy of Sciences 456 (1985), S. 0

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ISSN: 1749-6632

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Natural Sciences in General

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1749-6632.1985.tb14858.x

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2

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An equation for flow in the renal proximal tubule (1986)

Weinstein, Alan M.

Springer

Bulletin of mathematical biology 48 (1986), S. 29-57

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ISSN: 1522-9602

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Abstract Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02460061

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3

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Analysis of volume regulation in an epithelial cell model (1992)

Weinstein, Alan M.

Springer

Bulletin of mathematical biology 54 (1992), S. 537-561

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ISSN: 1522-9602

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Abstract An epithelial cell is modeled as a single compartment, bounded by apical and basolateral cell membranes, and containing two nonelectrolyte solute species, nominally NaCl and KCl. Membrane transport of these species may be metabolically driven, or it may follow the transmembrane concentration gradients, either singly (a channel) or jointly (a cotransporter). To represent the effect of stretch-activated channels or shrinkage-activated cotransporters, the membrane permeabilities and cotransport coefficients are permitted to be functions of cell volume. When this epithelium is considered as a dynamical system, conditions are indicated which guarantee the uniqueness and stability of equilibria. Experimentally, many epithelial cells can regulate their volume, and such volume regulatory capability is defined for this model. It is clearly distinct from dynamical stability of the equilibrium and requires more stringent conditions on the volume-dependent permeabilities and cotransporters. For a previously developed model of the toad urinary bladder (Strieteret al., 1990,J. gen. Physiol. 96, 319–344) the uniqueness and stability of its equilibria are indicated. The analysis also demonstrates that under some conditions a second stable equilibrium may appear, along with a saddle-node bifurcation. This is illustrated numerically in a modified model of the epithelium of the thick ascending limb of Henle.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02459634

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Modeling epithelial cell homeostasis: Steady-state analysis (1999)

Weinstein, Alan M.

Springer

Bulletin of mathematical biology 61 (1999), S. 1065-1091

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ISSN: 1522-9602

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Abstract Critical to epithelial cell viability is the homeostasis of cell volume and composition during changes in transcellular transport. In this study, two previously developed mathematical models (principal cell of the collecting duct and proximal tubule cell) are approximated by their linearizations about a reference condition. This yields matrices which estimate cell volume, cell composition, and transcellular fluxes in response to perturbations of bath conditions and membrane transporter activity. These approximations are themselves extended with the inclusion of linear dependence of membrane transport coefficients on cell variables (e.g., volume, solute concentrations, or electrical potential). This provides cell models with variable permeabilities, which may be homeostatic, and which can be examined systematically: sequentially testing each membrane permeability and its controlling cell variable. In the proximal tubule approximation, volume-mediated increases in peritubular K—Cl or Na—3HCO3 cotransport, and volume-mediated decreases in Na,K-ATPase activity are homeostatic; modulation of peritubular K permeability has little impact. In the principal cell model, volume homeostasis is afforded by volume-sensitive peritubular Na/H exchange or Cl− conductance. Predictions from the linear analysis are confirmed in the full models. This approach yields a systematic examination of homeostasis in an epithelial model, and identifies candidate control parameters.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1006/bulm.1999.0127

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5

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Weak acid permeability of a villous membrane: Formic acid transport across rat proximal tubule (1994)

Krahn, Thomas A. ; Aronson, Peter S. ; Weinstein, Alan M.

Springer

Bulletin of mathematical biology 56 (1994), S. 459-490

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ISSN: 1522-9602

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Abstract Chloride/formate exchange, in parallel with Na+/H+ exchange and nonionic diffusion of H2CO2, has been proposed as a mechanism of electroneutral transcellular Cl− reabsorption by the proximal tubule. However, the measured brush border H2CO2 permeability of the rat proximal tubule is at least an order of magnitude too low to support sufficient H2CO2 recycling. To investigate the possibility that an unstirred layer within the brush border might depress the measured H2CO2 permeability, we constructed a mathematical model of a villous membrane. Axial fluxes along villous and intervillous spaces were specified by Nernst-Planck diffusion equations. Model parameters were set to achieve agreement with ion and water fluxes measured in the rat proximal tubule. The equations were solved numerically to generate steady-state concentration profiles in the villous and intervillous spaces. An apparent brush border H2CO2 permeability was determined by perturbing luminal [H2CO2] and calculating the change in H2CO2 flux. Overall, the ratio of apparent brush border H2CO2 permeability to cell membrane H2CO2 permeability was greater than 90%. Contributing to the small decrease in apparent permeability are finite diffusion coefficients, folding of the membrane, and acidification of the luminal solution. An approximate analysis of this system shows the critical parameters of brush border formate transport to be the actual membrane H2CO2 permeability, and the diffusion coefficients of HCO 3 − and HCO 3 − . Nevertheless, decreasing the diffusion coefficients by one order of magnitude failed to depress apparent brush border H2CO2 permeability by more than an additional 25%. We conclude that although permeability is systematically underestimated across a villous membrane, unstirred layer effects in the brush border are still too small to resolve the discrepancy between the measured value of H2CO2 permeability and the value needed to allow recycling.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02460467

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6

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Dynamics of cellular homeostasis: Recovery time for a perturbation from equilibrium (1997)

Weinstein, Alan M.

Springer

Bulletin of mathematical biology 59 (1997), S. 451-481

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ISSN: 1522-9602

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Abstract In the collecting ductin vivo, the principal cell encounters a wide range in luminal flow rate and luminal concentration of NaCl. As a consequence, there are substantial variations in the transcellular fluxes of Na+ and Cl−, conditions which would be expected to perturb cell volume and cytosolic concentrations. Several control mechanisms have been identified which can potentially blunt these perturbations, and these entail cellular regulation of the luminal membrane Na+ channel and peritubular membrane K+ and Cl− channels. To illustrate the impact of these regulated channels, a mathematical model of the principal cell of the rat cortical collecting duct has been developed, in which ion channel permeabilities are either constant or regulated. In comparison to the model with fixed permeabilities, the model with regulated channels demonstrates enhanced cellular homeostasis following steady-state variation in luminal NaCl. However, in the transient response to a cytosolic perturbation, the difference in recovery time between the models is small. An approximate analysis is presented which casts these models as dynamical systems with constant coefficients. Despite the presence of regulated ion channels, concordance of each model with its linear approximation is verified for experimentally meaningful perturbations from the reference condition. Solution of a Lyapunov equation for each linear system yields a matrix whose application to a perturbation permits explicit estimation of the time to recovery. Comparison of these solution matrices for regulated and non-regulated cells confirms the similarity of the dynamic response of the two models. These calculations suggest that enhanced homeostasis by regulated channels may be protective, without necessarily hastening recovery from cellular perturbations.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02459460

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7

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Models of coupled salt and water transport across leaky epithelia (1981)

Weinstein, Alan M. ; Stephenson, John L.

Springer

The journal of membrane biology 60 (1981), S. 1-20

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ISSN: 1432-1424

Keywords: isotonic epithelial transport ; lateral intercellular space ; linearized Kedem-Katchalsky equations ; intraepithelial solute polarization

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Chemistry and Pharmacology

Notes: Summary A general formulation is presented for the verification of isotonic transport and for the assignment of a degree of osmotic coupling in any epithelial model. In particular, it is shown that the concentration of the transported fluid in the presence of exactly equal bathing media is, in general, not a sufficient calculation by which to decide the issue of isotonicity of transport. Within this framework, two epithelial models are considered: (1) A nonelectrolyte compartment model of the lateral intercellular space is presented along with its linearization about the condition of zero flux. This latter approximate model is shown to be useful in the estimation of deviation from isotonicity, intraepithelial solute polarization effects, and the capacity to transport water against a gradient. In the case of uphill water transport, some limitations of a model of fixed geometry are indicated and the advantage of modeling a compliant interspace is suggested. (2) A comprehensive model of cell and channel is described which includes the major electrolytes and the possible presence of intraepithelial gradients. The general approach to verification of isotonicity is illustrated for this numerical model. In addition, the insights about parameter dependence gained from the linear compartment model are shown to be applicable to understanding this large simulation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01870828

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