Modelling the swelling assay for aquaporin expression

Wet-tip versus dry-tip regimes of osmotically driven fluid flow

The secretion of osmolytes into a lumen and thereby caused osmotic water inflow can drive fluid flows in organs without a mechanical pump. Such fluids include saliva, sweat, pancreatic juice and bile. The effects of elevated fluid pressure and the associated mechanical limitations of organ function remain largely unknown since fluid pressure is difficult to measure inside tiny secretory channels in vivo. We consider the pressure profile of the coupled osmolyte-flow problem in a secretory channel with a closed tip and an open outlet. Importantly, the entire lateral boundary acts as a dynamic fluid source, the strength of which self-organizes through feedback from the emergent pressure solution itself. We derive analytical solutions and compare them to numerical simulations of the problem in three-dimensional space. The theoretical results reveal a phase boundary in a four-dimensional parameter space separating the commonly considered regime with steady flow all along the channel, here termed “wet-tip” regime, from a “dry-tip” regime suffering ceased flow downstream from the closed tip. We propose a relation between the predicted phase boundary and the onset of cholestasis, a pathological liver condition with reduced bile outflow. The phase boundary also sets an intrinsic length scale for the channel which could act as a length sensor during organ growth.

Growth of adult spinal cord in knifefish: Development and parametrization of a distributed model

The study of indeterminate-growing organisms such as teleost fish presents a unique opportunity for improving our understanding of central nervous tissue growth during adulthood. Integrating the existing experimental data associated with this process into a theoretical framework through mathematical or computational modeling provides further research avenues through sensitivity analysis and optimization. While this type of approach has been used extensively in investigations of tumor growth, wound healing, and bone regeneration, the development of nervous tissue has been rarely studied within a modeling framework. To address this gap, the present work introduces a distributed model of spinal cord growth in the knifefish Apteronotus leptorhynchus, an established teleostean model of adult growth in the central nervous system. The proposed model incorporates two mechanisms, cell proliferation by active stem/progenitor cells and cell drift due to population pressure, both of which are subject to global constraints. A coupled reaction-diffusion equation approach was adopted to represent the densities of actively-proliferating and non-proliferating cells along the longitudinal axis of the spinal cord. Computer simulations using this model yielded biologically-feasible growth trajectories. Subsequent comparisons with whole-organism growth curves allowed the estimation of previously-unknown parameters, such as relative growth rates.

The Water to Solute Permeability Ratio Governs the Osmotic Volume Dynamics in Beetroot Vacuoles

Plant cell vacuoles occupy up to 90% of the cell volume and, beyond their physiological function, are constantly subjected to water and solute exchange. The osmotic flow and vacuole volume dynamics relies on the vacuole membrane -the tonoplast- and its capacity to regulate its permeability to both water and solutes. The osmotic permeability coefficient (P_f ) is the parameter that better characterizes the water transport when submitted to an osmotic gradient. Usually, P_f determinations are made in vitro from the initial rate of volume change, when a fast (almost instantaneous) osmolality change occurs. When aquaporins are present, it is accepted that initial volume changes are only due to water movements. However, in living cells osmotic changes are not necessarily abrupt but gradually imposed. Under these conditions, water flux might not be the only relevant driving force shaping the vacuole volume response. In this study, we quantitatively investigated volume dynamics of isolated Beta vulgaris root vacuoles under progressively applied osmotic gradients at different pH, a condition that modifies the tonoplast P_f . We followed the vacuole volume changes while simultaneously determining the external osmolality time-courses and analyzing these data with mathematical modeling. Our findings indicate that vacuole volume changes, under progressively applied osmotic gradients, would not depend on the membrane elastic properties, nor on the non-osmotic volume of the vacuole, but on water and solute fluxes across the tonoplast. We found that the volume of the vacuole at the steady state is determined by the ratio of water to solute permeabilites (P_f /P_s ), which in turn is ruled by pH. The dependence of the permeability ratio on pH can be interpreted in terms of the degree of aquaporin inhibition and the consequently solute transport modulation. This is relevant in many plant organs such as root, leaves, cotyledons, or stems that perform extensive rhythmic growth movements, which very likely involve considerable cell volume changes within seconds to hours.

Human AQP1 is a constitutively open channel that closes by a membrane-tension-mediated mechanism

This work presents experimental results combined with model-dependent predictions regarding the osmotic-permeability regulation of human aquaporin 1 (hAQP1) expressed in Xenopus oocyte membranes. Membrane elastic properties were studied under fully controlled conditions to obtain a function that relates internal volume and pressure. This function was used to design a model in which osmotic permeability could be studied as a pressure-dependent variable. The model states that hAQP1 closes with membrane-tension increments. It is important to emphasize that the only parameter of the model is the initial osmotic permeability coefficient, which was obtained by model-dependent fitting. The model was contrasted with experimental records from emptied-out Xenopus laevis oocytes expressing hAQP1. Simulated results reproduce and predict volume changes in high-water-permeability membranes under hypoosmotic gradients of different magnitude, as well as under consecutive hypo- and hyperosmotic conditions. In all cases, the simulated permeability coefficients are similar to experimental values. Predicted pressure, volume, and permeability changes indicate that hAQP1 water channels can transit from a high-water-permeability state to a closed state. This behavior is reversible and occurs in a cooperative manner among monomers. We conclude that hAQP1 is a constitutively open channel that closes mediated by membrane-tension increments.

Water flux through human aquaporin 1: inhibition by intracellular furosemide and maximal response with high osmotic gradients

This work studies water permeability properties of human aquaporin 1 (hAQP1) expressed in Xenopus laevis oocyte membranes, applying a technique where cellular content is replaced with a known medium, with the possibility of measuring intracellular pressure. Consequences on water transport-produced by well-known anisotonic gradients and by the intracellular effect of probable aquaporin inhibitors-were tested. In this way, the specific intracellular inhibition of hAQP1 by the diuretic drug furosemide was demonstrated. In addition, experiments imposing anisotonic mannitol gradients with a constant ionic strength showed that the relationship between water flux and the applied mannitol gradient deflects from a perfect osmometer response when the gradient is higher than 150 mosmol kg (W) (-1) . These results would indicate that the passage of water molecules through hAQP1 may have a maximum rate. As a whole, this work demonstrates the technical advantage of controlling both intracellular pressure and medium composition in order to study biophysical properties of hAQP1, and contributes information on water channel behavior under osmotic challenges and the discovery of new inhibitors.

Regulatory volume decrease and P receptor signaling in fish cells: mechanisms, physiology, and modeling approaches

For animal cell plasma membranes, the permeability of water is much higher than that of ions and other solutes, and exposure to hyposmotic conditions almost invariably causes rapid water influx and cell swelling. In this situation, cells deploy regulatory mechanisms to preserve membrane integrity and avoid lysis. The phenomenon of regulatory volume decrease, the partial or full restoration of cell volume following cell swelling, is well-studied in mammals, with uncountable investigations yielding details on the signaling network and the effector mechanisms involved in the process. In comparison, cells from other vertebrates and from invertebrates received little attention, despite of the fact that e.g. fish cells could present rewarding model systems given the diversity in ecology and lifestyle of this animal group that may be reflected by an equal diversity of physiological adaptive mechanisms, including those related to cell volume regulation. In this review, we therefore present an overview on the most relevant aspects known on hypotonic volume regulation presently known in fish, summarizing transporters and signaling pathways described so far, and then focus on an aspect we have particularly studied over the past years using fish cell models, i.e. the role of extracellular nucleotides in mediating cell volume recovery of swollen cells. We, furthermore, present diverse modeling approaches developed on the basis of data derived from studies with fish and other models and discuss their potential use for gaining insight into the theoretical framework of volume regulation.

A simplest steady-state Munch-like model of phloem translocation, with source and pathway and sink

In the 80 years since its introduction by Münch, the pressure-driven mass-flow model of phloem translocation has become hegemonic, and has been mathematically modelled in many different fashions but not, to our knowledge, by one that incorporated the equations of hydrodynamics with those of osmosis and slice-source and slice-sink boundary conditions to yield a system that admits of an analytical steady-state solution for the sap velocity in a single sieve tube. To overcome this situation, we drastically simplified the problem by: (i) justifying a low Peclet number idealisation in which transverse variations could be neglected; (ii) justifying a low viscosity idealisation in which axial pressure drops could be neglected; and (iii) assuming a sink of strength sufficient to lower the photosynthate concentration at the extreme distal end of the sieve tube to levels at which it became unimportant. The resulting ordinary nonlinear second-order differential equation in sap velocity and axial position was of a generalised Liénard form with a single forcing parameter; and this is reason enough for the lack of a known analytic solution. However, since the forcing parameter was very large, it was possible to deduce approximate second-order solutions for behavior in the source, sink and transport regions: the sap velocity is zero at the slice-source, climbs with exponential rapidity to a plateau, maintains this plateau over most of the sieve tube, and then drops with exponential rapidity to zero at the slice-sink.