Modelling water and solute transport in Chara: a numerical study of the effects of unstirred layers on membrane parameter estimation

摘要

The cell pressure probe (CPP) is an apparatus used to measure membrane parametersudof cells, namely the hydraulic conductivity which indicates the permeability of theudmembrane to water, the permeability coefficient which indicates the permeability ofudthe membrane to solutes, and the reflection coefficient which indicates the extent toudwhich water and solute transport across the membrane is coupled. This thesis is audnumerical exploration of the impact of unstirred layers on the measurement of theseudparameters. Unstirred layers alter the effective concentration across the membrane,udand hence influence the calculation of the membrane parameters which are usuallyudobtained using the concentration value in the external bulk solution and assume audhomogeneous internal cell solution.udIn CPP experiments, cell pressure dynamics are changed by imposing either: a) audhydrostatic perturbation, where cell sap is injected into or removed from the cell, or b)udan osmotic perturbation, where permeable solutes are added to or removed from theudexternal solution. Outputs are pressure-time curves which are termed relaxationudcurves.udMuch of the CPP data has been obtained for Chara, a large-celled algae. The modeluddeveloped here will be applied to two sets of Chara data: one previously published,udand one unpublished and obtained from collaborators who freely contributed theiruddata to this study. Data from two types of CPP experiments were used to estimateudmembrane parameters by fitting both the classical and unstirred layer (UL) models.udThese were: hydrostatic pressure pulse experiments, and osmotic pressure pulseudexperiments using permeable solutes.udThis thesis comprises five chapters. Chapter 1 provides an introduction to the researchudarea, and gives an overview of the cell system, CPP experiments, and membraneudtransport theory. In Chapter 2 an analysis of predictions and limitations using theudclassical (i.e. usual) method of parameter estimation is made by applying it toudpublished data. This classical model makes simple assumptions about the system,ududallows analytical solutions to the membrane transport equations, and does not includeudunstirred layers. In Chapter 3, a model based upon the classical model butudincorporating unstirred layers, is outlined and its behaviour and predictions examined.udIn Chapter 4, the unstirred layer model is applied to unpublished CPP data, itsudpredictions compared with those from the classical model, and the overall predictionsudand behaviour of the unstirred layer model evaluated. Finally, in Chapter 5 anudassessment of usual practices and assumptions made in the parameter estimationudprocess using the CPP is carried out, and recommendations for future research areudgiven.udThe UL model was found to reproduce the observed CPP data to a high degree ofudaccuracy, and reproduced subtle details in the observed data better than the classicaludmodel. Estimated parameters from the two models differed significantly; the relativeuddifference in the parameters with respect to the UL model was up to 50% for osmoticudexperiments and 5% for hydrostatic experiments. This shows that unstirred layersudhave a significant impact on estimated parameters, and that the membrane parametersudcommonly estimated using the classical model may be in error by up to 50%.udData from three Chara cells were fit in Chapter 4. Significant inter-cell variation inudestimated parameters was found. Estimated parameters for experiments carried outudwithin the same cell were quite consistent, indicating that the UL model is predictingudthe membrane parameters well since parameters are expected to characterise a celludand its membrane. The behaviour of the UL model was also consistent withudexpectations from the Kedem and Katchalsky theory for membrane transport,udsuggesting that the UL model affects the estimated membrane parameters but not theudoverall behaviour predicted by the membrane transport equations.udCell pressure dynamics were found to be very sensitive to the thickness of theudunstirred layers in the system, so that estimated membrane parameters are dependentudon knowledge of the UL thicknesses. In Chapter 4, the UL model was used toudestimate the external UL thickness together with the membrane parameters, while theudinternal UL thickness was fixed at a value effectively equivalent to assuming theudwhole cell interior is a UL. The model estimated the external UL thickness to be inudthe range of 30-50 μm for fits to the unpublished data. Some variation in estimatedududparameters between types of CPP experiments (e.g. hydrostatic or osmoticudexperiments; experiments with positive or negative pressure perturbations) wereudfound, but the sample size was not sufficiently large for definite conclusions to beudmade. The UL model did not predict polarity in the membrane parameters (i.e.uddifferences in parameters between positive and negative pressure perturbations). Thisudsuggests that evidence of polarity found in the parameters is likely due to effects of audcomposite membrane (e.g. presence of a tonoplast) or of dehydration of theudmembrane, and not due to the presence of ULs.udData were also available from osmotic experiments where bubbles were used toudseparate the new and old external solutions during the solution changeover. Fits toudexperiments where bubbles are present were found to be more straightforward and toudgive more accurate estimates of membrane parameters, as the time for solutionudexchange was significantly shortened. Where bubbles were not present, the time forudsolution exchange could not be as effectively incorporated into the model due to lackudof experimental data regarding the duration and shape of the solution changeover.udResults clearly showed that some common assumptions regarding the effects of ULsudon CPP experiments are incorrect. External ULs are often assumed to primarilyudinfluence only the first few seconds of the relaxation curve, but the UL model showsudthat internal and external ULs influence the cell dynamics throughout the entireudcourse of a CPP experiment. Furthermore, the extent of the influence on ULs on CPPuddata can only be quantified numerically. Previous attempts at using solutions toudsteady-state diffusion equations, or using steady-state equations relating permeabilityudacross the membrane to permeability in the ULs to predict the impact of ULs onudestimated membrane parameters, are shown to be inaccurate. Published estimates ofudmembrane parameters for Chara are deemed to be in error, because even whereudeffects of ULs have been claimed to be taken into account, this has not been doneudnumerically. In addition, it is shown that relaxation curves can be fit using theudclassical model (which does not incorporate ULs) despite the presence of unstirredudlayers, because ULs do not change the fundamental shape of the relaxation curves,udand therefore the true effects of ULs are hidden.ududIt is recommended that the classical model no longer be used for parameterudestimation, and a more realistic model incorporating ULs be applied. This will lead touda more accurate estimation of membrane parameters. The model developed in thisudthesis, by taking into account effects of unstirred layers, can help to resolve the extentudto which ULs impact on estimated membrane parameters, and also the extent to whichudULs influence parameter variation among different types of experiments orudexperimental conditions. Currently, further experimental data is necessary for a widerudapplication of the UL model and fuller assessment of its predictions. The UL modeludmay also be extended in the future for application to more complicated systems suchudas root tissues.