A Mathematical Model for Trehalose Uptake in the Thermophilic Bacterium Rhodothermus marinus

Abstract

The aim of this work was to elucidate the mechanism of trehaloseuptake in the thermophilic halophilic bacterium Rhodothermus marinus.Mathematical modeling was employed to translate chemical networks describingsubsystems of the postulated trehalose uptake mechanism into coupleddifferential equations. Analytical functions resulting from these differentialequations were used for a multidimensional least-squares fit to experimentaldata, thus yielding values for fit parameters and serving as a test todecide between two models. The data used were kindly provided by Carla Jorgefrom the laboratory ofProf. Dr. Helena Santos at the Instituto de Tecnologia Quimica e Biologica (ITQB)in Oeiras, Portugal.Several data sets contributed information to resolve the issue: the experimentaldata consist of measurements of the uptake rate for radioactiveglucose analyzed in chapter 2, measurements of glucose release into the mediumdue to in vivo trehalase activitydealt with in chapter 3, uptake data for radioactive trehalose modeled inchapters 4 and 5, and cross-inhibition experiments with glucose and trehalosesimulated in chapter 6. In addition to these, in vitro inhibitionexperiments with purified trehalase have shown that glucose inhibits trehalaseactivity with a K_i of 12 mM.We have proposed two models for trehalose uptake: model 1 consists of a diffusionchannel for glucose and trehalose in the outer membrane, a periplasmic trehalasecleaving incoming trehalose into two units of glucose, and a glucose transporterin the cytoplasmic membrane. Model 2 contains an additional trehalose transporterin the inner membrane.Since the glucose transport system is a functionally independent part of bothtrehalose uptake models, the parameters obtained by fitting the glucose uptakedata alone can be used for the fit of the trehalose uptakeand enzymatic cleavage data. To describe the in vivo trehalase data fouradditional parameters are needed. The same four parameters are used in model 1for trehalose uptake; model 2 contains two more. Both experimental curves have tobe fitted together, since the same set of parameters has to describe bothmeasurements.One of the remaining parameters, z_2, can becalculated from the K_i for the in vitro glucose inhibition of trehalasementioned above and the K_m {gt} ofthe glucose transporter in the cytoplasmic membrane found in chapter 2.8.The theories for enzymatic cleavage and trehalose uptake provide restrictionscoupling the remaining fit parameters to the kinetic parametersK_m e and V_{max} e from the enzyme curve and K_m {tr} and V_{max} {tr}(model 1) or K_m {su} and V_{max}{su} (model 2) from the trehalose uptakecurve, for which we obtain an approximationby fitting a Michaelis-Menten function through the data. These restrictionstogether suffice to calculate all fit parameters in model 1, for model two anadditional scan over z_6 is needed.By optimizing the four kinetic parametersusing model 2 we have obtained a fit that describes all measurements. Model 1can either fit the cleavage data or the high concentration trehalose uptake data,but not both, and is unable to describe the trehalose uptake measurements at lowsubstrate concentrations. The inability of model one to coherently describeall experimental findings shows the necessity of the additional threhalosetransporter distinguishing model 1 from model 2.In order to further validate the model we have used the parameters from theglucose fit and from model 2 to simulate aninhibition experiment with a constant concentration of the substrate trehaloseand increasing concentrations of the inhibitor glucose. The simulationshows that in model 2 glucose inhibits the uptake of trehalose considerably inthe range of high trehalose concentrations, but at low trehalose concentrationseven a very high concentration of glucose causes only a slight inhibiting effect.This observation is due to the fact that the dominant uptake pathway atlow trehalose concentrations is the direct trehalose transporter which is notinhibited by glucose in our model.The result of the simulation is in qualitative agreement with experimentalfindings, but those show a tenfold inhibition oftrehalose uptake already at the low concentration of 1 µM. To be able totheoretically reproduce this experimental result quantitatively, an extension ofthe model network by a glucose mediated inhibition of the trehalose transporterin the cytoplasmic membrane should be adressed in further investigations.