A Thermodynamic Model of Monovalent Cation Homeostasis in the Yeast <i>Saccharomyces cerevisiae</i>

<div><p>Cationic and heavy metal toxicity is involved in a substantial number of diseases in mammals and crop plants. Therefore, the understanding of tightly regulated transporter activities, as well as conceiving the interplay of regulatory mechanisms, is of substantial interest. A generalized thermodynamic description is developed for the complex interplay of the plasma membrane ion transporters, membrane potential and the consumption of energy for maintaining and restoring specific intracellular cation concentrations. This concept is applied to the homeostasis of cation concentrations in the yeast cells of <i>S</i>. <i>cerevisiae</i>. The thermodynamic approach allows to model passive ion fluxes driven by the electrochemical potential differences, but also primary or secondary active transport processes driven by the inter- play of different ions (symport, antiport) or by ATP consumption (ATPases). The model—confronted with experimental data—reproduces the experimentally observed potassium and proton fluxes induced by the external stimuli KCl and glucose. The estimated phenomenological constants combine kinetic parameters and transport coefficients. These are in good agreement with the biological understanding of the transporters thus providing a better understanding of the control exerted by the coupled fluxes. The model predicts the flux of additional ion species, like e.g. chloride, as a potential candidate for counterbalancing positive charges. Furthermore, the effect of a second KCl stimulus is simulated, predicting a reduced cellular response for cells that were first exposed to a high KCl stimulus compared to cells pretreated with a mild KCl stimulus. By describing the generalized forces that are responsible for a given flow, the model provides information and suggestions for new experiments. Furthermore, it can be extended to other systems such as e.g. <i>Candida albicans</i>, or selected plant cells.</p></div

Prediction of second KCl stimulus.

<p>Model M2 with parameter set P2a was used to predict the reaction of the system to a second KCl stimulus following the glucose stimulus. As first stimulus the KCl concentrations 0.01, 0.1, 1 and 10 mM were used, in consistency with the data used for model fitting. The second stimulus was modeled as additional 10 mM KCl in all cases. The K⁺ flux is labeled in green, H⁺ flux in blue. Darker colors represent higher KCl concentrations used for the first KCl stimulus (applied to the system prior to time point 0). Glucose was added in this experiment at time point 660 s, the second KCl stimulus was at 1000 s.</p

Analysis of individual forces.

<p>Separation of <i>J</i>_K into a K⁺ (green) and a H⁺ (blue) dependent part for simulations with parameter sets a) P2a and b) P2b. c) Separation of <i>J</i>_K into a chemical (green) and an electrical (blue) potential dependent part with parameter set P2a. d) Ratio of the electrical and the chemical potential dependent part of <i>J</i>_K with P2a. Simulation of the membrane potential with parameter sets e) P2a and f) P2b.</p

Overview of transmembrane ion transporters and channels.

<p>Overview of transmembrane ion transporters and channels.</p

Additional file 2: Table S1. of Residual transpiration as a component of salinity stress tolerance mechanism: a case study for barley

Amount (μg cm−2) of different components of cuticular wax in three different positions of leaf of four barley genotypes (n = 4) (XLSX 12 kb)

Assignment of phenomenological coefficients to their realizing transporters.

<p>Assignment of phenomenological coefficients to their realizing transporters.</p

Initial concentrations, global quantities and volumes, and estimated parameters for P1.

<p>Estimated model parameters for stress with 4 different concentrations of KCl. All other <i>L</i>s could be set to 0 without affecting the goodness of fit.</p

Experimental data and simulation using model 2 with parameter set P2a.

<p>The model was used to reproduce the H⁺ and K⁺ flux data from MIFE experiments. It predicted the existence of Cl^- fluxes, which were verified in subsequent experiments. (a) Simulation of H⁺ and K⁺ fluxes during four different <i>in-silico</i> experiments with addition of KCl (0.01 mM, 0.1 mM, 1 mM, 10 mM) at 300 s followed by glucose addition at 660 s. (b) Experimental data (MIFE) used for fitting the model. (c) Predicted Cl^- fluxes during the four simulations. (d) Experimental validation of the existence of Cl^- fluxes. Here, KCl (0.01 mM, 0.1 mM, 1 mM, 10 mM) was added at 180 s followed by glucose addition at 300 s. The K⁺ flux is labeled in green, H⁺ flux in blue and Cl^- flux in red. Darker colors represent higher KCl concentrations used for the KCl stimulus.</p

Sketch of the system and the model-relevant key elements.

<p>Sketch of the system and the model-relevant key elements.</p

Uptake of soluble Aβ by wildtype and Tg2576 cortical neurons <i>in vitro</i>.

<p>Wildtype and Tg2576 cortical neurons were treated with 10 µM of monomeric Aβ_1-40, and immunostained for Aβ after 24 hours. In untreated Tg2576 neurons, Aβ was smoothly distributed throughout the cytoplasm and processes of all neurons (A). When Aβ_1-40 was applied to wildtype neurons, it was internalised and distributed in a punctate manner within the cytoplasm and processes (B). Notably, not all wildtype neurons internalised Aβ_1-40 (B). When Aβ_1-40 was applied to Tg2576 neurons, both smooth and punctately distributed Aβ was detected within neurons (C). scale bar  = 25 µm.</p