grofit: Fitting Biological Growth Curves with R

The grofit package was developed to fit many growth curves obtained under different conditions in order to derive a conclusive dose-response curve, for instance for a compound that potentially affects growth. grofit fits data to different parametric models and in addition provides a model free spline method to circumvent systematic errors that might occur within application of parametric methods. This amendment increases the reliability of the characteristic parameters (e.g.,lag phase, maximal growth rate, stationary phase) derived from a single growth curve. By relating obtained parameters to the respective condition (e.g.,concentration of a compound) a dose response curve can be derived that enables the calculation of descriptive pharma-/toxicological values like half maximum effective concentration (EC50). Bootstrap and cross-validation techniques are used for estimating confidence intervals of all derived parameters.

Potassium Starvation in Yeast: Mechanisms of Homeostasis Revealed by Mathematical Modeling

The intrinsic ability of cells to adapt to a wide range of environmental conditions is a fundamental process required for survival. Potassium is the most abundant cation in living cells and is required for essential cellular processes, including the regulation of cell volume, pH and protein synthesis. Yeast cells can grow from low micromolar to molar potassium concentrations and utilize sophisticated control mechanisms to keep the internal potassium concentration in a viable range. We developed a mathematical model for Saccharomyces cerevisiae to explore the complex interplay between biophysical forces and molecular regulation facilitating potassium homeostasis. By using a novel inference method (“the reverse tracking algorithm”) we predicted and then verified experimentally that the main regulators under conditions of potassium starvation are proton fluxes responding to changes of potassium concentrations. In contrast to the prevailing view, we show that regulation of the main potassium transport systems (Trk1,2 and Nha1) in the plasma membrane is not sufficient to achieve homeostasis

grofit: Fitting Biological Growth Curves with R

The following description of the package grofit was also published as Kahm et al. (2010). The grofit package was developed to fit many growth curves obtained under different conditions in order to derive a conclusive dose-response curve, for instance for a compound that potentially affects growth. grofit fits data to different parametric models and in addition provides a model free spline method to circumvent systematic errors that might occur within application of parametric methods. This amendment increases the reliability of the characteristic parameters (e.g.,lag phase, maximal growth rate, stationary phase) derived from a single growth curve. By relating obtained parameters to the respective condition (e.g.,concentration of a compound) a dose response curve can be derived that enables the calculation of descriptive pharma-/toxicological values like half maximum effective concentration (EC50). Bootstrap and cross-validation techniques are used for estimating confidence intervals of all derived parameters

Potassium starvation in yeast : mechanisms of homeostasis revealed by mathematical modeling

The intrinsic ability of cells to adapt to a wide range of environmental conditions is a fundamental process required for survival. Potassium is the most abundant cation in living cells and is required for essential cellular processes, including the regulation of cell volume, pH and protein synthesis. Yeast cells can grow from low micromolar to molar potassium concentrations and utilize sophisticated control mechanisms to keep the internal potassium concentration in a viable range. We developed a mathematical model for Saccharomyces cerevisiae to explore the complex interplay between biophysical forces and molecular regulation facilitating potassium homeostasis. By using a novel inference method ("the reverse tracking algorithm") we predicted and then verified experimentally that the main regulators under conditions of potassium starvation are proton fluxes responding to changes of potassium concentrations. In contrast to the prevailing view, we show that regulation of the main potassium transport systems (Trk1,2 and Nha1) in the plasma membrane is not sufficient to achieve homeostasis

Relationship of external and internal potassium.

<p>(A) Cells grown in 50 mM KCl were resuspended in 0.1, 0.2 and 0.5 mM KCl and the time course of internal potassium was monitored. The lines show the data fit obtained from the reverse tracking algorithm. (B) Internal potassium concentration in cells grown overnight at different external potassium concentrations. The steady state concentrations from (A) are indicated as squares.</p

Regulation of potassium starvation.

<p>(A) The tracking approach to detect potential regulators of homeostasis. Parameters which are constant in the minimal model are now considered as input functions. A parameter is called a potential regulator if it can be chosen to recover (“track”) the experimental time courses. (B,C) The predicted activity changes for Pma1 (B) and the bicarbonate reaction system (C) in response to potassium starvation. (D) Time course of ATPase activity for Pma1. (E) Time course of gene expression for the <i>NCE103</i> gene encoding carbonic anhydrase in the wild type strain. Confirmatory qRT-PCR measurements yield a fold increase of the mRNA level in the wild type after 60 minutes of potassium starvation. For comparison, the expression in non-starved <i>trk1,2</i> double mutant with respect to the wild type strain is depicted. The mRNA levels for <i>NCE103</i> in <i>trk1,2</i> double mutants growing at are higher by a factor of compared to the wild type strain (qRT-PCR measurements).</p

PMA1 mutants with decreased expression and ATPase activity.

<p>Strains RS514 (wild type, WT), RS515 (<i>pma1–204</i>) and RS516 (<i>pma1–205</i>) were grown in YNB-based medium (supplemented with adenine and histidine) with 2% galactose to maintain Pma1 activity from plasmid pYCp50-GALp::PMA1. Cells were diluted to an OD600 of 0.04 in Translucent -free medium (plus with 2% glucose) containing 1 mM or 50 mM KCl. Growth was monitored for 17 h. Data represent the growth ratio at 1 and 50 mM KCl and are mean SEM from 3 determinations.</p

Optical densities during starvation.

<p>Optical densities for the wild type and the <i>trk1,2</i> double mutant corresponding to the potassium starvation experiments of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002548#pcbi-1002548-g001" target="_blank">Figure 1A</a>.</p

Proposed mechanism of potassium homeostasis.

<p>Changes of the external potassium concentration are sensed by an unidentified sensor system either directly or indirectly, e.g, via the membrane potential, internal potassium or pH changes. The sensor signal triggers a modulation of proton fluxes using the bicarbonate reaction system and the Pma1 proton pump as regulators.</p