Membrane rigidity (Schaber, et al., 2010)
Initial total cellular osmolyte concentration.
Osmolytically active volume, derived from a total cell volume of 50 fl and a solid base volume of 41%.
Schaber2012 - Hog pathway in yeast The high osmolarity glycerol (HOG) pathway in the yeast Saccharomyces cerevisiae is one of the best-studied mitogen-activated protein kinase (MAPK) pathways and serves as a prototype signalling system for eukaryotes. This pathway is necessary and sufficient to adapt to high external osmolarity. A key component of this pathway is the stress-activated protein kinase (SAPK) Hog1, which is rapidly phosphorylated by the SAPK kinase Pbs2 upon hyper-osmotic shock, and which is the terminal kinase of two parallel signalling pathways, subsequently called the Sho1 branch and the Sln1 branch, respectively. Ensemble modelling (192 models) is used to study the yeast HOG pathway, a prototype for eukaryotic mitogen-activated kinase signalling systems. The best fit model (Model Nr.22: described here) provides new insights into the function of this system, some of which are then experimentally validated. This model is described in the article: Modelling reveals novel roles of two parallel signalling pathways and homeostatic feedbacks in yeast. Schaber J, Baltanas R, Bush A, Klipp E, Colman-Lerner A. Mol Syst Biol. 2012 Nov 13;8:622. Abstract: The high osmolarity glycerol (HOG) pathway in yeast serves as a prototype signalling system for eukaryotes. We used an unprecedented amount of data to parameterise 192 models capturing different hypotheses about molecular mechanisms underlying osmo-adaptation and selected a best approximating model. This model implied novel mechanisms regulating osmo-adaptation in yeast. The model suggested that (i) the main mechanism for osmo-adaptation is a fast and transient non-transcriptional Hog1-mediated activation of glycerol production, (ii) the transcriptional response serves to maintain an increased steady-state glycerol production with low steady-state Hog1 activity, and (iii) fast negative feedbacks of activated Hog1 on upstream signalling branches serves to stabilise adaptation response. The best approximating model also indicated that homoeostatic adaptive systems with two parallel redundant signalling branches show a more robust and faster response than single-branch systems. We corroborated this notion to a large extent by dedicated measurements of volume recovery in single cells. Our study also demonstrates that systematically testing a model ensemble against data has the potential to achieve a better and unbiased understanding of molecular mechanisms. This model is hosted on BioModels Database and identified by: MODEL1209110001 . To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models . To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.
〖2160f〗_n2μM: molecule numbers from http://yeastgfp.yeastgenome.org/
Active scaffold complex (Sho1 branch). Initial condition set such that a steady state of Hog1 phosphorylation is maintained.
〖6788f〗_n2μM: molecule numbers from http://yeastgfp.yeastgenome.org/
Simple cell surface area dependent binding of Pbs2 to Sho1. The complex is supposed to be the active form. With transient inhibition by activated Hog1.
Linear phosphorylation of Hog1 by either the scaffold complex (Sho1-branch) or activated Pbs2 (Sln1-branch).
Activated MAP kinase kinase (Sln1 branch). Initial condition set such that a steady state of Hog1 phosphorylation is maintained.
Single phosphorylated MAP kinase. Initial condition set such that a steady state of Hog1 phosphorylation is maintained.
Placeholder for phosphatases like Ppt1/2/3 and others. Initial value derived from measured number of Ptp3 molecules (769, http://yeastgfp.yeastgenome.org)
Constitutive phosphatase dependent deactivation.
Placeholder for Hog1-dependent proteins, especially Gpd1. Initial value derived from measured number of Gpd1 molecules (807, http://yeastgfp.yeastgenome.org)
Hydraulic conductivity (estimate from data from (Eriksson, et al., 2007)).
Intracellular glycerol, approximated by assuming a measured value of 0.1 mM/OD in 1 ml sample (Klipp, et al., 2005) and assuming 18•106 cells per ml sample culture and an average osmotic cell volume of 29.5 fl, i.e. 1/18/29.5•108.
Maximal Fps1 glycerol transport capacity.
2 param mod. add. constant flux MM (irrev)
Placeholder for transcribed genes. Initial value derived from data, i.e. initial percentage of maximum.
〖907f〗_n2μM: molecule numbers from http://yeastgfp.yeastgenome.org/
Gene transcription. Hog1 mediated transcription also involves other proteins that are potentially limiting a saturation kinetic is assumed.
Fraction of activated Hog1 molecule in the nucleous upon maximal activation.
Linear activation function for the Sln1 branch.
Membrane bound closed form of aquaglyceroporin Fps1 (assumed to be independent from volume change) . Initially half of the channels is assumed to be closed.
Constitutive dissociation of the scaffold complex.
Factor converting number of molecules in M concentrations per cell.
Osmotic salt shock. Starts at time t_s and has a certain mixing time t_m.
Linear activation function for the Sln1 branch with feedback.
Initial osmolarity of the medium (Schaber, et al., 2010)
Minimal cell volume (as fraction of total) (Schaber, et al., 2010)
〖2330f〗_n2μM: molecule numbers from http://yeastgfp.yeastgenome.org/
Intracellular osmolytically active concentration.
Membrane bound open form of aquaglyceroporin Fps1 (assumed to be independent from volume change). Initially half of the channels is assumed to be open.
Simple cell surface area dependent linear activation of Pbs2 through the Sln1 branch, with transient inhibition by activated Hog1.
Activated Hog1 inhibited channel opening, in conjunction with v15_5.
Extracellular osmolytically active concentration.
Constitutive phosphatase dependent de-phosphorylation.
Factor converting concentrations in  to pressures in MPa.
Turgor dependent closure of Fps1, in conjunction with v16_5, v16_6, v16_7, v16_8.
Gradient driven glycerol flow out of the cell, where k_tr characterises the state of the aquaglyceroporin channel Fps1 and k_s the maximal transport capacity of the channel.
Extracellular glycerol, assumed to be 100 times lower than 〖Gly〗_in.
Double phosphorylated, i.e. active, MAP kinase. It was derived from data that 2.23 % of the maximal phosphorylation is the steady state activation. f_n is the fraction in the nucleus at maximal phohsporylation.
Steady state activation of the Sln1 branch with feedback.
Glycerol production. As glycerol concentration also involves other proteins and cofactors that are potentially limiting a saturation kinetic is assumed. In addition, effective enzyme concentration can be enhanced as a function of activated Hog1.
Initial turgor pressure (Schaber, et al., 2010)
Initial non-permeable cellular osmolyte concentration.
Hill parameter of the turgor-activate Fps1 closure.
3 param activation with inhibition (iirev)