Data for the qualitative modeling of the osmotic stress response to NaCl in Escherichia coli

Qualitative modeling approaches allow to provide a coarse-grained description of the functioning of cellular networks when experimental data are scarce and heterogeneous. We translate the primary literature data on the response of Escherichia coli to hyperosmotic stress caused by NaCl addition into a piecewise linear (PL) model. We provide a data file of the qualitative model, which can be used for simulation of changes of protein concentrations and of DNA coiling during the physiological response of the bacterium to the stress. The qualitative model predictions are directly comparable to the available experimental data. This data is related to the research article entitled “Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens” (Metris et al., 2016) [1].


How data was acquired
Simulations were performed by means of the publicly available tool Genetic Network Analyzer Data format Equations, GNAML and SBML files Experimental factors Primary literature data

Experimental features
Gene expression and transcription factor binding sites of E. coli and Salmonella during osmotic stress response Data source location

Inria, Saint Ismier, France
Data accessibility The data is with this article

Value of the data
The reconstruction of the osmotic stress response network of E. coli provides a compilation of current knowledge on this process.
The piecewise-linear model of the network is useful to exploit the heterogeneous and scarce experimental data on hyper-osmotic stress: their comparison with the model predictions allow to verify if we have a good understanding of the network functioning or if additional hypotheses should be formulated to reconcile potential discrepancies.
The model can be easily extended to describe the response of E. coli to alternative osmotic stresses, caused for instance by other humectants and low moisture.

Data
The data provided in this article include a reconstruction of the hyper-osmotic stress response network of Escherichia coli and its translation into a piece-wise linear model. Files with the model equations in tow formats (GNAML and SBML) are also given, for computer simulation of the physiological response of E. coli to the presence or the absence of salt.

Experimental design, materials and methods
The PL modeling of the osmotic stress response network is briefly described below (see Batt et al. [2] and references therein for more information) and it is illustrated with a simple example in Fig. 1. Four steps were necessary before we could generate predictions on the network behavior that could be compared to experimental data.

Reconstruction of the osmotic stress response network
Our analysis of the physiological response of E. coli to hyper-osmotic stress is centered around proteins and markers known to play a key role in this process. Based on an extensive search of the literature and previous work [4,5], we have reconstructed a network of eight genes: the sigma factor RpoS, the transcription factors Fis, IHF, and CRP, the symporter ProP, the trehalose synthase OtsAB, and markers of the osmotic stress response, OsmY, and of cellular growth, the stable RNAs. The assumptions made to reconstruct the network and the role of the different network components and their interactions are summarized in Table 1. The reader is referred to Metris et al. [1] for additional information. An example is provided in Fig. 1A, in the case of the genes involved in the synthesis of the osmoprotectant trehalose, otsA and otsB. Expression of these genes is both osmotically and growth-phase regulated in a RpoS-dependent manner as determined by gene expression of mutants in Hengge-Aronis et al. [3]. Since the two genes are organized in an operon and share the same regulation [6], we consider OtsAB to be the product of a single gene otsAB, whose promoter P is recognized by RpoS.

Translation of the gene regulatory network into a PL model
We consider the network as composed of four different modules, each one accomplishing a specific task, that of setting (1) the concentration of the potassium salt of glutamate and the DNA supercoiling level; (2) the concentration of the general stress response factor RpoS; (3) the concentration of the complex CRP-cAMP; (4) the concentration of OsmY and the growth rate. We do not model explicitly the concentration of RNA polymerase nor the concentration of the σ 70 factor, as they are not known to vary in response to osmotic stress. We indicate in the table below the model equations and corresponding parameter ordering. The notations will follow the convention used above, k, representing protein synthesis rates, g, degradation rates, and t, threshold parameters.
Regulatory influences are described by means of step functions that change value at a threshold concentration. These functions simplify the sigmoidal Hill functions generally used to describe cooperative processes involved in the regulation of gene expression. For instance, the positive influence of RpoS on otsAB expression is described by a positive step function (see Panel B of Fig. 1). It evaluates to 1 when RpoS is above its threshold concentration t RpoS , and to 0 otherwise. Negative step functions are used to describe cooperative inhibition of gene expression. Hence, the auto-inhibition of IHF expression is described by the step function s À IHF; t 2

ihf
, which equals to 1 when IHF is below its threshold value t 2 ihf and to 0 otherwise (see Table 1). PL equations describe the rate of change of protein or RNA concentrations as the difference between their synthesis rate and their degradation rate. For instance, the PL equation for OtsAB in Panel C of Fig. 1 states that OtsAB is synthesized at a rate k otsAB when RpoS is above its threshold concentration, while the synthesis rate is null in the absence of RpoS. OtsAB is degraded at a basal rate g otsAB OtsAB. The concentration to which OtsAB tends when it is synthesized, k otsAB g otsAB , should be above its threshold level: k otsAB g otsAB 4t otsAB ; otherwise the protein would never reach a level above which it is able to produce trehalose and, indirectly, to affect the efflux of potassium.
We represent the input signal, i.e. the application of an osmotic stress to the system, by a step function s þ u; t u ð Þwhich equates to 1 upon osmotic shock. It captures the molecular changes induced

Qualitative simulation of the PL model
The model in Table 1 has been implemented in and simulated with the publicly available software tool Genetic Network Analyzer (GNA 8.4, Genostar, http://userclub.genostar.com/en/genostar-soft ware/gnasim.html). The corresponding model file is given in the supplementary data in GNAML and qualitative SBML formats [20]. An example of qualitative simulation with the simple network model is given in Panel D of Fig. 1.
Running the attractor search functionality of GNA shows that there are two stable steady states for the osmotic stress response model, one characteristic for normal growth in the absence of osmotic stress and one reached in case of osmotic stress. We can simulate how the system responds to salt addition and leaves the non-stressed state for the stressed one, by perturbing the state of normal growth with the signal of stress switched on u 4 t u ð Þ . The simulation returns a state transition graph composed of 192 states, showing all the possible dynamic behaviors of the system going from the initial state of normal growth to the stressed state.

Comparison of model predictions with experimental data
Each path in the state transition graph describes the evolution of protein and RNA concentrations, which can be confronted to the experimental data [1]. For instance, literature data summarized in Table 2 suggest an accumulation of OtsA and OtsB as trehalose accumulates after a hyper-osmotic stress induced by salt [21]. The expression varies with the conditions and the strains, however the pattern remains similar; a delay before increased expression during adaptation. The trend is also similar for E. coli and Salmonella typhimurium , so, in this case, the same equation may be used for both species. In the simple example of Fig. 1, the concentration of protein OtsAB is predicted to increase once RpoS accumulates in the cell. This prediction is hence consistent with experimental data. This type of analysis may be carried out for the different osmotic genes with more complex regulation as shown in Metris et al. [1].