Team:TU-Delft/Modeling/SingleCellModel

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Human Outreach

The single-cell pathway model of our system is composed of 4 modules, which are responsible for routing the signal from the receptor to the GFP sythesis. The mathematical models were developed on a scheme favoring the temporal order of processes, based on the current understanding of the pheromone signalling pathway from [1][2][3] and also on the feedback received from the experimentalists on the expected behaviour of the pathway, taking into consideration the aspects relevant to our project.

Contents

Assumptions

In all of the models developed certain assumptions were made due to the lack of data available on the new modified pathway and also due to the time constraints which limit the range of experiments that can be carried out. The assumptions made are listed below.

  • The rate constants and initial concentrations obtained from the literature are assumed to be the same for the new modified pathway.
  • The behaviour of the Ligand is assumed to be similar to the behaviour of the alpha pheromone.
  • The tuberculosis receptor is assumed to behave similar to the alpha-pheromone receptor.

Model of the G - Protein cycle

The concentration of free G-beta-gamma dimer is crucial for the activation of the MAP kinase cascade which in turn activates the
Figure 1: Reaction diagram of heterotrimeric G protein cycle[1]. The individual reactions comprising the key dynamics of heterotrimeric G proteins in yeast are represented along with the rate constants
expression of the GFP. The promoter used for the receptor along with initial concentration of the ligand are thus crucial parameters for the activation of the G-Protein Cycle. A model of the G-Protein cycle by Yi et al [1] was used to analyze the effects of the different promoter strengths of the receptor.

It can be seen that as the concentration of G-alpha-GDP increases the concentration of free G-beta-gamma dimer reduces, which motivates the use of a promoter which is weak or medium strength compared to a strong promoter.

File:PromoterStrengthAnalysis.gif
Figure 2: Effect of varying the strength of the promoter.

Model of the Yeast Pheromone Response

File:YeastPheromonePathwayKofahlKlipp.png
Figure 1: Yeast Pheromone Pathway[2].

The model of the yeast pheromone response was based on the model by Kofahl and Klipp[2]. This was used to test the effects of cell cycle arrest knockout on the transcription factor Ste12 which is crucial for the synthesis of GFP.

It can be seen from the plots that for an input concentration of 100nm, the knockout performed has no major influence on the concentration of the transcription factor.

File:CellCycleArrestKnockout.gif
Figure 2: Effects of the cell cycle arrest knockout on the transcription factor (Ste12active)

Model of the Snifformyces(Modified Yeast) Pathway

The model of the G-protein cycle lacked the description of MAP kinase cascade and the gene expression module.The model of the yeast pheromone response had a detailed description of the pathway but had two drawbacks, it did not incorporate the gene expression module and more importantly was too complex in terms of the number of parameters that were present in the model. Due to the large number of parameters, fitting the limited data available from the experiments to the highly complex pathway model in [2] we felt would not have been feasible.
Figure 5: Schematic of the modified yeast pheromone pathway

The above drawbacks motivated us to build a model, which would capture the crucial components of the pathway with a reduced degree of complexity i.e with lesser parameters to be estimated. Combining the knowledge from [1] and [2] and also using [3], We built a new model of the pathway.

The modifications done to the model are as follows,

  • The Receptor activation & the G - Protein cycle was retained from [1].
  • The simplified MAP kinase cascade was adopted from [3].
  • The activation of Ste12 was adopted from [2].
  • The gene expression modules was incorporated from [4].

For the initial analysis, the rates of this model uptil Fus3 activation were obtained by fitting the model to the data from [5]. The Ste12 activation and deactivation rates were taken from [2]. The rates for the gene expression module were obtained from [4].

It can be seen from the simulations that the model is capable of reproducing the Fus3 dynamics fairly accurately.

Parameter Estimation

Using the results from the sensitivity analysis, parameter estimation was performed to find the parameters of the model in order to fit the simulated data curves to the experimental data. The least squares method was performed for fitting by using the nonlinear regression function nlinfit in the Matlab statistical toolbox.

Figure 6: Results of the Parameter Estimation; Data values are scaled to the peak signal measured during the stimulation with only pheromone

Model Predictions

The model with the new estimated parameters was then used to make predictions on the behaviour of the pathway for different concentrations of the Ligand. The model was simulated for a range of input concentrations using the ode15s variable order solver from Matlab. The results of the simulation are in Figure 7.The GFP concentration increases linearly with the induced Ligand uptil a concentration of 2 micro Molar above which the output concentration saturates. These results could also be seen from the experiments. -- Place link

Figure 7: The response of the pathway to different input concentrations