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| <h2>Introduction</h2> | | <h2>Introduction</h2> |
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− | Mathematical modelling often gives useful insights into the behaviour of complex systems. Here, we model the synthetic gene oscillator circuit made by Stricker et al .(2008), where the protein product of the first gene (AraC) activates the expression of both the genes and the protein product of the second gene (LacI) inhibits expression of both the genes. It is expected that such a model would help test what modifications can be done in the mentioned oscillator, to couple it with other genes to achieve oscillations in their protein products, which are essential in the cell cycle. | + | Mathematical modelling often gives useful insights into the behaviour of complex systems. Here, we model the synthetic gene oscillator circuit made by Stricker et al.(2008), where the protein product of the first gene (AraC) activates the expression of both the genes and the protein product of the second gene (LacI) inhibits expression of both the genes. It is expected that such a model would help test what modifications can be done in the mentioned oscillator, to couple it with other genes to achieve oscillations in their protein products, which are essential in the cell cycle. |
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− | It is activated by the AraC protein in the presence of arabinose and repressed by the LacI protein in the absence of isopropyl β-d-1-thiogalactopyranoside (IPTG). We placed the araC, lacI and yemGFP (monomeric yeast-enhanced green fluorescent protein) genes under the control of three identical copies of plac/ara-1 to form three co-regulated transcription modules (Supplementary Information). Hence, activation of the promoters by the addition of arabinose and IPTG to the medium results in transcription of each component of the circuit, and increased production of AraC in the presence of arabinose results in a positive feedback loop that increases promoter activity. However, the concurrent increase in production of LacI results in a linked negative feedback loop that decreases promoter activity, and the differential activity of the two feedback loops can drive oscillatory behaviour
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| + | The oscillator described by Stricker et al. (2008) comprises of two genes AraC and LacI, placed downstream of a p_{lac/ara-1} hybrid promoter, which is activated by the binding of AraC protein in presence of arabinose and repressed by LacI protein in absence of IPTG. This forms a dual feedback loop that causes the levels of these proteins to oscillate periodically. |
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| Earlier attempts of reproducing the whole model using the Simbiology Toolbox in MATLAB R2015b were unsuccessful in reproducing the expected results. Possibly because of the complexity of the model and a huge number of reactions and their parameters. As a solution, a bottom-up approach of modelling was chosen, in which a simple model is built first and equations, parameters are added as required. The simple model, in this case, was chosen to be the cI-Lac oscillator described by \cite{Hasty}.The two first order coupled differential equations in the model were solved using < a href= "https://www.python.org/"> Python 3.6</a> in <a href="https://github.com/spyder-ide/spyder">Spyder 2.3.2</a>environment, a range of parameter values was scanned to obtain oscillations. On an average, the numerical integration took about 0.15 seconds to run an additional 0.30 seconds to output a graph. The main difference between the two oscillators is that the promoter in cI-Lac oscillator has two binding sites for cI protein and one for LacI tetramer, whereas the promoter in Ara-Lac oscillator has one binding site for AraC protein and two sites for LacI binding. The model was then modified to fit the ara-lac system and IPTG, and Arabinose inducibility was incorporated into the model. Four more differential equations, that of mRNA and unfolded proteins, were added, to introduce delay that is important for oscillations in proteins according to \cite{Stricker}. | | Earlier attempts of reproducing the whole model using the Simbiology Toolbox in MATLAB R2015b were unsuccessful in reproducing the expected results. Possibly because of the complexity of the model and a huge number of reactions and their parameters. As a solution, a bottom-up approach of modelling was chosen, in which a simple model is built first and equations, parameters are added as required. The simple model, in this case, was chosen to be the cI-Lac oscillator described by \cite{Hasty}.The two first order coupled differential equations in the model were solved using < a href= "https://www.python.org/"> Python 3.6</a> in <a href="https://github.com/spyder-ide/spyder">Spyder 2.3.2</a>environment, a range of parameter values was scanned to obtain oscillations. On an average, the numerical integration took about 0.15 seconds to run an additional 0.30 seconds to output a graph. The main difference between the two oscillators is that the promoter in cI-Lac oscillator has two binding sites for cI protein and one for LacI tetramer, whereas the promoter in Ara-Lac oscillator has one binding site for AraC protein and two sites for LacI binding. The model was then modified to fit the ara-lac system and IPTG, and Arabinose inducibility was incorporated into the model. Four more differential equations, that of mRNA and unfolded proteins, were added, to introduce delay that is important for oscillations in proteins according to \cite{Stricker}. |