<a href="#1st"><span id="tab"><b>1] Cell Growth Curve</b> </span></a>

<a href="#2nd"><span id="tab"><b>2] title??</b></span></a>

<a href="#3rd"><span id="tab"><b>3] title??</b></span></a>

<span id ="sub-sub-title">1] Cell Growth Curve</span></br></br>

<span id="little">Cell growth can be modeled using Logistic differential equation. The logistic equation is shown below.</span></br></br>

<span id="little">When we solve above equation with appropriate parameters(using MATLAB), we can get solution curve like below. This curve matches with our knowledge about cell growth.</span></br></br>

<div align="center" ><img src='#'/></div>

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<span id="sub-sub-title">2] Title???</span></br></br>

<span id="little">With GFP and RFP, we want to check whether our system really works or not. Since we cannot consider all of complicated biological phenomena, we assume our system simply follows reaction rate theory and mass balance equations. Below reactions are simplified version of our system, and we CONSIDER the production and degradation of mRNAs and Genes, but we IGNORE the polysome phenomena and any gene regulatory system that is occur in real biological system. Also, we CONSIDER that there is many copies of plasmids in <i>E.coli</i> and each plasmid can react with invertase to invert their gene sequence.</br>

Because every plasmid have equal probability that react with invertase, we assume plasmids follow uniform distribution. Also assume each plasmids are mutually independent, that is each  plasmid cannot affect invertase reaction of other plasmid.</br></br>

<span id='little'>Using these reaction, we construct mathematical model of our system that is shown below. Pg(gene probability), in our model, represents the number of plasmid which is inverted. And the rate of producing inverted gene is reduced as the remaining non-inverted gene is reduced.</span></br></br>

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