diff --git a/wiki/pages/model.html b/wiki/pages/model.html index 3a519adbdc5cd19f65c84628131aab547504f71a..f56bdcd9df1e3ae4cb4ad17ebd0d3e0be15d0237 100644 --- a/wiki/pages/model.html +++ b/wiki/pages/model.html @@ -213,10 +213,10 @@ pre{ <center><i>Figure 9. Output of concentrations of all related molecules in the butyrate negative feedback example.</i></center> <p></p> <h3 class="atx" id="conclusion">Conclusion</h3> - <p>Our calculator is capable of predicting any complex genetic circuit due to its generality, and its straightforward input system makes the calculator a simple tool for future iGEM teams to use. By inputting the structure of our team’s circuit and incorporating the basic mass action kinetic function and Hill function, the calculator predicts the results, visualizing the change of each substance and giving insights for experiments. It is also useful if we want to adjust the genetic circuit, preventing us from working from scratch and constructing a new model for the changed circuit. However, our current outputs are graphs of concentration as a function of time, which might be less accurate considering the chemical reactions in the circuit produce products that are described as probability distributions rather than expected values. Therefore, our future goal is to establish a probability distribution predicting calculator.</p> + <p>Our calculator is capable of predicting any complex genetic circuit due to its generality, and its straightforward input system makes the calculator a simple tool for future iGEM teams to use. By inputting the structure of our team’s circuit and incorporating the basic mass action kinetic function and fill function, the calculator predicts the results, visualizing the change of each substance and giving insights for experiments. It is also useful if we want to adjust the genetic circuit, preventing us from working from scratch and constructing a new model for the changed circuit. However, our current outputs are graphs of concentration as a function of time, which might be less accurate considering the chemical reactions in the circuit produce products that are described as probability distributions rather than expected values. Therefore, our future goal is to establish a probability distribution predicting calculator.</p> <p></p> <h2 class="atx" id="metabolic-stress-model">2. Metabolic Stress Model</h2> - <p>Concerned with the metabolic stress of the genetic pathways we integrated into the genome of our engineered <em>E. coli Nissle 1917</em> (EcN), we want to analyze whether this leads to reduced fitness in our engineered EcN so it may be outnumbered and outcompeted by existing gut microbiota. We also find estimating and simulating metabolic stress on expression systems commonplace across research projects, so our modeling process may provide insights for other iGEM projects.</p> + <p>Concerned with the metabolic stress of the genetic pathways we integrated into the genome of our engineered <em>E. coli</em> Nissle 1917 (EcN), we want to analyze whether this leads to reduced fitness in our engineered EcN so it may be outnumbered and outcompeted by existing gut microbiota. We also find estimating and simulating metabolic stress on expression systems commonplace across research projects, so our modeling process may provide insights for other iGEM projects.</p> <h3 class="atx" id="assumptions-and-parameters-1">Assumptions and Parameters</h3> <p>Throughout the modeling process, we've unified the units of concentration, time, and EcN population as <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:1em;vertical-align:-0.25em;" class="strut"></span><span class="mord"><span class="mord mathrm">millimoles</span></span><span class="mord">/</span><span class="mord"><span class="mord mathrm">liter</span></span></span></span></span>, hours, and <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.8333em;vertical-align:-0.15em;" class="strut"></span><span class="mord"><span class="mord"><span class="mord mathrm">OD</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.3011em;" class="vlist"><span style="top:-2.55em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">600</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span></span></span></span> respectively. Hence, we will refer to the following parameters:</p> <table class="table table-hover" style="text-align: center"> @@ -305,7 +305,7 @@ pre{ </li> </ol> <h3 class="atx" id="bacteria-logistic-growth">Bacteria Logistic Growth</h3> - <p>The growth of our engineered probiotic, <em>E. coli Nissle 1917</em> (EcN) is referred to repeatedly throughout our models. Moreover, EcN is a chassis widely utilized throughout biological research. Therefore, based on the comprehensive fluorescence kinetics data we've gathered (Figure. 10), we calculated the parameters <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.4306em;" class="strut"></span><span style="margin-right:0.02778em;" class="mord mathnormal">r</span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:0.6444em;" class="strut"></span><span class="mord">0.49700362</span></span></span></span>, <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.8333em;vertical-align:-0.15em;" class="strut"></span><span class="mord"><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.3011em;" class="vlist"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:0.6444em;" class="strut"></span><span class="mord">0.00121806</span></span></span></span> and <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.8333em;vertical-align:-0.15em;" class="strut"></span><span class="mord"><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.1514em;" class="vlist"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mtight">m</span><span class="mtight">a</span><span class="mtight">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:0.6444em;" class="strut"></span><span class="mord">0.66132188</span></span></span></span> with the following logistic growth model fitting:</p> + <p>The growth of our engineered probiotic, <em>E. coli</em> Nissle 1917 (EcN) is referred to repeatedly throughout our models. Moreover, EcN is a chassis widely utilized throughout biological research. Therefore, based on the comprehensive fluorescence kinetics data we've gathered (Figure. 10), we calculated the parameters <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.4306em;" class="strut"></span><span style="margin-right:0.02778em;" class="mord mathnormal">r</span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:0.6444em;" class="strut"></span><span class="mord">0.49700362</span></span></span></span>, <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.8333em;vertical-align:-0.15em;" class="strut"></span><span class="mord"><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.3011em;" class="vlist"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:0.6444em;" class="strut"></span><span class="mord">0.00121806</span></span></span></span> and <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.8333em;vertical-align:-0.15em;" class="strut"></span><span class="mord"><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.1514em;" class="vlist"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mtight">m</span><span class="mtight">a</span><span class="mtight">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:0.6444em;" class="strut"></span><span class="mord">0.66132188</span></span></span></span> with the following logistic growth model fitting:</p> <span class="katex-display"><span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:2.113em;vertical-align:-0.686em;" class="strut"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:1.427em;" class="vlist"><span style="top:-2.314em;"><span style="height:3em;" class="pstrut"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span></span></span><span style="top:-3.23em;"><span style="height:3em;" class="pstrut"></span><span style="border-bottom-width:0.04em;" class="frac-line"></span></span><span style="top:-3.677em;"><span style="height:3em;" class="pstrut"></span><span class="mord"><span class="mord mathnormal">d</span><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.686em;" class="vlist"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:2.4em;vertical-align:-0.95em;" class="strut"></span><span style="margin-right:0.02778em;" class="mord mathnormal">r</span><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span style="margin-right:0.1667em;" class="mspace"></span><span class="minner"><span style="top:0em;" class="mopen delimcenter"><span class="delimsizing size3">(</span></span><span class="mord">1</span><span style="margin-right:0.2222em;" class="mspace"></span><span class="mbin">−</span><span style="margin-right:0.2222em;" class="mspace"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:1.427em;" class="vlist"><span style="top:-2.314em;"><span style="height:3em;" class="pstrut"></span><span class="mord"><span class="mord"><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.1514em;" class="vlist"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mtight">m</span><span class="mtight">a</span><span class="mtight">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span style="height:3em;" class="pstrut"></span><span style="border-bottom-width:0.04em;" class="frac-line"></span></span><span style="top:-3.677em;"><span style="height:3em;" class="pstrut"></span><span class="mord"><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.836em;" class="vlist"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span style="top:0em;" class="mclose delimcenter"><span class="delimsizing size3">)</span></span></span></span></span></span></span> <p style="text-align: center;"><img src="https://static.igem.wiki/teams/5127/model/fig-model-metabostress-growth.webp" style="width: 100%"></p> <center><i>Figure 10. Data on logistic growth of EcN in vitro from fluorescence kinetics experiments.</i></center> @@ -432,7 +432,7 @@ pre{ <p>CATGAATAAAAATTCAAG</p> <p></p> <h2 class="atx" id="pharmacokinetics-model">5. Pharmacokinetics Model</h2> - <p>As our goal is to design a probiotic supplement that could mediate key metabolites in the gut environment in the long run, determining the optimum drug dosage and dosage regimen to optimize therapeutic benefit and its half-life is essential. We implemented the design of classical dose-response modeling to retain a balanced effective <em>E. coli Nissle 1917</em> (EcN) population above 90% of its maximum population with data from fluorescence kinetics experiments and literature reviews. We predict the optimum dosage regimen with <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.6833em;" class="strut"></span><span style="margin-right:0.13889em;" class="mord mathnormal">T</span></span></span></span> days between each dosage and the corresponding maximum EcN population, <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.8333em;vertical-align:-0.15em;" class="strut"></span><span class="mord"><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.1514em;" class="vlist"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mtight">m</span><span class="mtight">a</span><span class="mtight">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span></span></span></span>. To this end, we propose the following model based on logistic growth and population decay over time.</p> + <p>As our goal is to design a probiotic supplement that could mediate key metabolites in the gut environment in the long run, determining the optimum drug dosage and dosage regimen to optimize therapeutic benefit and its half-life is essential. We implemented the design of classical dose-response modeling to retain a balanced effective <em>E. coli</em> Nissle 1917 (EcN) population above 90% of its maximum population with data from fluorescence kinetics experiments and literature reviews. We predict the optimum dosage regimen with <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.6833em;" class="strut"></span><span style="margin-right:0.13889em;" class="mord mathnormal">T</span></span></span></span> days between each dosage and the corresponding maximum EcN population, <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.8333em;vertical-align:-0.15em;" class="strut"></span><span class="mord"><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.1514em;" class="vlist"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mtight">m</span><span class="mtight">a</span><span class="mtight">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span></span></span></span>. To this end, we propose the following model based on logistic growth and population decay over time.</p> <h3 class="atx" id="assumptions-and-parameters-2">Assumptions and Parameters</h3> <p>Throughout the modeling process, we've unified the units of time and drug concentration/EcN population as hours and <span class="katex"><span class="katex-mathml"></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:0.8333em;vertical-align:-0.15em;" class="strut"></span><span class="mord"><span class="mord"><span class="mord mathrm">OD</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.3011em;" class="vlist"><span style="top:-2.55em;margin-right:0.05em;"><span style="height:2.7em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">600</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.15em;" class="vlist"><span></span></span></span></span></span></span></span></span></span> respectively. Hence, we will refer to the following parameters:</p> <table class="table table-hover" style="text-align: center">