Team:Austin LASA/Model

const i = f => h(g.MathJax.Node, {inline: true, formula: f});
h(g.Page, {title: 'Model', prev: 'https://2018.igem.org/Team:Austin_LASA/Human_Practices', next: 'https://2018.igem.org/Team:Austin_LASA/Applied_Design', selector: [5, 1]},
  h('p', null, 'The LASA iGEM Team carried out the following modeling to count towards to Gold Medal Model criterion and Best Model Award:'),
  h(g.Section, {title: 'LAMP Modelling'},
    h('p', null, 'In order for our Cas12a-based assay to be used as an effective point-of-care diagnostic for HIV, we need a portable and inexpensive means of amplifying viral DNA. We chose to work with LAMP (Loop-Mediated Isothermal Amplification) because of its high selectivity, rapid amplification, and isothermal nature (rendering a thermal cycler unnecessary).'),
    h('p', null, 'After qualitatively narrowing down our pool of potential LAMP primers from four to six (See the graphs on our Design, Development, and Results page), we needed to choose which of the remaining four was the most effective in amplifying our HIV sample. We used kinetic modelling to compare the efficiency of each set of primers with the purified Bst enzyme. A recent article by  Subramanian and Gomez[1] proposed an empirical kinetic model for LAMP based on a generalized logistic curve. No ab initio model has been developed for the complex LAMP mechanism, but the logistic curve approximation can still be understood mechanistically in terms of the “competition between the so-called extended cauliflower-like structures and the complementary dumb bell structures in the cycling amplification step” [1] during the LAMP reaction.'),
    h(g.MathJax.Provider, null,
      h('p', null, 'The model proposed by Subramanian and Gomez is of the form:'),
      h(g.MathJax.Node, {formula: 'y(t) = a + \\frac{(k−a)}{(1+e^{−b(t−m)})},'}),
      h('p', null, 'where ', i('y(t)'), ' is the concentration of the amplicon at ', i('t'), ', ', i('a'), ' is the starting concentration,  is the maximum concentration, ', i('m'), ' is the time at which maximum growth occurs, and ', i('b'), ' is a free parameter representing how steep the growth is. We fit our data to this model using SciPy’s curve_fit function. It is also worth noting that our data and fitted parameters are actually in units of fluorescence, not concentration. We assumed that the two were proportional and worked in terms of fluorescence instead because that was the data we had readily available.'),
      h('p', null, 'Once the model parameters have been obtained, we can compute ', i('T_p'), ' by ', i('T_p = m-\\frac{2}{b}'), '[1].')  
    )
  )
);