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MATH3888

Semester 2

Interdisciplinary Project (Glycine Stream 2)

2021

WEEK 9 REPORT GUIDELINES

Submission:

As outlined in the information sheet of this interdisciplinary project course, you will create reports using the (maths) editing software LaTeX:

You are encouraged to use Overleaf to create your LaTeX report which you can access via your browser through your University of Sydney account:

Use the following basic setup for your LaTex file:

Submission of the corresponding pdf file is via turnitin (where it will be checked for plagariasm).

As outlined in the course info sheet, this report is worth 5% of your final mark.

Constraints:

The final submitted pdf document shall consist of no more than 5 pages (including figures,....). The ‘fontsize’ is strictly 11 points and the margins of the document are automatically set by the ‘fullpage’ package (as instructed above).

The other package (‘amsmath’) might be needed for the mathematical editing. Add any other packages, if needed.

In addition, you need to submit your Matlab/MatCont source file (*.m, *.mat).

Your glycine receptor model update

Based on the additional information you obtained since your week 7 submission:

1. Hypothesise the action of your group specific drug/modulator (OPOG) in biological terms with respect to your biological system. Support this with samples of experimental data (figures).

2. Incorporate the action of your drug/modulator (OPOG) to update your ODE model in week 7 homework that describes the kinetics/dynamics of your biological system under study. Provide your model parameter values and units in a LaTeX tabular environment.

3. Identify variable(s) and/or function(s) that describe (best) your experimental data (be specific)! Hypothesise the action of each agonist/drug/modulator on your ODE model, i.e. state which varia-tion of parameter (and/or function) models the action of each agonist/drug/modulator (be specific).

4. Implement your updated model system in Matlab/MatCont and show that it has the capability to create the desired output with respect to the agonist concentration, i.e. it replicates basic features of your experimental data.

5. Finally, implement an agonist/drug protocol in your model. Define each protocol in Matlab as a single discontinuous function (use Heaviside function). Check whether your agonist/drug hypothesis holds by comparing this model output with your experimental data, i.e. plot agonist/drug protocol, relevant model trajectories and corresponding experimental data. Provide (possible) explanations!

Your glycine transporter model update

Based on the additional information you obtained since your week 7 submission:

1. Hypothesise the action of altering ion and glycine concentrations in how the transporter functions in your model. Support this with samples of experimental data.

2. The glycine transporters GlyT1 or GlyT2 are electrogenic. Update your model in week 7 homework and define the transporter turnover rate accordingly. Provide your model parameter values and units in a LaTeX tabular environment.

3. Identify variable(s) and/or function(s) that describe (best) your experimental data (be specific)! Hypothesise the action of altering ion (sodium) and glycine concentrations on your model, i.e. state which variation of parameter (and/or function) models the action of each agonist/drug (be specific).

4. Implement your updated model system in Matlab/MatCont and show that it has the capability to create the desired output with respect to your agonist concentration, i.e. it replicates basic features of your experimental data.

5. Finally, implement an agonist/drug protocol in your model. Define each protocol in Matlab as a single discontinuous function (use Heaviside function). Check whether your agonist/drug hypothesis holds by comparing this model output with your experimental data, i.e. plot agonist/drug protocol, relevant model trajectories and corresponding experimental data. Provide (possible) explanations!