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MATH3888

Semester 2

Interdisciplinary Project (Glycine Stream 2)


WEEK 7 REPORT GUIDELINES

Submission:

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

https://en.wikibooks.org/wiki/LaTeX

You are encouraged to use the software Overleaf which you can access via any browser through your University of Sydney account:

https://www.overleaf.com

Use the following basic setup for your LaTex file:

\documentclass[11pt]{article}

\usepackage{fullpage,amsmath}

. . .

\begin{document}

. . .

\end{document}


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 4 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 pack-ages, if needed.)


Your glycine model

Based on your week 5 group presentation slides, define a first ODE model that describes the base dynamics of your biological model under study.

If your group project is on glycine receptors (an agonist-controlled ion channel), then

1. Provide a cartoon of the kinetic scheme (Markov model) of a base glycine receptor model, i.e. glycine is the only receptor agonist. Assume there are only 2 relevant glycine binding sites; look at the kinetic scheme for a GABAa recptor shown in, e.g. modelling lecture week 4. Furthermore, assume cooperativity. Indicate all reaction rates. Which reaction rates depend on the agonist concentration? How is cooperativity reflected in the reaction rates? (Please consult your MEDS students, if necessary.)

2. Define the current IGlyR through a population of such glycine receptors; assume that the receptors are ohmic resistors. Note, the conductivity of this population of glycine receptors depends on the fraction of open glycine receptors.

3. Write down a system of ODEs representing your base glycine receptor model. If you use a model from the literature, cite appropriately! Give a short description of all your variables and parameters in relation to your receptor model.

4. Identify conservation laws and reduce your model accordingly. Implement this model in Matlab/MatCont. Provide all parameter and initial values. (Please consult your MEDS students or literature for possible parameter values.) Set agonist (glycine) concentration equal zero; the receptor should not conduct at all, i.e. the fraction of open glycine receptors must be zero. Find the corresponding steady state numerically.

5. Continue this steady state with respect to the agonist (glycine) concentration. Provide the corresponding plot. How do you interpret this curve?

Note: this homework is NOT about any specific modulator! This will be your focus in the coming weeks.

If your group project is on glycine transporters (carrier-mediated transport), then

1. Provide a cartoon of your base glycine transporter models, GlyT1 and GlyT2. Sodium and chloride ions are involved in this process. Provide typical extra- and intracellular concentrations of each ion (sodium and chloride). What distinguishes GlyT1 and GlyT2? Are these uniports, symports or antiports? (Please consult your MEDS students, if necessary.)

2. Provide a simple kinetic scheme (Markov model) that describes these transporters. Follow the ideas from the textbook, section 2.4., i.e. assume 4 possible states at most. Indicate all reaction rates in the diagram. Which reaction rates depend on which ion concentration(s)? (Please consult your MEDS students, if necessary.)

3. Write down a system of ODEs representing your base glycine transporter model for GlyT1 or GlyT2; ignore electrogenic effects. If you use a model from the literature, cite appropriately! Give a short description of all your variables and parameters in relation to your transporter model. Define the glycine transporter turnover rate (flux).

4. Identify conservation laws and reduce your model accordingly. Implement your system in Matlab/MatCont. Provide all parameter and initial values. (Please consult your MEDS students or literature for possible parameter values.) Set extracellular glycine concentration equal zero. Find a steady state numerically. Then continue this steady state with respect to the extracellular glycine concentration.

5. Finally, plot the (steady state) turnover rate (flux) as a function of the extracellular glycine concentration. How do you interpret this curve? (Please consult your MEDS students, if necessary.)

Note: this homework is NOT about any specific pathological condition! This will be your focus in the coming weeks.