Instruksies

Handig $\text{'}$n Jupyter "notebook" in deur dit via

die Assignment funksie van SUNLearn op te

laai. Die "notebook" moet die berekeninge

uitvoer en grafieke trek soos hieronder beskryf.

L$$ernaam: jou$\_$studente$\_$nommer $.$ ipynb

Sperdatum: Maandag $27$ Mei $2024,23$ h$59.$

$($Geen laat inhandiging word aanvaar nie!$)$

Opdrag

Beskou $\text{'}$n oop sisteem van twee gekoppelde

reaksies wat $S$ na $P$ omsit via die koppel$-$

ingsmetaboliet $x$ :

$S{}^{v_1}x{}^{v_2}P$

Neem aan dat albei ensieme omkeerbare

Michaelis$-$Menten kinetika volg, terwyl die

eerste ensiem bykomend nog deur $x$ onkom$-$

peterend ge$$nhibeer word. Die kinetiese pa$-$

rameters vir die sisteem is as volg:

Instructions

Hand in a Jupyter notebook by uploading it

via the Assignment function of SUNLearn. The

notebook should perform the calculations and

draw the graphs as set out below.

File name: your$\_$student$\_$number.ipynb

Deadline: Monday $27$ May $2024,23$ h$59.$

$($No late submissions will be accepted!$)$

Assignment

Consider an open system of two coupled reac$-$

tions converting $S$ to $P$ via the linking metabo$-$

lite $x$ :

Assume that the both enzymes follow re$-$

versible Michaelis$-$Menten kinetics, while the

first enzyme is additionally inhibited uncom$-$

petitively by $x.$ The kinetic parameters for the

system are as follows:

Gebruik matplotlib om $\text{'}n$ stel snelheidsken$-$

merke vir hierdie sisteem te plot.

Definieer toepaslike funksies vir $v_1$ en

$v_2.$

Kies $\text{'}$n gepaste $x-$data omvang sodat

die bestendige toestand duidelik sig$-$

baar is$.$

Gebruik $\text{'}$n line$$re skaal vir die asse.

Kies voldoende datapunte om gladde

kurwes te gee.

Verskaf byskrifte vir lyne $($grafiekle$-$

gende$),$ onderskrifte en titels vir asse.

Using matplotlib, plot a set of rate characteris$-$

tics for this system.

Define appropriate functions for $v_1$ and

$v_2.$

Choose a suitable $x-$data range so that

the steady state is clearly visible.

Use a linear scale for the axes.

Choose sufficiently many data points to

give smooth curves.

Provide labels for the lines $($graph leg$-$

end$),$ axis labels and axis titles.Bepaal die ko$$rdinate $(\stackrel{}{x},J)$ van die

bestendige toestand punt.

Jy kan dit benader deur die $x-$datapunt

in jou omvang wat naaste aan die

bestendige toestand l$.$

Plot weer die stel snelheidskenmerke, maar

gebruik $\text{'}$n logaritmiese skaal vir die asse.

Verskaf weer by$-/$onderskrifte en titels.

Bereken ${}_x^{{}_1}$ en ${}_x^{{}_2}$ d$.$m$.$v$.$ line$$re regressie ron$-$

dom die bestendige toestand$-$punt.

Gebruik die antwoorde in Vraag $(4)$ om

die waardes van die kontrole$-$ko$$ffisi$$nte

$(C_{v_1}^J,C_{v_2}^J,C_{v_1}^x,C_{v_2}^x)$ te bereken.

Determine the coordinates $(x,J)$ of the steady

state point.

You can approximate it with the $x-$data

point in your range that lies closest to

the steady state.

Again plot the set of rate characteristics, but

use a logarithmic scale for the axes.

Again provide all labels and titles.

Calculate ${}_x^{v_1}$ en ${}_x^{{}_2}$ by means of linear regres$-$

sion around the steady state point.

Use the answers in Question $(4)$ to calcu$-$

late the values of the control coefficients

$(C_{v_1}^J,C_{v_2}^l,C_{v_1}^x,C_{v_2}^x)$

Let wel:

Wys duidelik alle Python kode.

Toon alle berekeninge.

N$.$B$.$:

Clearly show all Python code.

Show all calculations.