Plotting Mathematica: Michaelis-Menten Rate of Uptake

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SUMMARY

The discussion focuses on plotting the Michaelis-Menten rate of uptake in Mathematica using the formula \( R_0 = \frac{Q_{s_0}}{K_m+s_0} \), where \( K_m = \frac{k_{-1}+k_2}{k_1} \) and \( Q_{s_0} = k_2 e_0 s_0 \). Users sought assistance with plotting this equation and encountered issues with plot markings. A solution was provided using the Plot function in Mathematica, specifically employing the PlotLegends package to enhance the visual representation of the data.

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  • Understanding of the Michaelis-Menten kinetics model
  • Familiarity with Mathematica version 12.0 or higher
  • Basic knowledge of plotting functions in Mathematica
  • Experience with mathematical notation and functions
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  • Learn about the PlotLegends package in Mathematica
  • Study the implications of Michaelis-Menten kinetics in biochemical reactions
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Biochemists, data scientists, and Mathematica users interested in modeling and visualizing enzyme kinetics and related mathematical functions.

Dustinsfl
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dwsmith said:
So the Michaelis-Menten rate of uptake is
$$
R_0 = \frac{Q_{s_0}}{K_m+s_0}
$$
where $K_m=\dfrac{k_{-1}+k_2}{k_1}$ and $Q_{s_0}=k_2e_0s_0$

Q is the max velocity K_m is the Michaelis constant.

How can I plot this in Mathematica?
 
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dwsmith said:
How can I plot this in Mathematica?

Code: 
<< PlotLegends`
 Plot[{x*(1 + x)/(1 + x + x^2), x^2/(1 + x + x^2)}, {x, 0, 5}, 
 PlotLegend -> {"Michaelis-Mendel", "k_2=0"}, 
 LegendPosition -> {0, -.45}, Joined -> {True, True}, 
 PlotMarkers -> Automatic]

Plot markings aren't working. How can I get this to work?
 
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