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I was wondering what the constants in the Michaelis-Menten equation actually mean in experimental data of enzymes. How do I process the data to find Km and Kcat?

I did an experiment on catalase and its breakdown of hydrogen peroxide. I used a gas pressure sensor to track how much O2 was produced from the reaction over time. The following is an example raw plot of what I found. Point 0 is when I put the substrate and the reaction started (so I think I can call this the "maximum amount of substrate concentration" - in the Michaelis-Menten plot, it should be on the far right side.)

To find the speed of the reaction at each point, I thought of finding the slopes between each point, which basically equates to finding the derivative. Since the raw plot I found looks like a logarithm function, so I would predict that the derivative would look like a hyperbola (with x > 0). Indeed, this is the (crude) graph of the "derivative" of the previous plot, which looks like a hyperbola:

I believe that Kmax is the y-value of the first point in this graph - the initial velocity when the substrate is mixed with the enzyme. The substrate concentration is at highest at time 0, and the substrate concentration decreases as time increases.

So I thought, to make the Michaelis-Menten graph, I should flip the x-axis so that the substrate concentration is increasing along the x-axis. Yet, my problem was that if I do this, then the graph ends up not looking like the Michaelis curve…

What I would have wanted to find is the Michaelis-Menten curve, so that I can also derive the Km and Kcat values. Does anyone know how to do this? Or am I doing my steps wrong? Thank you very much for helping me!

Michaelis-Menten Curve:

Have you got data for different concentrations of hydrogen peroxode?

If so you should choose a time point that falls on the linear part of your time graph. And plot the rate at that time point for each substrate concentration.

That will give you a MM curve where you can calculate the values you desire. You cannot calculate them with just your time data that you have provided.