In a range of initial substrate concentrations at different reaction time of enzyme reaction plotting Michaelis menten equations and other linear equations including Linweaver-Burk, Woolf-Hans and Integrated Michaelis Menten equation result different Vm and km; ie for 5 initial substrate concentrations at 5 reaction times plotting 5 curves result in 5 different km and Vmax. The differences between kms and Vmaxs become more at longer time.
Also, At a certain time plotting different equations result different km and Vmax.
Does it show the reaction hasn't reached to its steady state and we should do the experiment for longer time? How could I show the unsteady condition in my results?
Hello Samira,
It is somewhat difficult to give you an answer, as you don't mention how your kinetic parameters vary with incubation time. However, it seems likely that your reaction kinetics tends to flatten at longer incubation times, which is often the case when you get substrate depletion, product inhibition, or enzyme inactivation. If this is the case, what you should strive for is to get the initial rate of the reaction at early times, when the rate of product formation vs time is nearly linear. To investigate pre-steady state kinetics, you would need very fast assay method such as stopped flow kinetics, but I suspect that this is not relevant to your case.
If you are trying to calculate Vm and Km, you should consider the linear range of your kinetic data. For rate calculation, the range where we do not get a linear graph is bound to give us inappropriate results. Also, considering the full time frame, i.e., from beginning till end is also going to give us similar outputs.
Hi there,
If in the proper condition of enzyme and substrate concentrations, the steady state (reaction rate is constant) is reached within seconds after mixing the reagents. What you have to check is how long is the steady state lasting. If you are using time points within this period, Km and Vm should be constant. If not it means that for some timepoints you are not in the condition of steady state kinetics.
Many thanks for your helpful answers. Here I attached the progressive curve of my data.
Besides plotting Linweaver-Burk and Woolf-Hans equations showed increasing reaction time causes higher Vmax and km (from 1st min to 2nd or 3rd min). using Woolf-Hans equation 10% and 50% increase in Vmax and km, respectively from 1st to 2nd min. In Linwearver-Burk plot in both Vmax and km there were about 50-60% increase from 1st to 2nd min of reaction.
In addition, there was no similarity in Vmax and km of the specific any specific time plotting with different equation.
I tried integrated Michaelis-Menten equation too, and it showed no real linear curve. There is a break point at substrate x- cordinate, ie. a linear part with an slope then it breaks (shifts) to another linear part with higher slope.
I also added the integrated plot for the first and second mins of the reaction.
From the kinetics you should include the origin for all kinetics and determine the tangent to each curve extrapolated at the origin. From your graphics you are systematically underestimating the velocity because you consider all the timepoints. Roughly I would only consider interval 0-2minutes for calculating initial velocities. I made a quick calculation with LB plot (with a nice correlation coefficient 0.9962) and found Vm=1.135mM/min and Km=10.2 (unit?)...
Special thanks dear Dr.Liger. As it is shown we have nodata for time less than 1min. As it is shown in the initial time the curves dont fit with linear curve. So, it should be right that with these data we couldn't determine initial rate.
About Vmax and km, have you plotted the LB for 1st min? Well, my question is if we consider it steady, why the Vmax and km are different while plotting with other equations like Woolf-Hans? Why the integrated plot is like this? Could you please send the LB curve which you have plotted?
I've roughly determined initial velocities using the datapoints at 2 min (for each curve, the points 0, 1min and 2 min are roughly aligned so the slope is the initial velocity). From one plot to another the bias on Km and Vm is different then the values do vary from one to another...
The other way of processing data is to perform non linear regression. Some free program are available online like this one :
http://faculty.gvsu.edu/carlsont/232lab/nonlin2.html
Using it I have obtained Vm and Km very close from those with LB plot (1.15mM/min and 10.79 respectively) which shows LB plot is quite reliable with your data.
Dear Dr.Liger
Many thanks for your attention and guides. for a series of data similar to previous treatment, I used L-B and Woolf-Hans equations (by excel) and it showed linear increase in curves with zero y-intersection. With that program you suggested the result was different with L-B, may be for my mistake as I havnt worked with that before.
It is obvious the substrate depletion couldnt be ignored. So, I plotted the data using integrated MM equation, and it resulted reasonable answers. There are differences between km and Vmax at different times. My question is, how should I know which of them are the best to report? And could I estimate the initial rate by these information?
I attached the progressive curve and integrated MM curve I obtained for different initial substrate concentrations at different times.
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