Good Day.
I'm working on enzyme kinetics and I require to plot Lineweave -burk/Eadie-Hofstee graphs/Hanes as my final results.
I have plotted a graph (absorbance against time ) for five substrate concentration at different time. I need to obtain the linear slope for the calculation of my initial velocity which will be then used in beer lambert law .
How do I obtain the slope from the polynomial equation? or should I use a linear trendline and work with the m value intial velocity?
Thank you in advance.
Hi Freddy,
You can use the initial linear phase of each of the plot and calculate slope using linear equation. I am not sure which instrument you are using. In general, the UV-Vis spectrometers have in built softwares to calculate slopes for a given specific time points. Once you get the slopes, you can calculate specific activities and proceed for your LB or EF plots.
Good luck!
Hi there,
To obtain initial velocity you have to restrain the kinetics to its linear part and calculate the slope on this laps of time only.
One other thing: Linearised plots like Lineweaver-Burk are very nice for data presentation, as the human eye is very good at detecting deviations from linearity. However, they are suboptimal for the determination of Vmax and Km, because taking reciprocals changes the error distribution (data loose "homoskedasticity"). Either use non-linear curve fitting (Marquardt-Levenberg or even better Nelder-Mead algorithms), or the direct plot of Eisenthal and Cornish-Bowden.
What your are asking is not standard (I have not seen anyone reporting so), but the maths are pretty simple:
A) Fit your [P] vs t or your [S] vs t curve to the polynomial of your choice.
B) The slope at any value of the independent variable is the first derivative of the curve, here described by your polynomial:
f(t)=A0+A1 t + A2 t2 + A3 t3 + ...
f'(t)=A1+2A2 t + 3A3 t2 + ...
When evaluated at zero time (initial velocity), you get:
f'(0)=A1
i.e. the initial velocity equals the coefficient of the first linear term.
Best wishes
Rogelio
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