Hi,
I have tested a substrate for my enzyme and want to include the Km value. I have calculated the Km via excel and also tried GraphPrism for it. However in both softwares I dont know how to get the SD. Can someone explain me how to calculate this?
The only possible solution, I come up with is this one: Lets say I have titrated the substrate 5 times and calculate for each experiment the Km. With those 5 Km values I could calculate SD but I am not sure if this would be an accurate way.
I would appreciate any suggestion. Thanks
The method you suggested is, in my opinion, the best approach: make the Km measurement multiple times in independent experiments and calculate the average and standard deviation of the multiple independent measurements.
The Origin (OriginLab) has a nice algorithm for non-linear regression (including Michaelis-Mentem Model). It automatically shows the standard deviation of all parameters.
It is important to distinguish between the standard deviation (usually reported as standard error) of a parameter computed by nonlinear regression from the standard deviation of repeated measurements of the parameter. The first one is a measurement of how much scatter there is in the raw data used to perform the regression within a single experiment. The second one is a measurement of variation of the measurement between experiments.
The classical method to determine Km and Vmax was linear regression after transformation (Lineweaver-Burk, Hanes or Eadie-Hofstee, all three originally proposed by Barnett Woolf and, due to his early death in a road accident, published in Haldane & Stern 1932). Linear regression, of course, gives error estimates for both slope and intercept. However, linear transformation leads to a change of weights of the data points, biasing both the parameter estimates and, in particular, their estimated errors. This is especially true if the dependent variable is transformed, as the independent variable is supposed to be error-free, its transformation is less critical.
Modern non-linear curve fitting uses the data without transformation, there are two important methods, Marquardt-Levenberg (doi:10.1137/0111030) and Nelder-Mead's simplex-method (10.1093/comjnl/7.4.308). Of these, ML works (oversimplified) by steepest descent and therefore requires the first derivative to be known and the second to exist and be smooth. In my experience, it is numerically less stable and often results in higher sum of squares than simplex. However, because the derivative is known, ML can calculate error margins for the parameters directly, just like linear regression. If you use the simplex method, you need to estimate the errors by bootstrapping (doi:10.1016/0076-6879(92)10009-3). On my first computer with a 80186 processor, this took several minutes; with a modern machine, of course, this is no longer a problem.
There is another alternative, which in your case may be the best choice: the direct plot of Eisenthal & Cornish-Bowden (doi:10.1042/bj1390715 and 10.1042/bj1390721). You connect the negative substrate concentration on the x-axis by a straight line with the corresponding velocity on the y-axis. Then all lines intersect in a point, whose coordinates are Km and Vmax.
As a non-parametric method, it works well even with error-containing data (typical for beginners), each pair of S/v then gives a separate intersection with all other pairs. You then determine the median of these as estimate for the parameters, and the 25% and 75% quartiles as estimate for the within-experiment error. My github-page (https://github.com/ebuxbaum) contains the Pascal-code to automate this.
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