Hello all,
We have an enzyme that must follow Michaelis-Menten kinetics (we
have an experimental way to avoid the inverse reaction), so we need to
estimate initial rates at different initial substrate concentrations,
then do the double reciprocal graph (Lineweaver-Burk).
Raw data from a spectrophotometer is absorbance x time ; OK, we can
relate absorbance to the amount of product formed.
The question is: is there a formal , statistical way, to evaluate
the point to which the rate is constant such that this one might be used
to approximate the *initial rate*. Event better, I wonder of a software
(very preferably free, even better if for linux) that might get the raw
data (Abs x time) and apply the statistics to estimate the initial rate
(we should have triplicates for several substrate concentrations - so,
several curves). Our doubt here is, considering that though one has a
good spectrophotometer, random oscillation might occur as in any
experimental measurement and the inherent characteristic of such an
experiment, id est, as the substrate concentration falls the rate falls
(not necessarily in a linear way) as well.
If such way is not available, I wonder how people have been
estimating initial rate for abs x time.
Thank you,
Agnes
There are several points here.
1. The Lineweaver -Burk plot or other linearizations of the Michaelis-Menten equation have the undesirable property of distorting the experimental error. For example, in the L-B plot, the point farthest from the origin in quadrant 1 corresponds to the slowest rate, which is likely to have a large error, yet because it is farthest from the origin it has a disproportionately large effect on the slope of the line.
2. Linear regression can be used to measure the slope of the initial rate portion of the progress curve (absorbance v. time), but some judgment is required to make sure that the initial rate is actually being measured, not a slightly smaller rate because data points were included from time points after the rate started to slow down. Collecting as many time points as possible at the start of the reaction is a way to have enough data to be sure that the initial rate is being measured. The best-fit line corresponding to the initial rate should be colinear with all the included data points. Removing the latest one or few should have no significant effect on the slope.
3. Using progress curve analysis, it is sometimes possible to obtain the kinetic constants from more of the progress curve than just the initial rate part, taking advantage of the curvature as the substrate is consumed. In this case, the progress curve is fit to the integrated form of the M-M equation using nonlinear regression. Preferably, this is done globally for a set of progress curves obtained at different substrate concentrations. The form of the progress curve is not a second order polynomial, it is logarithmic.
http://onlinelibrary.wiley.com/doi/10.1002/bmb.32/full
4. It is also possible to use numerical methods for progress curve analysis rather than nonlinear regression, using certain computer programs. I have used Kintek Global Kinetic Explorer for this purpose, for example.
This can help you, as a starting point:
http://elte.prompt.hu/sites/default/files/tananyagok/IntroductionToPracticalBiochemistry/ch09s03.html
All the best.
I do the easy thing and plot abosrbance vs. Time. I take the linear part of the curve and fit to a straight line using EXcel. That is about it. For lineweaver burke plots, etc and determining Km there is Prism software which you can get a trial run for free I think. There is a free program called Biokin which you can use to fit the complete progress curves if you like, which is a better method to use. But the program is more difficult. You can quantify total substrate, by measuring the initial absorbance, or if the product has abosrbance, you can convert everything to product and measure the final absorbance.
If you have measured many time points spaced closely together, you can make a plot of the slope versus time, using several adjacent time points to measure the slope (in other words, the 1st derivative of the absorbance versus time plot). Ideally, this would result in a graph with a constant y-value until the rate begins to slow down. You can then take this constant value as the initial rate.
I suggest not to do Lineveaver-Burk plots. CurveExpert is a good inexpensive software for nonlinear fitting. You can also run free trial. If do not see clearly linear part in the beginning of your time-curves you must fit them also to some reasonable nonlinear curve fprmula and determine the initial slope.
People keep saying that use non-linear regression to determine Km & Vmax and do not use linear transformation like Lineveaver-Burk plots. Yet people are recommending to use linear regression to determine initial velocities which I got absolutely confused. Can I use second order polynomial with Y-intercept to fit the data (Abs vs Time) then calculate derivative of the equation and put X=0 to get Vo (initial velocity) which would make more sense mathematically if I wanna still call it as "initial velocity". Practically speaking if I measure Abs vs Time on series of different enzyme concentrations [E], lower concentration would look like linear but higher concentration looks like Logarithmic. Therefore the more the high concentration, the more the value will be varies on linear regression. Isn't that weird... with same data (Abs vs Time) two different person will get slightly different Vo (259 or 244) depending on where their linear feeling is. in fact polynomial fitting gives 296 which is not varies by person's linear feeling. in the end ..I don't know I might be wrong but.... just let me know if you know any better way.
There are several points here.
1. The Lineweaver -Burk plot or other linearizations of the Michaelis-Menten equation have the undesirable property of distorting the experimental error. For example, in the L-B plot, the point farthest from the origin in quadrant 1 corresponds to the slowest rate, which is likely to have a large error, yet because it is farthest from the origin it has a disproportionately large effect on the slope of the line.
2. Linear regression can be used to measure the slope of the initial rate portion of the progress curve (absorbance v. time), but some judgment is required to make sure that the initial rate is actually being measured, not a slightly smaller rate because data points were included from time points after the rate started to slow down. Collecting as many time points as possible at the start of the reaction is a way to have enough data to be sure that the initial rate is being measured. The best-fit line corresponding to the initial rate should be colinear with all the included data points. Removing the latest one or few should have no significant effect on the slope.
3. Using progress curve analysis, it is sometimes possible to obtain the kinetic constants from more of the progress curve than just the initial rate part, taking advantage of the curvature as the substrate is consumed. In this case, the progress curve is fit to the integrated form of the M-M equation using nonlinear regression. Preferably, this is done globally for a set of progress curves obtained at different substrate concentrations. The form of the progress curve is not a second order polynomial, it is logarithmic.
http://onlinelibrary.wiley.com/doi/10.1002/bmb.32/full
4. It is also possible to use numerical methods for progress curve analysis rather than nonlinear regression, using certain computer programs. I have used Kintek Global Kinetic Explorer for this purpose, for example.
I deeply appreciate your prompt response Dr. Shapiro which cleared some confusion on my understanding
Thanks you all for great helps.
I love this place which is far ~~ better than google ^^
and goodnight all.
Sincerely
Choi
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