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Natural Science Forum / Biology / Microbiology / April 2004enzyme kinetics question
Hi, I have data from a set of competitive inhibition experiments. My data consists of substrate concentration [S] monitored over time (t) for various concentrations of inhibitor [I] at a certain enyme concentration [E]. I understand about getting the initial velocity (v0) from the raw data and using these v0 values to obtain a Ki value for the inhibitor, and I have done this. I was looking at the data again, and wondered why can't I fit the original raw data directly instead of attempting to extrapolate a v0? I'm sure that the fit to the data should be of the form: [S](t) = A*exp(-B*t) I know that this analysis is the more complicated way to solve for v0 or v, but I was just wondering if it was possible? Thanks. > Hi, > [quoted text clipped - 12 lines] > > Thanks. The velocity changes over time. Substrate is depleted. The concentration of the product increases, and the inverse reaction takes place. It is possible to get the rate of the forward reaction in other ways, but extrapolation to zero time is the easiest. >Hi, > [quoted text clipped - 10 lines] >I know that this analysis is the more complicated way to solve for v0 >or v, but I was just wondering if it was possible? There are often enough complications so that analyzing the full time course of [S] vs t isn't often a very good way of getting what you want. In fact, if there is any significant back reaction then [S] won't go to zero and you have two parameters to fit, not one. The reaction rate should not be so fast for you to get at least a few good data values in before the reactions slows significantly. If so, you should refine your techniques to start collecting data sooner and more frequently or else use less enzyme to slow the reaction a bit. It also depends on what level of experiment and analysis you are doing -- intro biology? research activity? For the purpose of teaching the biology of enzyme kinetics, simple straightforward analytic techniques are more effective. That is why Lineweaver-Burke plots are still used to calculate Km and Vmax even though more complex forms of data analysis are required for research level work. > Hi, > [quoted text clipped - 12 lines] > > Thanks. Hysterical Raisins. Back in the bad old days, it was hard to do stuff like fitting an exponential to experimental data, so everything got reworked to a linear equation and fit with a good old linear least squares regression. As background, remember that least squares minimizes the sum of the squares of the deviations (call it z). When you do a data transform, you end up minimizing some other quantity like 1/z or log(1/z) or something else. This tends to pull the regression line hither and yon and gives less than ideal values for Km and Vmax. We never really cared because: A) It's better than doing it *GASP* graphically. Does anybody out there still have any semilog or log-log graph paper?????? B) What would you do with the extra accuracy, sell it?. Your next sample of enzyme will have a specific activity different by a factor of 4 at least. Now that everybody is walking around with multi-Ghz computers, the calculation issue seems almost incomprehensible. Remember Scotty trying to talk to a Mac in Star Trek III, "A keyboard, How quaint". It's worse than that. So yes, fit your eqn. directly and you get better values. Just watch to be sure your fitting algorithm is correct and you are good to go. Cheers, Tony. > Hysterical Raisins. > Back in the bad old days, it was hard to do stuff like fitting [quoted text clipped - 24 lines] > Cheers, > Tony. I tend to aggree, Tony... The data I'm working with is for my primary research. I've been told by another postdoc that doing anything more than using the linear fit to get an initial velocity is a 'complete and utter waste of time.' I believe that he's wrong. I'm just trying to look for a good physical basis for writing a meaningful fitting equation. In my experiment, a chromogenic substrate is cleaved by a certain enzyme. The substrate changes it's absorbance wavelength when it is cleaved. I simply monitor the absorbance as a function of time to 'see' what's going on. I've done this experiment many times in the presence of different concentrations of a certain inhibitor (as well as in the absence of the inhibitor). I'm at a bit of a loss as to what fitting equation I should use for any ONE set of this data (that is, the decrease in the substrate's absorbance as a function of time - at a certain enzyme and inhibitor concentration). If I'm able to get a reasonable equation to fit one curve, I don't see why I can't fit all the curves simultaneously (using matlab) and generate a plot to determine a Ki value... Thanks again. >I tend to aggree, Tony... The data I'm working with is for my >primary research. I've been told by another postdoc that doing >anything more than using the linear fit to get an initial velocity is >a 'complete and utter waste of time.' I believe that he's wrong. >I'm just trying to look for a good physical basis for writing a >meaningful fitting equation. At least for the sake of discussion, let me agree with your post-doc colleague. My basic point/question is why do you want to make things more complicated? The more of the curve you use, the more assumptions you have to make. S is no problem. But you also have to assume that all other conditions relevant to your enzyme are constant. These would include things such as pH and O2, and the assumption that your product does not affect the enzyme. One reason for using the initial velocity is to minimize the possible effect of these confounding variables. If your intent is to explore these confounding variables, then comparing the results calculated one way vs another may be instructive. On the other hand, if you want to measure product inhibition, why not just do it directly? Using more data from the curve might in principle result in better accuracy of result. But there are two cautions there. One is whether that better accuracy is of any value to you. And the second is whether the assumptions behind using the additional data are valid -- and if you don't want to get into that then you are just kidding yourself by using the extra data. Keep it simple. Use initial velocity unless... ??? bob >>I tend to aggree, Tony... The data I'm working with is for my >>primary research. I've been told by another postdoc that doing [quoted text clipped - 27 lines] > >Keep it simple. Use initial velocity unless... ??? There is another reason to keep it simple. If you use initial velocity, the don't have to explain anything. If you use a more complex method, you are going to have to describe exactly what you did in your materials and methods section and then justify exactly why you modeled your equation exactly the way you did including describing all the assumptions that are either explicit or hidden and show just how you know all your assumptions are valid. Then you have to describe just what algorithm you used for the non-linear fit and run the gauntlet of the referees possibly being more sophisticated in numerical analysis than you and tearing down your methods! It isn't clear to me why you'd want to fit the entire kinetic curve(s) in the first place. Parameters such as Ki arise from the Michaelis-equation which relates (presumably) the forward rate as a function of [S] and the only true experimental measure of the forward rate is the initial velocity. So even if you could fit the entire kinetic curve(s) (OD vs. time) to some fancy exponential function the only relevant part is the initial slope. Modelling the whole curve may allow you to test hypothesis on the catalytic mechanism (e.g., presence of intermediates) but is quite unnecessary to get at empirical parameters such as Ki. On another note, the real advantage of nonlinear curve-fitting over fitting linearized equations is statistical in nature. When you linearize equations, you can severely skew the relative contibutions of the data points to the fit, such that well-spaced data for the original equation can exhibit highly skewed distributions in transformed scales and bias the fitting. Lineweaver-Burke is particularly nasty on this count. On yet another note, somebody mentioned semilog plots; if you were to be really rigorous, rectangular hyperbolas such as Michaelis-Menten should be fitted on a semilog scale, exactly the same as equilibrium binding curves, again for the reason above. On a linear scale, the fitted Km can be very unevenly bracketed by the measured data (because we're all try to make sure we've reached vmax).  SignatureGregory M. K. Poon, Ph.D., R.Ph., B.Sc.Phm. Departments of Pharmaceutical Sciences and Chemical Engineering University of Toronto Toronto, ON M5S 2S2 > > Hysterical Raisins. > > Back in the bad old days, it was hard to do stuff like fitting [quoted text clipped - 46 lines] > > Thanks again. |
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